title: The use of pseudo-inertia in asymptotic modelling of constraints in boundary value problems

authors: Ilanko, Sinniah

subjects: pseudo-inertia

abstract: In recent publications, the validity of using positive and negative inertial penalty parameters and the advantage of this approach over the conventional positive penalty function approach have been established for linear eigenvalue problems. This paper shows how this method may be applied to solve a boundary value problem. A steady-state 2-D heat transfer problem is used to demonstrate the method. First, the governing partial differential equation is modified by adding a pseudo-inertial term that results in an equation, which is mathematically identical to the equation governing the free vibration of a membrane. The essential boundary conditions of zero temperature along a specified line are imposed using inertial penalty parameters. The characteristic vibration modes found in this way are used to generate the complementary function to the heat transfer problem. This solution satisfies all natural boundary conditions (adiabatic) and zero temperature conditions using the inertial penalty parameter. To satisfy any additional temperature distribution imposed on the system, two sets of corrector terms are superimposed resulting in the final solution. The results are compared with constrained solutions obtained using the Lagrangian multiplier method and the ordinary penalty method.

text: The use of pseudo-inertia in asymptotic modelling of constraints in boundary value problems In recent publications, the validity of using positive and negative inertial penalty parameters and the advantage of this approach over the conventional positive penalty function approach have been established for linear eigenvalue problems. This paper shows how this method may be applied to solve a boundary value problem. A steady-state 2-D heat transfer problem is used to demonstrate the method. First, the governing partial differential equation is modified by adding a pseudo-inertial term that results in an equation, which is mathematically identical to the equation governing the free vibration of a membrane. The essential boundary conditions of zero temperature along a specified line are imposed using inertial penalty parameters. The characteristic vibration modes found in this way are used to generate the complementary function to the heat transfer problem. This solution satisfies all natural boundary conditions (adiabatic) and zero temperature conditions using the inertial penalty parameter. To satisfy any additional temperature distribution imposed on the system, two sets of corrector terms are superimposed resulting in the final solution. The results are compared with constrained solutions obtained using the Lagrangian multiplier method and the ordinary penalty method.

year: 2009

title: Hotspots: Modelling capacity for vector-borne disease risk analysis in New Zealand: A case study of Ochlerotatus camptorhynchus incursions in New Zealand

authors: de Wet, Neil

subjects: New Zealand

abstract: This Hotspots case study of Oc. camptorhynchus in New Zealand forms part of the wider aims and
objectives of the Hotspots project. The overall aims of the case study were:
1. To evaluate the performance of the Hotspots model as a risk analysis tool for Oc.
camptorhynchus;
2. To use and learn from the experience of the various incursions of Oc. camptorhynchus in
order to critically assess and improve the model;
3. To gain experience in using the model for risk analysis for Oc. camptorhynchus in
particular, and in so doing, also develop experience applicable to risk analysis for other
vectors of concern (Table 1); and,
4. To develop an experience and knowledge base as well as guidelines for future use of the
model in its various applications related to biosecurity, surveillance and risk assessment
and management.

text: Hotspots: Modelling capacity for vector-borne disease risk analysis in New Zealand: A case study of Ochlerotatus camptorhynchus incursions in New Zealand This Hotspots case study of Oc. camptorhynchus in New Zealand forms part of the wider aims and
objectives of the Hotspots project. The overall aims of the case study were:
1. To evaluate the performance of the Hotspots model as a risk analysis tool for Oc.
camptorhynchus;
2. To use and learn from the experience of the various incursions of Oc. camptorhynchus in
order to critically assess and improve the model;
3. To gain experience in using the model for risk analysis for Oc. camptorhynchus in
particular, and in so doing, also develop experience applicable to risk analysis for other
vectors of concern (Table 1); and,
4. To develop an experience and knowledge base as well as guidelines for future use of the
model in its various applications related to biosecurity, surveillance and risk assessment
and management.

year: 2005-04

title: Changing patterns of Otitis Media in the Waikato region during the Covid Pandemic

authors: Becker, Andre

subjects: COVID-19 pandemic

abstract: Introduction. Acute otitis media (AOM) is a common condition of children encountered in general practice. A proportion of children develop otitis media with effusion (OME), which may require tympanostomy and ventilation tube insertion. Aim. The aim of the study was to compare the incidence of AOM in Māori and New Zealand (NZ) European children in general practice and the referral practices to secondary care for tympanostomy and ventilation tube insertion. Methods. The study was conducted in two parts: (1) an analysis of the incidence of AOM and OME in a rural Waikato general practice (Ōtorohanga) with a high Māori population over a 2-year period; and (2) an analysis of all referrals to the otorhinolaryngology (ORL) department at Waikato District Health Board and tympanostomy and ventilation tube insertion by this service over the same period. Results. The incidence of AOM was similar in Māori compared with NZ European children. The incidence declined significantly between 2019 and 2020 and 50% of children with AOM were treated with antibiotics. Referral rates to the ORL department were greater for Māori compared with NZ European children as were tympanostomy and ventilation tube insertion rates. Discussion. Although AOM is common, OME was rarely diagnosed. The clinical guidelines regarding antibiotic use for common conditions are not being readily adopted and further research is needed into this matter. The COVID-19 pandemic had a substantial effect on demand both in general practice and in the hospital sector. This may have been due to a reduction in the incidence of AOM or due to system changes caused by the pandemic.

text: Changing patterns of Otitis Media in the Waikato region during the Covid Pandemic Introduction. Acute otitis media (AOM) is a common condition of children encountered in general practice. A proportion of children develop otitis media with effusion (OME), which may require tympanostomy and ventilation tube insertion. Aim. The aim of the study was to compare the incidence of AOM in Māori and New Zealand (NZ) European children in general practice and the referral practices to secondary care for tympanostomy and ventilation tube insertion. Methods. The study was conducted in two parts: (1) an analysis of the incidence of AOM and OME in a rural Waikato general practice (Ōtorohanga) with a high Māori population over a 2-year period; and (2) an analysis of all referrals to the otorhinolaryngology (ORL) department at Waikato District Health Board and tympanostomy and ventilation tube insertion by this service over the same period. Results. The incidence of AOM was similar in Māori compared with NZ European children. The incidence declined significantly between 2019 and 2020 and 50% of children with AOM were treated with antibiotics. Referral rates to the ORL department were greater for Māori compared with NZ European children as were tympanostomy and ventilation tube insertion rates. Discussion. Although AOM is common, OME was rarely diagnosed. The clinical guidelines regarding antibiotic use for common conditions are not being readily adopted and further research is needed into this matter. The COVID-19 pandemic had a substantial effect on demand both in general practice and in the hospital sector. This may have been due to a reduction in the incidence of AOM or due to system changes caused by the pandemic.

year: 2023