bluuebunny/crossref_metadata_2025 huggingface dataset:
A neural mass model of basal ganglia nuclei simulates pathological beta rhythm in Parkinson's disease
Authors: Liu Fei , Wang Jiang , Liu Chen , Li Huiyan , Deng Bin , Fietkiewicz Chris , Loparo Kenneth A.
Published: December 2016

An increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with movement disorder, such as Parkinson's disease. The motor cortex and an excitatory-inhibitory neuronal network composed of the subthalamic nucleus (STN) and the external globus pallidus (GPe) are thought to play an important role in the generation of these oscillations. In this paper, we propose a neuron mass model of the basal ganglia on the population level that reproduces the Parkinsonian oscillations in a reciprocal excitatory-inhibitory network. Moreover, it is shown that the generation and frequency of these pathological beta oscillations are varied by the coupling strength and the intrinsic characteristics of the basal ganglia. Simulation results reveal that increase of the coupling strength induces the generation of the beta oscillation, as well as enhances the oscillation frequency. However, for the intrinsic properties of each nucleus in the excitatory-inhibitory network, the STN primarily influences the generation of the beta oscillation while the GPe mainly determines its frequency. Interestingly, describing function analysis applied on this model theoretically explains the mechanism of pathological beta oscillations.
The “neutron channel design”—A method for gaining the desired neutrons
Authors: Hu G. , Hu H. S. , Wang S. , Pan Z. H. , Jia Q. G. , Yan M. F.
Published: December 2016

The neutrons with desired parameters can be obtained after initial neutrons penetrating various structure and component of the material. A novel method, the “neutron channel design”, is proposed in this investigation for gaining the desired neutrons. It is established by employing genetic algorithm (GA) combining with Monte Carlo software. This method is verified by obtaining 0.01eV to 1.0eV neutrons from the Compact Accelerator-driven Neutron Source (CANS). One layer polyethylene (PE) moderator was designed and installed behind the beryllium target in CANS. The simulations and the experiment for detection the neutrons were carried out. The neutron spectrum at 500cm from the PE moderator was simulated by MCNP and PHITS software. The counts of 0.01eV to 1.0eV neutrons were simulated by MCNP and detected by the thermal neutron detector in the experiment. These data were compared and analyzed. Then this method is researched on designing the complex structure of PE and the composite material consisting of PE, lead and zirconium dioxide.
Dynamo-driven plasmoid formation from a current-sheet instability
Authors: Ebrahimi F.
Published: December 2016

Axisymmetric current-carrying plasmoids are formed in the presence of nonaxisymmetric fluctuations during nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry. We utilize the helicity injection technique to form an initial poloidal flux in the presence of a toroidal guide field. As helicity is injected, two types of current sheets are formed from (1) the oppositely directed field lines in the injector region (primary reconnecting current sheet), and (2) the poloidal flux compression near the plasma edge (edge current sheet). We first find that nonaxisymmetric fluctuations arising from the current-sheet instability isolated near the plasma edge have tearing parity but can nevertheless grow fast (on the poloidal Alfven time scale). These modes saturate by breaking up the current sheet. Second, for the first time, a dynamo poloidal flux amplification is observed at the reconnection site (in the region of the oppositely directed magnetic field). This fluctuation-induced flux amplification increases the local Lundquist number, which then triggers a plasmoid instability and breaks the primary current sheet at the reconnection site. The plasmoids formation driven by large-scale flux amplification, i.e., a large-scale dynamo, observed here has strong implications for astrophysical reconnection as well as fast reconnection events in laboratory plasmas.
Maxwell stress to explain the mechanism for the anisotropic expansion in lithiated silicon nanowires
Authors: Boone Donald C.
Published: December 2016

This computational research study attempts to explain the process that leads to volume expansion during insertion of lithium ions into a silicon nanowire. During lithiation, electrons flow through the nanowire in the opposing direction of lithium ions insertion. This causes an applied electromagnetic field which is described as being a quantum mechanical version of photon density wave theory. A series of events are calculated as the individual electrons and photons travels through the lithiated silicon nanowire. The hypothesis that will be presented employs the Maxwell stress tensor to calculate the refractive indices in three orthogonal directions during lithiation. The quantum harmonic oscillator and the electromagnetic intensity will be utilized in this presentation to calculate the energy of electrons and optical amplification of the electromagnetic field respectively. The main focus of this research study will use electron scattering theory, spontaneous and stimulated emission theory to model the breaking of cohesion bonds between silicon atoms that ultimately leads to excessive volume expansion that is witnessed during the lithiation process in Si nanowires.
Control of Rayleigh-like waves in thick plate Willis metamaterials
Authors: Diatta André , Achaoui Younes , Brûlé Stéphane , Enoch Stefan , Guenneau Sébastien
Published: December 2016

Recent advances in control of anthropic seismic sources in structured soil led us to explore interactions of elastic waves propagating in plates (with soil parameters) structured with concrete pillars buried in the soil. Pillars are 2 m in diameter, 30 m in depth and the plate is 50 m in thickness. We study the frequency range 5 to 10 Hz, for which Rayleigh wave wavelengths are smaller than the plate thickness. This frequency range is compatible with frequency ranges of particular interest in earthquake engineering. It is demonstrated in this paper that two seismic cloaks’ configurations allow for an unprecedented flow of elastodynamic energy associated with Rayleigh surface waves. The first cloak design is inspired by some approximation of ideal cloaks’ parameters within the framework of thin plate theory. The second, more accomplished but more involved, cloak design is deduced from a geometric transform in the full Navier equations that preserves the symmetry of the elasticity tensor but leads to Willis’ equations, well approximated by a homogenization procedure, as corroborated by numerical simulations. The two cloaks’s designs are strickingly different, and the superior efficiency of the second type of cloak emphasizes the necessity for rigour in transposition of existing cloaks’s designs in thin plates to the geophysics setting. Importantly, we focus our attention on geometric transforms applied to thick plates, which is an intermediate case between thin plates and semi-infinite media, not studied previously. Cloaking efficiency (reduction of the disturbance of the wave wavefront and its amplitude behind an obstacle) and protection (reduction of the wave amplitude within the center of the cloak) are studied for ideal and approximated cloaks’ parameters. These results represent a preliminary step towards designs of seismic cloaks for surface Rayleigh waves propagating in sedimentary soils structured with concrete pillars.
Comparison of stocking methods for beef production in northern Australia: seasonal diet quality and composition
Authors: Hall Trevor J. , McIvor John G. , Jones Paul , Smith David R. , Mayer David G.
Published: December 2016

Managing and measuring the grazing and nutrition of cattle are required to improve the productivity and profitability of beef businesses in northern Australia. The quality and composition of the diet selected by cattle grazing in three stocking methods (continuous, extensive rotation and intensive (cell) rotation) on nine commercial properties in Queensland were estimated using near infrared reflectance spectroscopy analyses of fresh faeces; 585 faecal samples were analysed between 2005 and 2009. Sites were in two regions (north and south Queensland) and on two vegetation communities, namely brigalow (Acacia harpophylla F. Muell. ex Benth.) on clay soils and eucalypts on light-textured soil types. Pastures were dominated by perennial sown exotic grass species, predominantly Cenchrus ciliaris L. (buffel grass) at five sites and Urochloa mosambicensis (Hack.) (Sabi grass) at one site, and by native perennial tussock grasses at three sites. Seasonal profiles of dietary crude protein, dry matter digestibility, faecal nitrogen concentration, proportion of non-grass, ratio of crude protein to digestibility and an estimate of liveweight gain are presented for each stocking method. Overall, dietary crude protein, digestibility, faecal nitrogen, the crude protein : digestibility ratio and liveweight gain were significantly higher for animals grazed continuously, with short rest periods, than for animals in extensive or intensive rotations. There was a significant interaction between stocking method and pasture growing conditions, measured as a simulated growth index, for dietary crude protein and faecal nitrogen. There was no difference between stocking methods during periods when the index was <0.2, indicating no pasture growth, but during periods of active growth (index >0.5), crude protein and faecal nitrogen were higher with continuous grazing than in the extensive and intensive rotations. For cattle producers considering alternative stocking methods, the results suggest they can obtain similar ecological responses under any of the three methods and diet quality will be higher during the pasture growing period in continuously grazed pastures.
Effect of soil, machine, and working state parameters on the required draft force of a subsoiler using a theoretical draft-calculating model
Authors: Ahmadi Iman
Published: December 2016

One of the most important soil degradation agents in agriculture is compaction. To rehabilitate compacted fields, farmers usually use subsoilers to break compacted layers. Moreover, the required draft force of a subsoiler dictates the amount of energy needed to operate it. Therefore, measurement, calculation or prediction of the draft force of this machine is vital for designing an efficient subsoiler. In the present study, an analytical model was developed to calculate the subsoiler draft force. To verify the model developed herein, model outputs regarding the draft force of a subsoiler were compared with corresponding results from the American Society of Agricultural Engineers (ASAE) standard, as well as the results of literature studies. Moreover, the output of the model was compared with the measured draft force of subsoiling a silty clay loam soil. Furthermore, the results obtained regarding the quantitative effect of model inputs on the draft force of a subsoiler were checked from the viewpoint of compatibility with the expected trends or observed results in other studies. The data obtained from the developed model were compatible with those of the ASAE standard. Moreover, the draft force of a single-shank subsoiler was almost 10 kN, which is approximately 14% higher than the result obtained by the model (8.73 kN). Therefore, the model developed herein can be used to calculate the subsoiler draft force with reasonable accuracy. Of the machine parameters, subsoiler wingspan had an adverse effect on the specific draft of this machine. Moreover, for the range of working depths between 30 and 50cm, the minimum values of specific draft took place.
Subcellular distribution and cellular self-repair ability of fluorescent quantum dots emitting in the visible to near-infrared region
Authors: Peng Fei , Su Yuanyuan , Zhong Yiling , He Yao
Published: December 2016

Semiconductor II-VI quantum dots (QDs), as high-performance fluorescent biological probes, have garnered significant attention due to their superior optical properties. To enable QDs for wide-ranging bioapplications, concerns about their in vitro behavior need to be fully addressed. Herein, for the first time, cellular behaviors of aqueous synthesized-QDs (aqQDs), whose maximum emission wavelength (λ
emission) covers the visible to near-infrared spectral window, are systematically investigated. Our results demonstrate that three different sized aqQDs feature distinct cellular distributions, i.e. aqQD530 (aqQDs whose λ
emission is 530 nm) and aqQD620 (aqQDs whose λ
emission is 620 nm) mainly distribute in the cytoplasm and nucleus, while aqQD730 (aqQDs whose λ
emission is 730 nm) mainly accumulates in the cytoplasm. Most significantly, the phenomenon that cellular self-repair ability is dependent on diameters of aqQDs is revealed for the first time. In particular, small-sized QDs (e.g. aqQD530 and aqQD620) severely deteriorate cellular self-repair ability, leading to an irreversible decrease in cell viability. In striking contrast, large-sized QDs (e.g. aqQD730) have little effect on cellular self-repair ability, and the cell viability is restored after removal of aqQD730 from the culture medium. Our results provide invaluable information for QD-relevant biosafety analysis, as well as suggest available guidance for the design of biocompatible QDs for wide utilization in biological and biomedical studies.
Very thin ITO/metal mesh hybrid films for a high-performance
transparent conductive layer in GaN-based light-emitting diodes
Authors: Min Jung-Hong , Kwak Hoe-Min , Kim Kiyoung , Jeong Woo-Lim , Lee Dong-Seon
Published: December 2016

In this paper, we introduce very thin Indium tin oxide (ITO) layers (5, 10, and
15 nm) hybridized with a metal mesh to produce high-performance transparent
conductive layers (TCLs) in near-ultraviolet light-emitting diodes (NUV LEDs).
Using UV–vis–IR spectrometry, Hall measurement, and atomic force
microscopy, we found that 10 nm was the optimal thickness for the very thin ITO
layers in terms of outstanding transmittance and sheet resistance values as well
as stable contact properties when hybridized with the metal mesh. The proposed
layers showed a value of 4.56 Ω/□ for sheet resistance and a value of
89.1% for transmittance. Moreover, the NUV LEDs fabricated with the
hybrid TCLs achieved ∼140% enhanced light output power compared to
that of 150 nm thick ITO layers. Finally, to verify the practical usage of the
TCLs for industrial applications, we packaged the NUV LED chips and obtained
improved turn-on voltage (3.48 V) and light output power (∼116%)
performance.
Bounded and unbounded solutions of the von Kármán vortex trail
Authors: Lim Chjan , Sirovich Lawrence
Published: December 2016

The general initial value problem for the linearized von Karman vortex trail is solved. In particular, the fundamental differences between von Karman’s normal mode solutions and aperiodic solutions with compact support are discussed. Within the natural space

ℓ
2

{\ell _2}

, it is shown that the von Karman trail at its special aspect ratio (neutrally stable case) supports unbounded solutions. Two invariants of the equations determine whether a solution is bounded or unbounded. The asymptotic behaviour of aperiodic solutions is discussed. It is found that unbounded solutions grow at the rate

O

(

l
n
τ

)

O\left ( {ln \tau } \right )

in

ℓ
∞

{\ell _\infty }

while bounded solutions decay as

O

(

1

/

τ

)

O\left ( {1/\sqrt \tau } \right )

. In addition, a Loschmidt’s demon is constructed for the reversible dispersive equations which demonstrates the focussing effect in the von Karman trail.
ECE versus DISP electrochemical competition
Authors: Cole S. L. , Wilder J. W.
Published: December 2016

The ECE (Electrochemical, Chemical, Electrochemical) and DISP (DISProportionation) mechanisms describe electrochemical reactions between four species in a diffusive solution. The general set of reactions which encompass both mechanisms is modelled by:
\[

A
+

e
−

→
B

A + {e^ - } \to B

\]
(at the electrode) (i)
\[

B
⇌
C

B \rightleftharpoons C

\]
(throughout the solution) (ii)
\[

C
+

e
−

→
D

C + {e^ - } \to D

\]
(at the electrode) (iii)
\[

B
+
C
⇌
A
+
D

B + C \rightleftharpoons A + D

\]
(throughout the solution) (iv) in the case when the applied overpotential is large enough that only the forward steps in (i) and (iii) are present. The ECE mechanism follows the pathway (i), (ii), (iii). The DISP mechanism follows the pathway (i), (ii), (iv). These electrochemical mechanisms play an important role in many organic reactions such as cleavage processes and in inorganic reactions such as the production of forms of technicium used as a radiopharmaceutical. It is important to understand these mechanisms in order to better predict product synthesis and performance. This paper uses asymptotic expansion and perturbation techniques to provide rigorous, relatively simple analytic/numerical solutions for the (linear) ECE mechanism, the (weakly nonlinear) DISP mechanism and a (weakly nonlinear) “competition” mechanism involving all four pathway steps. It is shown that for large dimensionless time, the ECE mechanism evolves to a state with only two species present in order one quantities. Yet, the DISP mechanism retains all four species in order one amounts when step (iv) is reversible. The competition mechanism behaves like the ECE mechanism for small time yet evolves for large time to a form more similar to the DISP mechanism showing that nonlinear effects eventually dominate the mechanistic behavior.
Nonlinear waves and shock calculations for hyperelastic fluid-filled tubes
Authors: Moodie T. Bryant , Swaters Gordon E.
Published: December 2016

The propagation of both finite amplitude and weakly nonlinear waves in fluid-filled hyperelastic tethered tubes subjected to axial strain is investigated in some detail. Procedures based upon the methods of characteristics and relatively undistorted waves are deployed to compute the time and location of first shock formation in tubes having both constant and variable properties ahead of the wave. The influence of wall thickness changes in shock formation is explored and it is further found that if the transmural pressure ahead of the wave is zero then no shock can form on the lead characteristic for any model based on a rational theory of finite elasticity. This latter result is in disagreement with several earlier studies.
Thermo-mechanical evolution of shape memory alloys
Authors: Colli Pierluigi , Frémond Michel , Visintin Augusto
Published: December 2016

In certain alloys, after deformation the original shape can be recovered just by thermal means. This shape memory behaviour can be interpreted as the effect of an austenite-martensite phase transition. We model this phenomenon by assuming the free energy to depend on the volumetric proportions of the different phases.
A conformally invariant Oseen equation for flow at small Reynolds numbers
Authors: Ranger K. B.
Published: December 2016

Starting from a complex variable formulation of the exact Navier-Stokes equations for the steady two-dimensional motion of an incompressible viscous fluid, a Burgers type linearization is introduced at small Reynolds number which results in a conformally invariant Oseen equation. The independent variables are the velocity potential and stream function for the corresponding irrotational flow. There are certain analytical advantages in this approach for the determination of uniformly valid approximations to flow at small Reynolds numbers and the method is illustrated by various examples.
Intervals of electrohydrodynamic Rayleigh-Taylor instability: effect of a normal periodic field
Authors: Elshehawey Elsayed F.
Published: December 2016

The intervals of electrohydrodynamic Rayleigh-Taylor instability influenced by a periodic normal field are considered. It is shown that a linear model of the interface is governed by Hill’s differential equation. Characteristic values and intervals of stability are discussed. The special case of Mathieu differential equation type is obtained.
Expansion of the Green’s function in a cylindrical coordinate system
Authors: Wang Wan-xian
Published: December 2016

The expansions of the Green’s function

e

i
k

|

r
−

r
′

|

/

|

r
−

r
′

|

{e^{ik\left | {r - r’} \right |}}/\left | {r - r’} \right |

in spherical and spheroidal coordinate systems were studied by some researchers; however, because of its complexity this kind of expansion has not been performed in a cylindrical coordinate system. With the aid of the expressions of the Bessel functions

J

−
1

/

2

{J_{ - 1/2}}

and

J

1

/

2

{J_{1/2}}

and of the transformation from these functions to the spherical Bessel functions, the author has analytically derived the expansion of the Green’s function in the cylindrical coordinate system.
Optimal low-dimensional dynamical approximations
Authors: Sirovich L. , Knight B. W. , Rodriguez J. D.
Published: December 2016

We present a method for determining optimal coordinates for the representation of an inertial manifold of a dynamical system. The condition of optimality is precisely defined and is shown to lead to a unique basis system. The method is applied to the Neumann and Dirichlet problems for the Ginzburg-Landau equation. Substantial reduction in the size of the dynamical system, without loss of accuracy is obtained from the method.
Nonlinear groups of gravity-capillary waves
Authors: Yih Chia-Shun
Published: December 2016

Nonlinear groups of gravity-capillary waves in deep water are investigated by a systematic direct approach that can be applied to nonlinear groups of other dispersive waves. Two formulas in closed form expressing the variations of the phase velocity

c
c

of the basic waves and of their group velocity

c
g

{c_g}

with the amplitude of the waves are obtained. These are in terms of the wavenumber

ε
\varepsilon

of the envelope and

ε
2

{\varepsilon ^2}

can be determined by the present approach as a power series in

a
2

{a^2}

, if

2
a

2a

represents the amplitude of the waves. To the order of approximation achieved here,

ε
2

{\varepsilon ^2}

is determined as a multiple of

a
2

{a^2}

. If

k
k

is the wavenumber of the basic waves,

g
g

is the gravitational acceleration,

ρ
\rho

is the density of the fluid,

T
^

\hat T

is surface tension, and

β
=

T
^

k
2

/

ρ
g

\beta = \hat T{k^2}/\rho g

, then wave groups are possible for
\[

0
≤
β
>
0.1547

0 \le \beta > 0.1547

\]
or
\[

β
>

1
2

,

\beta > \frac {1}{2},

\]
although the analysis is valid only when

β
\beta

is not near

1
2

\frac {1}{2}

. The phase velocity increases with the amplitude in the former interval for

β
\beta

and decreases with the amplitude in the latter interval. The group velocity

c
g

{c_g}

decreases with the amplitude in the former interval for

β
\beta

, or for

1
2

>
β
>
1

\frac {1}{2} > \beta > 1

, but increases with the amplitude if

β
>
1

\beta > 1

. When the results of this paper are compared with the results of previous authors, wherever comparison is possible, complete agreement is found. (Previous authors did not give the variation of

c
g

{c_g}

with the amplitude.)
Equipartition of energy in linearized 3-D viscoelasticity
Authors: Dassios George , Zafiropoulos Filareti
Published: December 2016

A regular and compactly supported initial disturbance propagates in a homogeneous isotropic and linearized viscoelastic medium. The elasticities of the medium exhibit a simple exponential decay in time. General expressions for the energies are obtained and the decay and equipartition of the kinetic and strain energies, for both the longitudinal as well as the transverse wave, are demonstrated.
A characterization of the room index by means of functional equations
Authors: Alsina Claudi
Published: December 2016

By solving a system of functional equations we characterize the classical room index which is useful in architectural problems concerning room lighting.
The potential for a homogeneous cylinder in a cylindrical coordinate system
Authors: Wang Wan-xian
Published: December 2016

Some special cases of the potential for a homogeneous cylinder in a cylindrical coordinate system may be treated by virtue of simple integrals, for example, the potential for a straight rod or wire segment and that for a homogeneous cylinder at the point on its axis. However, because of the involved mathematical operations, the analytical formula of the potential for a homogeneous cylinder at an arbitrary point has not been seen from others. In order to solve the problem, the author has taken the following steps: (1) expanding Green’s function

e

i
k

|

r
′

−
r

|

/

|

r
′

−
r

|

{e^{ik\left | {r’ - r} \right |}}/\left | {r’ - r} \right |

in the cylindrical coordinate system; (2) transforming Green’s function

e

i
k

|

r
′

−
r

|

/

|

r
′

−
r

|

{e^{ik\left | {r’ - r} \right |}}/\left | {r’ - r} \right |

into Green’s function

1

/

|

r
′

−
r

|

1/\left | {r’ - r} \right |

by setting the wave number

k
k

to be zero and integrating the separated azimuthal function

cos
n

(

ϕ
′

−
ϕ

)

{\cos ^n}\left ( {\phi ’ - \phi } \right )

; (3) using the integral recursion relation for the function

r

′

2
m
+
1

/

[

(

z
′

−
z

)

2

+

r
′

2

+

r
2

]

(

4
m
+
1

)

/

2

{r’^{2m + 1}}/{\left [ {{{\left ( {z’ - z} \right )}^2} + {{r’}^2} + {r^2}} \right ]^{\left ( {4m + 1} \right )/2}}

with respect to

r
′

r’

and those for the functions

1

/

[

(

z
′

−
z

)

2

+

r
2

]

(

2
m
−
1

)

/

2

1/{\left [ {{{\left ( {z’ - z} \right )}^2} + {r^2}} \right ]^{\left ( {2m - 1} \right )/2}}

and

1

/

[

(

z
′

−
z

)

2

+

r
2

+

a
2

]

(

4
m
−
2
l
−
1

)

/

2

1/{\left [ {{{\left ( {z’ - z} \right )}^2} + {r^2} + {a^2}} \right ]^{\left ( {4m - 2l - 1} \right )/2}}

with respect to

z
′

z’

, then we can complete the integrals for the function

1

/

|

r
′

−
r

|

1/\left | {r’ - r} \right |

and obtain the analytical expression of the potential for the cylinder in the cylindrical coordinate system. For numerical comparison, we have calculated the potentials for the cylinder and the prolate or oblate spheroid with equivalent volume and same high aspect ratio at far field point. The results are satisfactory.
Estimation of growth rate distributions in size structured population models
Authors: Banks H. T. , Fitzpatrick B. G.
Published: December 2016

We propose models for size-structured populations which allow growth rates to vary with individuals (growth rate distribution across all possible individual growth rates). A theoretical framework for the estimation of the growth rate distribution from data of sized population densities is developed. Numerical examples are presented to demonstrate feasibility of the ideas.
On an electromagnetic inverse problem for dispersive media
Authors: von Wolfersdorf L.
Published: December 2016

Recently, R. S. Beezley and R. J. Krueger [1] (see also [2]) and I. Lerche [6] considered some electromagnetic inverse problems for dispersive media, where the constitutive relation between the displacement field and the electric field in a homogeneous, isotropic, dielectric, dispersive medium is determined from measurements on monochromatic electromagnetic plane waves within the medium. For this aim Beezley and Krueger used the reflection behavior of the plane waves in the time domain, whereas Lerche utilized the absorption behavior of the waves in the frequency domain stressing the fact that decrement measurements are relatively easy to perform compared to phase measurements. He reduced the corresponding inverse problem for the whole space to a nonlinear Riemann-Hilbert problem for a holomorphic function in the upper half-plane and (not quite exactly) to an equivalent nonlinear singular integral equation which he solved in a linear approximation.
An unfolding of the Takens-Bogdanov singularity
Authors: Hirschberg P. , Knobloch E.
Published: December 2016

A complete analysis for

|
μ
|

,

|
ν
|

≪
1

\left | \mu \right |, \left | \nu \right | \ll 1

of the equation
\[

x
˙

=
y
,

y
˙

=
μ
x
+
ν
y
+
M

x
2

+
Γ
x
y

\dot x = y, \dot y = \mu x + \nu y + M{x^2} + \Gamma xy

\]
describing a particular unfolding of the Takens-Bogdanov singularity is presented.
On the Mullins-Sekerka model for phase transitions in mixtures
Authors: Milic Natasa
Published: December 2016

The Mullins-Sekerka model for dynamical phase transitions in two-component mixtures is considered. Global growth conditions for the phase regions and the interface are obtained from underlying conservation laws. A quasi-static model is formulated and the solutions are discussed for totally isolated mixtures.
A complex variable integration technique for the two-dimensional Navier-Stokes equations
Authors: Ranger K. B.
Published: December 2016

Starting from a complex variable formulation for the two-dimensional steady flow equations describing the motion of a viscous incompressible liquid, a method is developed which carries out three integrations of the fourth order system in parametric form containing three arbitrary real functions.
Nonincrease of mushy region in a nonhomogeneous Stefan problem
Authors: Götz I. G. , Zaltzman B. B.
Published: December 2016

For an arbitrary bounded solution of the Stefan problem the mushy region is nonincreasing in time in a sense of the theory of sets. This result takes place for the nonhomogeneous Stefan problem under some conditions on the behavior of a heat source in the mushy region.
On caustics associated with hyperbolic systems
Authors: Gorman Arthur D.
Published: December 2016

The Lagrange manifold formalism is adapted to find asymptotic solutions for a class of hyperbolic systems near caustics.
A note on the existence of a waiting time for a two-phase Stefan problem
Authors: Tarzia Domingo Alberto , Turner Cristina Vilma
Published: December 2016

We consider a slab, represented by the interval

0
>
x
>

x
0

0 > x > {x_0}

, at the initial temperature

θ
0

=

θ
0

(
x
)

≥
0

(

o
r

ϕ
0

=

ϕ
0

(
x
)

≥
0

)

{\theta _0} = {\theta _0}\left ( x \right ) \ge 0\left ( {or {\phi _0} = {\phi _0}\left ( x \right ) \ge 0} \right )

having a heat flux

q
=
q

(
t
)

>
0

q = q\left ( t \right ) > 0

(or convective boundary condition with a heat transfer coefficient

h
h

) on the left face

x
=
0

x = 0

and a temperature condition

b

(
t
)

>
0

b\left ( t \right ) > 0

on the right face

x
=

x
0

x = {x_0}

(

x

0

x_{0}

could be also

+
∞

+ \infty

, i.e., a semi-infinite material). We consider the corresponding heat conduction problem and assume that the phase-change temperature is

0
∘

C

{0^ \circ }C

.
Finite-element convergence for contact problems in plane linear elastostatics
Authors: Gwinner Joachim
Published: December 2016

This paper presents a convergence analysis for the finite-element approximation of unilateral problems in plane linear elastostatics. We consider in particular the deformation of a body unilaterally supported by a frictionless rigid foundation, solely subjected to body forces and surface tractions without being fixed along some part of its boundary, and establish convergence of piecewise polynomial finite-element approximations for mechanically definite problems without imposing any regularity assumption. Moreover we study the discretization of the contact problem with given friction along the rigid foundation.
Cohesive elasticity and surface phenomena
Authors: Wu Chien H.
Published: December 2016

Cohesive elasticity is the grade-3 theory of elasticity developed by Mindlin in 1965. It has a modulus of cohesion that gives rise to surface-tension. The concept of adhesion is introduced, and interfacial energies and energy of adhesion are defined. The interfacial energy solution may also be used to define a grain boundary energy. Also presented are the thin film energy and the concept of an interface-phase. The stretching of a thin film is analyzed in detail; and it is found that the apparent Young’s modulus obtained from a film is higher than that obtained from a plate.
Existence and nonexistence results on the radially symmetric cavitation problem
Authors: Meynard François
Published: December 2016

We investigate the problem of radially symmetric cavitation for a hyperelastic ball in

R

n

,
n
≥
2

\mathbb {R}{^n} , n \ge 2

. The radial equilibrium equation is analyzed by a shooting argument. The basic formulation of the problem is the same as C. A. Stuart’s formulation in [10], but an asymptotic study of the solutions of the radial equilibrium equation allows us to enlarge the discussion of cavitation to cases that are excluded from the context of [10]. Finally, criteria for nonexistence to the problem of cavitation are briefly discussed. They have a physical interpretation through relations between the total energy and the radial stress.
Interface cracks in anisotropic dissimilar materials: general case
Authors: Ni L. , Nemat-Nasser S.
Published: December 2016

An interface crack in anisotropic dissimilar materials is considered for the general case where all three fracture modes may be coupled. Analytic solutions are obtained for two commonly used models of interface cracks: (1) the fully open crack; and (2) the Comninou model where, even under farfield tension normal to the crack face, the existence of very small contact zones near the crack tips is permitted. Conditions under which nonoscillatory singular solutions may exist, are discussed.
Scalar wave scattering of a prolate spheroid as a parameter expansion of that of a sphere
Authors: Acho Thomas M.
Published: December 2016

In this paper the scattering problem for the prolate spheroid,
\[

Δ

U
p

+

k
2

U
p

=
0

\Delta {U_p} + {k^2}{U_p} = 0

\]
, is solved by way of an asymptotic parameter expansion, where the spheroid is considered a perturbation of a sphere (which has an exact solution). The error of the asymptotic approximation is then estimated.
Phenomenological behavior of multipolar viscous fluids
Authors: Bellout Hamid , Bloom Frederick , Nečas Jindřich
Published: December 2016

A constitutive theory is formulated to describe the flow of viscous fluids: the theory of multipolar fluids exhibits nonlinear relations among the stress tensors and spatial derivatives of the velocity of order greater than one and is compatible with the basic principles of continuum mechanics and thermodynamics. For an isothermal, incompressible, dipolar fluid the velocity profiles for various steady flows, such as proper Poiseuille flow in a circular pipe, are computed; the results are compared with the velocity profiles obtained from the steady Navier-Stokes equations through an application of the Prandtl boundary-layer theory.
Hamel’s problem for steady plane orthogonal MHD flows
Authors: Nguyen P. V. , Chandna O. P.
Published: December 2016

Complex variable technique is used to study steady plane orthogonal magnetohydrodynamic flows of a viscous incompressible fluid of finite electrical conductivity. The problem of determining all possible flows such that the streamlines and their orthogonal trajectories form an isometric net is investigated.
Solutions of the Navier-Stokes equations in implicit form
Authors: Ranger K. B.
Published: December 2016

A method is described to determine exact solutions of general type in implicit form for the equations governing the steady two-dimensional motion of a viscous incompressible liquid.
Plane deformations of membranes and networks with circular cords
Authors: Shi Jingyu
Published: December 2016

Deformations of membranes and networks formed with two families of highly elastic cords are considered. The cords are along the radial and circumferential directions of concentric circles and are perfectly joined together at their intersection points so that there is no slip relative to each other. The deformations studied include: (1) symmetric deformation of circular arcs or annuli, (2) straightening of circular arcs and (3) inverse bending of circular arcs. It is found that the second is a universal deformation, which satisfies the equilibrium equations for any constitutive relations of the material of the cords.
On the question of global existence for reaction-diffusion systems with mixed boundary conditions
Authors: Hollis Selwyn L.
Published: December 2016

The question of global existence for solutions of reaction-diffusion systems presents fundamental difficulties in the case in which some components of the system satisfy Neumann boundary conditions while others satisfy nonhomogeneous Dirichlet boundary conditions. We discuss particular examples for which classical solutions are known to exist globally when all components satisfy the same type of boundary condition and yet either finite-time blowup occurs or else global existence is unknown when mixed boundary condition types are imposed on the system. Some positive results are presented concerning global existence in the presence of mixed boundary conditions if certain structure requirements are placed on the system, and these results are applied to some particular chemical reaction models.
On a class of Stokes flows inside a corrugated boundary
Authors: Hackborn W. W.
Published: December 2016

A study is made of a family of steady two-dimensional Stokes flows stirred by an infinitesimal rotating cylinder (a line rotlet) inside a corrugated boundary. Parameters govern the position of the stirrer and the number and sharpness of ridges in the boundary. A solution is found in terms of a finite combination of elementary functions. It is demonstrated that the flow exhibits some interesting dynamical features such as peculiar bifurcations and homoclinic orbits.
The damped Mathieu equation
Authors: Turyn Lawrence
Published: December 2016

We establish an asymptotic lower bound for the minimum excitation needed to cause instability for the damped Mathieu equation. The methods used are Floquet theory and Liapunov-Schmidt, and we use a fact about the width of the instability interval for the undamped Mathieu equation. Our results are compared with published numerical data.
Exponential stability of the semigroup associated with a thermoelastic system
Authors: Liu Zhuangyi , Zheng Song Mu
Published: December 2016

In this paper it is proved that the semigroup associated with the one-dimensional thermoelastic system with Dirichlet boundary conditions is an exponentially stable

C
0

{C_0}

-semigroup of contraction on the space

H
0
1

×

L
2

×

L
2

H_0^1 \times {L^2} \times {L^2}

. The technique of the proof is completely different from the usual energy method. It is shown that the exponential decay in

D

(
A
)

D\left ( A \right )

recently obtained by Revira is a consequence of our main result. An important application of our main result to the Linear-Quadratic-Gaussian optimal control problem is also discussed.
Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials
Authors: Allaire Grégoire , Kohn Robert V.
Published: December 2016

We consider linearly elastic composite materials made by mixing two possibly anisotropic components. Our main hypothesis is that the Hooke’s laws of the two components be well-ordered. For given volume fractions and average strain, we present optimal upper and lower bounds on the elastic energy quadratic form. We also discuss bounds on sums of energies and bounds involving complementary energy rather than elastic energy. Our arguments are based primarily on the Hashin-Shtrikman variational principle; however, we also discuss how the same results arise from the “translation method", making use of the analysis of Milton. Our bounds are equivalent to those established by Avelleneda and closely related to the “trace bounds” established by Milton and Kohn. The optimal energy bounds, however, are presented here as the extreme values of certain convex optimization problems. The optimal microgeometries are determined by the associated first-order optimality conditions. A similar treatment for mixtures of two incompressible, isotropic elastic materials has previously been given by Kohn and Lipton.
Bifurcation and stability analysis of a rotating beam
Authors: Gross Peter , Gürgöze Metin , Kliem Wolfhard
Published: December 2016

We discuss small oscillations of an elastic beam clamped radially to the interior of a rotating ring. It is well known that if the speed of rotation is sufficiently high, the trivial equilibrium of the beam may lose stability and the beam buckles.
Collapse of spherical bubbles in fluids with nonlinear viscosity
Authors: Brutyan M. A. , Krapivsky P. L.
Published: December 2016

An analysis is given of the collapse of a spherical bubble in a large body of a viscous incompressible fluid with strain-dependent nonlinear viscosity. Two types of asymptotic behaviors are found analytically, namely the collapse over finite time and viscous damping over infinite time.
Pure azimuthal shear of compressible non-linearly elastic circular tubes
Authors: Polignone Debra A. , Horgan Cornelius O.
Published: December 2016

The azimuthal (or circular) shear problem for a hollow circular cylinder, composed of homogeneous isotropic compressible nonlinearly elastic material, is described. The inner surface of the tube is bonded to a rigid cylinder. The deformation may be achieved either by applying a uniformly distributed azimuthal shear traction on the outer surface together with zero radial traction (Problem 1) or by subjecting the outer surface to a prescribed angular displacement, with zero radial displacement (Problem 2). For an arbitrary compressible material, the cylinder will undergo both a radial and angular deformation. These axisymmetric fields are governed by a coupled pair of nonlinear ordinary differential equations, one of which is second-order and the other first-order. The class of materials for which pure azimuthal shear (i.e., a deformation with zero radial displacement) is possible is described. The corresponding angular displacement and stresses are determined explicitly. Specific material models are used to illustrate the results.
Linear water waves over a gently sloping beach
Authors: Sun S. M. , Shen M. C.
Published: December 2016

The objective of this paper is to justify rigorously the ray method originally developed by Keller [6] for linear water waves over a two-dimensional gently sloping beach. The approximate formula for eigenvalues of the linear water wave problem and the uniform ray method expansion at and near a shoreline are all consequences of the justification.
Parametrization of general solutions for the Navier-Stokes equations
Authors: Ranger K. B.
Published: December 2016

A method is described for constructing general solutions of the steady two-dimensional Navier-Stokes equations governing the motion of a viscous incompressible liquid. The solution for the stream function is expressed in implicit parametric form containing two arbitrary complex functions or four arbitrary real functions.
Regularly and singularly perturbed cracks
Authors: Wu Chien H.
Published: December 2016

In a nondimensionalized rectangular Cartesian coordinate system

(

x
1

,

x
2

)

\left ( {{x_1}, {x_2}} \right )

let

x
2

=
ε

Y
±

(

x
1

)

{x_2} = \varepsilon {Y_ \pm }\left ( {{x_1}} \right )

denote the upper and lower surfaces of a hole where

|

x
1

|

≤
1

\left | {{x_1}} \right | \le 1

and

ε
\varepsilon

is a small parameter. As

ε
\varepsilon

tends to zero, the hole degenerates into a crack of length 2. The functions

Y
±

{Y_ \pm }

, together with their derivatives, are continuous and

Y
+

−

Y
−

≥
0

{Y_ + } - {Y_ - } \ge 0

. For

ε
\varepsilon

not equal to zero, the hole is called a regularly (singularly) perturbed crack if
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Y prime Subscript plus Baseline left-parenthesis plus-or-minus 1 right-parenthesis equals upper Y prime Subscript minus Baseline left-parenthesis plus-or-minus 1 right-parenthesis left-parenthesis upper Y prime Subscript plus Baseline left-parenthesis plus-or-minus 1 right-parenthesis not-equals upper Y prime Subscript minus Baseline left-parenthesis plus-or-minus 1 right-parenthesis right-parenthesis">

Y
+
′

(

±
1

)

=

Y
−
′

(

±
1

)

(

Y
+
′

(

±
1

)

≠

Y
−
′

(

±
1

)

)

{Y’_ + }\left ( { \pm 1} \right ) = {Y’_ - }\left ( { \pm 1} \right ) \left ( {Y’_ + } \left ( { \pm 1} \right ) \ne {Y’_ - }\left ( { \pm 1} \right ) \right )

. Regular perturbation procedures are applied to obtain the stress intensity factors existing at the tips of regularly perturbed cracks. It is shown that the second term of a two-term expansion is not always of the order of

ε
\varepsilon

. The notch-tip singularity associated with a singularly perturbed crack is obtained by the method of matched asymptotic expansions.
Behavior of solutions of Burgers’s equation with nonlocal boundary conditions. II
Authors: Deng Keng
Published: December 2016

We study the large-time behavior of positive solutions of Burgers’s equation

u
t

=

u

x
x

+
ε
u

u
x

,
0
>
x
>
1
,
t
>
0

(

ε
>
0

)

{u_t} = {u_{xx}} + \varepsilon u{u_x}, 0 > x > 1, t > 0\left ( {\varepsilon > 0} \right )

, subject to the nonlocal boundary condition:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="minus u Subscript x Baseline left-parenthesis 0 comma t right-parenthesis minus one half epsilon u squared left-parenthesis 0 comma t right-parenthesis equals a u Superscript p Baseline left-parenthesis 0 comma t right-parenthesis left-parenthesis integral Subscript 0 Superscript 1 Baseline u left-parenthesis x comma t right-parenthesis d x right-parenthesis Superscript q Baseline comma u left-parenthesis 1 comma t right-parenthesis equals 0 left-parenthesis 0 greater-than p comma q greater-than normal infinity right-parenthesis">

−

u
x

(

0
,
t

)

−

1
2

ε

u
2

(

0
,
t

)

=
a

u
p

(

0
,
t

)

(

∫
0
1

u

(

x
,
t

)

d
x

)

q

,
u

(

1
,
t

)

=
0

(

0
>
p
,
q
>
∞

)

- {u_x}\left ( {0, t} \right ) - \frac {1}{2}\varepsilon {u^2}\left ( {0, t} \right ) = a{u^p}\left ( {0, t} \right ){\left ( {\int _0^1 u \left ( {x, t} \right )dx} \right )^q},u\left ( {1, t} \right ) = 0 \\ \left ( {0 > p, q > \infty } \right )

. The steady-state problem is analyzed in detail, and the result about finite-time blow-up is proved.
A Liapunov function for four-dimensional positive feedback systems
Authors: Jiang Ji Fa
Published: December 2016

In this paper, we use elementary symmetric polynomials in parameters to construct a Liapunov function for four-dimensional positive feedback systems. By applying it, we give a sufficient condition for every positive-time trajectory to converge to an equilibrium.
Variational formulations for the vibration of a piezoelectric body
Authors: Yang J. S.
Published: December 2016

This paper presents a systematic discussion on the variational principles for the vibration of a piezoelectric body. It is shown that there exist four types of variational formulations depending on the internal energy, electric enthalpy, mechanical enthalpy, and enthalpy, respectively. The one depending on the internal energy is in a positive-definite form which immediately leads to a few important properties of the lowest resonant frequency.
Steady flows of nonlinear bipolar viscous fluids between rotating cylinders
Authors: Bloom Frederick , Hao Wenge
Published: December 2016

The boundary-value problem governing the steady Couette flow of a nonlinear bipolar viscous fluid is formulated and solved for particular, degenerate, values of the constitutive parameters; for the general situation, in which the relevant constitutive parameters are positive, we establish existence and uniqueness of solutions to the boundary-value problems. Continuous dependence of solutions, in appropriate norms, is also established with respect to the parameters governing the nonlinearity and multipolarity of the model as these constitutive parameters converge to zero.