ANZIAM 2018
54th Meeting
4-8 February, 2018
Hotel Grand Chancellor
Hobart, Tasmania

The abstracts of the talks in this handbook were provided individually by the authors. Only minor
typographical changes have been made by the editors. The opinions, findings, conclusions andrecommendations in this book are those of the individual authors.
We thank John Banks for his software allowing abstract submission and generation of LATEX files.
We also thank the organisers of the ANZIAM 2017 conference for providing their LATEX template files.
Editors: Michael Brideson, Andrew Bassom and Larry Forbes
Web: maths.utas.edu.au/anziam2018
ISBN: 978-0-9942562-6-3 (Softcover)
ISBN: 978-0-9942562-7-0 (Portable Document e-Format)

CONTENTS

1

Contents
1 Conference Details and History2

1.1

Organising Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.2

Invited Speakers Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.3

Invited Speakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.4

Past Conference Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.5

The T.M. Cherry Student Prize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.6

The Cherry Ripe Prize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.7

The J.H. Michell Medal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.8

The E.O. Tuck Medal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.9

The ANZIAM Medal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.10 The A. F. Pillow Applied Mathematics Top-Up Scholarship . . . . . . . . . . . . . . .

6

1.11 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62 Conference Events, Venues and Facilities

7

2.1

Conference Venue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.2

Conference Welcome Reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.3

Conference Banquet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.4

Refreshment Breaks and Lunches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.5Internet Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.6

Invited Lectures and Contributed Talks . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.7

Student Evening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.8

Women in Mathematical Sciences Lunch . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.9

Tuesday Afternoon - Explore Hobart . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

3 Conference Programme

10

4 Conference Abstracts

26

Index of Speakers and Session Chairs

133

Registered Conference Delegates

136

ANZIAM 2018 Conference Handbook

1

Conference Details and History

1.1

Organising Committee• Larry Forbes (University of Tasmania) — Director• Karen Bradford (University of Tasmania)• Andrew Bassom (University of Tasmania)• Michael Brideson (University of Tasmania)

1.2

Invited Speakers Committee• Tammy Lynch (Massey University) — Chair• Andrew Bassom (University of Tasmania)• Sophie Hautphenne (University of Melbourne)• Alex James (University of Canterbury)• Carlo Laing (Massey University)• Michael Small (University of Western Australia)• Sharon Stephen (University of Sydney)• Ian Turner (Queensland University of Technology)

1.3

Invited Speakers• Snezhana Abarzhi (University of Western Australia)• Alys Clark (University of Auckland) — 2017 J.H. Michell Medallist• Michael Plank (Canterbury University)• Louise Ryan (University of Technology, Sydney)• Kate Smith-Miles (University of Melbourne) — 2017 E.O. Tuck Medallist• Mandyam Srinivasan (University of Queensland)• Nick Trefethen (University of Oxford)

2

3

ANZIAM 2018 Conference Handbook

1.4

Past Conference Locations

SurfersmParadisemK97IwmQFK5TanundamK975
BarossamValleymQFFK

BroadbeachmK978
CaloundramQFF9

HahndorfmK99IwmQFK7AdelaidemK967

LeuramK979wmK988
KatoombamQFF8

CoolangattamK99FwmK998

PokolbinmK99R
NewcastlemQFKI

TerrigalmK977
SydneymQFFI
WollongongmK97Q
BundanoonmK98Q
WirrinamK986
BusseltonmK995
WaitangimQFFF
CanberramQFFQwmQFK6
MollymookmK999
KangaroomIslandmK966
BatemansmBaymK99Q
VictormHarbourmK969wmK98K
MerimbulamK98R
CoorongmK966
RotoruamQFKR
JindabynemK976
HallsmGapmK968
WairakeimK987
SmigginsmHolemK97K
NapiermQFF5
WarrnamboolmQFKQ
MansfieldmQFF6
BallaratmK989
MastertonmK996
LauncestonmK985
LornemK97FwmK97RwmK997
HanmermSpringsmK99K
CowesmK98F
HobartmQFFRwmQFK8PerthmK98I
FremantlemQFF7

GlenelgmQFKKQueenstownmQFKF

1966
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982

Kangaroo Island (Aug)
Coorong (Dec)
AdelaideHalls Gap
Victor Harbor
Lorne
Smiggin Holes
Wollongong
Surfers Paradise
Lorne
TanundaJindabyne
Terrigal
Broadbeach
Leura
Cowes
Victor Harbor
Bundanoon

1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000

Perth
Merimbula
Launceston
Wirrina
Wairakei
Leura
Ballarat
Coolangatta
Hanmer Springs
Batemans Bay
Hahndorf
Pokolbin
Busselton
Masterton
Lorne
Coolangatta
Mollymook
Waitangi

2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018

Barossa Valley
Canberra
SydneyHobartNapierMansfield
Fremantle
Katoomba
Caloundra
Queenstown
Glenelg
Warrnambool
Newcastle
Rotorua
Surfers Paradise
Canberra
Hahndorf
Hobart4

ANZIAM 2018 Conference Handbook

1.5

The T.M. Cherry Student Prize

An annual prize for the best student talk was introduced in 1969 at Victor Harbor. In May 1976 theDivision of Applied Mathematics titled it the “T.M. Cherry Student Prize” in honour of Professor Sir
Thomas MacFarland Cherry. Past recipients are listed below.
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1988
1987
1989
1990
1991
1992

1.6

R. Jones
J. Rickard
J. Jones
Not awarded
Not awarded
R. P. Oertel
R. E. Robinson
J. P. Abbott
J. Finnigan
S. Bhaskaran
B. Hughes
P. Robinson
J. R. Coleby
B. Hughes
M. Lukas
A. Plank
G. Fulford
J. GearP. Kovesi
A. Kucera
S. Wright
G. Fulford
F. Murrell
A. Becker
K. Thalassoudis
W. Henry
M. Rumsewicz
M. MyerscoughJ. Roberts
J. BestS. K. Lucas
S. F. Brown

U Adelaide
UCL
Mount Stromlo

1993
1994
1995
1996

U Adelaide
U Sydney
ANU
CSIRO
U Adelaide
ANU
UQ
U Adelaide
ANU
ANU
UNSW
UoW
U Melbourne
UWA
UoW
UQ
UoW
U Melbourne
Monash U
U Adelaide
ANU
U Adelaide
U Oxford
U Melbourne
UoW
U Sydney
UoW

1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017

D. Standingford
B. Barnes
A. Buryak
A. GoreD. Scullen
S. Cummins
J. Clark
T. Gourlay
E. Ostrovskaya
C. Reid
M. Haese
V. Gubernov
W. Megill
Not awarded
K. Mustapha
J. Looker
C. Fricke
S. Harper
E. Button
M. Haythorpe
S. Cohen
L. Mitchell
S. Butler
J. Caffrey
J. Nassios
D. Khoury
T. Vo
M. Chan
H. Tronnolone
D. Arnold
A. Jenner
C. Miller
E. Hester

U Adelaide
Monash U
ANU
U Newcastle
U Adelaide
Monash U
U Sydney
U Adelaide
ANU
Massey U
U Adelaide
ADFA
UBC/UoWUNSWU Melbourne
U Melbourne
Massey U
U Melbourne
UniSA
U Adelaide
U Sydney
U Sydney
U Melbourne
U Melbourne
UNSW
U Sydney
U Sydney
U Adelaide
U Adelaide
U Sydney
U Melbourne
U Sydney

The Cherry Ripe Prize

Since 1995 the students have run an alternative competition for the best non-student talk. Past
recipients are listed below.
1995
1996
1997
1998
1999
2000
2001
2002
2004
2005
2006

Natashia Boland
Andrew Pullan
Neville de Mestre
David Stump
Mark McGuinness
Joseph MonaghanAndy Philpott
Phil Broadbridge
Ernie Tuck
Larry Forbes
Stephen Lucas
Kerry Landman
Vicky Mak
James Sneyd

U Melbourne
U Auckland
Bond UUQ
VUW
Monash U
U Auckland
UoW
U Adelaide
U Tasmania
UniSAU Melbourne
Deakin U
U Auckland

2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017

Geoffry Mercer
Neville de Mestre
Philip Maini
Larry Forbes
Larry Forbes
Darren Crowdy
Martin Wechselberger
Scott McCue
Sheehan OlverPeter Kim
Not awarded
Matthew Simpson
Melanie Roberts
Christopher Green

USW
Bond UU Oxford
U Tasmania
U Tasmania
Imperial College
U SydneyQUT
U Sydney
U Sydney
QUT
IBM Research Australia
QUT

5

ANZIAM 2018 Conference Handbook

1.7

The J.H. Michell Medal

The J. H. Michell Medal is awarded to outstanding new researchers who have carried out distinguishedresearch in applied or industrial mathematics, where a significant proportion of the research work has
been carried out in Australia or New Zealand. Past recipients are listed below.
1999
2000
2001
2002
2004
2006
2007
2008

1.8

Harvinder Sidhu
Antoinette Tordesillas
Nigel Bean
Stephen Lucas
Mark Nelson
Sanjeeva Balasuriya
Yvonne Stokes
Carlo LaingUNSWU Melbourne
U Adelaide
UniSA
UoW
U Sydney
U Adelaide
Massey U

2009
2011
2012
2013
2014
2015
2016
2017

Scott McCue
Frances Kuo
Matthew Simpson
Terence O’Kane
Ngamta Thamwattana
Barry Cox
Joshua Ross
Alys Clark

QUT
UNSW
QUT
CMAR CSIROUoW
U Adelaide
U Adelaide
U Auckland

The E.O. Tuck Medal

In honour of the late Ernest Oliver Tuck, FAustMS, FTSE and FAA, ANZIAM has instituted a midcareer award for outstanding research and distinguished service to the field of Applied Mathematics.
The inaugural EO Tuck Medals were presented at ANZIAM 2013.
2013
2015
2017

1.9

Shaun Hendy
Geoffry Mercer
Troy Farrell
Kate Smith-MilesVUW and Callaghan Innovation
ANU
QUT
Monash U

The ANZIAM Medal

The ANZIAM Medal is awarded on the basis of research achievements or activities enhancing applied
or industrial mathematics and contributions to ANZIAM. The first award was made in 1995. Past
recipients are listed below.
1995
1997
1999
2001
2004
2006
2008
2010
2012
2014
2016

Renfrey Potts
Ian Sloan
Ernie TuckCharles Pearce
Roger Grimshaw
Graeme Wake
James Hill
Bob Anderssen
Robert McKibbin
Kerry LandmanFrank de Hoog

U Adelaide
UNSW
U Adelaide
U Adelaide
Loughborough U
Massey U
UoW
CSIRO
Massey U
U Melbourne
CSIRO Canberra

6

ANZIAM 2018 Conference Handbook

1.10

The A. F. Pillow Applied Mathematics Top-Up Scholarship

The A. F. Pillow Applied Mathematics Trust offers an annual “top-up” scholarship to a student holding
either an Australian Postgraduate Award (APA) or equivalent award for full-time research in Applied
Mathematics leading to the award of a PhD. The aim of the A. F. Pillow Applied Mathematics Top-up
Scholarship is to increase the quality of postgraduate students in the field of applied mathematics inAustralia. Past recipients are listed below.
2009
2010
2011
2012
2013
2014
2015
2016
2017

1.11

Christopher Lustri
Alex BadranMichael Dallaston
Hayden Tronnolone
Lisa Mayo
Audrey Markowskei
Pouya Baniasadi
Alexander Tam
Jody Fisher

QUT
UoW
QUT
U Adelaide
QUT
Macquarie U
Flinders U
U Adelaide
Flinders U

Acknowledgements

The Organising Committee gratefully acknowledges the financial support of Professor Nalini Joshi’s
Georgina Sweet Australian Laureate Fellowship.
The Organising Committee gratefully acknowledges John Banks for providing the conference registration
and abstract submission software, register!.
The Organising Committee is thankful for funding received from the ANZIAM Student Support Scheme
to assist the following students to attend the ANZIAM 2018 conference:
Rosemary Aogo
Sarah Belet
Chantelle Blachut
Calum Braham
Alexander Browning
Hilary Hunt
Claudio Ibarra
Adrianne Jenner
Matthew KingMaria Kleshnina
Tiffany Leung
Sha Lin
Meirian Lovelace-Tozer
Michael Lydeamore
Benjamin Maldon
Sean McInerney
Claire Miller
Liam Morrow

Samson Ogunlade
Pantea Pooladvand
James Reoch
Joseph Teague
Eloise Tredenick
Lachlan Tyrrell
Demival VasquesSean Vittadello
Collin Zheng

ANZIAM 2018 Conference Handbook

2

Conference Events, Venues and Facilities

2.1

Conference Venue

7

The conference is being held at the Hotel Grand Chancellor (HGC) in Hobart, Tasmania. The HGC is
at 1 Davey Street, overlooking Hobart Harbour and Constitution Dock.

The HGC is convenient to the Tasmanian Travel and Information Centre (corner of Elizabeth St andDavey St), Elizabeth St Mall, and the historic regions of Battery Point and Salamanca Place.

ANZIAM 2018 Conference Handbook

8

All conference rooms are located on Level 1 of the HGC; the floor plan is shown below. The fivemeeting rooms are the Grand Ballrooms 1, 2 and 3; Harbour View Room 2; and Chancellor Room 4.
Grand Ballrooms 2 and 3 will combine for the conference opening, closing, and plenary sessions.

2.2

Conference Welcome Reception

The welcome reception will be held from 6–8 pm on Sunday, February 4 in Harbour View Room 1. All
conference delegates and registered guests are invited.

2.3

Conference Banquet

The Conference Banquet will be held in the Grand Ballroom on Wednesday, February 7. Pre-dinner
drinks will be served on the Mezzanine from 6:30 pm, for a 7 pm start to the banquet.

2.4

Refreshment Breaks and Lunches

Arrival tea and coffee will be available on the Mezzanine prior to the Conference Opening on Monday
and 9 am invited Talks on the remaining days. Morning teas, afternoon teas and lunches will also be
set up on the Mezzanine. Lunches are included in the registration fee for delegates and their registered
guests.

2.5

Internet Access

Delegates will be provided with WiFi internet access throughout the conference. Connection details
will be provided at the conference.

ANZIAM 2018 Conference Handbook

2.6

9

Invited Lectures and Contributed Talks

All invited lectures will take place in Grand Ballroom 2–3 and are scheduled for 50 minutes, inclusiveof questions.
Contributed talks will be held in parallel sessions in Grand Ballroom 1, Grand Ballroom 2, Grand
Ballroom 3, Harbour View 2 and Chancellor 4. The duration of each contributed talk will be fifteen
minutes with an additional five minutes for questions and room change over.

2.7

Student Evening

All students are invited to BarCelona in Salamanca Square from 6:30 pm on Monday, February 5 for
the Student Evening. The Evening provides a chance to meet fellow students in an informal setting,with food provided and drinks available for purchase. This event has been organised by the ANZIAM
student representative Laura Karantgis.

2.8

Women in Mathematical Sciences Lunch

The 2018 Women in Mathematical Sciences ANZIAM Lunch will be held on Tuesday, February 6.
This event is being held under the umbrella of the Women in Mathematics Special Interest Group(WIMSIG) of the Australian Mathematical Society. It is free to all registrants at ANZIAM 2018 whowish to attend and is funded and supported by Prof. Nalini Joshi’s Georgina Sweet Australian Laureate
Fellowship. It is open to people of any gender.
The purpose of the lunch is to support women, and particularly early career researchers, to enter andestablish careers in mathematics. Come along and hear about the careers of the ANZIAM 2018 female
plenary speakers, to discuss issues concerning women in mathematics in Australia, and to network withfellow WIMSIG members and supporters. Check out the WIMSIG website (austms.org.au/WIMSIGQA) for information on/advice from the female plenary speakers at this and past ANZIAM and AustMS
conferences.
Please collect your lunch from the Mezzanine and then convene in Grand Ballroom 2.

ANZIAM 2018 Conference Handbook

2.9

10

Tuesday Afternoon - Explore Hobart

The Tuesday afternoon of ANZIAM conferences is traditionally set aside for free time. We encourage
you to use this time to explore some of the wonderful attractions in the Greater Hobart region.
The hotel foyer has a pamphlet display area for local attractions. More information can be obtained
from the Tasmanian Travel and Information Centre on the corner of Elizabeth St and Davey St(approximately 150 m from the HGC).
Here are some suggestions for activities:
Across the road from the HGC is the Tasmanian Museum and Art Gallery.
One block further along is the Maritime Museum of Tasmania.
MONA, the Museum of Old and New Art is the largest privately funded museum in Australia. The
building is carved into the landscape and the displayed art is often reviewed anywhere on the scalefrom disgusting to wonderful. A trip to the museum on the MONA ferry is an attraction in itself.
Unfortunately, the museum is closed on Tuesdays.
The historic regions of Salamanca Place and Battery Point are wonderful places to explore on foot, asis the Hobart Rivulet track which takes you into the foothills of kunanyi / Mount Wellington.
The World Heritage listed Female Factory Historic Site is also beside the Hobart Rivulet and justdownstream from the Cascade Brewery.
Sightseeing tours around Hobart are available on the Red Decker bus. Alternatively, see Hobart fromthe river with Hobart Historic Cruises.

3

Conference Programme

The program is shown on the following pages. Contributed talks should be no more than 15 minutes
and speakers will be provided a warning after 12 minutes. Talks must stop after 15 minutes to allow 3
minutes for questions and 2 minutes for room changes.

11:00–11:20

10:40–11:00

10:20–10:40

10:00–10:20

8:00–8:30
8:30–9:00
9:00–9:50

Registration — Mezzanine
Conference Opening, Grand Ballroom 2–3
Invited: Nick Trefethen, (University of Oxford), Grand Ballroom 2–3
Title: Mathematics of the Faraday Cage (#186, p. 120)
Chair: Larry Forbes
Grand Ballroom 1
Grand Ballroom 2Grand Ballroom 3
Harbour View 2
Chair: Roslyn Hickson
Chair: Jerome Droniou
Chair: Mark Flegg
Chair: Carlo Laing
Rebecca Chisholm
Peter Johnston
Jennifer Flegg
Bernd Krauskopf
Understanding how
Evaluating singular
A mathematical model of Robust chaos: blenders
immunity, strain
integrals for fun andthe use of supplemental
in a Hénon-like family
diversity and prevalence
profit (#85, p. 68)
oxygen to combat(#95, p. 73)
surgical site infection
interact in multi-strain
pathogens using(#51, p. 51)
agent-based modelling(#29, p. 41)
Sarah Belet*
Robert Scott
Anand
Andrus Giraldo
Models for the spread of Anderssen
Rampadarath*
Shilnikov-like chaos in
Wolbachia in mosquito
Modelling causality:
A Distribution-Moment
two nonlinear coupled
populations as a means
integral equations versus approximation forphotonic nanocavities
of suppressing dengue
ODEs (#6, p. 29)
coupled airway dynamics (#60, p. 56)
fever transmission (#16,of the airway wall andp. 34)
airway smooth muscle(#147, p. 100)
Saber Dini*
Barbara Johnston
Adel Ahmed
Elle Musoke*
Investigating the efficacy The ‘sinh’ transformation Almalki*
The geometry of aof antimalarial drugs
method for evaluating
An analysis of the first
three-dimensional
using a mathematicalnearly singular boundary order growthinvariant manifold in amodel (#39, p. 46)
element integrals (#84,
fragmentation equation
four-dimensional
p. 68)
for special divisionslow-fast system (#124,
kernels (#5, p. 28)
p. 88)
Morning tea - Mezzanine*student talkMonday Morning

Suha Al Ali*
Withdrawal of waterfrom within a sandcolumn (#4, p. 28)

Lidong Cui*Resonance, symmetry
and pattern selection in
Langmuir circulation(#36, p. 44)

Chancellor 4
Chair: Tony Roberts
Jim Denier
New results in the
instability ofcompressible boundary
layers (#38, p. 45)

ANZIAM 2018 Conference Handbook

11

Stuart Johnston
An analytical approachfor quantifying theinfluence of nanoparticle
polydispersity on cellulardelivered dose (#86,
p. 69)

12:00–12:20

Ian Sloan
Needlet approximationon the sphere (#164,
p. 108)Robert Cope
Graeme Wake
Multi-strain epidemic
Geometric Optimisation
models for transmission(#198, p. 126)and evolution of drug
resistant pathogens (#32,
p. 42)

Grand Ballroom 2
Chair: Linda Stals
Frank de Hoog
Iterative Deconvolution(#37, p. 45)

11:40–12:00

11:20–11:40

Grand Ballroom 1
Chair: Mick Roberts
Samson Ogunlade*
Modelling malaria
parasites’ survivability
the dry season (#132,
p. 92)

Elias Vera Siguenza*
A mathematical model
supports a key role foranion exchanger Ae4(Slc4a9) in salivary gland
fluid secretion (#195,
p. 124)
NgamtaThamwattana
Modelling phagocytosis(#182, p. 117)

Grand Ballroom 3
Chair: Matthew Simpson
Edward GreenCan the left ventricle getenough oxygen? (#66,
p. 59)*student talkChancellor 4
Chair: Scott McCue
John Harper
A Volterra equation witha physically but notmathematically uniquesolution: a bubble risingin a liquid with negative
surface activity (#71,
p. 61)
Liam Morrow*
A level set based
numerical scheme fordoubly connected
Hele-Shaw flow (#123,
p. 87)

Chantelle Blachut*
Lachlan Tyrrell*
Detecting andViscous fingeringcharacterising coherent
patterns driven by
structures and theirheterogeneous substrateevolution in
wettability (#190,
non-autonomous
p. 122)
dynamical systems (#18,
p. 35)

Andrew Keane
State-dependent delaysin the El Niño Southern
Oscillation system (#89,
p. 70)

Harbour View 2
Chair: Michael Small
MartinWechselberger
Two-stroke relaxation
oscillators (#203, p. 128)

Monday morning continued

ANZIAM 2018 Conference Handbook

121:00–2:00

12:40–1:00

12:20–12:40

Rosemary Aogo*
Modelling malaria
parasite development
before and after drug
treatment (#8, p. 30)

Grand Ballroom 1
David Khoury
Correctly assessing drug
efficacy in malaria relies
on understand parasite
kinetics before treatment(#90, p. 71)

Tony Roberts
Projective integration ofmultiscale ODEs via
Dynamic Mode
Decomposition (#155,
p. 104)Grand Ballroom 2
Jeremy Sumner
Lie-Markov models
derived from finite
semigroups (#172,
p. 112)Lunch - Mezzanine

Sean Trinity
Vittadello*
Mathematical models forcell migration withreal-time cell cycle
dynamics (#197, p. 125)

Robert Nawiekang
Otupiri*
Numerical modelling andcharacterisation of an
all-fibre laser withsaturable absorber(#135, p. 94)

Grand Ballroom 3
Harbour View 2Nathan Pages*
Soizic Terrien
A model of calcium
Pulsing dynamics in an
dynamics in anatomically excitable laser subject toaccurate parotid acinardelayed optical feedback
cells (#137, p. 95)(#181, p. 117)

*student talkMonday morning continued
Chancellor 4
Khanh Pham*On the evaluation of
Landau constants in
amplitude equations
away from a criticalpoint. Part 1:
supercritical regimes(#140, p. 96)
Sergey Suslov
On the evaluation of
Landau constants in
amplitude equations
away from a criticalpoint. Part 2: subcriticalregimes and a physicalexample (#173, p. 113)

ANZIAM 2018 Conference Handbook

13

3:40–4:00

3:20–3:40

3:00–3:20

2:00–2:50

Invited: Louise Ryan, (University of Technology, Sydney), Grand Ballroom 2–3
Title: But I’m a data scientist too, aren’t I? (#159, p. 106)
Chair: Barbara Holland
Grand Ballroom 1
Grand Ballroom 2Grand Ballroom 3
Harbour View 2
Chair: Ngamta
Chair: Geetika Verma
Chair: Amie Albrecht
Chair: Elliot Carr
Thamwattana
Bronwyn Hajek
Andrew Black
Meirian Sara
Tim Moroney
Analytic solutions for a
Importance sampling for Lovelace-Tozer*
A modern linear algebra
reaction diffusion model
partially observed
Modelling donor flow
library for C++17
of calcium waves on theMarkov models (#19,(#106, p. 79)(#122, p. 87)
surface of an egg (#69,
p. 36)
p. 60)
Wang Jin
Benjamin David
Erika Rana Gabriela
Atsushi Minamihata
The role of initial
Kaehler
Belchamber*
Accurate error bounds
geometry in experimental Full reconstruction of a
Stochastic optimal
for linear systems using
models of wound closing hidden variable model
control of a
H-matrices (#121, p. 86)(#83, p. 67)
with just two observed
solar-powered car (#15,
variables (#87, p. 69)
p. 34)
Afternoon tea - Mezzanine*student talkMonday afternoon

Stephen Walters
Viscous Rayleigh-Taylor
flows in two and three
dimensions using GPU
acceleration (#200,
p. 127)
Mohamed Nasser
A fast numerical method
for ideal fluid flow indomains with multiple
stirrers (#126, p. 89)

Chancellor 4
Chair: Yvonne Stokes

ANZIAM 2018 Conference Handbook

14

Vijay Rajagopal
The Cardiac Cell under
the Mathematical
Microscope (#145, p. 99)

5:00–5:20

6:30

4:40–5:00

Alexander Tam*
Investigating the effect ofnutrient-limited growth
on floral patternformation in yeast
biofilms (#177, p. 115)
Anna McGann*
Anomalous Diffusion on
a Growing Domain(#117, p. 84)

4:20–4:40

4:00–4:20

Grand Ballroom 1
Chair: Edward Green
Tertius Ralph*
Hard-core interactions in
one-dimensional velocity
jump models (#146,
p. 99)

Grand Ballroom 2Grand Ballroom 3
Harbour View 2
Chair: Andrew Black
Chair: Peter Taylor
Chair: Ian Sloan
Jessica Penfold*
Adelle Coster
Linda Stals
Using Approximate
Fat and muscle glucose
Domain Decomposition
regulation same-same or applied to the thin-plate
Bayesian Computation
to understand the impact different? (#34, p. 43)
spline saddle pointof climate in seasonal
problem (#169, p. 111)influenza in Australia(#138, p. 95)
Ashwani Kumar*Mark Fackrell
Craig Douglas
A sequential stochastic
A timely solution to theSolving high condition
mixed integer
nurse rostering problem: number systems (#41,
programming model for
an operations researchp. 47)
elective surgery
approach (#46, p. 49)
scheduling (#97, p. 74)
Demival Vasques
Ryan Loxton
Robert Lodder
Filho*
Switching time
The BEST Approach to
Look who’s talking:
optimization for switched the Search forbipartite networks as
systems with
Extraterrestrial
representations of a topic time-dependent andIntelligence (SETI)
model of New Zealandstate-dependent(#104, p. 78)
parliamentary speeches
switching conditions(#194, p. 124)(#107, p. 79)
Calum Braham*
Ali Tirdad
Sebastián Elı́as Graiff
LogarithmicallyImproving health
Zurita*discretised population
benefits of in-home care
Discrete mechanicalbalance models offor chronic patients
systems: existence of
aggregation andthrough optimal service
trajectories (#62, p. 57)
fragmentation (#21,
timing (#184, p. 118)
p. 37)ANZIAM Student Evening - BarCelona, Salamanca Square*student talkMonday afternoon continued

Sophie Calabretto
Objective detection ofrotationally coherent
vortices (#25, p. 39)

Matthew James
Hopwood*
Extensional flow of anaxisymmetrictransversely isotropic
fluid thread (#78, p. 65)
James Reoch*Thin-film multiphasemodelling of collagen gelmechanics (#149, p. 101)

Chancellor 4
Chair: Larry Forbes
Yvonne Stokes
Why oversized holes in
microstructured opticalfibres? (#171, p. 112)

ANZIAM 2018 Conference Handbook

15

Tiffany Ngo Nam
Leung*
Infection-acquired versus
vaccine-acquired
immunity in an SIRWS
model (#101, p. 76)

10:40–11:00

11:00–11:20

James Nicholas
Walker*A sequential approach todata-augmented MCMC(#199, p. 126)

Joseph Alex Teague*
Experimental featuredriven development formathematical models of
LiFePO4 batteries(#180, p. 116)

Troy Farrell
Towards accurate
real-time control oflithium ion batteries(#48, p. 50)

Alexander Paul
Browning*
A Bayesiancomputational approach
to explore the optimal
duration of a cellproliferation assay (#23,
p. 38)
Oleksii Matsiaka*
Continuum
approximations forlattice-free multi-species
models of collective cell
migration (#115, p. 83)
Morning tea - Mezzanine

Naoto Nakano
Revisiting
delay-embedding byusing Hilbert-Schmidt
integral operator theory
for dynamicalreconstruction (#125,
p. 88)
Debora Cristina
CorreaOn system behaviour
using complex networks
of a compression
algorithm (#33, p. 43)

Invited: Mandyam Srinivasan, (The University of Queensland), Grand Ballroom 2–3
Title: From birds and bees to flying machines (#168, p. 110)Chair: Mary MyerscoughGrand Ballroom 1
Grand Ballroom 2Grand Ballroom 3
Harbour View 2
Chair: Peter Kim
Chair: Mark Nelson
Chair: Catherine
Chair: Hinke Osinga
Penington
Roslyn Hickson
Jim Byrnes
Zoltan Neufeld
Cris Hasan*
A history-based
Active sonar remote
Modelling collective cell
Saddle slow manifolds
multi-outbreak influenza identification of
migration in a channel
and canard orbits in themodel (#75, p. 63)
materials (#24, p. 38)(#128, p. 90)
Hodgkin–Huxley model(#72, p. 61)

10:20–10:40

10:00–10:20

9:00–9:50*student talkTuesday morning

Caleb Gemmell*
Social network analysis
from obsidian artefacts(#59, p. 55)

Silvestru Sever
DragomirApproximation of
f -Divergence Measure inInformation Theory andApplications (#42, p. 47)
Caitlin Gray*
Generating connected
spatially embedded
graphs (#63, p. 57)

Chancellor 4
Chair: Elliot Carr

ANZIAM 2018 Conference Handbook

16

12:10–1:00

11:40–12:00

11:20–11:40

Nabil Fadai*
Asymptotic analysis of amultiphase drying model
motivated by coffee bean
roasting (#47, p. 49)

Grand Ballroom 2
Chair: Melanie Roberts
Catheryn Gray*
Tracking the location of
metabolic controllers:
Akt as a harmonic
oscillator (#64, p. 58)

Grand Ballroom 3
Chair: Adelle Coster

Harbour View 2
Chair: Martin
Wechselberger
Maria Kleshnina*
Nonlinear learning ingames with incompetence(#93, p. 72)

Eloise Tredenick*Adarsh Kumbhari*
Cecilia
Mathematical modelling Modelling the impact ofGonzalez-Tokmanof hydrophilic
T-cell avidity on cancer
Optimal mixing
agrochemical penetration vaccines (#98, p. 75)
enhancement by local
in astomatous plant
perturbation (#61,
cuticles: surfactant andp. 56)
hygroscopic effects(#185, p. 119)
Invited: Michael Plank, (University of Canterbury), Grand Ballroom 2–3
Title: The other end of the spectrum: size-based models of marine ecosystems and fishing (#142, p. 97)
Chair: Bronwyn Hajek

Michael Lydeamore*
Investigating the
dynamics of coupledmodels with applications
to Group A
Streptococcus andScabies (#110, p. 81)
Mick Roberts
Is your family pet asource of antibiotic
resistance? (#153,
p. 103)

Grand Ballroom 1
Chair: Tammy Lynch*student talkTuesday morning continued

Takuya Tsuchiya
Error analysis ofCrouzeix-Raviart andRaviart-Thomas finite
element methods (#189,
p. 121)

Siegfried Rump
Linear systems in Matlab
with zero residual (#158,
p. 105)Chancellor 4
Chair: Tim Moroney

ANZIAM 2018 Conference Handbook

17

Free time
ANZIAM AGM, Grand Ballroom 2
ANZIAM Executive Meeting, Chancellor 5

7:30–9:30

9:30–11:30

Women in Mathematical Sciences Lunch - Grand Ballroom 2

Lunch - Mezzanine

2:00–7:30

1:00–2:00

Tuesday afternoon and evening

ANZIAM 2018 Conference Handbook18

11:00–11:20

10:40–11:00

10:20–10:40

10:00–10:20

9:00–9:50

Invited: Alys Rachel Clark - 2017 J.H. Michell Medal Winner, (The University of Auckland), Grand Ballroom 2–3
Title: Pregnancy and beyond: how mathematical modelling could improve early life health (#30, p. 41)
Chair: Matthew Simpson
Grand Ballroom 1
Grand Ballroom 2Grand Ballroom 3
Harbour View 2
Chancellor 4
Chair: Philip
Chair: Murk Bottema
Chair: Noel Barton
Chair: Frank de Hoog
Chair: Song-Ping Zhu
Broadbridge
Kenji Kajiwara
Hilary Hunt*Mark Nelson
Elliot Joseph Carr
Anna Aksamit
Log-Aesthetic curves in
Mixed Signals:
Nitrogen removal in the
Calculating how long it
Additional information
Interaction between RyR activated sludge processindustrial design as
takes for diffusive
in robust approach toand IP3R mediatedsimilarity geometric(#127, p. 89)
processes to effectively
mathematical financecalcium release shapes
analogue of Euler’s
reach steady state(#3, p. 27)
the calcium transient forelastic curves (#88,
without computing thehypertrophic signallingp. 70)
transient solution:in cardiomyocytes (#79,
application to
groundwater flow (#26,
p. 65)
p. 39)
Guido Baardink*
Claire Miller*
Melanie Roberts
Scott McCue
Guiyuan Ma
Localizing softness and
The impact of stem cellFine-grained multi-factor Steady free-surface flow
An analytical solution for
stress in topologicaldivision models in
hail damage modellingover a bottom
the HJB equation arisingmetamaterials (#10,
epithelial multi-cellular(#152, p. 102)
obstruction in three
from the Merton
p. 31)
tissue modelling (#120,
dimensions (#116, p. 84) problem (#112, p. 82)
p. 86)
Matthew King*
Kengo Fujita*
Benjamin Ganim*
Sheehan Shakiban
Xiaoping Lu
Chaos and fluctuations
Construction of a
Forecasting maximum
Olver
Finite margin call stock
in a modified Ehrernfest mathematical model that power demand in NSW
Sparse spectral methods loan evaluation (#108,
wind-tree model (#92,
reproduces thewith SARIMA-regression for PDEs on triangles
p. 80)
p. 72)
mechanism ofmodel (#58, p. 55)
with multivariateclassification andorthogonal polynomials
memory of information(#133, p. 93)
using timeshift andphase states of brain
waves (#56, p. 54)
Morning tea - Mezzanine*student talkWednesday morning

ANZIAM 2018 Conference Handbook

19

1:00–2:00

12:40–1:00

12:20–12:40

12:00–12:20

11:40–12:00

11:20–11:40

James Murray Hill
Relating elasticity andgraphene folding
conformation (#76, p. 63)

Chair: Hayden Tronnolone
Arnold Reynaldi
Age-specific heterogeneity in
CD8+ T-Cell homeostasis(#151, p. 102)
Adrianne Jenner*
The effect of tumour
heterogeneity on cancer
treatments: the ninja virus(#81, p. 66)
David Waters*
Calcium Signalling in T-Cells(#201, p. 127)

Chair: Christopher Lustri
Nathan Paul Duignan*
On a conjecture about thesimultaneous binary collision(#44, p. 48)
Khongorzul Dorjgotov*
Exact invariant solutions oftime fractional evolution
systems with variable
coefficient (#40, p. 46)
Joe O’Leary*
The energy integral in thefirst post-Newtonian
approximation for generalrelativity (#130, p. 91)
Winston Sweatman
Symmetrical few-body orbits(#175, p. 114)

Ielyaas Cloete*
Calcium oscillations inhepatocytes: how are they
shaped? (#31, p. 42)

Pantea Pooladvand*
Do T-cells compete for
antigen? (#143, p. 98)

Grand Ballroom 2Grand Ballroom 1

Lunch - Mezzanine

Kenta Kobayashi
The relation between
Crouzeix-Raviart andRaviart-Thomas finite
element methods (#94, p. 73)
Benjamin Maldon*
Pressing charges: analyticalsolutions to the diffusion
model charge carriers in
dye-sensitized solar cells(#113, p. 82)
Jamilatuzzahro Abdul
Fatah*The determination of OpenScience, Open Innovation
paddy production inIndonesia using
geographically weighted
regression (#2, p. 26)

Chair: Troy Farrell
Steve Taylor
Preserving quality of milk
powder shipments (#179,
p. 116)
Mark Joseph
McGuinness
MMM, Microwaves Measure
Moisture (#118, p. 85)

Grand Ballroom 3*student talk

Jerome Droniou
Low order or high order?
Wisdom may be in the
middle... (#43, p. 47)

Marko Lange
Rigorous results in electronic
structure calculation (#100,
p. 76)

Chair: Peter Johnston
Dimetre Triadis
An integrable discrete model
for soil-water infiltration(#187, p. 120)
Eric William Hester*
Fluid-Structure interaction inpseudospectral codes: Thesmooth volume penalty
method (#74, p. 62)
Arthur George Suvorov*
The information geometry of
sensor management (#174,
p. 113)

Harbour View 2

Wednesday morning continued

Sue Ann Chen
Compliance for Personal
Financial Advice (#28, p. 40)

Song-Ping Zhu
American-style Parisian
options and their fair price(#209, p. 132)

Xin-Jiang He
How should a local
regime-switching model becalibrated? (#73, p. 62)

Chair: Anna Aksamit
Angus Hamilton Lewis*
Modelling South Australia’s
electricity prices (#102,
p. 77)
Sha Lin*
Pricing puttable convertible
bonds with integral equation
approaches (#103, p. 77)

Chancellor 4

ANZIAM 2018 Conference Handbook20

3:40–4:00

3:20–3:40

3:00–3:20

2:00–2:50

Invited: Kate Smith-Miles - 2017 E.O. Tuck Medal Winner, (The University of Melbourne), Grand Ballroom 2–3
Title: Optimization in the Darkness of Uncertainty: when you don’t know what you don’t know, and what you do know isn’t much!
(#167, p. 110)Chair: Troy Farrell
Grand Ballroom 1
Grand Ballroom 2Grand Ballroom 3
Harbour View 2
Chancellor 4
Chair: Arnold Reynaldi
Chair: Robert Cope
Chair: Andrew Keane
Chair: Boris Baeumer
Chair: Phil Howlett
Xueshan Yang*
Alexey Martyushev
Caroline Wormell*Philip Broadbridge
Geetika Verma
Dynamics of a coupled
Mathematical modelling Linear response in
Quantum mechanics
The replicator equation
calcium system (#206,
of HIV dynamics inweakly-coupled systems
from a classical fluids
in discrete time (#196,
p. 130)humanized mice (#114,(#205, p. 130)
perspective (#22, p. 37) p. 125)
p. 83)
Mythreye Krishnan*
Nick Beeton
Sam Jelbart*
Balazs Sandor*
Florian Wechsung*Network using
Modelling mange in the
Why there might be
Topographical
Shape optimization withMichaelis-Menton
common wombat (#14,
more slow-fast systems
uniqueness condition for geometric constraints
kinetics: an algorithm to p. 33)
than you thought there
the weak form of a linear using Moreau-Yosida
find target genes fromwere (#80, p. 66)
depth-averaged vorticity regularization (#204,
expression data (#96,
model (#161, p. 107)
p. 129)p. 74)
Afternoon tea - Mezzanine*student talkWednesday afternoon

ANZIAM 2018 Conference Handbook

21

6:30–11:00

5:00–5:20

4:40–5:00

4:20–4:40

4:00–4:20

Chair: Mary MyerscoughClaudio Arancibia*
The Holling-Tanner
predator-prey model withstrong Allee effect on prey(#9, p. 30)
Jonathan Eade*
An ODE model for thetransmission of the disease
Nosema ceranae in honey beecolonies with demographic
structure (#45, p. 48)
Zeaiter Zeaiter*
The effect ofthermoregulation on honeybee colony health andsurvival (#207, p. 131)

Chair: Rebecca Chisholm
Ishraq Uddin*
A multiphase model for
HDL-assisted stabilisation ofearly atherosclerotic plaques(#192, p. 123)
Sara Li-Yen Loo*
The evolution of hunting
effort in hunter-gatherer
populations (#105, p. 78)

Mykola Pinkevych
Dynamics of reactivation fromlatency in macaques infectedwith simian immunodeficiency
virus (#141, p. 97)

Grand Ballroom 2Grand Ballroom 1

Conference Banquet
6:30 Pre-dinner drinks - Mezzanine
7:00 Banquet - Grand Ballroom

Hinke Osinga
Global manifolds
parametrised by isochrons(#134, p. 93)

Chair: Gary Froyland
Timothy Roberts*
Neurons, temperature andtimescales: what GSPT mighttell us about temperature
regulation? (#154, p. 103)
Joshua Ross
Demography determines gene
drives success in eradicatingpests (#157, p. 105)

Grand Ballroom 3*student talk

Sean McInerney*
Evaluating burn damage andexploring first aid treatment
with partial differential
equations and in vivo Porcine
experiments (#119, p. 85)
Graeme Hocking
Plumes generated bydesalination outfalls (#77,
p. 64)

Owen Jepps
Modelling density-dependent
collective diffusion in
microporous Knudsen flows(#82, p. 67)

Chair: Mark McGuinness
Emma Greenbank*Modelling Surtseyan Ejecta(#67, p. 59)

Harbour View 2

Wednesday afternoon continued

Terry O’Kane
Non-stationary
nonparametric andregularised time series
analysis of observed
atmospheric dynamics (#129,
p. 90)

Lisa Reischmann*
A multiscale approximation ofa Cahn–Larché system withphase-separation on the
microscale (#148, p. 100)

Saima Gul*
A cell growth model adapted
for minimum cell size division(#68, p. 60)

Chair: Bruce van Brunt
Polwaththa Dilruk
Darshana Gallage*
Solving nonlinear PDEs forphase boundaries (#57, p. 54)

Chancellor 4

ANZIAM 2018 Conference Handbook22

11:00–11:20

10:40–11:00

10:20–10:40

10:00–10:20

9:00–9:50

Invited: Snezhana I. Abarzhi, (The University of Western Australia), Grand Ballroom 2–3
Title: On the fundamental of Rayleigh-Taylor instability and Rayleigh-Taylor interfacial mixing (#1, p. 26)
Chair: Larry Forbes
Grand Ballroom 1
Grand Ballroom 2Grand Ballroom 3
Harbour View 2
Chancellor 4
Chair: Nick Beeton
Chair: Andrew Bassom
Chair: Bernd Krauskopf Chair: Julia Piantadosi
Chair: Barbara Holland
Catherine Penington
Sharon Stephen
Carlo Laing
Jerzy Filar
Dion O’Neale
Ordered field property in Real beards & real
Modelling cell
Stability of the
Chimeras on spheres
proliferation times
non-Newtonian(#99, p. 75)
stochastic games (#50,
networks: a spin-glass
p. 51)(#139, p. 96)
asymptotic suction
model of interacting
boundary layer (#170,
individuals (#131, p. 92)
p. 111)
Christopher
Duncan Farrow
Gary FroylandPeter Gerrard Taylor Rowena Ball
Angstmann
Gravity current
FEM-based numerics for
The fundamental
Guessing how triangles
generated by saline
approximating the
Sampling without
equation of life (#12,
will split in half:
groundwater inflow (#49, dynamic Laplacian andreplacement: a story of
p. 32)
Laplacians and cellp. 50)
extracting coherent sets
noncentral
division (#7, p. 29)(#55, p. 53)
hypergeometric
distributions (#178,
p. 115)Matthew Simpson
Daisuke Tagami
Michael Small
Justin Tzou
Brendan Florio
Optimal quantification of Some remarks on a
Hunting for a moving
Mean first passage time
Tailings dewatering bycontact inhibition in cell time-explicit particle
target on a graph andproblems and localised
flocculation (#53, p. 52)
populations (#163,
methods for flowbuilding dynamicalpattern formation p. 108)
problems (#176, p. 114) systems from complex
analysis, results, andnetworks (#165, p. 109) surprising connections(#191, p. 122)
Morning tea - Mezzanine*student talkThursday morning

ANZIAM 2018 Conference Handbook

23

Tammy Lynch
Microbial co-existence
and selection in entericfermentation (#111,
p. 81)

Hayden Tronnolone
Diffusion-limited growth
limits in microbialcolonies (#188, p. 121)

Josephine Reyes
Modelling HIV latency
using distribution oflifespans of infected cells(#150, p. 101)

11:20–11:40

11:40–12:00

12:00–12:20

Grand Ballroom 1
Chair: David Khoury

Brendan Harding
Inertial force on particles
in curved microfluidic
ducts (#70, p. 60)

Ozge Ozcakir
Nonlinear exact coherent
structures in pipe flow(#136, p. 94)

Boris Baeumer
Maximal regularity forstochastic Volterra
integral equations (#11,
p. 31)

Grand Ballroom 2
Chair: Graeme Hocking

Multiphase modelling of
early fibrous cap
formation inatherosclerosis (#202,
p. 128)Peter Kim
Evolution of monogamy
in response to humanpost-menopausal
longevity (#91, p. 71)

Michael Greg Watson

Danya Rose
Who gets the girl? On
the operational sex ratio
as an index for malestrategy (#156, p. 104)

Grand Ballroom 3
Chair: Jennifer Flegg*student talkLuke Bennetts
Acoustic metamaterial
chains involving inertial
amplification (#17,
p. 35)

Harbour View 2
Chair: Winston
SweatmanChristopher Green
Using the Schottky-Klein
prime function tocompute harmonicmeasure distributionfunctions of a class ofmultiply connectedplanar domains (#65,
p. 58)
Bruce van Brunt
On a second order PDE
that models cell division(#193, p. 123)

Thursday morning and afternoon

David John Warwick
SimpsonThe sausage-string
structure ofmode-locking regions ofpiecewise-linear maps(#162, p. 107)

Christopher Lustri
Nonlocal solitary waves
in nearest-neighbour
particle chains (#109,
p. 80)

Andrey Pototsky
Shaping liquid drops byvibration (#144, p. 98)

Chancellor 4
Chair: Graeme Wake

ANZIAM 2018 Conference Handbook24

1:10–1:30
1:30–2:30

12:40–1:00

12:20–12:40

Murk Bottema
Cows and largest
connected sets (#20,
p. 36)

Grand Ballroom 1
Collin Zheng*
Mathematical models forcheckpoint blockade
treatments in cancer
immunotherapy (#208,
p. 131)

Mike Chen
Multiscale modelling offibre-reinforced hydrogels
for tissue engineering(#27, p. 40)

Grand Ballroom 3Mark Flegg
Interfacing diffusive
particle models between
various scales (#52,
p. 52)

John Elie Sader
Why does aninverted-flag flap in a
uniform steady flow?
(#160, p. 106)

Harbour View 2
Barry Cox
Graphene folding aroundcarbon nanotubes (#35,
p. 44)

Closing remarks, Grand Ballroom 2–3
Lunch - Mezzanine

Larry Forbes
Fluid mechanics and thegentle art of viscometry(#54, p. 53)0Grand Ballroom 2
Christian Thomas
Globally unstablebehaviour in therotating-disc boundary
layer (#183, p. 118)

*student talkThursday afternoon continued
Chancellor 4
Paul Smith
The effect induced in the
far-field pattern by therounding of corners of ascatterer illuminated bya plane wave
electromagnetic field(#166, p. 109)
Peter Ballard
The impact oftime-dependenttransmission rate on theprobability of epidemic
fade-out (#13, p. 32)

ANZIAM 2018 Conference Handbook

25

ANZIAM 2018 Conference Handbook

26

4

Conference Abstracts

1

On the fundamental of Rayleigh-Taylor instability and Rayleigh-Taylor interfacial
mixingSnezhana I. Abarzhi
The University of Western Australia
Timetable: p. 23

Rayleigh-Taylor instability (RTI) develops when fluids of different densities are accelerated against
their density gradient. Extensive interfacial mixing of the fluids ensues with time. The Rayleigh-Taylor(RT) mixing controls a broad range of processes in nature and technology. Examples include the
RTI that quenches ignition in inertial confinement fusion; blast wave induced RT mixing in corecollapse supernova that creates conditions for synthesis of heavy mass elements; RT unstable plasma
irregularities in the Earth’s ionosphere that result in climate change on regional scales; RT mixing ofwater and oil bounding efficiency of fossil fuel recovery; the RTI that governs material transformationof under impact in nano-electronics. Our ability to reliably model RT mixing with variable acceleration
can advance knowledge of fundamentals of nature and have a major positive impact on energy andenvironment.
Traditionally, it was presumed that the RTI leads to uncontrolled growth of small-scale perturbations,
single-scale nonlinear dynamics, and extensive turbulent mixing that is similar to canonical turbulence.
The recent success of the theory and experiments suggests an alternative scenario of RTI evolution. It
finds that the RT dynamics is multi-scale, well correlated and sensitive to the initial conditions, andthe laminarization of RT mixing can occur due to the effects of acceleration, interfaces, and accelerated
shear.
In this work, we focus on the classical problem RT mixing induced by variable acceleration with powerlaw time dependence. By applying group theory, we find symmetries, invariants, scaling, correlations
and spectra of the RT mixing, and quantify its sensitivity to the initial conditions. In a broad rangeof the acceleration parameters, critical points are identified at which the RT dynamics are ballistics,
quasi-Kolmogorov, steady flex, diffusive, and dissipative. For super-ballistics and super-Kolmogorov
dynamics, RT mixing has a greater degree of order when compared to canonical turbulence. For
up-steady-flex and super-diffusion - larger velocity fluctuations occur at larger scales, whereas for
sub-diffusion and dissipation - larger velocities correspond to smaller scales. The properties of RT
mixing depart substantially from those of canonical turbulence thus opening new perspectives forbetter understanding and control of RT dynamics in nature and technology.

2

The determination of Open Science, Open Innovation paddy production in Indonesia
using geographically weighted regression

Jamilatuzzahro Abdul Fatah
Bandung Institute of Technology
Timetable: p. 20

ANZIAM 2018 Conference Handbook

27

Indonesia is an agricultural country with a large proportion of its population living from cultivation or
farming, so agriculture is a sector that plays an essential role in the welfare of Indonesians. Rice is
one of the leading food crops that have a strategic value and a significant influence in the economic,
environmental, and socio-political sectors. The basic premise of Open Innovation is to open theinnovation process to all active players so that knowledge can circulate more freely and can betransformed into products and services that create new markets, fostering a stronger entrepreneurial
culture. Specific innovations can no longer be seen as a result of established and isolated innovation
activities but as a consequence of a complicated joint creation process that involves the flow of knowledge
across economic and social environments. Furthermore, Open Science is a new approach to scientificprocesses based on collaboration and a new way to spread knowledge using new digital technologies.
The collaboration between spatial, open science and open innovation can be effective to analyze thepotential of planting as well as production. Therefore, it is necessary to have a model for predicting
the amount of rice production, especially in Indonesia. The data used is the historical data of paddy
production and land area at 34 Province in Indonesia. In a nutshell, we were using Geographically
Weighted Regression (GWR) with AIC precision value of 980.3654 and R Square global of 0.9855874.
It means that 98.55% of variation occurred in the paddy production was influenced by the included
explanatory variables.

3

Additional information in robust approach to mathematical finance

Anna Aksamit
The University of Sydney
Timetable: p. 19

Robust approach to pricing and hedging derivatives has been an active field of research in mathematicalfinance over the recent years. In this approach, instead of choosing one model for price dynamics, one
considers superhedging simultaneously under a family of models, or pathwise on the set of feasible
trajectories. Typically dynamic strategy in stocks and static trading in some European options areallowed. Usually in the literature the focus is on the natural filtration F of the price process S. Here
we give an extension to a general filtration G which includes the natural filtration of the price process
F ⊂ G. Two filtrations can model asymmetry of information on the market. The larger filtration canbe obtained by considering additional market data and analyses. This talk is based on joint work with
Zhaoxu Hou and Jan Oblój.

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Withdrawal of water from within a sand column*

Suha Al Ali
Murdoch University
Co-authors: Graeme Hocking
Timetable: p. 11

We consider a free surface problem of flow in a vertical sand column when water is being withdrawn.
The problem is important in managing valuable underground water resources. One powerful methodof finding such a solution is to use conformal mapping and spectral techniques. The method is tocompute the solution for a line sink in the vertical duct and then use Fourier techniques to correct for
the nonlinear surface conditions. The results of the numerical solution for the steady case are comparedwith the analytic solution to the approximate, linearized equations. It is found that there is an increasein the depth of the dip in the free surface as the sink increases strength, and that no solutions are
possible if the flow rate is too large. The effect of the bottom starts to be important if the sink is morethan half of the depth. Some unsteady solutions using a similar technique will also be presented.

5

An analysis of the first order growth fragmentation equation for special division
kernels

Adel Ahmed Almalki
Massey University
Timetable: p. 11

The growth fragmentation equation is a linear integro-differential equation describing the evolution ofcohorts that grow, divide and die over time. In this talk we focus on a special choice of division kernelthat models size structured cell cohorts that divide into daughter cells of equal size. This problem
reduces to an initial-boundary value type that involves an advanced partial differential equation. There
are no general techniques for solving these problems. The constant growth rate case has been studied
by a number of researchers. In particular it was shown that the large time solutions converge to a
special solution; the separable solution. We look at the case when the growth rate is linear. This
problem can be solved analytically for monomial division rates. We show that the large time dynamics
for this case differ markedly from the previous case. Specifically, the solutions approach a time-periodic
attracting solution.

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Modelling causality: integral equations versus ODEs

Robert Scott Anderssen
CSIRO
Timetable: p. 11

In the modelling of viscoelasticity, the tradition is to work with the integral equation formulation
first proposed by Boltzmann which correspond to first kind Volterra (causal) convolution integral
equations. The earlier models proposed by Maxwell, Kelvin and Voigt were differential equation
models. The key observation of Boltzmann that led to his integral equation formulation was that,
unlike for a perfect elastic material where the reference state is the original state, the reference state
for a viscoelastic material has to be the current state, since it is impossible to return to the originalstate. The advantages of using first kind Volterra integral equations to model causal dynamics, which
includes linear viscoelasticity as a special case, rather than ODEs, will be discussed and illustrated.
The key is the step strain experiment. The advantage of using causal integral equation models inbiology will be illustrated with the modelling of the genetics of vernalization.

7

Guessing how triangles will split in half: Laplacians and cell division

Christopher Angstmann
University of New South Wales
Timetable: p. 23

There is a long history of empirical rules that describe the geometry of dividing cells. In many simple
cases, such as rod shaped bacteria like e.coli, the division will occur symmetrically. In more complicatedcell shapes it seems more difficult to intuit how exactly they will divide. In this talk I will show
how the division plane in many cases relates to the eigenfunctions of a Laplacian operator definedover the surface of the cell. The use of irregularly shaped cells, such as pleomorphic archaea, gives agreat example of the robustness of this connection. Whilst there are other possible reasons for thisempirical observation to exist, I will show how it naturally arises from a Turing instability in a set ofreaction-diffusion equations.

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Modelling malaria parasite development before and after drug treatment

Rosemary Aogo
University of New South Wales
Timetable: p. 13

The use of antimalarial drugs has significantly reduced mortality due to malaria, however, the emergenceof resistance to the most effective and widely used antimalarial drugs (artemisinin derivatives) impedes
this progress. Moreover, artesunate has been reported to have high treatment failure when not used in
combination with other drugs, and this may be due to a persisting population of parasites that goes
into an inert state and recovers later (dormancy). Further, we have observed previously that stress cancause parasites to mature more slowly, which is perhaps a general survival strategy of the parasite, anda similar effect has been observed after drug treatment. More recently artemisinin resistant parasites
have been studied and it has been found that they have an altered development pathway, which
protects parasites during treatment. Hence, we are interested in studying the development of parasites
through their life cycle without treatment and how treatment with different drugs perturb this normal
development. Here, using a novel experimental system, we track the progress in life stages of malaria
parasites taken from mice grown in culture. We do this by measuring the RNA and DNA content
of parasites over time. Our unique experimental set up allows us to track the parasite throughout
their life cycle after treatment with different doses of mefloquine and/or artesunate. By formulating
an age-structured partial differential equation model of parasite as well as fitting mixture models we
attempt to determine whether the action of antimalarial drugs on parasites i) slows down parasite
growth, ii) impairs a proportion of parasites which then mature slowly compared to the unaffected
fraction, or iii) arrests parasite development at a particular stage in their life cycle.

9

The Holling-Tanner predator-prey model with strong Allee effect on prey

Claudio Arancibia
Queensland University of Technology
Timetable: p. 22

In this work a Holling-Tanner predator-prey model is analysed incorporating a strong Allee effect onprey and with a functional response of Holling type II. The analysis of the model complements resultsof previous articles that consider the Holling-Tanner model with a weak Allee effect on prey.
We show the existence of significant differences compared with the well-known Holling-Tanner model,
since new equilibrium points can appear in the first quadrant. Besides, the model presents rich dynamics
for different parameter values and it is possible to prove the existence of:(i) a separatrix curve in the phase plane dividing the behaviour of the trajectories,(ii) a homoclinic curve generated by the stable and unstable manifolds of a positive equilibrium point.
When this curve breaks it generates a non-infinitesimal limit cycle,(iii) different kinds of bifurcations, such as: saddle-node, Hopf, Bogadonov-Takens and homoclinic.

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The system has solutions highly sensitive to initial conditions. To simplify the calculus, we considered
a topologically equivalent system with a small number of parameters. For this new model, we provethat for certain value of parameters the model exhibits multi-stability phenomenon since there exists a
stable limit cycle or a stable positive equilibrium point.

10

Localizing softness and stress in topological metamaterials

Guido Baardink
Kyushu University
Timetable: p. 19

The softness and rigidity of certain ball-spring networks can be described by a topologically protected
polarization field. By introducing dislocations to such a polarized lattice we can locally manipulate theyield response.

11

Maximal regularity for stochastic Volterra integral equations

Boris Baeumer
University of Otago
Co-authors: Markus Antoni and Petru Cioica-Licht
Timetable: p. 24

We present an approach to obtain maximal regularity estimates for solutions of stochastic Volterra
integral equations driven by a multiplicative Gaussian noise. The main part consists of the proof ofsuitable estimates for deterministic and stochastic convolution operators. Starting with the scalar-valued
case, we use functional calculi results to obtain the corresponding estimates for the operator-valued
setting. Once maximal regularity estimates for convolutions are obtained, appropriate Lipschitz
and linear growth assumptions on the nonlinearities will lead to unique mild solutions with Holder
continuous trajectories.

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32

The fundamental equation of life

Rowena Ball
Australian National University
Timetable: p. 23

The role of random fluctuations of a non-equilibrium flow in pre-biotic chemistry has received much lessattention than the non-equilibrium condition itself. Plausible environments for life’s origin were not
only strongly driven, to create sustained disequilibria, but temporally messy too, because input flows
through an inhomogeneous matrix were subject to fluctuations. But Brownian motions, or normally
distributed, random thermal fluctuations, occur regardless of whether a system is at macroscopic
equilibrium or not. It is self-evident that life cannot exist in an equilibrium setting.
We have modelled the putative hydrothermal rock pore setting for the origin of life on Earth as a
train of continuous flow units coupled in series. Perfusing through the train are reactants that giverise to thermochemical and pH oscillations, which drive the production of monomers and dimersfrom activated nucleotides. The dynamical equations that model this system are fully thermallyself-consistent. Crucially, we built stochasticity of the inputs into the model. Interrogating thecomputational results, we found (i) that Gaussian perturbations of the inputs to a system do not induce
Gaussian fluctuations in the outputs, and (ii) that the output fluctuations must exhibit a left-skewed,
right-weighted probability distribution for a prebiotic chemical system to evolve towards a living system.
This ‘Goldilocks’ distribution, when its moments and parameters are characterized, is the fundamental
equation of life. It tells us not only that fluctuations are essential for life to originate, but more:that for a prebiotic chemical system to live it must spend enough time at high temperatures to carryout essential high activation energy reactions, but not so much that reactant is totally consumed, or
destroyed, or catalytic surfaces degraded.
Our results have placed stochasticity explicitly at centre stage in the origin-of-life drama. They also
vindicate the general approach of constructing and running a simple toy model to learn important new
information about a complex system.

Ball, R.; Brindley, J. 2017. Toy trains, loaded dice, and the origin of life: Dimerization on mineralsurfaces under periodic drive with Gaussian inputs. Royal Society Open Science 4:17014. (doi:
10.1098/rsos.170141).

13

The impact of time-dependent transmission rate on the probability of epidemic fadeout

Peter Ballard
The University of Adelaide
Timetable: p. 25

Epidemic fade-out refers to the situation in which an infection dies out after the first wave of an
outbreak. Previous research has assumed constant parameters, but obviously some parameters canANZIAM 2018 Conference Handbook

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change over time. In particular, the transmission rate parameter is likely to vary over the course of theyear, both due to the climate, and due to changes in human behaviour patterns.
For the SIR-with-demography and SIRS infection models, I present a method for the calculation of theprobability of epidemic fade-out when the the parameters are not constant. I then present some results
for two different scenarios: flu-like parameters with a sinusoidal variation in transmission rate due tothe seasons; and measles-like parameters with a step change in transmission rate due to the switch
between school vacations and term time.

14

Modelling mange in the common wombat

Nick Beeton
University of Tasmania
Timetable: p. 21

Some Tasmanian populations of the common wombat (Vombatus ursinus) are threatened with extinction
by infection with sarcoptic mange, caused by the mite Sarcoptes scabiei. Little is known about why
only some populations, such as Narawntapu National Park (NNP) in the state’s north, are susceptible
whereas others only experience minor, non-threatening outbreaks.
In NNP, treatment of wombats is performed by installing flaps covered with insecticide on the entrance
to their burrows, so that they push through and receive a dose when entering or leaving.
In this talk, we describe two compartmental ODE models of the wombat-mite system. The first assumes
spatially homogenous, well-mixed populations of susceptible, pre-symptomatic, symptomatic, andrecovered wombats as well as fomites: substances (such as burrow soil) that support mites, which canthen infect wombats. The second instead assumes that only a proportion of burrows in the landscape
are infected with fomites at any given time, which are moved between burrows by infected wombats.
We examine both models, performing dynamical systems analysis as far as analytically possible, andpresent numerical sensitivity analyses, varying important parameters such as wombat treatment rate,
fomite mortality and fecundity.
We find the two models give sometimes complementary, sometimes contradictory and sometimes
surprising results, providing ideas for future disease management as well as a cautionary tale about theapplicability of results where model assumptions are not necessarily accurate.

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34

Stochastic optimal control of a solar-powered car

Erika Rana Gabriela Belchamber
University of South Australia
Timetable: p. 14

The World Solar Challenge (WSC) is a biennial event held in Australia, where solar cars are driven from
Darwin to Adelaide. The Australian Technology Network of Universities is designing and building asolar car to compete in 2019. The solar car must travel over 3000 km in only six days. This presentation
details work on a driving strategy the ATN team will use with their solar car.
The speed a solar car travels is restricted by the solar energy it collects. If the battery is empty andavailable solar energy is low, the car will have to drive slowly or stop. The car will then have to wait
until there is enough solar energy to power it at a higher speed. This disruption jeopardises the car’s
ability to complete the WSC. If solar energy is known in advance, an optimal driving strategy can befound so enough energy is collected for the car to travel at a high speed. When solar energy is notknown in advance, the driving strategy must cope with an unknown solar energy.
One possible driving strategy is minimax regret, where the maximum regret is minimised. In thispresentation, a minimax regret strategy is described and the distance travelled is compared with the
distance travelled in the optimal solution. We use historic solar energy data from stations along the
WSC route to test the minimax regret strategy and find the distance travelled is within 1% of the
optimal distance.

16

Models for the spread of Wolbachia in mosquito populations as a means of suppressing dengue fever transmission

Sarah Belet
Monash University
Timetable: p. 11

Dengue fever poses a major health issue in tropic environments. Particular breeds of mosquitoes,such as the aedes aegypti species common to areas including northern Queensland, carry the virus.
Humans contract the dengue virus when bitten by a mosquito that carries it and so, historically,
attempts at curtailing the spread of dengue have focused on controlling the size and spread of mosquito
populations. Several factors make this an astronomically difficult task to accomplish on any reasonable
scale, however, and so more novel methods of suppressing dengue outbreaks are being explored. One
such method is the introduction of parasitic bacteria called Wolbachia into mosquito populations, which
prevents mosquitoes from passing on blood-borne viruses to those it bites. A Wolbachia invasion has
strong potential to completely saturate mosquito populations due to a mechanism called cytoplasmic
incompatibility. The mathematical modelling problem here becomes twofold - first, the task of inferring
the position of mosquito populations, and then the modelling of Wolbachia spreading through these
populations. Here, we will be discussing the effects and mechanisms of Wolbachia in more detail,including the phenomenon of cytoplasmic incompatibility. Next, recent developments in modelling

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mosquito populations such as the use of semi agent-based models will be outlined, within the context
of predicting the spread of Wolbachia in order to prevent further dengue outbreaks.

17

Acoustic metamaterial chains involving inertial amplification

Luke Bennetts
The University of Adelaide
Timetable: p. 24

A desirable property of acoustic metamaterials is that they have wide and deep low-frequency bandgaps.
The standard method for generating low-frequency bandgaps is to use local resonators, but thisoften requires prohibitively heavy elements. A practical alternative is to induce anti-resonances usinginertial amplification, by equipping the structural elements with lightweight attachments that exert
inertial forces proportional to the vibrational forces. This presentation will outline the mechanism bywhich inertial amplification can be used to control the location and depth of bandgaps along infinite
mass-spring chains, via geometrical properties only. The theory will be illustrated by direct numericalsimulations.

18

Detecting and characterising coherent structures and their evolution in non-autonomous
dynamical systems

Chantelle Blachut
The University of Queensland
Timetable: p. 12

Manifestations of coherent structures are evident throughout the physical world. This research aims
at understanding and characterising the behaviour of such structures. We develop and implement
algorithms for the detection of minimally dispersive regions in a non-autonomous dynamical setting
and propose a method to characterise transport features of the underlying system.
Previous authors have shown that the singular value decomposition (SVD) of a transfer operator
induced by a dynamical system is useful for identifying the regions of phase space that exhibit minimal
dispersion over a time period of interest. Our work considers the SVD of a cocycle of numericallyestimated transition matrices for a time-dependent dynamical system, investigates the evolution of
singular vectors in association with Oseledets subspaces and develops algorithms to characterise thebehaviour of coherent structures in non-autonomous systems. Our results show that this method allows
one to retrieve important information about how and when such structures merge and split in thepresence of an underlying time-dependent chaotic flow.

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36

Importance sampling for partially observed Markov models

Andrew BlackThe University of Adelaide
Timetable: p. 14

Particle marginal Metropolis Hastings (pmMH) is a popular method for performing Bayesian inference
when it is only possible to simulate from the underlying model. This uses a particle filter to estimate
the likelihood, which is then used in a basic Metropolis Hastings algorithm. A well know problem withparticle filters is that the more accurate the observations of a system, the worse the filter performs. For
models where we observe a single component of the state exactly, the cost of producing simulations
becomes very high. In this talk I will discuss some recent work using importance sampling to generaterealisations of Markovian models that match observations exactly. When used in a pmMH scheme, theimportance of sampling is that it provides a large speed-up in terms of the effective sample size perunit of computational time compared to simple bootstrap sampling.

20

Cows and largest connected sets

Murk Bottema
Flinders University
Timetable: p. 25

Flecks of fat in steaks, called marbling, influence taste and consumer appeal. Marbling in beef is alsoof interest in understanding fat metabolism. In a previous study, the number of marbling flecks, theirsize distribution and shape characteristics were associated with levels of vitamin A in the animal’s
diet. When the study was extended to characterising marbling in three dimensions, the marbling was
found to comprise a single giant fleck accounting for roughly 80% of the total marbling, plus thousandsof small flecks. Whether this observation reflects the true structure of marbling in beef or whether
the observed large connected sets were due to the discretisation into voxels raised the following question:

Given a random binary array with a given density of ‘on’ voxels, what proportion of such voxels are
expected to form the largest connected component of the set of on voxels?

Several studies on the largest connected components in random graphs have appeared but the literaturedoes not report a clear answer to the question above. Indeed, a formula for the expected size of thelargest component has proved elusive. Simulations suggest that the size of connected marbling structure
observed in the data cannot be due to chance alone. Observations are consistent with marbling forming
a single connected structure. As do the cows, we continue to ruminate on the combinatorics question.

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37

Logarithmically-discretised population balance models of aggregation and fragmentation

Calum Braham
The University of Western Australia
Co-authors: Neville Fowkes, Brendan J. Florio, David M. Walker and Michael Small
Timetable: p. 15

Many physical systems can be modelled as a set of particles interacting through aggregation andfragmentation. All but the simplest models of such systems are intractable analytically and, as such,
simulations of the time evolution of particle size distributions generally require a discretised particle
size domain. The logarithmically-discretised aggregation population balance models of Hounslow et al(1988) and Litster et al (1995) are re-derived using a local, collision-based framework. This derivation
has advantages in simplicity and tractability, as local conservation of mass can be ensured without theneed for correcting factors or the consideration of intra-bin particle distributions. Unlike the original
derivation, appropriate evolution of particle numbers and conservation of mass can be demonstrated
without assuming size-independent collision kernels or an infinite size domain, showing the model isvalid for more general use. The model is also generalised to allow any logarithm base for the particle
size discretisation and a framework is developed to treat fragmentation consistently.

22

Quantum mechanics from a classical fluids perspective

Philip Broadbridge
La Trobe University
Timetable: p. 21

As shown by Madelüng in 1927, quantum mechanics can be fully described as a system consisting ofa real-valued probability density and a real-valued velocity field that satisfies a forced Burgers’ fluid
equation. It is envisaged that the coupling of a macroscopic measuring device introduces shear to
the fluid. With vorticity, the fluid has a vector potential as well as the single scalar potential that isa function of the Schrödinger wave function. This suggests a classical description of the mysterious
decoherence or collapse of the wave packet during which time the Schrödinger equation no longer
applies. After the dissipation of vorticity, quantum equilibrium is restored, the Born probability rules
again apply, and vorticity collapses to a few isolated point vortices which have long been acceptedwithin angular momentum eigenstates since the time of Bohr and Sommerfeld. It has been suggested
also that quantum disequilibrium in the early violent universe may explain some discrepancies in thecosmic microwave spectrum. This is not a usual type of ANZIAM talk but it shows that QM may be
open to discussion in the language of fluid mechanics.

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38

A Bayesian computational approach to explore the optimal duration of a cell proliferation assay

Alexander Paul Browning
Queensland University of Technology
Timetable: p. 16

Cell proliferation assays are routinely used to explore how a low-density monolayer of cells grows withtime. For a typical cell line with a doubling time of 12 hours (or longer), a standard cell proliferation
assay conducted over 24 hours provides excellent information about the low-density exponential growthrate, but limited information about crowding effects that occur at higher densities. To explore how we
can best detect and quantify crowding effects, we examine a stochastic individual based model where
cells proliferate according to a generalised logistic growth model. We then apply approximate Bayesiancomputation to quantify the decrease in uncertainty in the crowding mechanism as the experimental
duration is increased.

24

Active sonar remote identification of materials

Jim Byrnes
Prometheus Inc.
Timetable: p. 16

For sonar detection of submarines the baseline technologies incorporate Doppler and target motion
analyses as key parameters. However, these clearly will fail if the submarine is sitting on the bottom,
as those of several countries are known to do. To address this and other concerns, at the request of
Admiral Tom Eccles (Head of NAVSEA PEO Submarines at the time) Prometheus Inc. adapted its
MISAR (Material Identification Synthetic Aperture Radar) technology to the sonar environment. Ourdemonstrated solution, as recognized by the US DoD1 is known as MIRK (Material Identification
Reflectivity Kernel). As stated there, MIRK ‘Provides the warfighter the capability to reliably detectbottomed submarines and mines in real time with fewer false alarms, significantly increasing the fleet’s
ability to defeat Anti-Access / Area Denial (A2/AD) threats.’
Echo returns from active sonar interrogation of an underwater object contain reflectivity kernel (RK)clues. We discuss our novel time-domain deconvolution technique and additional signal processing
tools that yield, in a highly stable and real-time manner, reliable RK estimates. Thus MIRK is able toclassify active sonar contacts based on this material discrimination technique.
We further discuss enabling requirements for MIRK, specific real-world examples of its use, environments
where it has proven successful, and limitations on its applicability.
1 http://www.defenseinnovationmarketplace.mil/RIF.html, FY 2011 cell F41

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39

Objective detection of rotationally coherent vortices

Sophie Calabretto
Macquarie University
Timetable: p. 15

The detection and forecasting of ocean vortices is important in the field of geophysical fluid dynamics
as these eddies tend to play a major role in the underlying flow dynamics of the ocean. We approach
the issue of ocean eddy identification from a rotational-coherence basis via the identification of elliptic
Lagrangian coherent structures (LCSs), and seek the boundaries of rotationally coherent Lagrangianvortices, which are formed by tubes of deforming fluid elements that complete equal bulk material
rotation relative to the mean rotation of the deforming fluid volume.

26

Calculating how long it takes for diffusive processes to effectively reach steady state
without computing the transient solution: application to groundwater flow

Elliot Joseph Carr
Queensland University of Technology
Timetable: p. 19

When a diffusive process is disturbed from an initial state of equilibrium by a sudden change inboundary conditions, it takes an infinite amount of time to return to an equilibrium (steady) state.
While this is strictly true, because the transient solution of the underlying PDE approaches the steadystate solution exponentially, there exists a finite time at which the diffusive process is effectively atsteady state (i.e. the difference between the transient and steady state solutions is less than a small
specified tolerance). A common measure of this so-called finite transition time is the mean action
time, which is the expected time of the process calculated by identifying a cumulative distributionfunction that tracks the progress of the transient solution towards steady state. In this talk, I extend
the concept of mean action time and show how the higher order moments can be used to calculate
the finite transition time without computing the transient solution. This approach provides a uniquemathematical connection with the heuristic argument that the time required for a one-dimensional
linear homogeneous diffusion problem to reach steady state is proportional to L2 /D, where L is thelength of the medium and D is the diffusivity. A case study involving flow through heterogeneous
porous media, where the saturated hydraulic conductivity varies spatially, confirms the accuracy andefficiency of the method.

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40

Multiscale modelling of fibre-reinforced hydrogels for tissue engineering

Mike ChenThe University of Adelaide
Co-authors: Laura Kimpton, Jonathan Whiteley, Miguel Castilho, Jos Malda, Colin Please, Sarah Waters and Helen
Byrne
Timetable: p. 25

Tissue engineering aims to grow artificial tissues in vitro to replace those in the body that have beendamaged through age, trauma or disease. A recent approach to engineer artificial cartilage involves
seeding cells within a scaffold consisting of an interconnected three dimensional printed lattice ofpolymer fibres combined with a cast or printed hydrogel, and subjecting the construct (cell-seededscaffold) to an applied load in a bioreactor. A key question is to understand how the applied load is
distributed throughout the construct to the mechanosensitive cells.
To address this, we employ homogenisation theory to derive macroscale governing equations for theeffective material properties of the composite, where we treat the fibres as a linear elastic material
and the hydrogel as a poroelastic material and exploit the disparate length scales (small inter-fibre
spacing compared with construct dimensions). This description reflects the orthotropic nature of
the composite. To validate the model, solutions from finite element simulations of the macroscale,homogenised equations are compared to experimental data describing the unconfined compression offibre-reinforced hydrogels.

28

Compliance for Personal Financial Advice

Sue Ann Chen
IBM Research Australia
Timetable: p. 20

In recent years, Australian financial advice licencees have had to pay hundreds of millions of dollars infinancial penalties and compensation, in addition to having to undertake extensive audit programs
due to provision of non-compliant financial advice. Existing procedures to assess the compliance of aStatement of Advice (SoA) document are not only time-consuming, but are also severely limited bysampling issues. By leveraging deep learning and natural language processing techniques, our project
aims to automatically identify the at-risk documents, thus allowing for a more efficient and thoroughcompliance assessment procedure.

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41

Understanding how immunity, strain diversity and prevalence interact in multistrain pathogens using agent-based modelling

Rebecca Chisholm
The University of Melbourne
Co-authors: Nicholas Geard
Timetable: p. 11

Infectious diseases are frequently caused by pathogens that exist in multiple phenotypically distinct
strains that may differ in traits including drug resistance, virulence, and by the expression of antigens
that trigger different host immune responses. The ability of multi-strain pathogens to trigger strainspecific and cross-strain immune responses poses challenges for understanding their transmission andcontrol. These challenges are amplified for pathogens with very large numbers of circulating strains(high diversity). In this talk I will outline how we are using agent based models to generate newunderstanding of how strain-specific and cross-strain immunity may interact with strain diversity tosustain the transmission of such multi-strain pathogens. I will discuss our results in the context ofunderstanding the transmission of Group A Streptococcus (GAS), an obligate human pathogen withover 200 molecular types, and a major cause of death and disability globally. Our results indicate thatstrain-specific immunity and low levels of cross-strain immunity may be a contributing factor to thehigh endemicity of GAS skin infections that exist in settings of poverty, where there is generally highstrain diversity and no predominant strains.

30

Pregnancy and beyond: how mathematical modelling could improve early life health

Alys Rachel Clark
The University of Auckland
Timetable: p. 19

Pregnancy and early life is a time of rapid physiological development: organs form and develop overtime periods of weeks and months. It is also one of the most difficult periods of life to observe as many
clinical techniques used to examine adults bodies in disease are too risky to use in pregnancy and earlychildhood. So how do we identify risk of poor outcome in early life with relatively low resolution clinicaltools? Data defining risk are acquired across many disciplines (such as medicine and cell biology) andprovide only snapshots of development. Mathematical modelling potentially provides the missing link
between these diverse data sources to improve metrics of health in early life.
In this talk I will present our strategies to model physiological systems in early life, with a focus onmodelling oxygen transport and exchange. I will discuss how we use models to better understand thephysiological process of oxygen exchange in health and disease, the development process itself, and thepotential of mathematical models to improve clinical decision making.

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42

Calcium oscillations in hepatocytes: how are they shaped?

Ielyaas Cloete
The University of Auckland
Timetable: p. 20

Calcium in hepatocytes (liver cells) modulate diverse functions, including bile secretion, glucose andenergy metabolism and vesicular trafficking. A major question in the study of calcium signalling in
hepatocytes is how these distinct cellular processes are controlled and organised via coordinated spatial
and temporal calcium signals.
Downstream cellular responses are controlled via intracellular calcium oscillations but the underlying
mechanisms which shape these oscillations have yet to be elucidated. We will determine the effects
calcium feedbacks on Phospholipase C (PLC), inositol trisphosphate kinase, as well the feedbacksof protein kinase C (PKC) on the hormone receptor have on the whole-cell calcium signals. The
data suggests that hormone-induced calcium oscillations require positive calcium feedback on PLC
to generate inositol trisphosphate oscillations, yielding cross-coupling between calcium and inositol
trisphosphate. Furthermore, there is also a negative feedback pathway, cross-coupling PLC activation
to PKC which serves to terminate calcium spikes.
To show this we will construct a model of calcium oscillations in hepatocytes which will include thenecessary feedback mechanisms.

32

Multi-strain epidemic models for transmission and evolution of drug resistant pathogens

Robert Cope
The University of Adelaide
Timetable: p. 12

The evolution of antimicrobial resistance in endemic infectious diseases is of substantial public healthconcern, particularly in developing countries. New drug-resistant strains are continually emerging,and this can occur in a variety of ways, depending on characteristics of the disease or the available
treatments. We describe a general stochastic epidemic model for the emergence and transmissionof drug-resistant disease strains in a population, wherein upon receiving (unsuccessful) treatment,
individuals may transition into a different infectious class. We investigate the ways in which different
parameter choices can describe different potential evolutionary dynamics, and how simple building
blocks can be combined to produce more complex behaviours.

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43

On system behaviour using complex networks of a compression algorithm

Debora Cristina Correa
The University of Western Australia
Co-authors: David M. Walker and Michael Small
Timetable: p. 16

We construct complex networks of scalar time series using a data compression algorithm. The structureand statistics of the resulting networks can be used to help characterize complex systems and one
property, in particular, appears to be a useful discriminating statistic in surrogate data hypothesis
tests. We demonstrate these ideas on systems with known dynamical behaviour and also show that ourapproach is capable of identifying behavioural transitions within EEG recordings as well as changes
due to a bifurcation parameter of a chaotic system. The technique we propose is dependent on acoarse grained quantization of the original time series and therefore provides potential for a spatial
scale-dependent characterization of the data. Finally the method is as computationally efficient as
the underlying compression algorithm and provides a compression of the salient features of long timeseries.

34

Fat and muscle glucose regulation same-same or different?

Adelle Coster
University of New South Wales
Timetable: p. 15

Insulin regulates glucose uptake in mammalian fat and muscle cells. The extracellular insulin concentration controls the distribution of the glucose transporter protein GLUT4. We have previously shownthat the regulation of glucose uptake in fat cells can be described by a compartmental system of ODEs
with six steps: 1) endocytosis, 2) sorting/recycling from endosomes back to the cell surface, 3) rescue
from degradation, 4) sequestration into storage vesicles, 5) release from retention in the storage vesicles
and 6) fusion of the storage vesicles to the plasma membrane. Insulin stimulates three of these steps infat cells.
Can the network structure of the model for the fat cell also describe the dynamics of translocation of
GLUT4 in muscle cells? Five experimental data sets from different protocols are used simultaneously to
optimise the model parameters and determine the main regulatory differences between fat and muscle
cells. Predictions are then made about the effects of different biochemical perturbations on the system.

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44

Graphene folding around carbon nanotubes

Barry CoxThe University of Adelaide
Co-authors: Tom Dyer and Ngamta Thamwattana
Timetable: p. 25

Folding graphene materials have the potential to create complex structures with new properties.
Intercalating molecules into these folds is a method of one-dimensional functionalisation of the graphenesheet. Here we investigate the effects of incorporating a single-walled carbon nanotube in a graphenefold. Balancing the van der Waals interactions and the elastic energy leads to a curved structure that
we derive using a variational approach. Results are compared with molecular dynamics simulations.

36

Resonance, symmetry and pattern selection in Langmuir circulation

Lidong Cui
Swinburne University of Technology
Co-authors: William R.C. Phillips
Timetable: p. 11

I undertake a weakly nonlinear analysis of resonant interactions of Langmuir circulation (LC), which is alarge (up to stadium sized) roll-like pattern in water bodies that arises due to wave-current interactions.
LC helps mix the upper ocean and is thus important in climate dynamics. In this regard, it is crucial
to understand LC’s scale and geometry. LC is described by an averaged set of partial differential
equations known as the CL-equations. From the CL-equations we derive amplitude equations by boththe multiple-scale method and the amplitude expansion method. With the amplitude equations, we
discuss the 1:2 and the 1:3 resonances, and we also discuss the Eckhaus stability. We find, among
other things, that the preferred spacing of LC rolls can be doubled, or even tripled, due to resonance.
Resonance can also lead to mixed-modes as well as travelling waves, and can modify the Eckhaus
stability. In the analyses, we consider various boundary conditions with different symmetry properties.

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37

Iterative Deconvolution

Frank de Hoog
CSIRO
Timetable: p. 12

In many practical situations, the recovery of information about some phenomenon of interest f reduces
to performing a deconvolution on indirect measurements g that often take the form of the Fourier
convolution of f with a known point spread function p; namelyZ∞p(x − y)f (y)dy.

g(x) =−∞

Examples include the frequency response of the stress and strain in rheological oscillatory shear
measurements and the frequency response of electronic amplifiers, of microphones and loudspeakers,
and of brain waves.
However in practice, only discrete measurements, on a limited domain are available and this limits thetechniques that can be used to obtain approximations. Specifically, if the available data is relatively
local, then the approximations to the solution also need to be local. When the point spread function p
is narrow, iterative techniques will provide such local approximations if the number of iterations issmall.
A property required to ensure that the deconvolution of g is unique (given that it exists), is that
the Fourier transform of the point spread function p is positive. It is also a key property to take
into consideration when constructing appropriate discretization of the Fourier convolution and for theconstruction of appropriate iterations. These will be discussed in the presentation.

38

New results in the instability of compressible boundary layers

Jim Denier
Macquarie University
Timetable: p. 11

I discuss how and when compressible boundary layer transition from a laminar to a turbulent stateis of extreme importance in the design of a new generation of high speed transports. This talk will
present some new results on this topic, in which we demonstrate a new mode of instability that occurs
when the fluid physics is such that the boundary layers achieve “supervelocities”. How these occur,and why they might be important will be explained.

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46

Investigating the efficacy of antimalarial drugs using a mathematical model

Saber Dini
AMSI/University of Melbourne
Timetable: p. 11

Malaria is one of the deadliest infectious diseases in the world, causing around 500,000 deaths each year.
Artemisinin-based combination therapies (ACTs) have been used for two decades as effective first-line
treatment for malaria. However, the efficacy of these drugs has declined recently, due to the emerging
resistance of malaria parasites to ACTs. This is hence threatening the lives of people in malaria endemic
regions such as South-East Asia, and warrants developing alternative antimalarial treatments. Triple
artemisinin-based combination therapy (TACT) has been suggested as a novel strategy to overcome
the declining efficacy of ACT. Some pharmacological and clinical studies are underway, investigating
the efficacy, safety and tolerability of TACTs. In this work, we use mathematical modelling to provide
insights into how different mechanisms of resistance influence the efficacy of TACT. Of particularinterest, we investigate which dosing scheme of a TACT suffices to produce World Health Organisation(WHO) recommended cure rates.

40

Exact invariant solutions of time fractional evolution systems with variable coefficient

Khongorzul Dorjgotov
Kyushu University
Timetable: p. 20

Lie symmetry analysis is widely used in the study of ordinary and partial differential equations andsystems due to its efficiency and algorithmic nature. We consider the fractional diffusion-wave systems,
in which the derivatives in time variable is replaced by fractional derivative of arbitrary order. The time
fractional systems that we studied describes from diffusion process to the wave process, when the orderof fractional derivative varies from 12 to 1. We explicitly give the group invariant solutions to a class ofRiemann-Liouville time fractional evolution or diffusion-wave systems with variable coefficients. These
solutions correspond to each element in an optimal system of Lie algebra of infinitesimal symmetriesof the evolution system under consideration. We express the solutions using three kinds of special
functions: Mittag-Leffler functions, generalized Wright functions and Fox H-functions, and include somepreviously known solutions for particular cases. These solutions also solve time fractional diffusion-wave
equations with variable coefficients. For comparison of the behavior of solutions , we illustrate plots
subject to the order of fractional derivative.

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47

Solving high condition number systems

Craig Douglas
University of Wyoming
Timetable: p. 15

This talk presents results that combine two theoretically sound methods (spectral projection andmultigrid methods) together to attack ill conditioned linear systems. Our preliminary results show thatthe proposed algorithm applied to a Krylov subspace method takes many fewer iterations for solving
an ill-conditioned problem downloaded from a popular online sparse matrix collection. All previous
methods that are similar are for specific applications while our results are completely general.

42

Approximation of f -Divergence Measure in Information Theory and Applications

Silvestru Sever Dragomir
Victoria University
Timetable: p. 16

One of the important issues in many applications of probability theory & statistics is finding anappropriate measure of distance (or difference or discrimination ) between two probability distributions.
In this presentation we provide some approximations for the Csiszar f -divergence measure in information
theory. Some particular instances of interest such as Kullback-Leibler divergence, Jeffrey’s distance,
Hellinger discrimination etc. are also given. For preprint versions of this work please see the ResearchGroup in Mathematical Inequalities & Applications website http://rgmia.org/index.php.

43

Low order or high order? Wisdom may be in the middle...

Jerome Droniou
Monash University
Co-authors: Daniel Anderson
Timetable: p. 20

Tertiary oil recovery is a process through which a solvent, injected through a well in an undergroundoil reservoir, reduces the oil viscosity and thus enables it to flow through a production well. The
mathematical model is a non-linear, coupled system of an elliptic and a parabolic equation, the latterbeing advection-dominated. Low order numerical schemes for advection-dominated models rely on
upwinding for stability reasons, but said upwinding introduces additional numerical diffusion that
reduces the accuracy of the approximation. High-order methods coupled with upwinding ensures boththe stability of the scheme, and its accurate capture of the advection process... at an obvious increased
computational cost.

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In this talk, I will show that neither low-order nor high-order methods are the most efficient ones forsuch a coupled non-linear model, and that a middle-order method can realise the optimal accuracy/cost
ratio. The demonstration will be carried out using the Hybrid High-Order method, which is designed
to be applicable on generic meshes as encountered in practical applications, in which mesh elements
can have complex geometry that prevent the usage of usual conforming/non-conforming/mixed finite
element method.

44

On a conjecture about the simultaneous binary collision

Nathan Paul Duignan
The University of Sydney
Co-authors: Holger Dullin
Timetable: p. 20

This work explores a conjecture in celestial mechanics about the nature of the singularity at asimultaneous binary collision in the 4-body problem. The conjecture states that any attempt to remove
this singularity via block regularisation will result in a regularised flow that is no more than C 8/3
differentiable with respect to initial conditions. By restricting our attention to planar vector fields, we
examine how, despite the smoothness of a vector field, this curious loss of differentiability can occur.
We discuss how this work extends to higher dimensions and whether it will resolve the conjecture.

45

An ODE model for the transmission of the disease Nosema ceranae in honey beecolonies with demographic structure

Jonathan Eade
The University of Sydney
Timetable: p. 22

I present a mathematical model for the transmission of the disease Nosema ceranae through a honeybee colony. N.ceranae is a parasite which attacks the midgut of a honey bee, and has been posited asa contributing factor in the honey bee colony collapse disorder which is affecting agricultural sectors
worldwide. We formulate a system of ordinary differential equations, based on standard SIR diseasemodels, that includes important demographic features of the colony. The addition of food, brood
and an implicit age structure allows colony failures to be simulated on the same rapid time scale asobserved colony collapses. Results show how the disease can weaken honey bee colonies and increase
their susceptibility to other external stressors. A colony with a pre-existing infection may collapse
under an external stressor where a healthy colony would not. Multi-year colony failures have also been
simulated, in which an infected colony under stress is not strong enough post-winter to survive thetransition to spring conditions.

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49

A timely solution to the nurse rostering problem: an operations research approach

Mark Fackrell
The University of Melbourne
Co-authors: Ria Szeredi and Peter Taylor
Timetable: p. 15

The quality of a nurse roster has a great impact on the quality of patient care, due to its influenceon nurse work performance. Furthermore, the numerous conflicting objectives of the hospital makethe task of producing a high quality roster extremely difficult to undertake manually. Research into
efficient ways to produce high quality nurse rosters is thus crucial. Motivated by the lack of applicationof theoretical research to the real world, we investigate a particular case of the nurse rostering problem
at a major Victorian hospital. We present a mixed integer programming model that captures thereal-world scenario as closely as possible. Upon implementation with real hospital data, we demonstrate
the success of the model in achieving the various objectives of the hospital. Moreover, we find that themodel significantly outperforms the manual process for creating rosters, in terms of both the quality of
the resulting rosters and the time spent producing them.

47

Asymptotic analysis of a multiphase drying model motivated by coffee bean roasting

Nabil Fadai
University of Oxford
Co-authors: Colin P. Please and Robert A. Van Gorder
Timetable: p. 17

Coffee bean roasting has, with the exception of a few studies, been largely unexplored from a mathematical point of view. However, recent modelling of coffee bean roasting suggests that in the early stages ofroasting, within each coffee bean, there are two emergent regions: a dried outer region and a saturated
interior region. The two regions are separated by a transition layer (or drying front). In this talk, we
consider the asymptotic analysis of a multiphase model of this roasting process which was recently
put forth and studied numerically, in order to gain a better understanding of its salient features. The
model consists of a PDE system governing the thermal, moisture and gas pressure profiles throughout
the interior of the bean. By obtaining asymptotic expansions for these quantities in relevant limits ofthe physical parameters, we are able to determine the qualitative behaviour of the outer and interior
regions, as well as the dynamics of the drying front. Although a number of simplifications and scaling
are used, we take care not to discard aspects of the model which are fundamental to the roastingprocess. Indeed, we find that for all of the asymptotic limits considered, our approximate solutions
faithfully reproduce the qualitative features evident from numerical simulations of the full model.

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50

Towards accurate real-time control of lithium ion batteries

Troy Farrell
Queensland University of Technology
Co-authors: Ngoc Tham Tran, Mahinda Vilathgamuwa and San Shing Choi
Timetable: p. 16

We present a reduced order model for a lithium ion battery in which Padé approximants are used
to simplify the complicated transfer functions associated with a detailed electrochemical model ofthe battery. The results from our reduced model are shown to compare favorably to those from thefull model, with significant savings in computational time. Importantly, the form of the reduced
model means that variables can be evaluated at specific discrete locations within the cell domain,
without the need to compute all values of the variable at all discrete locations, as is the case with thespatial discretization methods most commonly used to implement partial differential equation models
of battery operation. We show that this results in further significant time savings and enhances thesuitability of the model for real-time battery control applications.

49

Gravity current generated by saline groundwater inflow

Duncan Farrow
Murdoch University
Co-authors: Andrew Bassom
Timetable: p. 23

Some freshwater lakes are in contact with saline groundwater. As saline groundwater seeps into a lakewith a sloping boundary, a gravity current forms. The thickness and speed of this gravity current
increases as more saline water seeps into the lake. This talk considers a model for the form andhydrodynamic stability of this gravity current.

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51

Ordered field property in stochastic games

Jerzy Filar
The University of Queensland
Timetable: p. 23

Modern Game Theory dates back to von Neumann’s 1928 proof of the minimax theorem for matrix
games and the 1944 seminal treatise Theory of Games and Economic Behavior by von Neumann& Morgenstern. Despite many advances in Game Theory resulting from its subsequent popularity,
perturbation theory for dynamic and stochastic games is still in its infancy. A fundamental issue
pertinent to the development of such perturbation theory is the ordered field property (OFP) originallyraised by Weyl who proved that for matrix games the game value and extreme optimal strategies lie inthe same closed ordered field as data defining the game, in particular the rationals. Shapley’s remark
in his seminal 1953 paper on stochastic games pointing out that they lack that property stimulated aline of research aimed at characterising the largest subclass of these games possessing OFP. In thispresentation, without any assumptions on the structure of the game, we show that the ordered field
property holds for both discounted and limiting average stochastic games over the field of algebraic
numbers.

51

A mathematical model of the use of supplemental oxygen to combat surgical site
infection

Jennifer Flegg
The University of Melbourne
Timetable: p. 11

Infections are a common complication of any surgery, often requiring a recovery period in hospital.
Supplemental oxygen therapy administered during and immediately after surgery is thought to enhance
the immune response to bacterial contamination. However, aerobic bacteria thrive in oxygen-richenvironments, and so it is unclear whether oxygen has a net positive effect on recovery. Here, wedevelop a mathematical model of post-surgery infection that predicts the efficacy of supplemental
oxygen therapy on surgical-site infections.
A four-species coupled set of non-linear partial differential equations that describes the space-timedependence of neutrophils, bacteria, chemoattractant and oxygen is developed and numerical solutions
obtained. We quantify the efficacy of different supplemental oxygen regimes on the treatment ofsurgical site infections in wounds of different initial bacterial load. A sensitivity analysis is performed toinvestigate how robust the predictions are to changes in the model parameters. Our findings illustrate
how the nature of the contaminant and its initial density influence bacterial infection dynamics in thewound.

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52

Interfacing diffusive particle models between various scales

Mark Flegg
Monash University
Timetable: p. 25

In many emergent fields of mathematical modelling a recurring difficulty can be systems which operate
on multiple scales and require different mathematical frameworks in different parts of the domain.
For systems of diffusive particles, I present methods for interfacing between continuum, lattice-based
and lattice-free methods of simulation. These methods are widely useful beyond just particle systems,
for example interfacing SSA and CME frameworks in chemistry, since they treat each trajectoryindividually rather than using flux-averaging techniques which are common in fields such as fluid
dynamics.

53

Tailings dewatering by flocculation

Brendan Florio
CSIRO
Timetable: p. 23

In minerals processing it is often advantageous to separate the solid and liquid components of a slurry.
For example, water from waste tailings can be re-used in processing, while the dewatered slurry becomes
thicker and easier to dispose of in a green way. Separation is commonly achieved by flocculation in a
gravity thickener whereby long-chain polymers are introduced to adsorb to the surface of solid particles,binding them together in large aggregates. Large aggregates then sink swiftly leaving a clear fluid at
the top. Modelling the entire system requires knowledge of many facets, including population balances,
the fractal nature of the aggregates, consolidation of the sediments and mixing of the viscous flocculant.
A summary of the current state of these elements will be presented.

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53

Fluid mechanics and the gentle art of viscometry

Larry Forbes
University of Tasmania
Timetable: p. 25

Whenever we solve a problem in viscous fluid mechanics, we need a value for the dynamic viscosity
coefficient µ that features in the Navier–Stokes equation of motion. It is interesting to think about
how this number is measured in practice. Viscometers are devices that use exact (simple) solutions of
the Navier–Stokes equation to infer the dynamic viscosity µ based on some property of the flow; forexample, one such device uses the Stokes solution for flow around a falling sphere to calculate µ basedon how fast a sphere falls through the viscous fluid. Here, I am interested in a non-Newtonian fluid, thatis governed by the Reiner–Rivlin equation, instead of the Navier–Stokes equation, and a brief reason
for this interest will be mentioned in the talk. Such a fluid has two viscosity coefficients and standard
viscometry is not applicable. Poiseuille flow in concentric cylinders still applies for Reiner–Rivlin fluids
but in this talk I want instead to look at a classical problem of flow between rotating plates. A famous
similarity solution due to von Kármán can be extended to the Reiner–Rivlin case, and might offer
a way of measuring both viscosity coefficients. However, there are subtle numerical problems to be
overcome first.

55

FEM-based numerics for approximating the dynamic Laplacian and extracting coherent sets

Gary Froyland
University of New South Wales
Timetable: p. 23

Transport and mixing properties of aperiodic flows are crucial to a dynamical analysis of a flow, andoften have to be carried out with limited information. Finite-time coherent sets provide a skeleton
of distinct regions around which more turbulent flow occurs. In the purely advective setting this isequivalent to identifying sets whose boundary interfaces remain small throughout their evolution. These
sets manifest in geophysical systems in the forms of e.g. ocean eddies, ocean gyres and atmosphericvortices. In real-world settings, often observational data is scattered and sparse, which makes thedifficult problem of coherent set identification and tracking even more challenging. I will describe an
FEM-based numerical method to efficiently approximate the dynamic Laplace operator, and rapidly
and reliably extract finite-time coherent sets from models or scattered, possibly sparse, and possibly
incomplete observed data.

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54

Construction of a mathematical model that reproduces the mechanism of classification and memory of information using timeshift and phase states of brain waves

Kengo Fujita
Kyushu University
Timetable: p. 19

Different parts of the brain play different roles. For example, the frontal lobe is responsible for thoughts
and judgments, and temporal lobes and parietal lobes for memory. According to the experiment of
Kawasaki, it was found that the frontal lobes and temporal lobes are active when thinking aboutauditory information, and the frontal lobe and the parietal lobe are active. When the frontal lobeclassifies the input information, features were found in the phase states of the α-wave and the θ-wave
included in the brain waves in the frontal lobe, the temporal lobe, and the parietal lobe. These results
suggest that the brain uses phase states of brain waves when processing information. Furthermore,
Fukami has proposed a mechanism for distributing information using the phase difference between
the α-wave and the θ-wave. However, in the previous research, there is a problem that the activity ofbrain waves stops and accumulation of the memory ceases when the information input disappears. In
this presentation, we propose a mechanism that can accumulate information using a mathematicalmodel. We set a connection as input to the frontal lobe from the temporal lobe and parietal lobe witha time shift, and made loops with temporal lobe and parietal lobe and frontal lobe. As a result of
simulation, only external inputs of a specific cycle could be accumulated. This result suggests that it ispossible to process information using the time shift of information transmission and the difference inphase state of brain waves.

57

Solving nonlinear PDEs for phase boundaries

Polwaththa Dilruk Darshana Gallage
La Trobe University
Timetable: p. 22

Some exact multi-dimensional time-dependent solutions are constructed for a fourth-order nonlinear
parabolic partial differential equation by using a nonclassical symmetry led by a single relationshipbetween the diffusion term and the reaction term. This models a phase field that describes a two-phasesystem near the critical temperature. Solutions are given for the changing phase of a cylindrical or
spherical inclusion.
Using an inverse approach, exact solutions to a nonlinear second order evaporation-condensation
equation and a fourth-order surface diffusion equation at axi-symmetric three-dimensional phase of asolid are constructed.

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55

Forecasting maximum power demand in NSW with SARIMA-regression model

Benjamin Ganim
The University of Newcastle
Co-authors: Terry Perkins
Timetable: p. 19

Accurately predicting power demand is essential for ensuring the lights stay on for consumers. Electricity
used by consumers is strongly influenced by the state of the weather which follows a clear seasonalpattern. These time correlated patterns can be examined using time series analysis and effectively
modelled by a Seasonal Autoregressive Integrated Moving Average (SARIMA) model to present a
simple but powerful model. The choice of SARIMA model is presented.
Given the potential for increasing unpredictability in weather events and base-load electrical supply,
understanding the relation between these systems is crucial. We show that on the day electricity
demand is strongly influenced by the real feel of the weather and exploit this result to construct a
SARIMA-regression model for electricity demand. The model output reveals that regression in thelinear and quadratic using on the day weather variables from Sydney Airport significantly improve theunderlying SARIMA model over a 52-week horizon.

59

Social network analysis from obsidian artefacts

Caleb Gemmell
The University of Auckland
Timetable: p. 16

Obsidian artefacts were an important stone resource that was used for a variety of tools in pre-European
Māori society. By using data from pXRF analysis to determine the original sources of these artefacts,
we can create a bipartite network of the obsidian source locations and the locations of the archaeologicalsites. A social network analysis of this spatial and temporal distribution data provides an insight into
the movement and interactions of these groups, as well as a method to test various hypotheses that
explain the unique distribution of obsidian throughout the Northland and Auckland regions. Using
further tools such as similarity measures, projected networks and community detection allows us toanalyse which regions were behaving in similar patterns. Ultimately we aim to gain new information
about the complexities of Māori society and iwi interactions, as well as what possibly influenced how
these groups gathered resources; whether geographic, economic or social factors.

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56

Shilnikov-like chaos in two nonlinear coupled photonic nanocavities

Andrus Giraldo
The University of Auckland
Co-authors: Bernd Krauskopf , Neil G. R. Broderick, Maia Brunstein, Alejandro M. Yacomotti and Juan A. Levenson
Timetable: p. 11

Recent experiments have shown that two coupled photonic crystal (PhC) nanocavities exhibit spontaneous symmetry breaking and bistable behaviour. In particular, bistability has been extensively studied
in the last decades due to its usefulness for optical memories and logical switching. Theoretically,bistability and symmetry breaking have been observed in the Bose–Hubbard model, which describes
the dynamics of the two coupled PhC nanocavities.
We consider an extension of the Bose–Hubbard model for the slowly varying amplitudes A and B of
the electric fields in each nanocavity. It is given as a set of two complex ordinary differential equations
determined by a photon lifetime τ , linear couplings between the cavities κ and γ, a detuning from thecavity resonance δ, and a coherent driving term f .
Our work focusses on the overall dynamics of this extended Bose–Hubbard model and, in particular,
the existence and disappearance of periodic solutions. As more energy is pumped into the system,
represented by an increase of the coherent driving term f , periodic solutions arise from Hopf bifurcations,which then disappear in sequences of homoclinic bifurcations. In particular, we find chaotic Shilnikov
bifurcations and the appearance of chaotic attractors. They imply complicated dynamics taking placein the individual cavities, or both of them simultaneously. We present the overall changes of thissystem, from simple to chaotic dynamics, as a function of the coherent driving term and the detuningfrom the cavity resonance. More specifically, we present the bifurcation diagram in the (f, δ)-plane as
the other parameter values are fixed at experimental values. Our global bifurcation analysis of the two
coupled photonic crystal nanocavities predicts types of (chaotic) dynamics well within the range of
future experiments.

61

Optimal mixing enhancement by local perturbation

Cecilia Gonzalez-Tokman
The University of Queensland
Timetable: p. 17

We consider the problem of how to apply local perturbations to optimally enhance the mixingof a (possibly time-dependent) dynamical system. We show a flexible modeling approach basedon the transfer operator of the dynamical system, and pose the problem in the language of convex
optimization. The optimal local perturbations can then be efficiently computed, at discrete time instants,
by standard convex optimization techniques. The local perturbations satisfy physical constraints, suchas preservation of the invariant measure of the dynamics (for example, for incompressible fluid flow, theperturbations preserve volume), and a variety of other physical constraints can also be easily enforced.
We show that one can achieve surprisingly large speedups in mixing via optimizing the diffusion, as
compared to fixed diffusion protocols.

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57

Discrete mechanical systems: existence of trajectories

Sebastián Elı́as Graiff Zurita
Kyushu University
Co-authors: Kenji Kajiwara
Timetable: p. 15

In this talk I am going to show that discrete mechanical systems, when viewed as discrete-time
dynamical systems, may behave in one of three different ways. Given an initial condition such a system
can have no solution, a unique solution, or multiple solutions. But, given a mechanical system, we
can construct a one-parameter family of discrete mechanical systems that have a unique solution, in aneighborhood of a given initial condition, for all values of the parameter. Our construction uses thealternative formulation of discrete mechanical system given in [1], which is different from the usual
construction (see, for example, [2]), but equivalent in some sense. Finally, I will discuss briefly theerror analysis for these systems, and I will show that it is possible to extend all the analysis to discretemechanical systems with forces.

[1] G. W. Patrick, C. Cuell. Error analysis of variational integrators of unconstrained Lagrangiansystems. Numer. Math. 113 (2009) 243-264.
[2] J. E. Marsden, M. West. Discrete mechanics and variational integrators. Numerica Acta 10 (2001)
357-514.

63

Generating connected spatially embedded graphs

Caitlin Gray
The University of Adelaide
Timetable: p. 16

Random networks are useful in providing insights into the formation of real-world networks and are used
as underlying models in many fields. However, many random networks do not guarantee connectedness.
This is not realistic as many real-world networks are inherently connected. In this talk, I will present an
MCMC algorithm to produce connected spatially embedded random networks and study convergenceproperties through numerical simulation.

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58

Tracking the location of metabolic controllers: Akt as a harmonic oscillator

Catheryn Gray
University of New South Wales
Timetable: p. 17

Akt/PKB (Protein Kinase B) is a key signalling molecule in the mammalian cell. As a major cross-talknode shared between several signalling pathways, it is involved in a variety of cellular processes,
including glucose metabolism, cell growth and apoptosis. The dysregulation of Akt is implicated in arange of human disorders, from diabetes to cancer.
As a key nutrient sensor, Akt derives signalling specificity from both its biochemical state and, justas importantly, its intracellular location. Initially, Akt is synthesised in the unactivated state in theinterior of the cell. However, activation (phosphorylation) of the nascent Akt only occurs at thecell membrane, necessitating the translocation of Akt from the interior to the periphery of the cell.
Currently, knowledge concerning Akt translocation is rudimentary, although there is evidence that it isa staged process.
We have developed a deterministic, three-compartment, ordinary differential equation (ODE) model of
Akt translocation. Given a conservation relation implicit in the model, it can be shown that this system
is equivalent to the harmonic oscillator equation; a classic, well-studied ODE. With this framework, we
elucidate the different modes of behaviour of the Akt translocation system, and derive conditions on
the model for the manifestation of these modes. The results are also applicable to other signalling
molecules where it can be assumed that a conservation relation holds true.

65

Using the Schottky-Klein prime function to compute harmonic measure distributionfunctions of a class of multiply connected planar domains

Christopher Green
Macquarie University
Co-authors: Marie A Snipes and Lesley A Ward
Timetable: p. 24

Consider releasing a Brownian particle from a basepoint z0 in a planar domain Ω ⊂ C. What is the
chance, denoted hΩ,z0 (r), that the particle’s first exit from Ω occurs within a fixed distance r > 0 ofz0 ? The function of r suggested by this question, denoted hΩ,z0 : [0, ∞) → [0, 1], is called the harmonicmeasure distribution function, or h-function, of Ω with respect to z0 . We can think of the h-function asa signature that encodes the geometry of the boundary of Ω. In the language of PDEs, the h-function
can also be formulated in terms of a suitable Dirichlet problem on Ω. For simply connected domains,
the theory of h-functions is now quite well developed and several explicit results are known. However,until recently, for multiply connected domains the theory of h-functions has been almost entirely outof reach.
We will show how to construct explicit formulae for the h-functions of symmetric multiply connected
slit domains Ω̂ whose boundaries consist of an even number of colinear slits. We will employ the special

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function theory of the Schottky-Klein prime function ω(ζ, γ) and its associated constructive methods
in conformal mapping to build explicit formulae for the h-functions of domains Ω̂ with any finite evennumber of slits.

66

Can the left ventricle get enough oxygen?

Edward GreenThe University of Adelaide
Timetable: p. 12

I present a mathematical model for oxygen transport in the left ventricle, the main chamber of theheart which pumps blood around the body. The model was parameterised for goats and sheep using
data gathered from microscopic examination of the heart tissue by our experimental collaborators. The
work rate of the heart was measured in two situations: with the animal at rest, and whilst running on atreadmill. The mathematical model was used to estimate the oxygen demand from the left ventricle ineach case. The results suggest that oxygen demands are easily satisfied at rest, but only just satisfied
during simulated heavy exercise. So, the answer to the question is ’Yes, it can’, but evolution appears
to have matched supply closely to demand.

67

Modelling Surtseyan Ejecta

Emma Greenbank
Victoria University of Wellington
Timetable: p. 22

Eruptions through crater lakes or shallow sea water, known as sub-aqueous or Surtseyan eruptions,are often some of the most dangerous eruptions in the world. These eruptions can cause tsunamis,
lahars, base surges and the phenomenon of interest to our research, the Surtseyan ejecta. Surtseyan
ejecta occur when a slurry of previously erupted material and water is washed into the volcanic vent.
This slurry is incorporated into the magma and ejected from the volcano inside a ball of lava. There
are two opposing processes affecting the ejectas behaviour: the first is the evaporation of the water in
the inclusion, increasing the pressure, and the second is the vapour escaping through the pores of themagma.
In this talk I will focus on improved modelling of the behaviour of the ejecta. This model has a more
systematic reduction of the resulting coupled nonlinear partial differential equations that arise frommass, momentum and energy conservation.

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60

A cell growth model adapted for minimum cell size division

Saima Gul
Massey University
Timetable: p. 22

In this talk I present a cell growth model with a division function that models cells dividing only after
they have reached a certain minimum size. In contrast with the earlier cases studied by Hall and Wake,the determination of the steady size distribution requires an eigenvalue that is not known explicitly,
but is defined through a continuity condition. We show that there is a steady size distribution solution
to this problem.

69

Analytic solutions for a reaction diffusion model of calcium waves on the surface ofan eggBronwyn Hajek
University of South Australia
Timetable: p. 14

When an amphibious egg is fertilised, a wave of calcium ions travels around the egg to help prevent theentry of multiple sperm. This process can be described with a nonlinear reaction-diffusion equation
with a cubic reaction term. Providing the nonlinear diffusion is related to the reaction term in a certain
way, the nonclassical symmetry method may be used to find a transformation that will linearise andseparate (time and space) the reaction-diffusion equation. Analytic solutions are then constructed, andvarious types of phenomena, including spirals, can be observed.

70

Inertial force on particles in curved microfluidic ductsBrendan Harding
The University of Adelaide
Timetable: p. 24

When particles are suspended in fluid flow through a microfluidic device they are perturbed fromstreamlines by inertial lift forces. Much of the work on calculating these forces is performed in
the context of straight ducts having a circular or rectangular cross-section. The problem becomessignificantly more complex in the case of curved ducts. In this talk I will discuss some of the challenges
that arise due to the curved geometry and show some preliminary results for the lift forces acting on
the particle.

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61

A Volterra equation with a physically but not mathematically unique solution: abubble rising in a liquid with negative surface activity

John Harper
Victoria University of Wellington
Timetable: p. 12

Much is known about convective diffusion around a bubble rising in a liquid when the solute lowers
the surface tension of the liquid. Some solutes, e.g. many salts in water, increase the surface tension
even when very dilute if many (but not all) physical chemists are to be believed. The theory leads
to a linear Volterra integral equation of the third kind. Its mathematical solution is non-unique, butphysical constraints force uniqueness. Finding the solution numerically is easiest in the case which
is both the most difficult by previously known methods and the most physically realistic: very weaknegative surface activity.

72

Saddle slow manifolds and canard orbits in the Hodgkin–Huxley model

Cris Hasan
The University of Auckland
Co-authors: Bernd Krauskopf and Hinke Osinga
Timetable: p. 16

Many physiological phenomena have the property that some processes evolve much faster than others.
For example, neuron models typically involve observable differences in time scales. The Hodgkin-Huxleymodel is well known for explaining the ionic mechanism that generates the action potential (a pulse of
the voltage) in the squid giant axon. Rubin and Wechselberger nondimensionalized this model andobtained a singularly perturbed system an explicit time-scale ratio that separates two fast, two slow
variables. The dynamics of this system are very complex and feature periodic orbits with a series ofaction potentials separated by small-amplitude oscillations. Such periodic orbits are also referred toas mixed-mode oscillations. The system features two-dimensional locally invariant manifolds calledslow manifolds, which can be either attracting or of saddle type. We introduce a general method forcomputing two-dimensional saddle slow manifolds as well as so-called canard orbits. Our method
is first tested and implemented for a four-dimensional extended normal form of a folded node. We
then illustrate how slow manifolds and associated canard orbits organize mixed-mode oscillations anddetermine the firing rates of action potentials in the Hodgkin-Huxley model.

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62

How should a local regime-switching model be calibrated?

Xin-Jiang He
University of Wollongong
Co-authors: Song-Ping Zhu
Timetable: p. 20

Local regime-switching models are a natural consequence of combining the concept of a local volatility
model with that of a regime-switching model. However, even though Elliott et al (2015) have derived aDupire formula for a local regime-switching model, its calibration still remains a challenge. This is
primarily due to the fact that the derived volatility function for each state involves all the state pricevariables whereas only one market price is available for model calibration, and a direct implementationof Elliott et al’s formula may not yield stable results. In this talk, a closed system for option pricing
and data extraction under the classical regime-switching model is proposed with a special approach,splitting one market price into two “market-implied state prices”. The success of our approach hinges
on the recovery of the two local volatility functions being transformed into an optimal control problem,
which is solved through the Tikhonov regularization. In addition, an efficient algorithm is proposed
to obtain the optimal solution by iteration. Our numerical experiments show that different shapes of
local volatility functions can be accurately and stably recovered with the newly-proposed algorithm,
and this algorithm also works quite well with real market data.

Elliott, R. J., Chan, L. and Siu, T. K. (2015), A Dupire equation for a regime-switching model,International Journal of Theoretical and Applied Finance 18(04), 1550023.

74

Fluid-Structure interaction in pseudospectral codes: The smooth volume penalty
methodEric William Hester
The University of Sydney
Timetable: p. 20

Fluid-structure interactions (FSI) pervade applied mathematics, science and engineering, yet are often
too complex to solve analytically. Animal swimming and flight, glacier-ocean interactions, blood
circulation, geodynamics and volcanoes, dune formation and erosion, are a handful of important such
examples. Standard numerical approaches utilise body-conforming grids. However, they are difficult togenerate, update, and program, and often of limited accuracy. Pseudospectral methods are an exciting
alternative for their exponential accuracy, but are restricted to regular geometries. The volume penalty
method is a simple and flexible tool to incorporate arbitrarily shaped boundaries into existing codes.
We examine the method, demonstrate its application to several interesting FSI problems, and showthat the majority of the error stems from a ”displacement length”, which can easily be corrected.

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63

A history-based multi-outbreak influenza model

Roslyn Hickson
IBM Research Australia
Co-authors: A.J. Swan
Timetable: p. 16

There is evidence that susceptibility to infection during an influenza outbreak is dependent on thenumber of previous influenza infections and/or how recent the infections were. We construct a multioutbreak influenza model to explore the effect of these two factors modifying population susceptibilityon the outbreak dynamics.
Classic deterministic compartment modelling of infectious disease spread divides the population into
fully susceptible and fully immune compartments which are homogeneous. In reality, the population has
differing degrees of immunity due to unique infection histories of individuals. There are two approaches
within the deterministic compartmental modelling framework to address this issue; one is to have many
compartments reflecting different levels of immunity, and the other is to capture the heterogeneity
within a single susceptibility compartment in the model. The first approach has been well explored in
the literature. We focus on the second approach by building a history-based compartmental modelwith the between outbreak immunological timescale modelled using a map between disease states. Thismap of immunity loss incorporates antigenic drift, births-deaths, and decreases in antibody response in
the weeks-months timescale.
We use our developed model to explore fundamental questions on how the different susceptibility
hypotheses and other key model parameters affect the outbreak dynamics. There are several limitations
to our modelling approach to answer these questions. These include the limitation of only explicitly
considering a single strain circulating within a season, which is not appropriate if there are crossimmunity effects, and the assumption of homogeneity in importance of history length and immune
response. Despite these limitations we are able to provide important insights into these fundamental
questions.

76

Relating elasticity and graphene folding conformation

James Murray Hill
University of South Australia
Co-authors: Barry J. Cox, Duangkamon Baowan and Wolfgang Bacsa
Timetable: p. 20

The variational calculus is employed to determine the folding behaviour of a single graphene sheet.
Both elastic and van der Waals energies are taken into account, and from these considerations theshape of the curve is determined. By prescribing that the separation distance between the folded
graphene in the parallel region is 3.32 Angstroms, an arbitrary constant β arising by integrating theEuler-Lagrange equation is determined. Furthermore, the full parametric representations for the folding
conformation is derived, so that the folded graphene may be depicted graphically. Using typical values

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64of the bending rigidity in the range of 0.8-1.6 Electron Volts, the shortest stable folded graphene sheets
are required to be at least 6.5 - 10 nanometers in length for the folded conformation.

B. J. Cox, D. Baowan, W. Bacsa and J. M. Hill, “Relating elasticity and graphene folding conformation.”
RSC Advances, 5 (2015) 57515-57520.
J. S. Bunch, A. M. van der Zande, S. S. Verbridge, I. W. Frank, D. M. Tanenbaum, J. M. Parpia, H.
G. Craighead and P. L. McEuen, Electromechanical resonators from grapheme sheets, Science, 2007,
315, 490-493.
K.-T. Lam, C. Lee and G. Liang, Bilayer graphene nanoribbon nanoelectromechani-cal system device:a computational study, Appl. Phys. Lett., 2009, 95, 143107.

77

Plumes generated by desalination outfalls

Graeme Hocking
Murdoch University
Co-authors: Shaymaa Shraida
Timetable: p. 22

A bi-product of the desalination process is water of high salinity. In the West Australian desalination
plants, this water is pumped into Cockburn Sound where it is (optimistically) believed to disperse. In
this talk I will consider the flow of such a saline plume when the outfall is raised off the bed. Only
two-dimensional flows will be considered, but these provide some interesting solutions. The usual
Nekrasov integral equation formulation for free surface flow problems proves to work very well andsteady solutions will be presented over a range of flow conditions. Future work will be discussed.

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65

Extensional flow of an axisymmetric transversely isotropic fluid thread

Matthew James Hopwood
The University of Adelaide
Timetable: p. 15

Biological materials exhibit complex behaviours, including viscoelasticity and anisotropy. In manycases, these behaviours can be attributed to the material having a fibrous microstructure e.g. collagengel and cervical mucus. We study a class of anisotropic materials that are known as ‘transversely
isotropic’, where the material’s physical properties are isotropic in the plane normal to some axis (e.g.
the fibre direction). Motivated by potential applications to understanding the changes to the structureof cervical mucus throughout the menstrual cycle and its role in providing regulation to the passage of
spermatoza, we consider the extensional flow of an axisymmetric, inertialess, transversely isotropic
viscous fluid thread. A reduced set of governing equations is obtained by exploiting the thin geometryof the thread. We then present results for the special cases where the fibre alignment is nearly axial orradial.

79

Mixed Signals: Interaction between RyR and IP3R mediated calcium release shapes
the calcium transient for hypertrophic signalling in cardiomyocytes

Hilary Hunt
The University of Melbourne
Co-authors: Gregory Bass, Llewelyn Roderick, Christian Soeller, Vijay Rajagopal and Edmund Crampin
Timetable: p. 19

Calcium plays a central role in mediating the contractile function of heart cells. However, calcium
is also the second messenger in a wide variety of other intracellular signalling pathways, including
hypertrophic signalling in cardiomyocytes. How intracellular calcium can encode several different,
specific signals at once is not well understood.
Under hypertrophic stimulation, calcium released from IP3R channels triggers dephosphorylation andnuclear import of the transcription factor NFAT, with resulting gene expression linked to cell growth.
Yet this must occur on a background of rising and falling cytosolic calcium which controls each heart
beat.
Modelling these two signals within a single heart cell, we combine our knowledge of calcium channels
with the evidence from a recent study on NFAT response to identify the key signal-carrying componentof the IP3-dependent hypertrophic signalling pathway in cardiomyocytes.

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66

Why there might be more slow-fast systems than you thought there were

Sam Jelbart
The University of Sydney
Timetable: p. 21

Geometric singular perturbation theory (GSPT) provides a well established framework for the studyof slow-fast dynamical systems. For the most part, however, this framework has been applied only
for systems in which the slow-fast structure derives from a separation of slow/fast variables. Not
all slow-fast systems have such a structure, however, and as such applications of GSPT to slow-fastsystems without such a structure are rare in the literature. We show how traditional GSPT can begeneralised so that it may be applicable to a larger class of problems, and illustrate the method byapplying it to prove results about a slow-fast limit cycle in a planar slow-fast system that cannot betreated using the traditional framework.

81

The effect of tumour heterogeneity on cancer treatments: the ninja virus

Adrianne Jenner
The University of Sydney
Timetable: p. 20

Heterogeneity within tumours has been identified as the major culprit impeding treatment efficacy. The
heterogeneous nature of tumour geometry arises from an over-proliferation of mutated cells within aconfined space. Over-proliferation of cells leads to a limited number of treatment entry points resulting
in a less effective treatment. Currently, the challenge in the field is to develop a cancer treatmentthat overcomes both the heterogeneous tumour microenvironment and limited treatment entry points.
Cancer-killing viruses can overcome most tumour heterogeneity obstacles; however, limited treatment
diffusion is regularly observed experimentally. Using a Voronoi cellular automaton, we investigate theeffects of tumour heterogeneity on cancer-killing viruses and propose a new generation of cancer-killingviruses: the ninja virus. The ninja virus is developed with time-dependent infection, where for a fixed
initial period no infection will occur. This allows for further treatment diffusion and improves treatment
efficacy dramatically. From our work, we illustrate the importance that mathematical modelling holds
in cancer research and propose a novel innovative treatment.

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67

Modelling density-dependent collective diffusion in microporous Knudsen flows

Owen Jepps
Griffith University
Co-authors: Marsel Gokovi
Timetable: p. 22

Knudsen flows can arise in applications of microporous materials, such as filtration, when external
conditions induce low-density transport. Over a decade ago, we proposed a model (Jepps, Bhatia
and Searles, PRL 91:126102, 2003) to predict the collective diffusion of Knudsen flows in uniform
micropores (such as some microporous carbons and silicas). This model works in the zero-density (highKnudsen-number) limit, and has proven popular as a means of estimating Knudsen transport in thislimit, and as a basis for developing density-dependent models. Most of these density-dependent models
extend the zero-density model using approaches that are very different in philosophy to the originalmodel. In this presentation, I will show how the original model can be adapted to include density
dependence more rigorously, and compare its predictions with existing and new data.

83

The role of initial geometry in experimental models of wound closing

Wang Jin
Queensland University of Technology
Timetable: p. 14

Standard wound healing assays often deal with just one initial wound shape, and it is unclear whether
varying it might impact how we interpret results from these experiments. Here, we use a new kindof wound healing assay, called a sticker assay, to explore the role of the initial shape. We examine
healing with square, circular and triangular wounds. Measurements of the area as a function of timeshow that the rate of wound closure depends on the initial shape. This is interesting because the only
aspect of the assay we change is the initial wound shape, and the reason for different closure rates is
unclear. To provide more insight we calibrate a typical mathematical model to match the data. Thisshows that the rates of cell motility and proliferation associated with different initial wound shapes areapproximately the same, implying that the differences in the closure rates are consistent with a typicalmathematical model of wound healing. Therefore, parameter estimates from an experiment with aparticular wound shape can be used to predict the development of wounds of different initial shape.

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68

The ‘sinh’ transformation method for evaluating nearly singular boundary element
integrals

Barbara Johnston
Griffith University
Timetable: p. 11

When implementing the boundary element method, three types of integrals (regular, ‘nearly’ singularand singular) must be evaluated, and these can be categorised by the distance between the source
point and the boundary element in question. The most troublesome to evaluate is the subject of thistalk, the ‘nearly’ singular integral. This integral occurs when the source point is close to, but not on,
the element of integration, resulting in a sharply peaked integrand.
In 2004, David Elliott suggested applying a transformation, based on the sinh function, to smooth the
integrand. The ‘sinh’ transformation was designed to automatically take into account the projection of
the source point onto the element of integration and also the distance between the two. Applying thistransformation to one-dimensional ‘nearly’ singular integrals gave relative errors that were several ordersof magnitude lower than those for conventional Gauss-Legendre quadrature. David also calculated
asymptotic error estimates for the truncation errors, based on work that he had previously publishedback in 1972.
This talk will trace the evolution of the ‘sinh’ transformation method, and its associated error estimates,
as it was successfully applied in both one and two dimensions to weakly and strongly nearly singular
integrals, and in various geometries.

85

Evaluating singular integrals for fun and profit

Peter Johnston
Griffith University
Timetable: p. 11

The accuracy of the boundary element method is heavily reliant on accurate evaluation of singular
integrals. Over a long period of time, many researchers have proposed a variety of approaches toovercome this problem. The most common of these approaches are splitting the interval of integration,transformation methods and a combination of both.
During this talk I will provide an excursion through several complicated transformations to aid in theevaluation of singular integrals that arise in the boundary element method. Eventually, I will arrive ata very simple transformation that yields very interesting error behaviour.
Throughout this journey all the numerical analysis and error estimates were provided by David, always
harking back to the pioneering work of “Donaldson and Elliott, 1972”.

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69

An analytical approach for quantifying the influence of nanoparticle polydispersity
on cellular delivered dose

Stuart Johnston
The University of Melbourne
Timetable: p. 12

Nanoparticles provide a promising approach for the targeted delivery of therapeutic, diagnostic andimaging agents in the body. However, it is not yet fully understood how the physico-chemical propertiesof the nanoparticles influence cellular association and uptake. Cellular association experiments
are routinely performed in an effort to determine how nanoparticle properties impact the rate ofnanoparticle-cell association. To compare experiments in a meaningful manner, the association data
must be normalised by the quantity of nanoparticles that arrive at the cells, a measure referred to as
the delivered dose. The delivered dose is calculated from a model of nanoparticle transport throughfluid. A standard assumption is that all nanoparticles within the population are monodisperse, namely,
the nanoparticles have the same physicochemical properties. We present a semi-analytic solution to amodified model of nanoparticle transport that allows for the nanoparticle population to be polydisperse.
This solution allows us to efficiently analyse the influence of polydispersity on the delivered dose.
Combining characterisation data obtained from a range of commonly-used nanoparticles and ourmodel, we find that the delivered dose changes by more than a factor of two if realistic amounts ofpolydispersity are considered.

87

Full reconstruction of a hidden variable model with just two observed variables

Benjamin David Kaehler
Australian National University
Timetable: p. 14

Consider a stochastic model with a number of observed variables that are independent only if we
condition on a hidden variable. Several authors have written on the restriction that at least threeobserved variables are required for the parameters of the model to be fully recoverable from the joint
probability distribution of the observed variables. I am interested in this question from the perspectiveof phylogenetics, where the observed random variables are the DNA of living species and the hidden
variable is the DNA of a common ancestor. The restriction to three observed variables means thattrees that model evolutionary relationships must be unrooted. That is, the properties of the mostrecent common ancestor of a fixed set of species are unknowable. I will show how this situation canbe remedied by introducing some biologically justifiable constraints, so that the minimum number ofobserved variables drops to two and the root can be discovered.

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70

Log-Aesthetic curves in industrial design as similarity geometric analogue of Eulers
elastic curves

Kenji Kajiwara
Kyushu University
Co-authors: Jun-ichi Inoguchi, Kenjiro T. Miura and Wolfgang K. Schief
Timetable: p. 19

The class of plane curves called the Euler’s elastic curves is one of the most important geometric objects
and serves as a basic model in the elastic theory. It can be characterized (1) as a critical point of theelastic energy where it is given by the square of the Euclidean curvature, (2) as the stationary flow
with respect to the isoperimetric deformation of plane curves in the Euclidean geometry governed by
the modified KdV equation, which is one of the most typical integrable systems. In this talk, I considera class of plane curves called the log-aesthetic curves (LAC) and their generalization which is used inindustrial design. We investigate those curves under the similarity geometry and characterize themas stationary integrable flow on plane curves which is governed by Burgers’ equation. We introduce“fairing energy” and propose a variational formulation of those curves whose Euler-Lagrange equation
yields the stationary Burgers’ equation. Our result suggests that the LAC and their generalization canbe regarded as the similarity geometric analogue of the Euler’s elastic curves, which provides a newmathematical framework of those curves and would yield various generalizations. As an example, wewill mention the integrable discretization of LAC which may be useful for numerical implementation.

89

State-dependent delays in the El Niño Southern Oscillation system

Andrew Keane
University of Auckland
Co-authors: Bernd Krauskopf
Timetable: p. 12

Delay differential equations (DDEs) have been used successfully in the past to model climate systems at
a conceptual level. An important aspect of these models is the existence of feedback loops that feature
a delay time, usually associated with the time required to transport energy through the atmosphere
and/or oceans across the globe. So far, the values of the delays are generally assumed to be constant.
Recent studies have demonstrated that even simple DDEs with nonconstant delay times, which change
depending on the state of the system, can produce surprisingly rich dynamical behaviour. Here, we
identify physical arguments for the existence of such state-dependent delays in a DDE model for
the El Niño Southern Oscillation climate system. We then conduct a bifurcation analysis by meansof continuation software to investigate the effects of state-dependent delays on the dynamics of thesystem.

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71

Correctly assessing drug efficacy in malaria relies on understand parasite kinetics
before treatment

David Samuel Khoury
University of New South Wales
Co-authors: James McCarthy and Miles P Davenport
Timetable: p. 13

The two most prevalent species of malaria parasites are Plasmodium falciparum and Plasmodium vivax.
P. falciparum causes the greater mortality, and so is morefrequently the focus of malaria research.
However, P. vivax is still widespread and contributes significantly to the global disease burden. We
aim to translate insights gained from the numerous studies of P. falciparum infection to further our
understanding of P. vivax infection.
About 24% of people with P. falciparum infection experience an increase in parasite concentrations
after receiving the recommended antimalarial treatment. Rises in parasite concentration occur when apatient is given treatment when they have many mature parasites that are about to proliferate (produce
progeny), and treatment is unable to prevent this process completely. Proliferation of parasites is
associated with inflammation and illness in malaria. Hence preventing rises in parasite concentration
is likely important for reducing illness and mortality rates. Interestingly, in P. vivax malaria, < 2%of individuals have a rise in parasite concentration after treatment with the same antimalarial. We
explore the reasons for this difference. Are drugs more effective against P. vivax? Or is there someother explanation for this difference? Using data from volunteers that received an experimental P. vivax
and P. falciparum infection we construct a PDE model of parasite proliferation and using that model,
and parameter estimates, we simulate the effect of drugs in the two parasite species. We find that avery fundamental difference in sequestration (hiding) between the two species is a critical consideration
when interpreting data on the effects of drugs in these two species.

91

Evolution of monogamy in response to human post-menopausal longevityPeter Kim
The University of Sydney
Timetable: p. 24

The human species is unique among mammals in its tendency towards monogamy, or pair bonding, a
trait which also exists in hunter-gathering societies. Traditional explanations for this evolution havefocused on the presence of paternal care and the needs of our offspring; however, recent research has
challenged this claim, contending that the significant effects of mating competition on male choice
result in evolutionary equilibria with high promiscuity and little mate guarding or pair bonding. We
develop an ordinary differential equation model to investigate this question and determine conditions
for mate guarding or pair bonding to supersede multiple-mating (promiscuous) strategies as the optimal
allocation of male reproductive effort. Various situations were considered including the variation of
reproduction rate, sex ratio, end of female fertility, and the effect of grandmother help in providing
for offspring. While our results confirmed previous findings that pair bonding triumphs in response

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to partner scarcity and male-biased populations, it was found that this effect only occurred in theextreme case of a 1:10 or higher female to male ratio. In contrast, the introduction of post-menopausal
longevity combined with a grandmother effect provided a significantly more realistic and mechanism
for monogamy to evolve.

92

Chaos and fluctuations in a modified Ehrernfest wind-tree model

Matthew King
Griffith University
Co-authors: Owen G Jepps
Timetable: p. 19

The non-equilibrium Ehrenfest wind-tree model is an interesting model for testing fluctuation relations,because it was believed to be a non-chaotic system that obeyed fluctuation relations. More recently, it
was shown that over short times the dynamics is chaotic, but at almost all field strengths trajectories
are eventually periodic. We have considered perturbations of the Ehrenfest wind-tree model that do not
permit these eventually periodic orbits, and studied the Lyapunov exponents and fluctuation relationsin these systems. For some perturbations the system remains chaotic for all times investigated, and thefluctuation relations are obeyed. However, we will also present results on some systems which appear
to remain non-trivially non-chaotic at long times.

93

Nonlinear learning in games with incompetence

Maria Kleshnina
The University of Queensland
Timetable: p. 17

In this talk I will extend my results on games with linear incompetence to the cases with different
nonlinear learning processes. We will show that the speed and the steepness of improvement may
change the population time-dynamics dramatically. We also examine the long-time behaviour of thereplicator dynamics under incompetence and show how this idea affects games’ equilibiria.
This research is funded by ARC discovery grants DP160101236 and DP150100618.

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94

The relation between Crouzeix-Raviart and Raviart-Thomas finite element methods

Kenta Kobayashi
Hitotsubashi University
Timetable: p. 20

We discuss the lowest degree Crouzeix-Raviart and Raviart-Thomas finite element methods applied
to the Poisson equation with a piecewise constant righthand function f . Let uCR
and (ph , uRThh ) bethe Crouzeix-Raviart and Raviart-Thomas finite element solution respectively. Then, for the twodimensional case, it is well-known that these two finite element solutions have a close relation. In
particular, for each triangular element K in the proper triangulation Th , the following relation holds:
3

0 CR
uRT
h = πK uh +f X
|xi − xK |2 ,48

ph = ∇uCR
h −

i=1

f
(x − xK )2

0 is the piecewise constant projection operator, x are the vertices of K and x is the centre
where πKiKof gravity of K. In our research, we generalize this relation to any dimension and proved the following:
d+1

0 CR
uRT
h = πK uh +Xf|xi − xK |2 ,d2 (d + 1)(d + 2)
i=1

ph = ∇uCRh −f(x − xK )dwhere d denotes the space dimension.

95

Robust chaos: blenders in a Hénon-like family

Bernd Krauskopf
University of Auckland
Co-authors: Stephanie Hittmeyer, Hinke Osinga and Katsutoshi Shinohara
Timetable: p. 11

Blenders are geometric objects that allow one to construct complicated dynamics and robust homoclinic
tangencies in the theoretical setting of nonuniformly hyperbolic dynamics. A defining feature of ablender is the property that its invariant manifolds behave as geometric objects of a higher dimension.
We consider an explicit example of a blender, which arises in a family of three-dimensional Hénon-like
maps. We employ advanced numerical techniques to compute one-dimensional stable and unstablemanifolds of saddle points to very considerable arclengths. In this way, we not only present the firstimages of an actual blender but also obtain a convincing numerical test for the blender property. This
allows us to determine when and how the blender disappears when a system parameter is changed.
The relevance of the blender property for chaotic attractors will be discussed.

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74

Network using Michaelis-Menton kinetics: an algorithm to find target genes fromexpression data

Mythreye Krishnan
The University of Western Australia
Co-authors: Michael Small, Anthony Bosco and Thomas Stemler
Timetable: p. 21

The most challenging aspect of gene expression data analysis is to process the large and complex
data using mathematical models and find biologically relevant information that gives insight to theunderlying mechanism. We derived a simple ordinary differential equation using Michaelis-Menton
kinetics to process the microarray data. Different biological systems of asthma and allergy in humans
and cancer in mice have been studied. The resulting analysis extracts highly linked target genes, thechanges in which might cause change in the other genes, in other words, potential experimental targets
that can be exploited for studies such as gene therapy. Our aim is to identify novel targets that can beanalyzed further in addition to the previously identified nodes. We present a method that can be used
to process the microarray data to find target genes using relevant links between them.

97

A sequential stochastic mixed integer programming model for elective surgery schedulingAshwani Kumar
The University of Melbourne
Co-authors: Alysson Costa, Mark Fackrell and Peter Taylor
Timetable: p. 15

Demand for healthcare services is growing rapidly in Australia and across the world, and rising
healthcare expenditure is increasing pressure on the sustainability of the government-funded healthcare
system. To keep up with the rising demand, we need to be more efficient in delivering surgical services.
In this talk, we will discuss a stochastic mixed integer programming model to optimise the master
surgery schedule (MSS) in order to achieve a better patient flow under downstream capacity constraints.
We optimise the process over several scheduling periods and we use various sequences of randomly
generated patients’ length of stay scenario realisations to model the uncertainty in the process. Thismodel has the particularity that the scenarios are chronologically sequential, not parallel. We use a very
simple approach to enhance the non-anticipative feature of the model and we empirically demonstratethat our approach is useful in achieving the desired objective. We use simulation to show that themost frequently optimal schedule is the best schedule for implementation. Furthermore, we analyse theeffect of varying the penalty factor, an input parameter that decides the trade-off between the numberof cancellations and occupancy level on the patient flow process. We demonstrate empirically that if we
can operate on elective surgery patients over weekends, then we can achieve a better throughput andmore efficient utilisation of resources. Finally, we develop a robust MSS to maximise the utilisationlevel while keeping the number of cancellations within acceptable limits.

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Modelling the impact of T-cell avidity on cancer vaccines

Adarsh Kumbhari
The University of Sydney
Timetable: p. 17

Therapeutic vaccines treat cancers that have already developed by stimulating cytotoxic T-cells.
Despite showing promise, positive clinical outcomes have yet to be realised. Vaccines elicit a low-avidity
T-cell response and the mere presence of low-avidity T-cells can inhibit cancer killing by tumour-lytic
high-avidity T-cells via the stripping of surface antigen on target cells. This may explain the observed
inefficacy of therapeutic cancer vaccines. We look at a variety of T-cell profiles and how the parametersthat characterise these profiles affect tumour progression.

99

Chimeras on spheres

Carlo Laing
Massey University
Timetable: p. 23

We consider a network of nonlocally coupled heterogeneous phase oscillators lying on the surface of asphere. This network was previously studied with identical oscillators and spatiotemporal patterns
known as chimeras were found, mostly as a result of direct numerical simulation. Here we take thecontinuum limit of an infinite number of oscillators and use the Ott/Antonsen ansatz to derive acontinuum level evolution equation for an order parameter-like quantity. Most of the patterns previously
found in these types of network correspond to relative fixed points of this evolution equation, and weshow the results of numerical investigations of these fixed points: their existence and stability, and thebifurcations involved in their loss of stability as parameters are varied. Our results answer a number ofquestions posed by previous authors who studied such networks, and provide a better understanding ofthese networks dynamics.

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76

Rigorous results in electronic structure calculation

Marko Lange
Waseda University
Co-authors: Denis Chaykin, Christian Jansson, Frerich Keil, Kai Torben Ohlhus, Siegfried M. Rump
Timetable: p. 20

Electronic structure calculations, in particular the computation of the ground state energy, are ofenormous importance in quantum chemistry. Minimization methods for computing the ground stateenergy can be developed by employing a variational approach, where the second-order reduced density
matrix defines the variable. This concept leads to large-scale semi-definite programming problems
that provide a lower bound for the ground state energy. Upper bounds of the ground state energy arecalculated for instance with the Hartree-Fock method.
However, Nakata et al observed that, due to numerical errors the solver produced erroneous resultswith a lower bound larger than the Hartree-Fock upper bound. Violations within one mhartree wereobserved. I present here a method for computing tight rigorous error bounds without violations asmentioned above.

101

Infection-acquired versus vaccine-acquired immunity in an SIRWS model

Tiffany Ngo Nam Leung
The University of Melbourne
Timetable: p. 16

Waning immunity is known to occur for some infectious diseases after natural infection and vaccination.
We present a susceptible-infectious-recovered-susceptible (SIRS)-type transmission model that includes
the waning and boosting of immunity. We allow the duration of infection-acquired immunity to differ
from that of vaccine-acquired immunity. We evaluate its impact on (i) the proportions of primaryand secondary infections, and (ii) the epidemiological patterns of an infectious disease (pertussis as
an example), focussing on the peaks and period of the epidemic cycles that characterise the average
infection prevalence.
Our results show that the effectiveness of a vaccine to reduce infection prevalence increases moreby extending the duration of infection-acquired immunity than extending that of vaccine-acquired
immunity. We find that increasing vaccine uptake (i) always lowers the proportion of primary infections
but may lead to an increase in overall transmission, and (ii) raises the peaks and lengthens the periodof the epidemic cycles. Our study highlights that for a particular disease and associated vaccine, adetailed understanding of how the duration of protection can influence infection prevalence is important
as we seek to optimise vaccination strategies.

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77

Modelling South Australia’s electricity prices

Angus Hamilton Lewis
The University of Adelaide
Timetable: p. 20

Electricity spot prices are known to exhibit characteristics not often observed in other financial markets- seasonality on multiple scales, mean reversion, large price spikes, price drops and negative prices.
These characteristics are largely attributed to the lack of effective storage options for electricity. The
goal of my research is to capture the aforementioned characteristics using a stochastic model. Such amodel is useful to help market participants manage risk and for valuation of financial contracts andreal options for investment.
We use a regime-switching time-series model, which is an extension of a hidden Markov model, tomodel prices. A subtle but important part of our model is that we require each regime to be completely
independent. This coupled with the fact that the regime sequence is not directly observable, makes
parameter estimation difficult as the likelihood function is not computable for realistic datasets, hence,
we use data-augmented MCMC for Bayesian inference.
In this talk I will present our modelling process for the South Australian electricity market, touchingon model inference and model selection. South Australia is a particularly interesting case study due to
its relative isolation, high prices and huge price spikes (up to AUD$14000 compared to the average
price of around AUD$80).

103

Pricing puttable convertible bonds with integral equation approaches

Sha Lin
University of Wollongong
Timetable: p. 20

American-style puttable convertible bonds are often priced with various numerical solutions because
the predominant complexity arises from the determination of the two free boundaries together with thebond price. In this talk two forms of integral equation are derived to price a puttable convertible bondon a single underlying asset. The first form is obtained under the Black-Scholes framework by using an
incomplete Fourier transform. However, this integral equation formulation possesses a discontinuity
along both free boundaries. An even worse problem is that this representation contains two first-orderderivatives of the unknown exercise prices, which demands a higher smoothness of the interpolation
functions used in the numerical solution procedure. Thus, a second integral equation formulation isdeveloped based on the first form to overcome those problems. Numerical experiments are conducted
to show several interesting properties of puttable convertible bonds.

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78

The BEST Approach to the Search for Extraterrestrial Intelligence (SETI)

Robert Lodder
University of Kentucky
Timetable: p. 15

The Bootstrap Error-adjusted Single-sample Technique (BEST) is shown to perform better than the
Mahalanobis distance metric in analysis of SETI data from a Project Argus near-infrared telescope. The
BEST algorithm is used to identify unusual signals, and returns a distance in asymmetric nonparametricmultidimensional central 68% confidence intervals (equivalent to standard deviations for 1-D data thatare normally distributed, or Mahalanobis distance units for normally distributed data of d dimensions).
The BEST algorithm is designed for high-speed parallel processing supercomputers, but is also shown
to operate efficiently on single processors. Calculation of the Mahalanobis metric requires matrix
factorization and is O(d3 ). In contrast, calculation of the BEST metric does not require matrix
factorization and is O(d). Furthermore, the accuracy and precision of the BEST metric are greaterthan the Mahalanobis metric. Using synthetic multivariate data, the bias and RSD of the BESTand Mahalanobis metrics are compared as a function of the number of dimensions in hyperspace andthe number of training samples in the calibration set. Full near-IR spectra of a stellar system (KIC
8462852, or ”Tabby’s star”) are analyzed successfully using the BEST to identify unusual signals.

105

The evolution of hunting effort in hunter-gatherer populations

Sara Li-Yen Loo
The University of Sydney
Timetable: p. 22

The evolution of large-game hunting in human life history is a counter-intuitive behaviour. Despite
low daily success probabilities and large proportions of sharing, hunter-gatherer males make greater
investments in large-game hunting and food sharing. While costly, investment into these behaviours
pays off with more successful hunters being deemed as better partners, thus increasing their likelihood ofpaternity. It is the effort with which, and time where, an individual invests their energy that determines
one’s status. We therefore model the effect of a hunting effort on male hierarchy and investigate
the evolution of this large-game hunting behaviour as it trades off with fertility. We investigate theintergenerational dynamics of a population defined by a probability density in two traits, hunting effort
and hierarchical status, and analyse the mechanisms by which such large-game hunting behaviour canevolve.

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79

Modelling donor flow

Meirian Sara Lovelace-Tozer
The University of Melbourne
Timetable: p. 14

Due to its short shelf-life, blood is a limited resource, yet sufficient and quality supply from blood
donors is vital to meet demand for blood transfusions. The Australian Red Cross is the primary blood
service provider Australia-wide, and depends on voluntary, non-remunerated donors. To maximise
donor retention rates, it is paramount that donors have a satisfactory donation experience. Donor
feedback indicates that wait times play a significant role in their decision to return.
The goal of this project is to establish a model which accurately represents the flow of donors throughan Australian Red Cross blood service centre.

107

Switching time optimization for switched systems with time-dependent and statedependent switching conditions

Ryan Loxton
Curtin University
Timetable: p. 15

Switched systems operate by switching among various different modes. Determining the optimal times
at which the mode switches should occur is a fundamental problem in systems and control, withparticular importance to the numerical solution of optimal control problems. This talk will discuss theswitching time optimization problem for two classes of switched systems: those with time-dependent
switching conditions (where the switches are directly controllable), and those with state-dependent
switching conditions (where the switches occur when the system hits certain switching surfaces in thestate space). It is often claimed in the literature that standard numerical optimization techniques
struggle when applied to switching time optimization problems. In this talk we present new results
showing that this challenge is over-stated; contrary to popular belief, switching times can in fact be
optimized effectively using standard optimization methods. We verify this with a numerical example
involving a switched system model for the production of 1,3-propanediol, an industrial polymer used inpaints, adhesives and lubricants.

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80

Finite margin call stock loan evaluation

Xiaoping Lu
University of Wollongong
Timetable: p. 19

A stock loan is a financial contract that allows the borrower to obtain a loan with stocks as collateral.
In this talk, we will discuss the American connection between stock loans and options, and showthat the problem of finite maturity margin call stock loans can be evaluated as the corresponding
American barrier options with rebate. The governing partial differential equation is established underthe Black-Scholes framework. Mathematically, the valuation problem is a moving boundary problem,
which does not have an analytical solution except for special cases. I show that the problem canbe solved semi-analytically with great accuracy and efficiency. Numerical examples are presented todemonstrate my solution procedure.

109

Nonlocal solitary waves in nearest-neighbour particle chains

Christopher Lustri
Macquarie University
Timetable: p. 24

Systems consisting of a chain of particles that interact only with their nearest neighbours often produce
solitary wave solutions. However, inhomogeneous chains in which the particle parameters vary, such as
period-2 dimer chains, exhibit more complicated behaviour. Experimental and numerical studies ofdimer particle chains indicate that we can observe nonlocal solitary waves, in which the wavefront isfollowed by a small-amplitude oscillations that do not decay in amplitude away from the wave-front.
These are known as nanoptera.
I will consider 2-periodic particle chains (dimers) in which neighbouring particles interact througha Toda potential, and particles alternate between heavy and light. In particular, I will perform an
asymptotic analysis in the small mass ratio limit.
Using exponential asymptotic techniques, I will show that these systems contain Stokes lines, andby carefully considering the exponentially small solution components, will determine the form of thetrailing oscillations produced behind the traveling wave. Finally, I will show that there is a simple
formula that can be used to identify dimer configurations that produce purely localised solitary wave
solutions without far-field oscillations, which are more robust and decay more slowly than generalsolutions containing nanoptera.

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81

Investigating the dynamics of coupled models with applications to Group A Streptococcus and Scabies

Michael Lydeamore
The University of Melbourne
Co-authors: James M. McCaw, Patricia T. Campbell and Jodie McVernon
Timetable: p. 17

Infections with Group A Streptoccocus (GAS) are highly prevalent in remote communities in the
Northern Territory. One of the primary drivers of GAS infection is scabies, a small mite which causes a
break in the skin layer, potentially allowing GAS to take hold. This biological connection is reaffirmedby the observation that mass treatment for scabies in these remote communities sees a reduction in theprevalence of GAS infection, despite GAS not being directly targeted. In the most extreme case, it has
been hypothesised that the eradication of scabies in remote communities may lead to an eradication of
GAS related infection thereafter.
We present a biologically informed model of scabies infection, which captures the life-cycle dynamics
of the scabies mite and the effects of treatment. We then investigate two reduced models for scabies:
one which notes only the key stages of mite development, and the second deduced from a fast-slow
analysis. We investigate the differences in the transient dynamics between these models, particularly
after a mass drug administration, where a large proportion of the population is treated rapidly, in an
Approximate Bayesian Computation (ABC) framework.
Finally, we couple these scabies models to a susceptible-infected-susceptible (SIS) model that isrepresentative of GAS infections, where individuals who are infected with scabies are assumed to havea greater susceptibility to GAS through the use of a multiplier known as an enhanced susceptibility
factor. We investigate the impact of varying this enhanced susceptibility factor and determine feasible
ranges for the duration of GAS infection, incorporating the posterior distributions from the scabies
model investigation. Finally, we investigate whether the “eradicate scabies eradicate GAS” scenario is
possible under our modelling assumptions.

111

Microbial co-existence and selection in enteric fermentation

Tammy Lynch
Massey University
Timetable: p. 24

In this talk we present a mathematical model created to allow for testing of developing knowledgeof enteric fermentation. The model uses concepts from chemostat modelling and enzyme kinetics
and thermodynamics to model dynamic control of microbe growth. The addition of thermodynamic
control that includes both substrate and product inhibition on the rate of biochemical processes,
produces substrate thresholds below which metabolism stops as has been seen experimentally. It
allows for fermentation pathway selection based on rumen environment and can lead to coexistence ofdifferent species consuming the same substrate but using different fermentation pathways, providing an

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explanation for observed microbial diversity in the rumen that is not dependent on spatial or temporalchanges in the system.

112

An analytical solution for the HJB equation arising from the Merton problem

Guiyuan Ma
University of Wollongong
Timetable: p. 19

An analytical solution of the well-known HJB (Hamilton-Jacobi-Bellman) equation that arises from
the Merton problem subject to some general utility functions is presented for the first time. In theliterature only when the utility function is of some specific form can an analytical solution be obtained.
The solution presented in this talk is written in the form of a Taylor series expansion and constructed
through the homotopy analysis method. The fully nonlinear HJB equation is decomposed into an
infinite series of linear PDEs which can be solved analytically.
To demonstrate convincingly the success of applying the homotopy analysis method to solve this fully
nonlinear HJB equation, which has many applications beyond mathematical finance, four examples arepresented. The first few of these show the accuracy of the homotopy analysis method; while the latter
two demonstrate the versatility of this solution approach.

113

Pressing charges: analytical solutions to the diffusion model charge carriers in
dye-sensitized solar cells

Benjamin Maldon
University of Wollongong
Timetable: p. 20

Dye-Sensitized Solar Cells (DSSCs) have attracted great academic interest since their debut in O’Regan
and Grätzels seminal 1991 paper, owing largely to their reduced cost and unconventional approachto renewable energy. Researchers in the area are confident that methods for optimising efficiency in
DSSCs have not been completely exhausted, but the mathematical modelling in this area is limited. In
this talk we will explore the dominant diffusion model, derive a new analytical solution and use it tocalculate the efficiency of a DSSC.

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83

Mathematical modelling of HIV dynamics in humanized miceAlexey Martyushev
Kyushu University
Timetable: p. 21

Human immunodeficiency virus (HIV) infects and replicates primarily in CD4 T-cells, a subtype of
immune system cells. A dramatic loss of CD4 T-cells within the first months post infection does
not immediately disorder the host immune system that remains protective against other pathogens
for many years, before occurring acquired immune deficiency syndrome (AIDS). The slow diseaseprogression with maintaining functional immunity in chronic HIV infection is a poorly understoodprocess, but it determines the survival of patients, limited in antiretroviral drug (ART) use. To
understand the process, a mathematical model governed by ordinary differential equations (ODEs)
was fitted to the time series data of the CD4 T-cell count and viral load in the peripheral blood ofexperimentally infected humanized mice. In the experiment, two groups of the animals were infectedwith two different HIV strains: (i) eight animals were infected with a wild-type (WT) virus, and (ii) six
animals were infected with a genetically modified virus, deficient in the Vpu protein production. The
experimental data exposed both a rapid increase of the viral load and a progressive decline of the CD4
T-cell count in the WT infected mice. Interestingly, most of the hosts infected with the Vpu-deficientvirus sustained the baseline CD4 T-cell level during the trial period of 105 days, while the viral load
peaked slower than in the WT group. The modelling results revealed that neither a self-proliferation
rate nor a recruitment rate of CD4 T-cells from precursors can explain the difference between the two
experimental groups. However, a lower production rate of infectious virions by infected cells due tothe Vpu-deficiency can explain the observations. The results of this study demonstrate the protection
mechanism of the CD4 T-cell level in HIV infection.

115

Continuum approximations for lattice-free multi-species models of collective cell
migration

Oleksii Matsiaka
Queensland University of Technology
Timetable: p. 16

Cell migration within tissues involves the interaction of many cells from distinct subpopulations. In
this work we present a discrete model of collective cell migration where the motion of individual cells isdriven by random forces, short range repulsion forces to mimic crowding, and longer range attraction
forces to mimic adhesion. This discrete model can be used to simulate a population of cells that iscomposed of K > 1 distinct subpopulations. To analyse the discrete model we formulate a hierarchy of
moment equations that describe the spatial evolution of the density of agents, pairs of agents, tripletsof agents, and so forth. To solve the hierarchy of moment equations we introduce two forms of closure:(i) the mean field approximation, which effectively assumes that the distributions of individual agentsare independent; and (ii) a moment dynamics description that is based on the Kirkwood superposition
approximation. The moment dynamics description provides an approximate way of incorporating
spatial patterns, such as agent clustering, into the continuum description. Comparing the performanceANZIAM 2018 Conference Handbook

84of the two continuum descriptions confirms that both perform well when adhesive forces are sufficiently
weak. In contrast, the moment dynamics description outperforms the mean field model when adhesive
forces are sufficiently large. This is a first attempt to provide an accurate continuum description of alattice-free, multi-species model of collective cell migration.

116

Steady free-surface flow over a bottom obstruction in three dimensions

Scott McCue
Queensland University of Technology
Co-authors: Nicholas Buttle, Ravindra Pethiyagoda and Timothy Moroney
Timetable: p. 19

The problem of steady free-surface flow over a bottom obstruction in two dimensions has received
significant attention in the literature. The linear version of the problem has an exact solution that
I learnt of as an Honours student. With this solution many of the key features can be understood,
such as qualitative differences between slower flows with a train of waves downstream (subcritical) andfaster flows without waves (supercritical). The nonlinear version presents computational challenges
that have been revisited a number of times (starting with Larry Forbes and Len Schwartz in 1982). In
this talk I will consider the three-dimensional version of this problem which, at least in the nonlinear
case, has not received much attention. For three-dimensional flows the wave system appears like a ship
wake. I will discuss qualitative features of the waves and the effects that nonlinearity have on the flow.

117

Anomalous Diffusion on a Growing Domain

Anna McGann
University of New South Wales
Timetable: p. 15

Subdiffusive transport has been observed in many physical and biological systems leading to intensive
efforts to provide robust theoretical models for this phenomenon. Additionally many physical andbiological phenomena occur on domains which evolve with time. We have derived a diffusion equation,using a continuous time random walk, for particles on a domain that grows with time. This allows us toconstruct models that represent physical and biological systems which incorporate both diffusion and adomain that is growing. The resulting equations feature fractional derivatives. The implementation of
the master equation is illustrated with a simple model of subdiffusing proteins in a growing membrane.

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85

MMM, Microwaves Measure MoistureMark Joseph McGuinness
Victoria University of Wellington
Co-authors: Sean Bohun, William Lee and Vincent Cregan
Timetable: p. 20

Measure the moisture content of bauxite in real time on a conveyor belt as it is offloaded from a ship this is the challenge that alumina company Rusal Aughinish brought to a European Study Group with
Industry, held during one week in June last year at the Univeristy of Limerick in Ireland. Rusal areusing a recently installed microwave analyser, and they sought our judgement on the reliability of the
moisture measurements produced by the analyser. If you come to this talk, you will hear how we tackled
the data and information provided, and what we learned about the physics of microwaves propagating
through a field of polarisers. Come, and be amazed at the twist and turns of our negotiations of thepath to enlightenment.

119

Evaluating burn damage and exploring first aid treatment with partial differential
equations and in vivo Porcine experiments

Sean McInerney
Queensland University of Technology
Co-authors: Matthew Simpson and Elliot Carr
Timetable: p. 22

A burn is a common injury which inflicts a high proportion of people at some point in their life. Despite
this, many people are uncertain of what to do if they or someone they are responsible for is inflictedwith a burn. Through the use of mathematical modelling, in conjunction with experimental data, thistalk will begin to address how to measure potential damage to tissue and the effectiveness of different
first aid treatments. In particular, the type of burn that is investigated is a scald burn on in vivo pigs,
where the wound is treated using water of varying temperatures, applied for different periods of time.
Due to how thin the skin is, a single probe is placed below the tissue to track temperature over time.
This limitation in spatially variable data necessitates a single layer, one dimensional model, to allow forparameter inference to be performed. By calibrating the mathematical model to the experimental data,approximations of thermal diffusivity and other model parameters are obtained. With the calibrated
model, a temperature profile can be extended in space and time to infer information not captured in
the experimental data. A novel metric for potential damage to tissue is also proposed in an attempt toquantify harm and explore the effects of different scenarios. This metric incorporates the amount oftissue that exceeds some threshold temperature and for how long. This metric, alongside the calibrated
mathematical model, provides insight into the damage caused by burns and different approached toreduce this damage.

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86

The impact of stem cell division models in epithelial multi-cellular tissue modelling

Claire Miller
The University of Melbourne
Timetable: p. 19

Proliferation of stem cells is critical to normal healthy function in epithelial tissues. These tissues
have very specific structures depending on their type. Using the skin, specifically the epidermis, as
an example stem cells proliferate only in a single basal layer of the tissue. Consequently, being able
to maintain the stem cell population in this layer during division is an important consideration formathematical models of the tissue under normal homeostatic conditions.
We have developed an agent-based multi-cellular computational model to simulate tissue homeostasis in
the epidermis. We have identified that division modelling methodologies that are currently used cause
loss of stem cells from the proliferative layer and, ultimately, from the tissue completely. A common
fix for this issue is to artificially pin the stem cells to the basal layer. This is, however, unphysiological,
and we suggest an alternative more mechanistic approach which uses a rotational force during thedaughter cell separation phase of the cell division model.
In this talk we will explain why stem cell loss occurs from a base proliferative layer using traditional
division models and then present our new approach. We will also compare the impact of the approaches
on simulated epidermal tissue function.

121

Accurate error bounds for linear systems using H-matrices

Atsushi Minamihata
National Institute of Advanced Industrial Science and Technology
Co-authors: Takeshi Ogita and Shin’ichi Oishi
Timetable: p. 14

A used verification method for a linear system Ax = b uses an approximate inverse matrix R. We
need to evaluate an inclusion of RA in this method. We focus on an inclusion of RA by using amatrix multiplication with rounding down for lower bounds and a priori error estimation of matrix
multiplication for upper bounds, and present an accurate error bounds.

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87

A modern linear algebra library for C++17

Tim Moroney
Queensland University of Technology
Timetable: p. 14

Numerical linear algebra underpins much of computational science. Software such as MATLAB has
demonstrated the benefit of providing linear algebra facilities to practitioners in a natural, mathematicalinspired language. For C++, libraries such as Eigen and Armadillo have served the community wellfor many years. But these libraries were designed and written for a much different language: modern
C++ includes features such as auto type deduction, move semantics and most recently class templateargument deduction that have quickly changed the idioms and expectations of programmers. We
present a linear algebra library for C++17 that comes as close as possible to MATLAB, but no closer
in its syntax and semantics, while retaining the look and feel of a modern C++ library. Expression
templates with hooks for BLAS and LAPACK provide the implementations for the underlying low-levelroutines. We demonstrate how straightforward it is to translate MATLAB code to this environment,
and the immediate performance gains provided by doing so.

123

A level set based numerical scheme for doubly connected Hele-Shaw flow

Liam Morrow
Queensland University of Technology
Timetable: p. 12

A Hele-Shaw cell is an experimental apparatus consisting of two flat plates separated by a small gap
filled with a viscous fluid and a inviscid fluid is injected. Significant attention has been devoted to thestudy of fingering patterns which develop in a Hele-Shaw cell due to the Saffman-Taylor instability.
Mathematically, these problems are typically treated by assuming the inviscid fluid is surrounded by an
infinite body of viscous fluid. Here I consider a related problem when the inviscid bubble is surrounded
by a finite amount of fluid such that we have two interfaces to solve for. While this problem has
previously been studied analytically, there is a lack of numerical schemes which solve the full nonlinear
moving boundary problem. Here we present a robust level set based scheme in both radial and channel
geometries. We show that this scheme is able to replicate the characteristic fingering patterns up to
the point where one of the interfaces bursts through the other.

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88

The geometry of a three-dimensional invariant manifold in a four-dimensional slowfast system

Elle Musoke
The University of Auckland
Timetable: p. 11

Neurons, electric circuits and chemical reactions are examples of systems in which some variables
change much more slowly than others. When a system has the defining characteristic of variables
evolving on different time scales, we say that it is slow-fast. We consider the four-dimensional Olsenmodel for peroxidase-oxidase reaction that does not have a clear split into slow and fast variables.
Fenichel theory guarantees the existence of so-called slow manifolds and associated stable and unstablemanifolds that are locally invariant. Previous studies focused on a reduced three-dimensional version of
the Olsen model with a one-dimensional saddle slow manifold having a two-dimensional stable manifold.
Building on this work, we use numerical continuation methods in conjunction with appropriately
defined boundary-value problems to compute two-dimensional submanifolds of the largely unexplored
three-dimensional stable manifold of a slow manifold in the full four-dimensional system.

125

Revisiting delay-embedding by using Hilbert-Schmidt integral operator theory for
dynamical reconstruction

Naoto Nakano
Kyoto University
Timetable: p. 16

Delay embedding is well-known for non-linear time-series analysis, and it is used in several research
fields. Takens theorem ensures validity of the delay embedding analysis: embedded data preserves the
topological properties possessed by the original dynamics so long as one embeds it within some phasespace of sufficiently large dimension. This means that, for example, an attractor can be reconstructedby the delay coordinate system topologically. However, configuration of embedded data may easily varywith the delay width and the delay dimension, namely, “the way of embedding. Here, we investigate
the mathematical structure of the framework of delay-embedding to provide ansatz to choose theappropriate way of embedding, in order to utilise for time-series prediction. In short, mathematicaltheories of the Hilbert-Schmidt integral operator and the corresponding Sturm-Liouville eigenvalue
problem underlie the framework. We will show some numerical results of the present method.

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89

A fast numerical method for ideal fluid flow in domains with multiple stirrers

Mohamed Nasser
Qatar University
Co-authors: Christopher C. Green
Timetable: p. 14

A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix
or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid
stirrers are two-dimensional, the mathematical problem of resolving the flow field - given a particular
distribution of any finite number of stirrers of specified shape and speed - can be formulated as a
Riemann-Hilbert problem. I show that this Riemann-Hilbert problem can be solved numerically using
a fast and accurate algorithm for any finite number of stirrers based around a boundary integral
equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, andmy numerical scheme is shown to handle highly multiply-connected domains (i.e. systems of many
fluid stirrers) with minimal computational expense.

127

Nitrogen removal in the activated sludge process

Mark Nelson
University of Wollongong
Timetable: p. 19

The activated sludge process is the most widely used process for the biological treatment of both
domestic and industrial wastewaters. Wastewater treatment plants based on the activated sludge
process are in widespread use in both developed and developing countries.
The activated sludge model number 1 is an internationally accepted standard for activated sludge
modeling. This model describes nitrogen and chemical oxygen demand within suspended-growthtreatment processes, including mechanisms for nitrification and denitrification.
We analyse the biological treatment of a wastewater when a cascade of three reactors is used. The
reactor configuration consists of an anaerobic reactor followed by an anoxic reactor followed by anaerobic reactor. The process configuration includes one settling unit and two recycle units. The settlingunit is placed after the aerobic reactor and its recycle stream is fed into the anoxic reactor. The recycle
units transfer to and fro between the anoxic and the anaerobic reactors.
A combination of direct numerical integration with continuation methods is used to investigate thesteady-state behaviour of the system. We investigate how the operation of the recycle units effects theconcentration of total nitrogen in the effluent stream and identify conditions for effective nitrificationand denitrification to occur in the reactor.
In addition to identifying operating conditions which minimise the total nitrogen in the effluent stream
we conclude that continuation methods provide the right tool to investigate how changes in processparameters effect outputs in a systematic manner

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90

Modelling collective cell migration in a channel

Zoltan Neufeld
The University of Queensland
Co-authors: Ross Bennett
Timetable: p. 16

The coordinated collective migration of cells during embryogenesis is key to the development ofvertebrates, and improper migration can lead to severe developmental diseases and deformities. As asimple model for such cell migration we study the particle based Vicsek model in a channel geometry
with a constant input flux. The simulations produce two distinct types of motion - one corresponds todesired, well-ordered migration, while the other corresponds to undesirable and disordered migration.
We characterise the different types of collective behaviours and propose a theoretical description todetermine the conditions for coherent collective cell migration.

129

Non-stationary nonparametric and regularised time series analysis of observed atmospheric dynamics

Terry O’Kane
CSIRO
Co-authors: DP Monselesan, JS Risbey, I Horenko and CLE Franzke
Timetable: p. 22

For many atmospheric phenomena, low frequency variability manifests as transitions between quasistationary states or regimes, often initiated by weak stochastic forcing of the large scale slow modes by
the fast-noisy small scales, or through the organised amplification of initially small disturbances via
the inverse energy cascade such as occurs in quasi-two dimensional geophysical flows. In multi-scale
systems time dependence of the model parameters can be induced by the influence of the unresolved
scales leading to large scale regime transitions between quasi-stationary states.
When pre-filtering has been performed, intrinsic variability on timescales shorter than the averaging
period is removed and causal connections are affected. Analysis based solely on methods where thedimensionality is reduced such that only the leading few modes are retained, often justified in terms
of projection onto an arbitrarily determined slow manifold, can also be interpreted as a form ofpre-filtering. Where scale separation is absent, arbitrary filtering and truncation of the underlying
data, common to many studies of low frequency climate variability, can lead to the misrepresentationof the relative importance of the drivers of variability at given spatio-temporal scales. In general, moresophisticated stochastic approaches to mode reduction must be applied and, in particular, where someform of parameterization of the unresolved scales is incorporated. Determining the parameters of the
optimal stochastic model in the relatively short timeseries of the available (atmospheric reanalysis)
data represents a challenge.
Here, we apply a data-driven multiscale method that allows for approximation to non-stationary
dynamical processes, including parameterization of subgrid scales by stochastic forcing. This work

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applies the finite element, bounded variation, vector autoregressive method (FEM-BV-VARX), to
fit a non-stationary stochastic model to the data and then apply information theoretic criteria todetermine the optimal set of time evolving free model parameters. Specifically, we examine the full
three-dimensional structure of the troposphere. The severe computational challenge requires dimension
reduction in order to avoid ill-conditioning. Our focus is on the consequences of various dimension
reduction strategies. We show that a careful and systematic approach to the problem can in fact leadto a deeper insight into the major atmospheric circulation modes and progress toward a more unified
approach to analysing observational data.

130

The energy integral in the first post-Newtonian approximation for general relativity

Joe O’Leary
University of South Australia
Timetable: p. 20

The general theory of relativity is now widely accepted as providing the most accurate theory of gravity.
However, the field equations of General Relativity (GR) are a system of ten non-linear, coupled partial
differential equations where known solutions often exhibit such high degrees of symmetry that modelling
realistic astrophysical situations is often restricted. In order to combat the complexities associatedwith Einstein’s non-linear theory of gravity, linear approximation methods have been developed todetermine n-body equations of motion and approximate solutions to the field equations of GR. The
post-Newtonian (PN) approximation for general relativity is widely adopted by the geodesy andastronomy communities. Presently, the levels of accuracy required in geodetic techniques require thatreference frames, planetary/satellite orbits and signal propagation be treated within the PN regime. In
this talk, we present a novel derivation of the energy associated with a test particle in the first PN
approximation. The integral obtained is deduced by seeking a Jacobi-like integral associated with thePN equations of motion.

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92

Real beards & real networks: a spin-glass model of interacting individuals

Dion O’Neale
The University of Auckland
Timetable: p. 23“I want to be different, just like all the other different people” sang the band King Missile. Whether
they are the Beatniks of the 1950s, the punks of the 1970s, or the hipsters of today, non-conformists
often tend to look the same, seemingly at odds with their goal of non-conformity. The spin-glass model,
originally developed to describe the interaction of magnetic spins, and since applied to situations asdiverse as the electrical activity of networks of neurons, to trades on a financial market, has recently
been used in social science to study populations of interacting individuals comprised of a mix of bothconformists and anti-conformists - or hipsters. Including delay effects for the interactions between
individuals has been shown to give a system with non-trivial dynamics with a phase transition fromstable behaviour to periodic switching between two states (let’s call them bushy bearded and clean
shaven). Analytic solutions to such a model are possible, but only for particular assumptions about
the interaction and delay matrices. In this work we will show what happens when the interactions in
the model are based on real-world networks with “small-world” effects and clustering.

132

Modelling malaria parasites’ survivability the dry season

Samson Ogunlade
UNSW Sydney
Timetable: p. 12

In many malaria endemic areas, seasonal transmission occurs such that during the wet season, individuals
are highly exposed to infection, but not in the dry season, when mosquito numbers decline. We seek toinvestigate how parasites survive the dry season without ongoing transmission. By extending an existing
stochastic mathematical model, we simulated individuals who were repeatedly exposed to malaria
infection over their lifetime. In our model, general and strain specific immunity were generated by thehost at a rate proportional to the concentration of parasites. Hence, previous exposure to parasites
reduced the parasite growth rates of subsequent infections. Our simulation predicts that individuals
more exposed to malaria infection generate more general immunity which, counter-intuitively, leads tolonger infection that could span the entire dry season.
The predictions of these simulations were tested using data from a cohort study. Individuals from acommunity were determined to be either infected or uninfected at the end of the dry season. Infectedindividuals were then treated and regular follow-ups were conducted to determine when individuals
became infected. Survival analysis was used to determine the rate of exposure to new infections forpeople who were infected at the end of the dry season and people who were not infected. This analysis
showed that those who were infected fastest in the study were also those who had the highest levels of
infection at the start of the study (i.e. at the end of the previous dry season). Results from our work
provide support for the hypothesis that highly exposed individuals may be responsible for the parasite
carriage in the dry season.

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93

Sparse spectral methods for PDEs on triangles with multivariate orthogonal polynomials

Sheehan Shakiban Olver
Imperial College London
Timetable: p. 19

Univariate orthogonal polynomials have a long history in applied and computational mathematics,
playing a fundamental role in quadrature, spectral theory and solving differential equations with
spectral methods. Unfortunately, while numerous theoretical results concerning multivariate orthogonal
polynomials exist, they have an unfair reputation of being unwieldy on non-tensor product domains andtheir use in applications has been limited. In reality, many of the powerful computational aspects of
univariate orthogonal polynomials translate naturally to multivariate orthogonal polynomials, including
the existence of Jacobi operators, fast evaluation of expansions using Clenshaws algorithm and theability to construct sparse partial differential operators, a la the ultraspherical spectral method [Olver& Townsend 2012]. We demonstrate these computational aspects using multivariate orthogonal
polynomials on a triangle, including the fast solution of general partial differential equations.

134

Global manifolds parametrised by isochrons

Hinke Osinga
The University of Auckland
Timetable: p. 22

Isochrons are sets of points in the basin of a stable periodic orbit that have the same asymptotic
phase, that is, these points synchronise with a given point on the periodic orbit. We generalise thisnotion to periodic orbits of saddle type by considering the parametrisations of the stable manifold byforward-time isochrons and of the unstable manifold by backward-time isochrons. Computing thesefamilies of isochrons as (un)stable submanifolds of the period-map allows us to find, represent andillustrate two-dimensional global invariant manifolds in a new and efficient way.

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94

Numerical modelling and characterisation of an all-fibre laser with saturable absorber

Robert Nawiekang Otupiri
The University of Auckland
Timetable: p. 13

We present a detailed experimental and numerical study of self-pulsations in an all-fibre laser withsaturable absorber. Pulses are generated in a process known as Q-switching, and we show how thepulsing behaviour depends on a variety of parameters including the pump power, the strength ofabsorption, as well as the decay times of gain and absorber media. To this end, we consider a systemof three differential equations, initially developed by Yamada and adopted here to the experimental
laser system, which consists of an erbium-doped fibre generating the required gain in combination witha thulium-doped fibre providing the necessary absorption. The dynamics exhibited by this laser system
are studied with a focus on the strength of absorption; this is realised by considering, for different
absorber lengths, how the system behaves as a function of the pump power. We demonstrate good
agreement between the analysis of the model and experimental observations, in terms of the originof Q-switched pulsations in a Hopf bifurcation, as well as regarding the influence of the strength ofabsorption on the overall behaviour of the system.

136

Nonlinear exact coherent structures in pipe flow

Ozge OzcakirMonash University
Timetable: p. 24

There is little computational work on travelling wave computations in pipe flows at very large R
in existing literature apart from those reported in Ozcakir (2016). In this talk, we present resultsthat extend reliable travelling wave computations through greater efficiency to a far greater Reynolds
number (up to R = 5 × 105 ) regime than previously reported. Firstly, we confirm that travellingwaves states which are referred to as C1 and C2 in Ozcakir (2016) are indeed finite R realization of
nonlinear viscous core states because of much closer agreement of numerical results with asymptotics.
The second part of the talk concerns determination of a new branch of solution (WK2) which connects
to Wedin-Kerswell (WK) when continued to sufficiently large R. that ascertains that it is a finite
R realisation of asymptotic VWI states, with peak roll, wave, and stream amplitudes scaling as
R−1 , R−5/6 and O(1) respectively. In the last part or the talk linear stability of travelling waves are
discussed. We extend linear stability calculations to large enough R so that asymptotics of unstableeigenvalues are apparent. These scalings are in agreement with the R−1/2 , R−1 asymptotics for edge
and meandering modes predicted by Deguchi & Hall (2016) for uni-directional shear flow. Finally, we
present preliminary travelling wave calculations for non-Newtonian fluids.

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95

A model of calcium dynamics in anatomically accurate parotid acinar cells

Nathan Pages
The University of Auckland
Timetable: p. 13

We construct an anatomically-accurate three-dimensional model of calcium oscillation in a cluster ofparotid gland acinar cells.
Parotid acinar cells are responsible for the secretion of saliva. Olfactory and gustatory stimuli provoke
the release of agonists that bind to the basal membranes of the acinar cells. This triggers a cascade ofevents that results in the production of IP3 , which, in turn, releases calcium ions from intracellularcompartments.
The major current question in the modelling of saliva production and calcium oscillation is whether or
not the complex spatial structure of the acinus, or the spatial heterogeneities within each acinar cell,
have any significant effect on the calcium oscillations possible mechanism.
We will discuss how we built a computational model to answer this question. Preliminary results
suggest that the spatial structure impose severe constraints on the possible mechanism that could
cause calcium oscillation.

138

Using Approximate Bayesian Computation to understand the impact of climate inseasonal influenza in Australia

Jessica Penfold
The University of Adelaide
Timetable: p. 15

Influenza in humans exhibits a strong seasonal cycle in temperate climates, with a peak of varying
intensity appearing each winter. However, the exact cause of this seasonal cycle remains poorly
understood. We aim to develop a climate-based SIR model to understand influenza seasonality
by developing a functional form of transmissibility using climate data. Using a variety of existingclimate-based functional forms of transmissibility from current literature, we use modern Approximate
Bayesian Computation model selection methods to choose the best functional form for climatedependent transmissibility. By analysing a unique dataset comprising ten years of GP-reported
influenza surveillance data in Sydney, we explore the problem of ensemble prediction using a weighted
ensemble of models to predict future influenza seasons.

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96

Modelling cell proliferation times

Catherine Penington
Macquarie University
Timetable: p. 23

Typically, discrete stochastic models of cell proliferation use a rate to determine whether or not acell proliferates at a particular time, producing an exponential distribution for the time between
proliferation events. Actual experiments, however, suggest that cells have a Gaussian distribution
in their time to proliferation, with a relatively small standard deviation. This talk will discuss thesimilarities and differences in the group behaviour depending on the proliferation model: both thesurprising match after a single time step, and the large differences as simulations progress.

140

On the evaluation of Landau constants in amplitude equations away from a criticalpoint. Part 1: supercritical regimes

Khanh Pham
Swinburne University of Technology
Co-authors: Sergey A. Suslov
Timetable: p. 13

A classical weakly nonlinear stability analysis of shear fluid flows based on a perturbation amplitude
expansion is re-considered to derive Stuart-Landau type equations that model a temporal evolutionof disturbance amplitude in linearly unstable flow regimes. A robust computational procedure for
evaluating Landau coefficients appearing in such amplitude equations is suggested that incorporates a
generalized amplitude normalisation condition. It is proved rigorously that such a condition recovers
the standard solvability condition at the critical point, where the basic flow first becomes unstablewith respect to infinitesimal disturbances. It is also shown that the use of this generalised condition
results in a well-posed problem for the determination of coefficients of Stuart-Landau series both at thecritical point and a finite distance away from it. It is emphasised that the choice of the normalization
condition required to define the Landau coefficients away from the critical point is not unique. In
conjunction with the suggested computational procedure this offers a flexibility to adjust a weakly
nonlinear projection of the full problem solution onto the space spanned by the basic flow vector andthe eigenvector of the linearized problem to focus on the specific flow features of interest.

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97

Dynamics of reactivation from latency in macaques infected with simian immunodeficiency virus

Mykola Pinkevych
UNSW Sydney
Co-authors: Fennessey C., Keele B. and Davenport M.
Timetable: p. 22

HIV can be effectively controlled by anti-retroviral therapy, but cannot be eradicated due to thepresence of HIV in latently infected CD4+ cells that cause the reactivation of virus if a patient stops
anti-retroviral treatment. However there is a lack of knowledge about the basic dynamics of reactivationof latently infected cells, because this occurs at levels below our threshold of detection. In order toanswer these questions we combined mathematical modelling with a novel experimental method ofsequence barcoded viruses to track the reactivation of individual latently infected cells.
Rhesus macaques were infected intravenously with a sequence-tagged SIV-M virus with ≈ 10, 000
different clonotypes. Animals were treated with antiretroviral therapy for a various times prior totreatment interruption. After interruption serum samples were subjected to gene sequencing in order to
identify the frequency of individual tagged viruses. We developed a mathematical model incorporating
latent cell reactivation and viral growth to analyse the experimental data. Using this model we estimatethat the frequency of re-activation from latency ranges from around 20 re-activations per day to 0.5
re-activations per day, depending on the timing and duration of treatment. A single reactivated latentcell can produce an average viral load equivalent to ≈ 0.1 − 0.5 viral copies/ml of virus, depending on
assumption about duration of drug action.
The combination of the monkey model with mathematical analysis is a useful tool to understand the
dynamics of reactivation from latency, the estimation of the efficacy of treatment and as a guide as towhat interventions may be effective at early control of reactivation.

142

The other end of the spectrum: size-based models of marine ecosystems and fishing

Michael Plank
University of Canterbury
Timetable: p. 17

Many marine fish species can grow in body mass more than seven orders of magnitude over their
lifetime. As fish grow, their target prey and their growth, mortality and reproduction rates change
drastically with body mass. This means that body mass is a crucial variable in any mathematicalmodel. Size-spectrum models put body mass foremost by doing a bookkeeping of biomass as it flows
from prey to predator, and from parent to offspring. This is a different paradigm from the classicalspecies-based predator-prey model. This talk will give an overview of size-spectrum models and theinsights they have given us into marine community dynamics. Size-spectrum models are based ona generalisation of the McKendrick-von Foerster equation to a nonlinear, partial integro-differential
equation. I will show some theoretical results about the equilibrium size structure and stability, as

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well as applications in fisheries management and fisheries-induced evolution. Size-spectrum models are
particularly suited to investigating the effects of different distributions of fishing mortality over bodymass and species, which is a key question for ecosystem-based fisheries management.

143

Do T-cells compete for antigen?

Pantea Pooladvand
The University of Sydney
Timetable: p. 20

When antigen is presented to helper T-cells, the immune response is two-fold. First, the T-cells
will go through rapid expansion, followed by a contraction phase which subsequently contributes toimmunological memory.
It is difficult to assess the contribution of precursor frequency to the T-cell numbers at the peak of the
response due to the widely differing views in recent publications. Does the initial number of T-cells
determine the peak or is the T-cell response limited by the amount of antigen present?
Inspired by new experimental results from our collaborators, we introduce a simple system of ODEs
to investigate this problem by considering that the T-cells compete for limited amount of antigen.
We propose that this competition between T-cells limits the peak of response and we compare thedynamics from this system to our collaborators’ data.

144

Shaping liquid drops by vibration

Andrey Pototsky
Swinburne University of Technology
Timetable: p. 24

We present and analyze a minimal hydrodynamic model of a vertically vibrated liquid drop that
undergoes dynamic shape transformations. In agreement with experiments, a circular lens-shaped
drop is unstable above a critical vibration amplitude, spontaneously elongating in horizontal direction.
Smaller drops elongate into localized states that oscillate with half of the vibration frequency. Larger
drops evolve by transforming into a snake-like structure with gradually increasing length. The worm
state is long-lasting with a potential to fragment into smaller drops.

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99

The Cardiac Cell under the Mathematical Microscope

Vijay Rajagopal
The University of Melbourne
Timetable: p. 15

Diseases of the heart such as cardiac hypertrophy and diabetes induced cardiomyopathy are symptoms of
sub-cellular deregulation and remodelling of biochemical processes that govern heart muscle contraction.
It is often noted that morphological and structural changes also occur in parallel to these biochemicalchanges. However, whether these structural changes are minor, adaptive or pathological responses tothe changing conditions is largely unknown. We are developing in-silico finite element models of theheart cell that are derived from state-of-the-art structural microscopy data to investigate the role ofsub-cellular structural remodelling on heart cell function. I will present results from a modelling study
we conducted to investigate the effect of mitochondrial remodelling on cardiac cell bioenergetics. I will
also present tools we are building to make the development of these models easier and more widelyadoptable for similar investigations in other cell types.

146

Hard-core interactions in one-dimensional velocity jump models

Tertius Ralph
The University of Auckland
Co-authors: Steve Taylor
Timetable: p. 15

Excluded-volume effects can play an important role in determining transport properties in the diffusionof particles through crowded environments. Here, the diffusion of finite-sized hard-core inter-acting
particles is considered systematically using the method of matched asymptotic expansions. We will use
the Langevin approach to diffusion where stochastic increments are applied to the velocity rather than
to the space variable. The result is a non-linear PDE for the one-particle probability density function
taking into account crowding effects. Stochastic simulations will be used for a comparison with theanalytic/numerical solutions derived. The analytic/numerical solutions compare well with stochastic
simulations provided the excluded volume fraction is small.

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100

A Distribution-Moment approximation for coupled airway dynamics of the airway
wall and airway smooth muscle

Anand Rampadarath
The University of Auckland
Co-authors: GM Donovan
Timetable: p. 11

Asthma is fundamentally a disease of airway constriction. Due to a variety of experimental challenges,
the dynamics of airways are poorly understood. Of specific interest is the narrowing of the airway due
to forces produced by the airway smooth muscle (ASM) wrapped around each airway. The interaction
between the muscle and the airway wall is crucial for the airway constriction which occurs during anasthma attack. While crossbridge theory is a well-studied representation of complex smooth muscle
dynamics, and these dynamics can be coupled to the airway wall, this comes at significant computational
cost – even for isolated airways. Because many phenomena of interest in pulmonary physiology cannot
be adequately understood by studying isolated airways, this presents a significant limitation. We present
a distribution moment approximation of this coupled system as well as comparative results between
this approximation and the full PDE based model. These results show that in many situations the
distribution moment approximation is a viable option which provides an orders of magnitude reduction
in computational complexity; this is valuable not only for isolated airway studies, but moreover offers
the prospect that rich ASM dynamics might be incorporated into interacting airway models wherepreviously this was precluded by computational cost.

148

A multiscale approximation of a Cahn–Larché system with phase-separation on the
microscale

Lisa Reischmann
University of Augsburg
Timetable: p. 22

We consider the process of phase-separation of a binary system under the influence of mechanicaldeformation and we derive a mathematical multiscale model, which describes the evolving microstructure
taking into account the elastic properties of the involved materials. Motivated by phase-separation
processes observed in lipid monolayers in film-balance experiments, the starting point of the model is
the Cahn–Hilliard equation coupled with the equations of linear elasticity, the so-called Cahn–Larchésystem. Owing to the fact that the mechanical deformation takes place on a macroscopic scale whereas
the phase separation happens on a microscopic level, a multiscale approach is imperative. We assume
the pattern of the evolving microstructure to have an intrinsic length scale associated with it, which,after nondimensionalisation, leads to a scaled model involving a small parameter ε > 0, which is suitablefor periodic-homogenisation techniques. For the full nonlinear problem the so-called homogenised
problem is then obtained by letting ε → 0 using the method of asymptotic expansion. Furthermore,
we present a linearised Cahn–Larché system and use the method of two-scale convergence to obtain
the associated limit problem, which turns out to have the same structure as in the nonlinear case, in amathematically rigorous way. Properties of the limit model will be discussed.

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101

Thin-film multiphase modelling of collagen gel mechanics

James Reoch
The University of Adelaide
Timetable: p. 15

Cells are often grown within collagen gels in vitro for applications in tissue engineering. The behaviourof cells is regulated by their mechanical environment; however the forces exerted by cells in turn affectthe mechanical behaviour of the gel. We aim to gain more insight into the interactions between thecells and the gel using mathematical modelling. We have developed a multiphase model for this system,
incorporating cells and their traction forces alongside chemical effects like osmosis. We have modelled
this problem to date in one-dimensional Cartesian and spherical coordinates, mimicking experiments
performed with spheres of collagen gel. However, often these gels are produced in Petri dishes, resulting
in a thin disc. We have therefore modified our model to explore this type of geometry. We showhow, in certain parameter regimes, we are able to exploit thin-film approximations and reduce thetwo-dimensional system to a leading-order, one-dimensional model.

150

Modelling HIV latency using distribution of lifespans of infected cells

Josephine Reyes
University of New South Wales
Timetable: p. 24

Understanding the mechanisms of HIV latency is important in the development of strategies for
managing infection. Time from infection until production of virus has been shown to vary among
infected cells, hence challenging the dichotomous assumption that cells are either latent or productively
infected at time of infection. We will explore the implications of an alternative hypothesis that times
from infection to producing virus (reactivation) follow a probability distribution, of which latency isjust an extreme of this spectrum. We show the emerging dynamics from this mathematical model andtest its ability to explain features or reservoir formation and decay observed in SIV data. Analysis of
SIV DNA levels in macaques that start treatment at different times shows that the decay rates of cells
are different in early and late initiation of treatment. Modelling suggests that data can be explainedby a spectrum of time-to-viral production by infected cells.

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102

Age-specific heterogeneity in CD8+ T-Cell homeostasis

Arnold Reynaldi
UNSW Sydney
Co-authors: Norah L. Smith, Timothy E. Schlub, Vanessa Venturi, Brian D. Rudd and Miles P. Davenport
Timetable: p. 20

Infants and the elderly are more susceptible to infection as a result of an immature or senescent immune
system. However, little is understood about the development, persistence and death of immune cells
over the lifespan. CD8+ killer T-cells are a subset of the immune cells that is important in controlling
infections by killing infected cells. In this study, we aim to understand the maintenance of T-cells overthe lifespan. Recently, we have developed a novel mouse model in which we can track the survival of
T-cells produced at various stages of development. This provided numbers of cells produced at different
ages, and how long they persisted. Comparing various mathematical models of varying complexity, thepopulation of T-cells can be described by a three-parameter model including an initial rate of decay(of cells produced at birth), how this initial decay rate slows with age of the animal, and how, for cells
produced at any age, the rate of decay slows with the age of the cell. T-cells produced during infancy
showed the most rapid early decay (half-life of 14 days). However, the decay of these cells slowed, anda population of T-cells produced at birth persisted for the life of the animal. Cells produced laterin life (produced at 25 weeks) display a high level of persistence. A mathematical model was also
developed to understand how cell production and survival leads to a developmental layering of cells
produced at different ages, and how this contributes to the total T cell pool in adult life. Based on
the model, in a 100-day-old mouse, 43% of its T-cells were produced from the thymus within the last
30 days. In contrast, in a 300-day-old mouse, only 20% of the cells were produced within the last 30
days. Overall, this modeling indicates that the age at which cells were produced contributes to theheterogeneity observed in the adult T-cell population.

152

Fine-grained multi-factor hail damage modelling

Melanie Roberts
IBM Research Australia
Timetable: p. 19

A fine-grained multi-factor estimation of crop-hail damage is required to progress from manual
inspection of crops post-event to automated assessment and accurate forecasting of the expected impact
on agricultural areas. Such automated processes will enable more accurate claims processing, improvecustomer satisfaction and reduce insurance losses. This paper demonstrates the value of Gaussian
processes for the construction of such a multi-factor model of crop-hail damage. This is underpinned bya survey of public datasets and a description of the target dataset to support an operational crop-haildamage model.

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103

Is your family pet a source of antibiotic resistance?

Mick Roberts
Massey University
Timetable: p. 17

Antibiotics are used extensively to control infections in domestic pets, either in the form of a course oforal tablets or a single injection. There are several methods by which bacteria can develop resistantstrains, including mutation during reproduction and horizontal gene transfer. We present a model forthe development of antibiotic resistance within a single host animal. We derive criteria for a mutant
strain to replace the existing wild-type bacteria, and for co-existence of the wild-type and mutant.
Where resistance develops through horizontal gene transfer, we derive criteria for the resistant strain
to be excluded or co-exist with the wild-type. We show how resistance may develop during antibiotic
treatment when either or both mechanisms operate.

154

Neurons, temperature and timescales: what GSPT might tell us about temperature
regulation?

Timothy Roberts
The University of Sydney
Co-authors: Martin Wechselberger
Timetable: p. 22

The human body can only survive if its core temperature lies within a narrow range of permissible
values. Thus, regulation of core body temperature is a critical task for the body to perform. The
preoptic area and anterior hypothalamus (PO/AH) of the brain is thought to play a key role in thisprocess, acting as an integrative centre for temperature regulation. It is responsible for monitoring
the body’s core temperature, collecting information about ambient environmental temperature (viacommunications from neurons elsewhere in the body) and integrating this data to determine and control
how the body should respond to changing conditions. Current electrochemical models of PO/AH
neuron function appear to be able to describe the varied behaviours required to monitor core bodytemperature; however, the mathematical and physiological mechanisms that allow this are not fully
understood. In this talk I will look at how the methods of bifurcation theory and geometric singular
perturbation theory (GSPT) might help us to understand how model neurons function and what thiscan tell us about the physiological mechanisms underlying temperature sensitivity.

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104

Projective integration of multiscale ODEs via Dynamic Mode Decomposition

Tony Roberts
The University of Adelaide
Timetable: p. 13

Multiscale ODEs commonly arise in discretisations of PDEs, in agent based methods, and in molecularsimulations. The so-called projection integration uses short bursts of such detailed microscale simulations, followed by extrapolation over a macroscale time, to efficiently compute simulations over longtimes. Here I introduce using Dynamic Mode Decomposition (DMD) to perform the extrapolation.
DMD fits a low rank sum of exponentials to the microscale simulation and so should distinguish microscale and macroscale modes for better filtering, and hence make better forecasts over the macroscale
simulation.

156

Who gets the girl? On the operational sex ratio as an index for male strategy

Danya Rose
The University of Sydney
Timetable: p. 24

The operational sex ratio (OSR) is defined as the ratio of eligible males to fertile females in a population.
If males compete with each other for paternities according to their father’s strategy, does mating withas many females as possible (multiple-mating), or does preventing other males access to one’s own
mate (mate-guarding) win out? We build a two-strategy ODE model of a primate-like population inwhich males inherit their father’s mating strategy when they mature, and investigate the correlation
between OSR and dominant strategy.

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105

Demography determines gene drives success in eradicating pests

Joshua Ross
The University of Adelaide
Co-authors: Kym Wilkins, Thomas Prowse, Phill Cassey and Paul Thomas
Timetable: p. 22

Synthetic, selfish gene drives may offer a novel solution to the control of invasive, alien species.
Mathematical modelling of these systems is important for a variety of reasons, from ensuring the risks
to non-target populations is low, to determining if the biased inheritance and gene-drive strategy
is able to outcompete the rise of resistance alleles in the population, hence leading to a suitablestrategy. Most models to date have assumed mass action mating. This form of reproduction isinappropriate for vertebrate pest populations (e.g., mice), and we find it gives rise to overly optimistic
conclusions regarding gene drive efficacy. More realistic polygynous mating demonstrates that standard
implementations of gene-drive strategies will be unsuccessful in the absence of an Allee effect. An Allee
effect may assist gene drive success, but efficacy appears to be highly sensitive to the strength of theAllee effect. Our results indicate that a detailed understanding of the demography of the species isnecessary for evaluating gene drive strategies.

158

Linear systems in Matlab with zero residual

Siegfried Rump
Technical University Hamburg
Timetable: p. 17

Several examples of linear systems are given for which the residual of the computed approximation(computed in working precision) is precisely zero. Nevertheless, the computed approximation by
Matlab’s backslash operator is highly inaccurate, and often no warning is issued. Examples for matrix
inversion in that spirit are given. Moreover, it is demonstrated that rounding the exact real result tothe nearest floating-point numbers may be worse than using an approximation computed by somefloating-point algorithm.

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106

But I’m a data scientist too, aren’t I?

Louise Ryan
University of Technology, Sydney
Timetable: p. 14

The statistics profession is in a period of disruptive change, heralded by explosive growth in information
technology and the big data revolution. New specialties such as machine learning, data science andanalytics seem to go from strength to strength and sometimes it seems like statistics is being discarded
like one of last decades fashion embarrassments. In this presentation, I will offer some perspectives on
the changing landscape for statistical science. I will draw on some of my own recent projects where
statistics as usual fall short and outline some of the areas where I think there are great opportunities
for bringing a statistical perspective to the broader data science arena. I have already given several
versions of this presentation at venues around the world, but have updated it with some recent new
developments.

160

Why does an inverted-flag flap in a uniform steady flow?

John Elie Sader
The University of Melbourne
Timetable: p. 25

The dynamics of a cantilevered elastic sheet, with a uniform steady flow impinging on its clamped
end, have been studied widely and provide insight into the stability of flags and biological phenomena.
Recent measurements show that reversing the orientation of the sheet, with the flow impinging on
its free-edge, dramatically alters its dynamics. In contrast to the conventional flag, which exhibits(small-amplitude) flutter above a critical flow speed, the inverted-flag displays large-amplitude flapping
over a finite band of flow speeds. In this talk, a combination of mathematical theory, scaling analysis,numerical simulations and measurement is used to investigate the origin of this large-amplitude flapping
motion. Flapping is found to be a vortex-induced vibration and is predominantly periodic, with atransition to chaos as flow speed increases. These findings have implications to leaf motion and otherbiological processes, such as the dynamics of hairs, because they also can present an inverted-flag
configuration.

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107

Topographical uniqueness condition for the weak form of a linear depth-averaged
vorticity model

Balazs Sandor
Griffith University
Timetable: p. 21

The vorticity form of the depth-averaged shallow water equations are considered and simplified up to alinear model based on ongoing research of the authors. In this talk we would like to examine this minimalmodel from the mathematical point of view. Using the Lax-Milgram theorem, a uniqueness condition
has been deduced for the weak form of the model. This uniqueness condition has straight geometricalconsequences on the bed topography of the fluid body. We would like to present this result and also
some of the first application attempts. We have open questions about the connection of the uniquenessof the solutions and the evolution of circulating domains via the variation of topographical parameters
and whether a solution which describes splitting circulating domains is necessarily non-unique.

162

The sausage-string structure of mode-locking regions of piecewise-linear maps

David John Warwick Simpson
Massey University
Timetable: p. 24

Mode-locking regions are subsets of parameter space where a dynamical system is entrained to a
fixed frequency or rotation number. In two-parameter bifurcation diagrams they appear as narrow
regions ordered by rotation number. For piecewise-linear maps they have pinch points, called shrinking
points, and an overall structure that resembles a string of sausages. This has been identified in models
of diverse systems, including power converters, neurons, and economics, and remains incompletely
understood. In this talk I will explain how each shrinking point organises the bifurcation structure
locally. A handful of key scalar quantities assigned to a shrinking point govern the relative size,
properties, and arrangement of nearby mode-locking regions. In sectors radiating from a shrinking
point, periodic, quasiperiodic, and chaotic dynamics are accurately captured by a one-dimensionalskew sawtooth map.

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108

Optimal quantification of contact inhibition in cell populations

Matthew Simpson
Queensland University of Technology
Timetable: p. 23

Contact inhibition refers to a reduction in the rate of cell migration and/or cell proliferation inregions of high cell density. Under normal conditions contact inhibition is associated with the proper
functioning tissues, whereas abnormal regulation of contact inhibition is associated with pathologicalconditions, such as tumour spreading. Unfortunately, standard mathematical modeling practices mask
the importance of parameters that control contact inhibition through scaling arguments. Furthermore,
standard experimental protocols are insufficient to quantify the effects of contact inhibition because
they focus on data describing early time, low-density dynamics only. Here we use the logistic growthequation as a caricature model of contact inhibition to make recommendations as to how best to
mitigate these issues. Taking a Bayesian approach we quantify the trade-off between different featuresof experimental design and estimates of parameter uncertainty so that we can re-formulate a standard
cell proliferation assay to provide estimates of both the low-density intrinsic growth rate, λ, and thecarrying capacity density, K, which is a measure of contact inhibition.

164

Needlet approximation on the sphere

Ian Sloan
University of New South Wales
Timetable: p. 12

Spherical needlets are highly localized radial polynomials on the sphere Sd ⊂ Rd+1 , d ≥ 2, with centres
at the nodes of a suitable quadrature rule. The original spherical needlet approximation as proposed
by Narcowich, Petrushev and Ward makes use of coefficients defined by inner product integrals. In thistalk I first review the needlet construction, and then report on recent joint work with Yu Guang Wang,
Q Thong Le Gia and Robert Womersley, which uses an appropriate quadrature rule to construct afully discrete (and hence truly constructible) needlet approximation. We prove that the global fully
discrete approximation has rates of convergence in Sobolev spaces Wsp (Sd ), for 2 ≤ p ≤ ∞, that fors > d/p are exactly the same as for the original needlet approximation. We also demonstrate thatthese rates are achieved in numerical practice.

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109

Hunting for a moving target on a graph and building dynamical systems fromcomplex networks

Michael Small
The University of Western Australia
Timetable: p. 23

I introduce the problem of hunting for a moving target on a complex network (a large graph withheterogeneous and long-tailed degree distribution). In particular: how long will it take, on averagefor the hunter to capture the target? A related question, in the particular case where nodes of thegraph may be thought of as states of the dynamical systems and links as observed transitions (in thedeterministic setting, but where we have only been allowed finitely much data), is how does one move
about the graph so that the sequence of observed states best emulate independent output of the same
deterministic dynamical system?

166

The effect induced in the far-field pattern by the rounding of corners of a scatterer
illuminated by a plane wave electromagnetic field

Paul Smith
Macquarie University
Co-authors: Audrey Markowskei
Timetable: p. 25

When a perfectly electrically conducting two-dimensional scatterer, which is smooth except at finitely
many sharp corner points, is illuminated by an E-polarised electromagnetic plane wave, the surface
current density exhibits singularities at those corner points, whilst in the H-polarised case the surface
density exhibits singularities in its derivative at those points. Once the corners are rounded, the surface
density becomes non-singular. It is of interest to examine the impact of this rounding upon observed
physical quantities such as the far-field as the rounding becomes more pronounced.
An integral equation formulation is a satisfactory basis of numerical studies of the scattering of planewaves by a smooth obstacle; its solution provides a surface density from which all physical quantities
can be calculated. Whilst this approach can be adapted to accommodate obstacles with sharp corners,
efficient methods for the calculation of the desired surface density depend upon the introduction ofgraded meshes. In this presentation, we describe the appropriate modifications that are subsequently
employed to quantify the changes induced in the far-field pattern when the corners are rounded. We
examine the difference of the far-field pattern from that of the unrounded structure as a function of theparameter kρ where k is the wavenumber and ρ is the radius of curvature of the rounded corner. It isfound that the difference is O((kρ)m ) as kρ approaches zero, for some positive exponent m depending
upon boundary and other conditions. A number of structures with single or multiple corners are
examined with a variety of boundary conditions: E- or H-polarised cases as well as the impedance
loaded case.

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110

Optimization in the Darkness of Uncertainty: when you don’t know what you don’tknow, and what you do know isn’t much!

Kate Smith-Miles
The University of Melbourne
Timetable: p. 21

How do we find the optimal solution for a constrained multi-objective optimisation problem when we
have no analytical expression for the objective functions, and very limited function evaluations within
the huge search space due to the expense of measuring the objective functions? Calculus cant help you,and trial and error is not an option! This talk will describe a common practical optimization problem
found in many industrial settings with these challenges, and introduce some methods for expensive
black-box optimization. Finally, we will address the question of how best to evaluate the performanceof such methods by generating new test instances with controllable characteristics.

168

From birds and bees to flying machines

Mandyam Srinivasan
The University of Queensland
Timetable: p. 16

Flying insects and birds are remarkably adept at seeing and perceiving the world and navigating
effectively in it. This presentation will describe our recent progress in understanding how honeybees
and birds (budgerigars) use their vision to control and regulate their flight speed, measure travel
distance, negotiate narrow passages safely, avoid mid-air collisions and perform smooth landings, using
computational principles that are often elegant and unprecedented. It will conclude with an updateof our advances in the design and testing of biologically inspired vision systems for the guidance ofautonomous aerial vehicles.

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111

Domain Decomposition applied to the thin-plate spline saddle point problem

Linda Stals
Australian National University
Timetable: p. 15

Data fitting is an integral part of a number of applications including data mining, 3D reconstruction ofgeometric models, image warping and medical image analysis. A commonly used method for fitting
functions to data is the thin-plate spline method. This method is popular because it is not sensitive tonoise in the data.
We have developed a discrete thin-plate spline approximation technique that uses local basis functions.
With this approach the system of equations is sparse and its size depends only on the number of points
in the discrete grid, not the number of data points. Nevertheless the resulting system is a saddle point
problem that can be ill-conditioned for certain choices of parameters. In this talk I will present a
domain decomposition based preconditioner that results in a well conditioned system for a wide choiceof parameters.

170

Stability of the non-Newtonian asymptotic suction boundary layer

Sharon Stephen
The University of Sydney
Co-authors: Paul Griffiths
Timetable: p. 23

The stability of an asymptotic suction boundary layer is considered to investigate the effect of nonNewtonian viscosity on the transition process from a laminar to a turbulent flow at large Reynolds
number. As such, we investigate the flow past a flat plate, with uniform suction applied at the surface,
for a non-Newtonian flow. Suction is applied in practical situations to delay transition to turbulence.
This flow exhibits a constant boundary-layer thickness, making it attractive to numerical and theoreticalanalysis. For a Newtonian flow, recent interest has been in identifying coherent structures [1] anda self-sustaining vortex/Tollmien-Schlichting wave interaction [2]. The focus here is the effect of a
non-Newtonian fluid and is motivated by applications to use non-Newtonian flows to delay transition
to turbulence. In this first investigation for non-Newtonian flows we consider the effect on the linear
stability of lower branch neutral modes that are governed by a triple-deck structure.
[1] Deguchi, K. and Hall, P. 2014 Free-stream coherent structures in parallel boundary-layer flows. J.
Fluid Mech., 752, 602-625.
[2] Dempsey, L. J. and Walton, A. G. 2017 Vortex/Tollmien-Schlichting wave interaction states in theasymptotic suction boundary layer. Q. Jl Mech. Appl. Math, 70, 187-213.

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112

Why oversized holes in microstructured optical fibres?

Yvonne Stokes
The University of Adelaide
Co-authors: Michael Chen
Timetable: p. 15

A microstructured optical fibre (MOF) is a long and thin glass fibre, typically around 150µm in
diameter and more than a km in length, containing a pattern of air holes, with diameters comparable
to the wavelength of light, that run parallel to the axis of the fibre. Such a fibre is made by heating andstretching a preform of 1–3cm in diameter and 10–20cm in length, with appropriate internal structure,a process known as fibre drawing. For a desired set of optical properties, the holes in the fibre musthave specific shapes be arranged in a specified pattern. Mathematical modelling is essential for solving
the inverse problem of determining the preform geometry and draw parameters required to obtain adesired fibre.
Asymptotic techniques have been used to obtain an efficient model of fibre drawing yielding solutions
that match well with experiments. However, at times the air channel diameters seen in experiments
are significantly larger than predicted by the model, most notably for air channels of larger initial
diameter and when the fibre is drawn using a high tension or draw ratio. Using a modified model, thattakes account of the air in the channels and the temperature gradient along the neck-down region from
preform to fibre, we will investigate the possibility that the air in the channels results in a pressure
that, in turn, causes channel diameters larger than would otherwise be seen.

172

Lie-Markov models derived from finite semigroups

Jeremy Sumner
University of Tasmania
Timetable: p. 13

In recent years, our research group has developed mathematical methods to construct “Lie-Markov”
models and explored their particular application to phylogenetics. These models occur as continuoustime Markov chains and satisfy the strong condition that the associated transition matrices are closed
under matrix multiplication. In this talk, I will present a general method for deriving a Lie-Markov
model from a given finite semigroup presented in abstract form. If the degree of the semigroup isk, the resulting model is a Markov chain on k states and multiplicatively closure follows manifestly
from the product rule in the semigroup. Remarkably for k = 2, 3, 4 states, we found that the resulting
Markov chains are irreducible if and only if the underlying semigroup occurs as a direct product of
cyclic groups and/or left-zero semigroups. Whether this property continues to hold for any number ofstates is an open problem.

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113

On the evaluation of Landau constants in amplitude equations away from a criticalpoint. Part 2: subcritical regimes and a physical example

Sergey Suslov
Swinburne University of Technology
Timetable: p. 13

We show how the procedure for deriving Stuart-Landau type equations that model a temporal evolutionof disturbance amplitude (as outlined in Part 1 of our talk) is extended to include linearly stable flow
regimes. Specifically, here we focus on deriving a low-dimensional model capable of predicting thethreshold disturbance amplitude below which the solution returns to its undisturbed state and above
which it undergoes the transition to a different nonlinear state in systems bifurcating subcritically.
Unlike supercritical flows subcritical systems are prone to resonances that are traced back to theinteraction between the mean flow distortion induced by the decaying fundamental disturbance harmonicand other decaying disturbance modes. Here we illuminate the reasons why such difficulties are notencountered in supercritical systems and suggest a methodology of deriving a two-equation dynamicalsystem of coupled amplitude equations with non-singular coefficients. Such a model resolves resonances
and is capable of predicting the threshold amplitude for disturbed weakly nonlinear subcritical flows.
As an example, the developed procedure is applied to subcritical plane Poiseuille flow. The developedmodel predictions are found to be in a reasonable agreement with experimentally detected threshhold
amplitudes reported in literature.

174

The information geometry of sensor management

Arthur George Suvorov
RMIT University
Timetable: p. 20

In problems of parameter estimation from sensor data, the Fisher metric allows for a measure of
the information content of a particular configuration. However, when measurements are drawn from
distributions which are dependent on the positions, velocities and angles made between the sensors,a family of Fisher metrics arise. The problem then turns from optimising a given Fisher metric, toidentifying an optimal member from a family, once a suitable definition of optimality is obtained. It has
been shown that the collection of all Fisher metrics on a manifold itself forms a Riemannian manifold,often referred to as the sensor manifold. Each point of this sensor manifold corresponds to a Fisher
metric. We show that the distance measure on this manifold provides a means of finding an optimal,
dynamical sensor configuration from an information-theoretic standpoint. We also show that geodesics
on this space have physical interpretations related to sensor management, and provide several worked
examples to demonstrate the mathematical machinery.

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114

Symmetrical few-body orbits

Winston Sweatman
Massey University
Timetable: p. 20

In this talk I will consider some few-body orbits of the gravitational N-body problem. Althoughsomewhat artificial, orbits with symmetry or in lower dimension space can provide insight and inspiration
for the more general problem.

176

Some remarks on a time-explicit particle methods for flow problems

Daisuke Tagami
Kyushu University
Timetable: p. 23

We have recently obtained error estimates of a generalised particle method for convection-diffusion
problems, and have now continued to estimate it for the incompressible Navier–Stokes equations.
When introducing an implicit scheme in time based on the predictor-corrector strategy to particle
methods for the incompressible Navier–Stokes equations, we need to solve the pressure Poisson equation
at each time step. However, the pressure Poisson equation causes the increasing of computationalcosts, especially in case of huge computational models appearing in High-Performance Computing(HPC) fields. Therefore, many researchers in HPC fields introduce explicit schemes in time based onan equation of state of gas.
In this talk, we regard one of such explicit schemes as a perturbation problem derived from thecompressible Navier–Stokes equations, and give some remarks on the relations between them andthe incompressible Navier–Stokes equations. Moreover, we show some numerical results by using atime-explicit particle methods for the incompressible Navier–Stokes equations.

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115

Investigating the effect of nutrient-limited growth on floral pattern formation inyeast biofilms

Alexander Tam
The University of Adelaide
Timetable: p. 15

Yeast species have a huge effect on human life, and in many applications it would be advantageous tocontrol their growth. For example, yeasts are used extensively in food and drink production and inbiotechnology, but are also a leading cause of persistent hospital-acquired infections. It is therefore ofinterest to understand the fundamental mechanisms that determine colony morphology. Yeast biofilms
are complex systems in which growth is influenced by nutrient consumption, fluid flow, and mechanicalforces. In this work, we investigate the hypothesis that nutrient-limited growth is the mechanism bywhich patterns form. Analysis of experimental images shows that biofilms expand radially at a roughly
constant speed, and undergo a transition from circular to floral morphology, which is characterisedby the formation of finger-like ‘petals’. We use this data to parametrise a reaction-diffusion modelwith non-linear degenerate cell diffusion. In doing this, we show that two-dimensional travelling wave
solutions to our model are linearly unstable to transverse perturbations for experimentally feasible
parameters. There is good agreement between experimental floral patterns and predictions using themost unstable wave number of this analysis. Our model, which incorporates nutrient-limited growthalone, therefore provides a potential explanation for petal formation in yeast biofilms.

178

Sampling without replacement: a story of noncentral hypergeometric distributionsPeter Gerrard Taylor
The University of Melbourne
Co-authors: S. Loertscher and E.V. Muir
Timetable: p. 23

In elementary probability and statistics courses, we are taught how to derive the distribution of thenumber X of marked objects we see when we sample without replacement n objects from a populationof N objects, D of which are marked. This distribution, known as the hypergeometric distribution, finds
application in many areas, among which are analysis of card games, capture-recapture experiments
and sample surveys.
A basic assumption in this derivation is that marked objects are just as likely to be selected as
unmarked objects. It is easy to think of situations where this assumption does not hold, for example acapture/recapture experiment where the experience of being captured makes an animal less likely to
be captured a second time. This leads us to the concept of a noncentral hypergeometric distribution inwhich marked and unmarked objects can have different probabilities of being selected.
It turns out that surprisingly little has been written about this generalisation: there are two noncentral
hypergeometric distributions known in the literature, attributed to Fisher and Wallenius respectively.
In this talk I shall make some observations about these distributions and then introduce a third classof noncentral hypergeometric distribution, motivated by an application in microeconomics.

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116

Preserving quality of milk powder shipments

Steve Taylor
The University of Auckland
Timetable: p. 20

Milk powder can undergo a complexity of chemical reactions, all influenced by oxygen, moisture andtemperature. Yet, even small changes in milk powder lead to noticeable changes in its flavour. Whenmilk powder is shipped around the world, it is subjected to diverse environmental conditions forprolonged periods of time. We discuss how mathematical modelling sheds light on what can be done
to preserve its flavour under these conditions.
(This problem was a challenge from Fonterra to the mathematics in industry study group MINZ 2016.
Problem moderators: Luke Fullard, Valerie Chopovda, Steve Taylor.)

180

Experimental feature driven development for mathematical models of LiFePO4
batteries

Joseph Alex Teague
Queensland University of Technology
Timetable: p. 16

The internal operation of a lithium ion battery is difficult to measure experimentally, due in part to its
intricate nature and the instability of the electrolyte solution, requiring the battery to be well sealed.
A mathematical model that accurately simulates battery usage would be useful, both in optimisingbattery usage for efficiency or extended lifetime, and to inform battery design. However, to date, eventhe most sophisticated models fail to accurately recover the dynamics of battery charge and discharge
cycling. Additionally, most attempts at validation only include a single charge or discharge of thebattery at a time, and ignore effects occurring at the end of these events. In this presentation, we
discuss the incorporation of qualitative features observed in experimental charge/discharge cycling
data in the development of a mathematical model and numerical simulation of a LiFePO4 battery. We
also discuss the links between these observations and the dynamics within the cell and present the key
outcomes of our model, including our ability to validate against challenging, multi-cycle, experimental
data.

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117

Pulsing dynamics in an excitable laser subject to delayed optical feedback

Soizic Terrien
The University of Auckland
Timetable: p. 13

Controllable sources of short pulses of light are key elements in many applications, including telecommunications and optical signal processing. We consider here an excitable semiconductor laser subject
to delayed optical feedback. In such a device, recent experiments have shown that trains of short pulsesof light can be triggered independently by external perturbations. In particular, several pulses canbe sustained simultaneously, with different timing in between pulses. A mathematical model in theform of a system of delay differential equations describes the pulsing dynamics in very good agreementwith the experiment. A bifurcation analysis shows the coexistence of one stable equilibrium withseveral periodic solutions, which all correspond to pulsing regimes with equidistant pulses. Most ofthem are only weakly stable, and we demonstrate that all pulsing dynamics correspond to very longtransients toward one of these periodic solutions. Consequently, all pulses become equidistant in thelong term. Moreover, we investigate the effect of external perturbations on the stable pulsing regimes,
which relates to the basins of attraction of the different periodic solutions. We show that pulse trains
can be individually and reliably switched on and off through external perturbations. These results
pave the way to fast all-optical control of pulsing regimes in lasers. Moreover, since the mechanism
for self-pulsations relies only on excitability and self-feedback our results might be of more generalinterest, beyond laser dynamics.

182

Modelling phagocytosis

Ngamta Thamwattana
University of Wollongong
Timetable: p. 12

Phagocytosis refers to a process in which one cell type fully encloses and consumes unwanted cells,
debris or particulate matter. It plays an important role in immune systems through the destruction ofpathogens and the inhibiting of cancerous cells. In this study, we combine models on cell-cell adhesion
and on predator-prey modelling to generate a new model for phagocytosis that is capable of relating
the interaction between cells in both space and time. Numerical results are presented, demonstrating
the behaviours of cells during the process of phagocytosis.

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118

Globally unstable behaviour in the rotating-disc boundary layer

Christian Thomas
Monash University
Co-authors: Christopher Davies
Timetable: p. 25

Linear disturbance development in the von Kármán boundary layer over a rotating-disc is investigatedfor an extensive range of azimuthal mode numbers n. The study expands upon earlier investigations
that were limited to those values of n nearer to the onset of absolute instability (Lingwood 1995), where
disturbances to the genuine inhomogeneous flow were shown to be globally stable (Davies & Carpenter
2003). Numerical simulations for sufficiently large n display a form of global instability that is similar
in appearance to that found on the rotating-disc with mass suction (Thomas & Davies 2010). Solutions
indicate that a change in the response of the global behaviour arises for n ∈ [80 : 100] that is marginallygreater than those disturbances studied previously. Furthermore, the corresponding Reynolds number
coincides with the upper bound of experimental predictions for transition, which would suggest thattransition to turbulence is unlikely to be observed beyond that reported experimentally, as globally
unstable disturbances will have become fully established. These new stability characteristics are directly
related to the Huerre & Monkewitz (1990) local-global stability criterion that requires the regionof local absolute instability (for a fixed n) exceed a certain threshold size before globally unstablebehaviour can be established. Coupling solutions of the linearized complex Ginzburg-Landau equation
with numerical simulations based on the radially homogeneous flow approximation, conditions arederived that can be used to predict the azimuthal mode number needed to establish global instability.
The response is governed by a detuning effect, based on radial variations of the temporal frequency
and matching shifts in temporal growth that increases for larger n, eventually becoming big enoughto engineer globally unstable characteristics. Finally, we conclude that these newly observed linear
global modes are unlikely to have a strong bearing on the long term disturbance development of theimpulse response. This is because a global mode would be unlikely to establish itself over an extended
radial range before nonlinear effects were triggered by the huge growth associated with the wavepacket
maxima of the lower n-valued convective instabilities.

184

Improving health benefits of in-home care for chronic patients through optimal
service timing

Ali Tirdad
The University of Melbourne
Co-authors: Peter Taylor, Mark Fackrell and Jing Fu
Timetable: p. 15

We provide an Markov Decision Process (MDP) model for delivery of an in-home care service forpatients with chronic conditions in Melbourne, called MonashWatch. In this program patients receive
calls frequently from their health coaches, and are directed to necessary health services. The idea is tokeep patients with chronic conditions healthier at home to prevent/reduce avoidable hospitalisations andvisits to the emergency department. We assume that the reduction in number of unscheduled admissions

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119will be the consequence of having healthier patients. To do so, we look into how MonashWatch canmaximise the health benefits, measured with QALYs (Quality Adjusted Life Years), of its service forall the patients by optimally allocating its resources to the patients. We model the MonashWatch
program as an MDP, and provide the optimal policy to call the patients at the beginning of eachperiod (e.g. day) based on the health state of a patient on the last call, health behaviour of a patient,and the passed time from the latest call. To generate the policies, we use Whittle index policy whichis efficient and flexible to later variation in the model inputs, such as changes in registered patients’
number in the program, patients’ behaviour, and capacity of the program.

185

Mathematical modelling of hydrophilic agrochemical penetration in astomatous
plant cuticles: surfactant and hygroscopic effects

Eloise Tredenick
Queensland University of Technology
Timetable: p. 17

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds toreduce their environmental impact and increase financial returns. One way to improve efficacy is byenhancing foliar penetration. The plant leaf cuticle is the most significant barrier to agrochemical
diffusion within the plant leaf. The importance of a mechanistic model has been noted previously
in the literature, as each penetration experiment is dictated by its specific parameters, namely plant
species, environmental conditions such as relative humidity and spray formulation including adjuvant
addition. Here we develop a model to incorporate the effects of adjuvant addition, ion binding andevaporation with the hygroscopic nature of deliquescent ionic solutions, along with the ability to vary
the active ingredient concentration and type, relative humidity and plant species. We validate ourmodel results against two experimental data sets. Furthermore, we discuss the key model sensitivities
and relate theoretical predictions to physical mechanisms.

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120

Mathematics of the Faraday Cage

Nick Trefethen
University of Oxford
Timetable: p. 11

Everybody has heard of the Faraday cage effect, in which a wire mesh does a good job of blocking electricfields and electromagnetic waves. Surely the mathematics of such a famous and useful phenomenon
has been long ago worked out and written up in the textbooks?
It seems to be not so, and indeed, one of the few treatments to be found in the textbooks, by Feynman,
is incorrect. The shielding effect turns out to be not as simple as one might expect: it depends on
the wires having finite radius. Nor is it as strong as one might imagine: it improves only linearly as
the wire spacing decreases. This talk will present results on electrostatic Faraday shielding by Jon
Chapman, Dave Hewett and myself, published in SIAM Review. Mathematically, this is a problem of
harmonic measure. Physically, Faraday shielding cage can be regarded as electrostatic induction by asurface of limited capacitance.

187

An integrable discrete model for soil-water infiltration

Dimetre Triadis
Kyushu University
Co-authors: Philip Broadbridge, Kenji Kajiwara and Kenichi Maruno
Timetable: p. 20

We have recently presented an integrable discrete model of one-dimensional soil water infiltration.
It is based on the continuum model by Broadbridge and White: a nonlinear convection-diffusion
equation with a nonlinear flux boundary condition at the surface. This is transformed to the Burgers
equation with a time-dependent flux term by the hodograph transformation. Our discrete model
preserves underlying integrability, and takes the form of a self-adaptive moving mesh scheme. The
discretisation builds on linearisability of the Burgers equation, producing the linear diffusion equation.
Naı̈ve discretisation of the linearised equation using the Euler scheme is often used in the theory of
discrete integrable systems, but this does not necessarily produce a good numerical scheme for theoriginal equation. Taking desirable properties of a numerical scheme into account, we propose analternative discrete model that produces solutions with similar accuracy to direct computation on theoriginal nonlinear equation, but with clear benefits regarding computational cost.

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121

Diffusion-limited growth limits in microbial colonies

Hayden Tronnolone
The University of Adelaide
Co-authors: Benjamin J. Binder
Timetable: p. 24

When placed on a solid substrate, many types of microbes, such as bacteria and fungi, grow intocolonies comprising numerous individual cells. The shape of these colonies is highly dependent on
the availability of nutrients diffusing throughout the substrate. When nutrient is limited, the colony
may undergo diffusion-limited growth (DLG), which typically manifests itself as a non-uniform colony
growth pattern. Such a change can occur without any change in the behaviour of individual cells,such as observed in the bacterium Bacillus subtilis; however, certain microbes may instead respondactively to low nutrient levels. Dimorphic yeasts, such as Saccharomyces cerevisiae, transition to thepseudohyphal growth mode, which consists of a change in the cell budding pattern, an elongation of
the cells, and the ongoing adhesion of mother and daughter cells. As both responses produce visuallysimilar patterns, the relative contributions of of pseudohyphal growth and DLG to the colony shape
are not known. To resolve this uncertainty, a combination of discrete and continuous mathematicalmodels are used to identify the conditions under which DLG is expected to occur. Using the results
produced by these models, representative experimental examples of microbial colonies are examined to
identify which colony morphologies are likely to have arisen due to DLG and, ultimately, which species
are influenced by this effect.

189

Error analysis of Crouzeix-Raviart and Raviart-Thomas finite element methods

Takuya Tsuchiya
Ehime University
Co-authors: Kenta Kobayashi
Timetable: p. 17

We discuss the error analysis of the lowest degree Crouzeix-Raviart and Raviart-Thomas finite element
methods applied to a two-dimensional Poisson equation. To obtain error estimations, we utilize thetechniques developed by Babuska-Aziz and the authors. We present error estimates in terms of thecircumradius and the diameter of triangles in which the constants are independent of the geometricproperties of triangulations. Numerical experiments confirm the obtained results.

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122

Viscous fingering patterns driven by heterogeneous substrate wettability

Lachlan James Tyrrell
Queensland University of Technology
Timetable: p. 12

A Hele-Shaw cell is an experimental apparatus which consists of a pair of parallel glass plates held close
together and filled with a viscous fluid. Notably, a fingering pattern occurs when a less viscous fluid
is forced into the cell, due to Saffman-Taylor instability. Motivated by understanding the fingering
behaviour driven by a non-uniform wettability along one of the Hele-Shaw plates, we have investigatedthe effect of perturbing the transverse contact angle where the viscous fluid meets the plates. To
do so, we have introduced a small perturbation term that alters the pressure and causes differing
behaviour in the evolution of fingering patterns. Linear stability analysis suggests that the effect ofthe perturbation term will cause an initially flat surface to evolve into a fingering pattern rather thanremaining flat. The focus of this presentation will be on describing preliminary linear stability analysis
and fully nonlinear solutions which are computed using a complex variable formulation and conformal
mapping techniques.

191

Mean first passage time problems and localised pattern formation - analysis, results,
and surprising connections

Justin Tzou
Macquarie University
Timetable: p. 23

Mean first passage time (MFPT) problems, a classic example of which is the gambler’s ruin problem,
generally ask the question - how long on average does it take for a random walker to first encountera set of targets? Analysis of these problems in the past has been restricted to the scenario wheretargets are stationary. In this talk, we discuss how to derive and analyse the boundary-value problem
associated with moving targets, and report some counter-intuitive results. For localised spot patterns
in reaction-diffusion systems, we will demonstrate a hybrid asymptotic-numerical method for obtaining
key analytic results for their stability and dynamics. Finally, we draw some surprising links between
these two seemingly very different problems.

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123

A multiphase model for HDL-assisted stabilisation of early atherosclerotic plaques

Ishraq Uddin
The University of Sydney
Timetable: p. 22

Atherosclerosis is among the leading causes of death worldwide due to its implication in heart attacks
and strokes. The disease is characterised by the localised thickening of artery walls due to the buildup of
fatty cholesterol-filled streaks. A key factor in determining whether an atherosclerotic plaque becomesproblematic is the interplay between low density lipoprotein (LDL) and high low density lipoprotein(HDL), which are responsible for transporting cholesterol around the body: LDL is pro-atherogenic
and its buildup in the artery wall will trigger an immune response whereby the recruited immune
cells become engorged on lipid and remain in the artery wall, whereas HDL has the atheroprotective
properties of enabling lipid export and the egress of immune cells from the plaque. Plaque dynamics
consist of many nonlinear interactions between various cellular and biochemical species including theinteractions between immune cells and lipoproteins.
In this talk, I present a multiphase PDE model for an early stage atherosclerotic plaque. The modelaccounts for interactions between macrophages, apoptotic cells and lipids, modelling the plaque space
as a one dimensional domain with a moving boundary. Our model is based on a multiphase framework,
and incorporates the effects of cell crowding by having the domain expand or contract according to thetotal amount of material. We discuss how this model gives insight into how early plaque growth andstabilisation depends on the levels of LDL and HDL in the bloodstream.

193

On a second order PDE that models cell division

Bruce van Brunt
Massey University
Co-authors: Graeme Wake, Ali Zaidi and Messoud Efendiev
Timetable: p. 24

In this talk we examine a second order functional partial differential equation that models size structured
cell division and growth. The problem is of the initial boundary value type and the differential equation
features a simple nonlocal term in the form of a rescaling. The simplest equation of this type withlinear growth can be solved analytically. We present a solution method and use the result to establish
the existence of a long time attracting solution (the SSD solution). The long time dynamics can change
dramatically if we consider the exponential growth case. We look briefly at a critical case where there
is no (classical) SSD solution.

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124

Look who’s talking: bipartite networks as representations of a topic model of New
Zealand parliamentary speeches

Demival Vasques Filho
University of Auckland
Timetable: p. 15

Quantitative methods that describe the participation to debate of Members of Parliament and theparties they belong to are lacking. Here we propose a new approach that combines topic modellingwith complex networks techniques, and use it to characterise the political discourse at the New ZealandParliament. We implement a Latent Dirichlet Allocation model to discover the thematic structure of
the government’s digital database of parliamentary speeches, and construct from it two-mode networks
linking Members of the Parliament to the topics they discuss. Our results show how topic popularity
changes over time and allow us to relate the trends followed by political parties in their discourses withspecific social, economic and legislative events. Moreover, the community analysis of the two-mode
network projections reveals which parties dominate the political debate as well as how much they tendto specialize in a small or large number of topics. Our work demonstrates the benefits of performing
quantitative analysis in a domain normally reserved for qualitative approaches, providing an efficient
way to measure political activity

195

A mathematical model supports a key role for anion exchanger Ae4 (Slc4a9) insalivary gland fluid secretion

Elias Vera Siguenza
The University of Auckland
Timetable: p. 12

We construct a dynamical model of a salivary gland acinar cell with the objective of investigating therole of two anion exchangers, the Ae2 (Slc4a2) and Ae4 (Slc4a9), in fluid secretion.

Transepithelial chloride movement drives water transport in salivary gland acinar cells. A basolateral
sodium-potassium adenosine-triphosphatase pump (NaK-ATPase) and the sodium-potassium-chloride
co-transporters (Nkcc1) are primarily responsible for concentrating the intracellular space with chloride
well above its equilibrium potential. Gustatory and olfactory stimuli induce the release of calcium ionsfrom the internal stores of acinar cells, which trigger saliva secretion. Calcium-dependent chloride andpotassium channels promote ion secretion into the luminal space thus creating an osmotic gradientthat promotes water movement in the secretory direction. The current model for saliva secretion
proposes that chloride-bicarbonate anion exchangers, coupled with basolateral sodium-proton (Nhe1)
anti-porters, regulate intracellular pH and act as a secondary chloride uptake mechanism.

Recent studies demonstrated that Anion exchanger 4 (encoded by the Slc4a9 gene - Ae4) deficient
mice exhibit an approximate 30% decrease in gland salivation. Surprisingly, the same study revealed
that absence of Anion exchanger 2 (encoded by the Slc4a2 gene - Ae2) does not impair salivation, as

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previously suggested. These results seem to indicate that the Ae4 is responsible for the majority of thesecondary chloride uptake and thus a key mechanism for saliva secretion.

Our model produces mathematical support for such controversial findings. Our results suggest that theexchanger’s co-transport of monovalent cat-ions is key in establishing the osmotic gradient necessary
for optimal saliva secretion.

196

The replicator equation in discrete time

Geetika Verma
University of South Australia
Co-authors: Amie Albrecht, Kostia Avrachenkov and Phil Howlett
Timetable: p. 21

The replicator equation is used to understand the dynamic evolution of populations in both continuous
time and discrete time. In this talk I consider a simple model with two species and use the replicator
equation to study discrete time evolution of the population in the presence of small random ordeterministic perturbations to each generation caused either by genetic mutation or migration. Our
most important observation is that for small perturbations the model contains two important capture
regions that ensure stability of the iterated map describing the evolution but that for larger perturbations
one or both of these regions may disappear. Our future research will try to extend our analysis to
more complex models.

197

Mathematical models for cell migration with real-time cell cycle dynamics

Sean Trinity Vittadello
Queensland University of Technology
Co-authors: Scott W. McCue, Gency Gunasingh, Nikolas K. Haass and Matthew J. Simpson
Timetable: p. 13

Fluorescent ubiquitination-based cell cycle indicator, also known as FUCCI, allows the visualisation of
the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes,
so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI
reveals real-time information about cell cycle dynamics of individual cells, and can be used to explore
how the cell cycle relates to the location of individual cells, local cell density, and different cellular
microenvironments. In particular, FUCCI is used in experimental studies examining cell migration,such as malignant invasion and wound healing. Here we present new mathematical models which
can describe cell migration and cell cycle dynamics as indicated by FUCCI. The fundamental model
describes the two cell cycle phases, G1 and S/G2/M, which FUCCI directly labels. The extended
model includes a third phase, early S, which FUCCI indirectly labels. We present experimental data

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from scratch assays using FUCCI-transduced melanoma cells, and show that the predictions of spatial
and temporal patterns of cell density in the experiments can be described by the fundamental model.
We obtain numerical solutions of both the fundamental and extended models, which can take the formof travelling waves. These solutions are mathematically interesting because they are a combination ofmoving wavefronts and moving pulses. We derive and confirm a simple analytical expression for theminimum wave speed, as well as exploring how the wave speed depends on the spatial decay rate of
the initial condition.

198

Geometric Optimisation

Graeme Wake
Massey University
Timetable: p. 12

A largely forgotten piece of classical, but very useful, geometry will be described: that of Steiner
symmetrisation. This is a very elegant piece of quite straightforward mathematics, essentially precalculus in its simplicity. Answers to elementary questions like “What is the largest paddock you can
enclose with given length of fence?” are established essentially by construction. Recently it has beenvery successfully applied to several important optimisation problems for objects such as bubbles, drums
and bombs. It is used by myself and others in the insurance industry to predict shape factors as ameasure of the likelihood of the occurrence of spontaneous fires, see Wake (1973). This much harderquestion prompted the development of an extension of Jacob Steiner’s work, which will be explained.
Wake G.C. Estimation of critical parameters in thermal ignition, Combustion and Flame, J. Combustion
Institute 21 (1973) 19-2l.

199

A sequential approach to data-augmented MCMCJames Nicholas Walker
The University of Adelaide
Timetable: p. 16

Data-augmented MCMC (DA-MCMC) is an effective strategy for inferring parameters of state spacemodels where transitions are largely unobserved. The algorithm requires that inference is started anew
each time our data set is updated; this means that DA-MCMC can become slow for large data sets.
An alternative algorithm for this kind of inference problem is Sequential Monte Carlo (SMC); thisallows estimates to be updated as the data set is updated, but suffers from inefficiencies if too little ofthe process is observed. This talk outlines a new sequential data-augmented MCMC algorithm whichallows for estimates to be updated as in an SMC algorithm, but has the efficient steps of a DA-MCMC
algorithm. Applications of this algorithm are shown in the context of epidemic models.

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127

Viscous Rayleigh-Taylor flows in two and three dimensions using GPU acceleration

Stephen Walters
University of Tasmania
Timetable: p. 14

The Rayleigh-Taylor instability describes the situation where a denser fluid sits atop a less dense fluid.
If the interface between the fluids is perfectly flat and horizontal, an unstable equilibrium exists. Any
small perturbation to this interface will grow. Initially this growth will be exponential, but viscosity
will eventually cause the interface to roll over. In this talk, a spectral method is presented whichguarantees certain boundary conditions are met. The method is computationally expensive, but has
been found to run faster using parallel processing on a Graphical Processing Unit. Run time has been
reduced by factors in the hundreds. This increase in computational power and the accuracy of thespectral method enabled the forward integration of the model well past the ‘roll-over’ time, and ispresented in a few short videos.

201

Calcium Signalling in T-Cells

David Waters
The University of Auckland
Timetable: p. 20

Calcium oscillations are ubiquitous in many cell types and control a wide range of cellular activities.
Particularly, in T-cells, calcium oscillations are known to control cell differentiation, proliferation, andactivation. Very puzzling experimental results from the 1990s showed that blocking certain calcium
pumps initiated calcium oscillations. This behaviour is odd and fairly unique to T-cells, yet remains
without theoretical explanation. We construct and study theoretical models of T-cell calcium signallingin an attempt to provide an explanation. We study the bifurcation structure of our models whichallows us to describe a theoretical mechanism for this behaviour.

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128

Multiphase modelling of early fibrous cap formation in atherosclerosis

Michael Greg Watson
The University of Sydney
Co-authors: Mary R Myerscough, Helen M Byrne and Charlie Macaskill
Timetable: p. 24

Advanced atherosclerotic plaques are characterised by the accumulation of cellular debris and extracellular fat in the arterial intima. Smooth muscle cells (SMCs) are recruited from the media to synthesisea cap of fibrous tissue that sequesters this thrombogenic material from the bloodstream and contributes
to the prevention of plaque rupture. The fibrous cap therefore provides crucial protection from clinicalevents such as heart attack and stroke, but the mechanisms that underlie cap formation remain poorly
understood. Evidence suggests that certain plaques will remain strong and stable, while others become
fragile and dangerously vulnerable to rupture.
Using a multiphase approach with non-standard boundary conditions, we investigate early fibrous
cap formation in the intima by modelling SMC migration from the media in response to chemicalsignalling from the endothelium. Simulations indicate that the emergence of a cap-resembling SMC
profile requires a critical balance between the relative rates of cell supply from the media, chemotactic
migration within the intima and cell loss by apoptosis (or phenotype change). We identify a number of
disease-associated parameters that may be linked to variations in cap stability.

203

Two-stroke relaxation oscillators

Martin Wechselberger
The University of Sydney
Timetable: p. 12

In classic van der Pol-type oscillator theory, a relaxation cycle consists of two slow and two fast orbit
segments per period (slow-fast-slow-fast). A possible alternative relaxation oscillator type consists of
one slow and one fast segment only. In electrical circuit theory, Le Corbeiller (published in IEEE 1960)
termed this type a “two-stroke” oscillator (compared to the “four-stroke” vdP oscillator).
I will provide examples of such oscillators that are common in biochemical oscillator theory and discussthese problems from a geometric singular perturbation theory (GSPT) point of view “beyond thestandard form”. It is worth mentioning that Fenichel’s seminal work on GSPT (published in JDE
1979) discusses this more general setting, but it has not received much attention in the literature.

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204

Shape optimization with geometric constraints using Moreau-Yosida regularization

Florian Wechsung
University of Oxford
Co-authors: Patrick Farrell
Timetable: p. 21

Shape optimization has received significant interest from both a theoretical and an applied point ofview over the last decades. The approaches used can be roughly categorized into those based on using
a parametrization for the shape or its deformation and then applying an optimization algorithm to thediscretized problem (discretize-then-optimize) and those that formulate the problem as optimization
over an infinite-dimensional space of shapes or deformations and then discretize afterwards (optimizethen-discretize). We follow the latter approach and search for diffeomorphisms T ∈ [W 1,∞ (Ω)]d that
deform an initial shape Ω. The optimization problem then reads as follows
minimize J(T (Ω)).
T ∈X ∩K(1)

We choose X = {T ∈ [W 1,∞ (Ω)]d : T is a W 1,∞ -diffeomorphism} as the space of admissible deformations as Lipschitz regularity of the domain is needed by many problems in which a PDE constraint isincluded in the optimization problem.
Furthermore we want to include certain geometric constraints; this is represented by the requirement
T ∈ K. A classical example for a geometric constraint that is often considered is volume/massconservation, i.e. K = {T ∈ X : vol(T (Ω)) = vol(Ω)}. In our work we investigate constraints of theform
K = {T ∈ X : T (∂Ω) ⊂ C}(2)
for some convex set C ∈ Rd . A classical application where this is relevant is wing design in Formula 1,
where the teams are given bounding boxes in which the wing needs to be contained.
To include this constraint, we begin by considering the indicator function φ : L2 (∂Ω) → (−∞, +∞],
defined via(
0,
if T (∂Ω) ⊂ C
φ(T ) =
(3)+∞, otherwise,and observe that (1) is equivalent tominimize J(T (Ω)) + φ(T ).
T ∈X

(4)

Classically the Moreau-Yosida regularization of φ is then used to implement path-following methods;
in the context of shape optimization this has been done in [1]. However, in [2] it was shown that theMoreau-Yosida regularization of φ can also be used to formulate augmented Lagrangians. We adapt
the latter approach to the case of PDE constrained shape optimization and present numerical examples
implemented in the Firedrake finite element software.
[1] M. Keuthen and M. Ulbrich: Moreau-Yosida regularization in shape optimization with geometricconstraints, Computational Optimization and Applications, 62, 2014. [2] K. Ito and K. Kunisch:
Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces, Nonlinear
Analysis: Theory, Methods & Applications, 41, 2000.

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130

Linear response in weakly-coupled systems

Caroline Wormell
The University of Sydney
Co-authors: Georg A. Gottwald
Timetable: p. 21

It is assumed by many practitioners that complex chaotic systems have physical measures which varydifferentiably under a perturbation in the flow of the system. This assumption appears to bear out tosome extent in practice, but is largely unexplained, especially as certain simple chaotic systems such as
the logistic map are known to not have this so-called linear response.
We analyse a weak-coupling model, made up of J simple, independent “heat-bath” chaotic maps driving
a distinguished chaotic map. We find that when J is large and the heat-bath maps are sufficiently
heterogeneous, the distinguished variable has a linear response regardless of whether any of the maps
taken by themselves do. However, depending on the kind of coupling, the region of validity of Taylor
approximations to the response may be very small, and in the infinite J limit the system may not havelinear response.

206

Dynamics of a coupled calcium system

Xueshan Yang
The University of Auckland
Timetable: p. 21

Many models have been built to study the behaviour of calcium oscillations in spatially homogeneous
cells. In these models, all the variables of interest are assumed to evolve in time only, without
spatial dependence. However, in a variety of cell types, intercellular calcium oscillations are observed.
Furthermore, it has been observed that the calcium dynamics in one cell can influence the dynamics inneighbouring cells. Motivated by this observation, we are interested in building a model of intercellular
calcium oscillations to help understand the mechanisms underlying interactions between cells. This
talk presents preliminary results about the dynamics of a coupled pair of calcium oscillators, focusing
on the differences resulting from varying the coupling type and strength.

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131

The effect of thermoregulation on honey bee colony health and survival

Zeaiter Zeaiter
The University of Sydney
Timetable: p. 22

In recent years honey bee colonies have been experiencing increased loss of hives. One cause of hive
loss is colony collapse disorder (CCD). Colony collapse disorder is characterised by a previously healthy
hive having few or no adult bees but with food and brood still present. This occurs over several weeks.
It is not known if there is an exact cause of CCD but rather it is thought to be the accumulationof multiple stressors placed on a hive. One of these stressors is the breakdown of thermoregulation
inside the hive. the bee life cycle begins with eggs that hatch into larvae that become brood. The
hive contains combs which are made up of multiple cells; these cells house the brood. Pupal cells arecapped off by adult bees (and so are known as capped brood) and they undergo changes to develop
into an adult bee. In order for these capped brood to develop correctly, physically and mentally, thetemperature within the hive must be regulated by the hive bees to ensure optimal development of thecapped brood. Variations in the temperature, caused by the breakdown of thermoregulation, lead to
deformations in the adults that emerge from capped brood. This later leads to these bees becoming
inefficient foragers which also have shorter life spans. We model the effect of thermoregulation on hive
health using a system of DDEs which gives insights into how varying hive temperatures have an effecton the survival of the colony. Most notably adding the dynamics of hive thermoregulation creates anAllee effect. We approximate the DDE model by an ODE system to gain further insights into the
dynamics of the problem.

208

Mathematical models for checkpoint blockade treatments in cancer immunotherapy

Collin Zheng
The University of Sydney
Timetable: p. 25

Cytotoxic T-lymphocytes, commonly called killer T-cells, are among our immune systems most potent
and well-understood weapons against cancer. However receptors such as CTLA-4 and PD-1 on
the surfaces of T-cells inhibit their activation and proliferation. Antibody drugs, called checkpoint
blockades, can block these negative checkpoint receptors. We will present a mathematical model on
tumour-lymphocyte dynamics in the presence of a CTLA-4 blockade, discuss its implications to future
treatment direction and more broadly discuss the current modelling efforts in this area.

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132

American-style Parisian options and their fair priceSong-Ping Zhu
University of Wollongong
Timetable: p. 20

In this talk, pricing of various American-style Parisian options will be discussed. After showing thefundamental difference between American-style “in” and “out” Parisian options, I shall demonstrate
how a closed-form analytic solution for American-style up-and-in Parisian options can be worked out,
which does not explicitly involve a moving boundary as far as the mother option is concerned. For
American-style up-and-out Parisian options, a very efficient numerical approach is proposed, based on
the moving window technique developed by Zhu and Chen (2013), in order to simplify the solution
procedure. Preliminary numerical results are presented to show some very interesting features ofAmerican-style Parisian options.

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Index
Abarzhi, Snezhana I., 23, 26
Abdul Fatah, Jamilatuzzahro, 20, 26
Aksamit, Anna, 19, 20, 27
Al Ali, Suha, 11, 28
Albrecht, Amie, 14
Almalki, Adel Ahmed, 11, 28
Anderssen, Robert Scott, 11, 29
Angstmann, Christopher, 23, 29
Aogo, Rosemary, 13, 30
Arancibia, Claudio, 22, 30
Baardink, Guido, 19, 31
Baeumer, Boris, 21, 24, 31
Ball, Rowena, 23, 32
Ballard, Peter, 25, 32
Barton, Noel, 19
Bassom, Andrew, 23
Beeton, Nick, 21, 23, 33
Belchamber, Erika Rana Gabriela, 14, 34
Belet, Sarah, 11, 34
Bennetts, Luke, 24, 35
Blachut, Chantelle, 12, 35
Black, Andrew, 14, 15, 36
Bottema, Murk, 19, 25, 36
Braham, Calum, 15, 37
Broadbridge, Philip, 19, 21, 37
Browning, Alexander Paul, 16, 38
Byrnes, Jim, 16, 38
Calabretto, Sophie, 15, 39
Carr, Elliot, 14, 16
Carr, Elliot Joseph, 19, 39
Chen, Mike, 25, 40
Chen, Sue Ann, 20, 40
Chisholm, Rebecca, 11, 22, 41
Clark, Alys Rachel, 19, 41
Cloete, Ielyaas, 20, 42
Cope, Robert, 12, 21, 42
Correa, Debora Cristina, 16, 43
Coster, Adelle, 15, 17, 43
Cox, Barry, 25, 44
Cui, Lidong, 11, 44de Hoog, Frank, 12, 19, 45
Denier, Jim, 11, 45
Dini, Saber, 11, 46
Dorjgotov, Khongorzul, 20, 46
Douglas, Craig, 15, 47

Dragomir, Silvestru Sever, 16, 47
Droniou, Jerome, 11, 20, 47
Duignan, Nathan Paul, 20, 48
Eade, Jonathan, 22, 48
Fackrell, Mark, 15, 49
Fadai, Nabil, 17, 49
Farrell, Troy, 16, 20, 21, 50
Farrow, Duncan, 23, 50
Filar, Jerzy, 23, 51
Flegg, Jennifer, 11, 24, 51
Flegg, Mark, 11, 25, 52
Florio, Brendan, 23, 52
Forbes, Larry, 11, 15, 23, 25, 53
Froyland, Gary, 22, 23, 53
Fujita, Kengo, 19, 54
Gallage, Polwaththa Dilruk Darshana, 22, 54
Ganim, Benjamin, 19, 55
Gemmell, Caleb, 16, 55
Giraldo, Andrus, 11, 56
Gonzalez-Tokman, Cecilia, 17, 56
Graiff Zurita, Sebastian Elias, 15, 57
Gray, Caitlin, 16, 57
Gray, Catheryn, 17, 58
Green, Christopher, 24, 58
Green, Edward, 12, 15, 59
Greenbank, Emma, 22, 59
Gul, Saima, 22, 60
Hajek, Bronwyn, 14, 17, 60
Harding, Brendan, 24, 60
Harper, John, 12, 61
Hasan, Cris, 16, 61
He, Xin-Jiang, 20, 62
Hester, Eric William, 20, 62
Hickson, Roslyn, 11, 16, 63
Hill, James Murray, 20, 63
Hocking, Graeme, 22, 24, 64
Holland, Barbara, 14, 23
Hopwood, Matthew James, 15, 65
Howlett, Phil, 21
Hunt, Hilary, 19, 65
Jelbart, Sam, 21, 66
Jenner, Adrianne, 20, 66
Jepps, Owen, 22, 67

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ANZIAM 2018 Conference Handbook

Jin, Wang, 14, 67
Johnston, Barbara, 11, 68
Johnston, Peter, 11, 20, 68
Johnston, Stuart, 12, 69
Kaehler, Benjamin David, 14, 69
Kajiwara, Kenji, 19, 70
Keane, Andrew, 12, 21, 70
Khoury, David, 24
Khoury, David Samuel, 13, 71
Kim, Peter, 16, 24, 71
King, Matthew, 19, 72
Kleshnina, Maria, 17, 72
Kobayashi, Kenta, 20, 73
Krauskopf, Bernd, 11, 23, 73
Krishnan, Mythreye, 21, 74
Kumar, Ashwani, 15, 74
Kumbhari, Adarsh, 17, 75
Laing, Carlo, 11, 23, 75
Lange, Marko, 20, 76
Leung, Tiffany Ngo Nam, 16, 76
Lewis, Angus Hamilton, 20, 77
Lin, Sha, 20, 77
Lodder, Robert, 15, 78
Loo, Sara Li-Yen, 22, 78
Lovelace-Tozer, Meirian Sara, 14, 79
Loxton, Ryan, 15, 79
Lu, Xiaoping, 19, 80
Lustri, Christopher, 20, 24, 80
Lydeamore, Michael, 17, 81
Lynch, Tammy, 17, 24, 81
Ma, Guiyuan, 19, 82
Maldon, Benjamin, 20, 82
Martyushev, Alexey, 21, 83
Matsiaka, Oleksii, 16, 83
McCue, Scott, 12, 19, 84
McGann, Anna, 15, 84
McGuinness, Mark, 22
McGuinness, Mark Joseph, 20, 85
McInerney, Sean, 22, 85Miller, Claire, 19, 86
Minamihata, Atsushi, 14, 86
Moroney, Tim, 14, 17, 87
Morrow, Liam, 12, 87
Musoke, Elle, 11, 88
Myerscough, Mary, 16, 22
Nakano, Naoto, 16, 88
Nasser, Mohamed, 14, 89

Nelson, Mark, 16, 19, 89
Neufeld, Zoltan, 16, 90
O’Kane, Terry, 22, 90
O’Leary, Joe, 20, 91
O’Neale, Dion, 23, 92
Ogunlade, Samson, 12, 92
Olver, Sheehan Shakiban, 19, 93
Osinga, Hinke, 16, 22, 93
Otupiri, Robert Nawiekang, 13, 94
Ozcakir, Ozge, 24, 94
Pages, Nathan, 13, 95
Penfold, Jessica, 15, 95
Penington, Catherine, 16, 23, 96
Pham, Khanh, 13, 96
Piantadosi, Julia, 23
Pinkevych, Mykola, 22, 97
Plank, Michael, 17, 97
Pooladvand, Pantea, 20, 98
Pototsky, Andrey, 24, 98
Rajagopal, Vijay, 15, 99
Ralph, Tertius, 15, 99
Rampadarath, Anand, 11, 100
Reischmann, Lisa, 22, 100
Reoch, James, 15, 101
Reyes, Josephine, 24, 101
Reynaldi, Arnold, 20, 21, 102
Roberts, Melanie, 17, 19, 102
Roberts, Mick, 12, 17, 103
Roberts, Timothy, 22, 103
Roberts, Tony, 11, 13, 104Rose, Danya, 24, 104
Ross, Joshua, 22, 105
Rump, Siegfried, 17, 105
Ryan, Louise, 14, 106
Sader, John Elie, 25, 106
Sandor, Balazs, 21, 107
Simpson, David John Warwick, 24, 107
Simpson, Matthew, 12, 19, 23, 108
Sloan, Ian, 12, 15, 108
Small, Michael, 12, 23, 109
Smith, Paul, 25, 109
Smith-Miles, Kate, 21, 110
Srinivasan, Mandyam, 16, 110
Stals, Linda, 12, 15, 111
Stephen, Sharon, 23, 111
Stokes, Yvonne, 14, 15, 112
Sumner, Jeremy, 13, 112

ANZIAM 2018 Conference Handbook

Suslov, Sergey, 13, 113
Suvorov, Arthur George, 20, 113
Sweatman, Winston, 20, 24, 114
Tagami, Daisuke, 23, 114Tam, Alexander, 15, 115
Taylor, Peter, 15
Taylor, Peter Gerrard, 23, 115
Taylor, Steve, 20, 116
Teague, Joseph Alex, 16, 116
Terrien, Soizic, 13, 117
Thamwattana, Ngamta, 12, 14, 117
Thomas, Christian, 25, 118
Tirdad, Ali, 15, 118
Tredenick, Eloise, 17, 119
Trefethen, Nick, 11, 120
Triadis, Dimetre, 20, 120
Tronnolone, Hayden, 20, 24, 121
Tsuchiya, Takuya, 17, 121
Tyrrell, Lachlan James, 12, 122
Tzou, Justin, 23, 122
Uddin, Ishraq, 22, 123
van Brunt, Bruce, 22, 24, 123
Vasques Filho, Demival, 15, 124
Vera Siguenza, Elias, 12, 124
Verma, Geetika, 14, 21, 125
Vittadello, Sean Trinity, 13, 125
Wake, Graeme, 12, 24, 126
Walker, James Nicholas, 16, 126
Walters, Stephen, 14, 127
Waters, David, 20, 127
Watson, Michael Greg, 24, 128
Wechselberger, Martin, 12, 17, 128
Wechsung, Florian, 21, 129
Wormell, Caroline, 21, 130
Yang, Xueshan, 21, 130
Zeaiter, Zeaiter, 22, 131
Zheng, Collin, 25, 131
Zhu, Song-Ping, 19, 20, 132

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ANZIAM 2018 Conference Handbook

Registered Conference Delegates
Name
Snezhana I. Abarzhi
Jamilatuzzahro Abdul Fatah
Anna Aksamit
Suha AL Ali
Amie Albrecht
Adel Ahmed A Almalki
Robert Scott Anderssen
Christopher Angstmann
Rosemary Aogo
Claudio Arancibia
Azam Asanjarani
Guido Baardink
Boris Baeumer
Rowena Ball
Peter Ballard
Noel Barton
Andrew Bassom
Nick Beeton
Erika Rana Gabriela Belchamber
Sarah Belet
Luke Bennetts
Chantelle Blachut
Andrew BlackPeter Blennerhassett
Murk Bottema
Calum Braham
Michael Brideson
Philip Broadbridge
Phillip James Brown
Alexander Paul Browning
Jim Byrnes
Sophie Calabretto
Elliot Joseph Carr
Mike Chen
Sue Ann Chen
Rebecca Chisholm
Alys Rachel Clark
Ielyaas Cloete
Robert Cope
Debora Cristina Correa
Jason Michael Cosgrove
Adelle Coster
Barry Cox
Lidong Cui
Frank de Hoog
Jim Denier

Affiliation
The University of Western Australia
Bandung Institute of Technology
The University of Sydney
Murdoch University
University of South Australia
Massey University
CSIRO
University of New South Wales
University of New South Wales
Queensland University of Technology
AMSI/University of Melbourne
Kyushu University
University of Otago
Australian National University
The University of Adelaide
Retired
University of Tasmania
University of Tasmania
University of South Australia
Monash University
The University of Adelaide
The University of Queensland
The University of Adelaide
UNSW Sydney
Flinders University
The University of Western Australia
University of Tasmania
La Trobe University
The University of Adelaide
Queensland University of Technology
Prometheus Inc.
Macquarie University
Queensland University of Technology
The University of Adelaide
IBM Research Australia
The University of Melbourne
The University of Auckland
The University of Auckland
The University of Adelaide
The University of Western Australia
University of Tasmania
University of New South WalesThe University of Adelaide
Swinburne University of Technology
CSIRO
Macquarie University

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ANZIAM 2018 Conference Handbook

Name
Saber Dini
Khongorzul Dorjgotov
Craig Douglas
Silvestru Sever Dragomir
Jerome Droniou
Nathan Paul Duignan
Jonathan EadeDavid Elliott
Mark Fackrell
Nabil Fadai
Troy Farrell
Duncan Farrow
Jerzy Filar
Jennifer Flegg
Mark Flegg
Brendan Florio
Larry Forbes
Andrew Francis
Gary Froyland
Kengo Fujita
Polwaththa Dilruk Darshana Gallage
Benjamin Ganim
Caleb Gemmell
Andrus Giraldo
Cecilia Gonzalez-Tokman
Sebastin Elas Graiff Zurita
Caitlin Gray
Catheryn Gray
Christopher Green
Edward Green
Emma Greenbank
Saima Gul
Bronwyn Hajek
Brendan Harding
John Harper
Cris Hasan
Xin-Jiang He
Eric William Hester
Roslyn HicksonJames Murray Hill
Graeme Hocking
Barbara Ruth Holland
Matthew James Hopwood
Phil Howlett
Hilary Hunt
Nur Insani
Jim Isenberg
Sam Jelbart

Affiliation
AMSI/University of Melbourne
Kyushu University
University of Wyoming
Victoria University
Monash University
The University of Sydney
The University of Sydney
University of Tasmania
The University of Melbourne
University of Oxford
Queensland University of Technology
Murdoch University
The University of Queensland
The University of Melbourne
Monash University
CSIRO
University of Tasmania
Western Sydney University
University of New South Wales
Kyushu University
La Trobe University
The University of Newcastle
The University of Auckland
The University of Auckland
The University of Queensland
Kyushu University
The University of Adelaide
University of New South Wales
Macquarie University
The University of Adelaide
Victoria University of Wellington
Massey University
University of South Australia
The University of Adelaide
Victoria University of Wellington
The University of Auckland
University of Wollongong
The University of Sydney
IBM Research Australia
University of South Australia
Murdoch University
University of Tasmania
The University of Adelaide
University of South Australia
The University of Melbourne
RMIT University
University of Oregon
The University of Sydney

138

ANZIAM 2018 Conference Handbook

Name
Adrianne Jenner
Owen Jepps
Wang Jin
Barbara Johnston
Peter Johnston
Stuart Johnston
Nalini Joshi
Zlatko JovanoskiThomas Jungling
Benjamin David Kaehler
Kenji Kajiwara
Laura Karantgis
Andrew Keane
David Samuel KhouryPeter Kim
Matthew KingMaria Kleshnina
Kenta Kobayashi
Bernd Krauskopf
Mythreye Krishnan
Ashwani Kumar
Adarsh Kumbhari
Carlo Laing
Marko Lange
Tiffany Ngo Nam Leung
Angus Hamilton Lewis
Jessica Liebig
Sha LinDennis Liu
Robert Lodder
Sara Li-Yen Loo
Meirian Sara Lovelace-Tozer
Ryan Loxton
Xiaoping Lu
Christopher Lustri
Michael Lydeamore
Tammy Lynch
Guiyuan Ma
Benjamin Maldon
Alexey Martyushev
Oleksii Matsiaka
James McCaw
Scott McCue
Anna McGann
Mark Joseph McGuinness
Sean McInerney
Jody McKerral
Claire Miller

Affiliation
The University of Sydney
Griffith University
Queensland University of Technology
Griffith University
Griffith University
The University of Melbourne
The University of Sydney
University of New South Wales Canberra
The University of Western Australia
Australian National University
Kyushu University
La Trobe University
University of Auckland
University of New South WalesThe University of Sydney
Griffith University
The University of Queensland
Hitotsubashi University
University of Auckland
The University of Western Australia
The University of Melbourne
The University of Sydney
Massey University
Waseda University
The University of Melbourne
The University of Adelaide
CSIRO
University of Wollongong
The University of Adelaide
University of Kentucky
The University of Sydney
The University of Melbourne
Curtin University
University of Wollongong
Macquarie University
The University of Melbourne
Massey University
University of Wollongong
University of Wollongong
Kyushu University
Queensland University of Technology
The University of Melbourne
Queensland University of Technology
University of New South Wales
Victoria University of Wellington
Queensland University of Technology
Flinders University
The University of Melbourne

139

ANZIAM 2018 Conference Handbook

Name
Terence Mills
Atsushi Minamihata
Tim Moroney
Liam Morrow
Elle Musoke
Mary MyerscoughNaoto Nakano
Abrahim Steve Nasrawi
Mohamed Nasser
Mark Nelson
Neset Neset Ozkan TAN
Zoltan Neufeld
Behrooz Niknami
Terry O’Kane
Joe O’Leary
Dion O’Neale
Samson Ogunlade
Sheehan Shakiban Olver
Hinke Osinga
Robert Nawiekang Otupiri
Ozge Ozcakir
Nathan Pages
Jessica Penfold
Catherine Penington
Terry Edward Perkins
Khanh Pham
Julia Piantadosi
Mykola Pinkevych
Michael Plank
Pantea Pooladvand
Andrey Pototsky
Vijay Rajagopal
Tertius Ralph
Anand Rampadarath
Lisa ReischmannJames Reoch
Josephine Reyes
Arnold Reynaldi
Melanie Roberts
Mick Roberts
Timothy Roberts
Tony Roberts
Danya Rose
Joshua Ross
Siegfried Rump
Louise RyanJohn Elie Sader
Balazs Sandor

Affiliation
Deakin University
National Institute of AIST - Japan
Queensland University of Technology
Queensland University of Technology
The University of Auckland
The University of Sydney
Kyoto University
Monash University
Qatar University
University of Wollongong
The University of Auckland
The University of Queensland
The University of Melbourne
CSIRO
University of South Australia
The University of Auckland
UNSW Sydney
Imperial College London
The University of Auckland
The University of Auckland
Monash University
The University of Auckland
The University of Adelaide
Macquarie University
The University of Newcastle
Swinburne University of Technology
ANZIAMUNSW Sydney
University of Canterbury
The University of Sydney
Swinburne University of Technology
The University of Melbourne
The University of Auckland
The University of Auckland
University of Augsburg
The University of Adelaide
University of New South WalesUNSW Sydney
IBM Research Australia
Massey University
The University of Sydney
The University of Adelaide
The University of Sydney
The University of Adelaide
Technical University Hamburg
University of Technology, Sydney
The University of Melbourne
Griffith University

140

ANZIAM 2018 Conference Handbook

Name
Harvinder Sidhu
David John Warwick Simpson
Matthew Simpson
Ian Sloan
Michael Small
Paul Smith
Kate Smith-Miles
Mandyam Srinivasan
Linda Stals
Sharon Stephen
Tim Stokes
Yvonne Stokes
Jeremy SumnerSergey Suslov
Arthur George Suvorov
Winston Sweatman
Daisuke Tagami
Alexander Tam
Peter Gerrard Taylor
Steve Taylor
Joseph Alex Teague
Soizic Terrien
Ngamta Thamwattana
Hansani Thanippuli Kankanamalage
Christian Thomas
Ali Tirdad
Eloise Tredenick
Nick Trefethen
Dimetre Triadis
Hayden Tronnolone
Takuya Tsuchiya
Lachlan James Tyrrell
Justin Tzou
Ishraq Uddin
Bruce van Brunt
Demival Vasques Filho
Elias Vera Siguenza
Geetika Verma
Thiripura Vino
Sean Trinity Vittadello
Stephen Wade
Indu Wadhawan
Graeme Wake
James Nicholas Walker
Stephen Walters
David Waters
Michael Greg Watson
Martin Wechselberger

Affiliation
University of New South Wales
Massey University
Queensland University of Technology
University of New South WalesThe University of Western Australia
Macquarie University
The University of Melbourne
The University of Queensland
Australian National University
The University of Sydney
University of Waikato
The University of Adelaide
University of Tasmania
Swinburne University of Technology
RMIT University
Massey University
Kyushu University
The University of Adelaide
The University of Melbourne
The University of Auckland
Queensland University of Technology
The University of Auckland
University of Wollongong
University of South Australia
Monash University
The University of Melbourne
Queensland University of Technology
University of Oxford
Kyushu University
The University of Adelaide
Ehime University
Queensland University of Technology
Macquarie University
The University of Sydney
Massey University
University of Auckland
The University of Auckland
University of South Australia
The University of Melbourne
Queensland University of Technology
Cancer Council New South Wales
University of South Australia
Massey University
The University of Adelaide
University of Tasmania
The University of Auckland
The University of Sydney
The University of Sydney

141

ANZIAM 2018 Conference Handbook

Name
Florian Wechsung
Caroline Wormell
Xueshan Yang
Zeaiter Zeaiter
Collin Zheng
Song-Ping Zhu

Affiliation
University of Oxford
The University of Sydney
The University of Auckland
The University of Sydney
The University of Sydney
University of Wollongong