bluuebunny/crossref_metadata_2025 huggingface dataset:
Asymptotic analysis of the Ginzburg-Landau model of superconductivity: reduction to a free boundary model
Authors: Chapman S. J.
Published: December 2016

A detailed formal asymptotic analysis of the Ginzburg-Landau model of superconductivity is performed and it is found that the leading-order solution satisfies a vectorial version of the Stefan problem for the melting or solidification of a pure material. The first-order correction to this solution is found to contain terms analogous to those of surface tension and kinetic undercooling in the scalar Stefan model. However, the “surface energy” of a superconducting material is found to take both positive and negative values, defining type I and type II superconductors respectively, leading to the conclusion that the free boundary model is only appropriate for type I superconductors.
The Cahn-Hilliard equation as degenerate limit of the phase-field equations
Authors: Stoth Barbara E. E.
Published: December 2016

We show that the Cahn-Hilliard equation occurs as a special scaling limit of the phase-field equation.
On statically admissible stress fields for a plane masonry-like structure
Authors: Angelillo Maurizio , Rosso Fabio
Published: December 2016

Explicit and directly verifiable nonlocal conditions for the existence of a statically admissible stress field in an ideal plane body that does not support tension in the absence of body forces are presented. These conditions are sufficient for nonconvex bodies and become necessary and sufficient restricting to convex bodies and to loads different from zero at any point of the boundary.
The vibration of an elastic dielectric with piezoelectromagnetism
Authors: Yang J. S. , Wu X. Y.
Published: December 2016

This paper presents a few results on the free vibration of a finite elastic dielectric with linear piezoelectromagnetism. Following the proof of selfadjointness, the orthogonality of modes corresponding to different frequencies is proved. A variational principle is given in Rayleigh quotient form for the natural frequency. The variational principle is mixed in the sense that all field variables can be varied independently, and it can be used to generate other variational principles.
Thermomechanics and the formulation of the Stefan problem for fully faceted interfaces
Authors: Gurtin Morton E. , Matias José
Published: December 2016

This paper develops a thermomechanics of two-phase heat conductors in which the interface between phases is fully faceted. The theory is based on balance of forces, balance of energy, and growth of entropy in conjunction with constitutive equations for the interface; and the chief result is a free-boundary problem of Stefan type in which the classical interface condition

u
=
0

u = 0

is replaced by a condition relating the integral of

u
u

over each facet to the normal velocity of that facet.
Integral equations of the first kind in plane elasticity
Authors: Constanda Christian
Published: December 2016

A modified single layer potential is used to solve the interior and exterior Dirichlet problems of plane strain by means of integral equations of the first kind for all smooth boundary curves, including those on which the classical method fails to operate.
On the exponential stability of linear viscoelasticity and thermoviscoelasticity
Authors: Liu Zhuangyi , Zheng Songmu
Published: December 2016

The exponential stability of the semigroup associated with one-dimensional linear viscoelastic and thermoviscoelastic equations with several types of boundary conditions is proved for a class of kernel functions, including the weakly singular kernels.
Turing bifurcation in nonlinear competition models with delay
Authors: Roy Choudhury S. , Fosser C.
Published: December 2016

Turing instability in reaction-diffusion and predator-prey models including diffusion and Volterra-type distributed delays in the interspecies interaction terms is considered. For general functional forms of the reaction terms/prey birth rate-predator death rate, and delays modeled by the “weak” generic kernel

a
exp
⁡

(
−
a
U
)

a \exp \left ( - aU \right )

and the “strong” generic kernel

a
2

U
exp
⁡

(
−
a
U
)

{a^2}U \exp \left ( - aU \right )

, the necessary and sufficient conditions for Turing instability are derived and are found to be significantly different from the classical conditions with no delay. The structure of the resulting Turing space, where steady states may be diffusionally driven unstable initiating spatial patterns, is delineated for four specific models, and compared to the corresponding regimes in the absence of delay. An alternative bifurcation-theoretic derivation of the boundary of the Turing-unstable domain is also presented.
Unsteady asymptotic solutions of the two-dimensional Euler equations
Authors: Srinivasan Radhakrishnan
Published: December 2016

A technique is described for deducing a class of unsteady asymptotic solutions of the two-dimensional Euler equations. In contrast to previously known analytical results, the vorticity function

[

ω

(

x
,
y
,
t

)

]

\left [ {\omega \left ( {x, y, t} \right )} \right ]

for these solutions has a complicated dependence on the spatial coordinates

(

x
,
y

)

\left ( {x, y} \right )

and time

(
t
)

\left ( t \right )

. The results obtained are in implicit form and are valid in those regions of space and time where

t
ω
→

o
+

t\omega \to {o^ + }

or

t
ω
→
+
∞

t\omega \to + \infty

. These asymptotic solutions may be split into an unsteady, two-dimensional and irrotational basic flow and a disturbance that is strongly nonlinear at appropriate locations within the domain of validity. The generality and complexity of these solutions make them theoretically interesting and possibly useful in applications.
A comparison of time domain boundary conditions for acoustic waves in wave guides
Authors: Banks H. T. , Propst G. , Silcox R. J.
Published: December 2016

We consider several types of boundary conditions in the context of time domain models for acoustic waves. Experiments with four different duct terminations (hardwall, free radiation, foam, wedge) were carried out in a wave duct from which reflection coefficients over a wide frequency range were measured. These reflection coefficients are used to estimate parameters in the time domain boundary conditions, and a comparison of the relative merits of the models in describing the data is presented. Boundary conditions that yield a good fit of the model to the experimental data were found for all duct terminations except the wedge.
Solutions for an infinite compressible nonlinearly elastic body under a line load
Authors: Warne Paul G. , Polignone Debra A.
Published: December 2016

The axisymmetric deformation of a nonlinearly elastic isotropic compressible infinite elastic body subjected to a concentrated vertical line load is considered. We first derive the solution to this problem within the context of the linear theory of elasticity. We then obtain the governing equations for the nonlinear problem via the Principle of Stationary Potential Energy, and use these equations to obtain classes of compressible finite elasticity solutions for the line load problem. Finally, a comparison with finite anti-plane shear of compressible isotropic materials is made.
Transient response of an impulsively loaded plastic string on a plastic foundation
Authors: Mihăilescu-Suliciu M. , Suliciu I. , Wierzbicki T. , Hoo Fatt M. S.
Published: December 2016

The problem of an impulsive loading of a long rigid-plastic string resting on a rigid-plastic foundation is studied. A closed form solution is obtained by disregarding the longitudinal motion and considering an arbitrarily large transversal motion. Expressions for the final shape of the string are derived in terms of the magnitude of the applied impulse. It is found that the stress and the foundation reaction force are not uniquely determined, while the shape of the string is.
Similarity solutions to rotating Couette flow of non-Newtonian fluids in the presence of a magnetic field
Authors: Pascal J. P. , Pascal H.
Published: December 2016

We study the rotating Couette flow of conducting power law fluids in the presence of a magnetic field. We analyze the coupled effects of the rheology and the magnetic field on the angular velocity and shear stress distributions for the case when an infinite long cylinder rotates in an unbounded fluid. For shear thickening fluids our exact similarity solutions exhibit traveling wave characteristics determining the existence of a moving shear front. We investigate the electrorheological effect on the propagation of the shear disturbances front.
Adiabatic invariants for strongly nonlinear dynamical systems described with complex functions
Authors: Cveticanin L.
Published: December 2016

In this paper the adiabatic invariants for strongly nonlinear dynamical systems with two degrees of freedom described by complex functions are obtained. The method [1] developed for dynamical systems with one degree of freedom is extended to systems with two degrees of freedom. The method is based on Noether’s theory and the use of Krylov-Bogolubov-Mitropolski (KBM) and elliptic-Krylov-Bogolubov (EKB) asymptotic techniques. The adiabatic invariants for two types of strong nonlinearities are constructed: the pure cubic nonlinearity and quasi-cubic nonlinearity. The adiabatic invariants are used to obtain the approximate solution to the equations of motion.
On the dual boundary conditions of the fourth derivative operators
Authors: Yao Peng-Fei
Published: December 2016

A dual relationship between the boundary condition of the fourth derivative operator
\[

A
u
=

∂
4

u

∂

x
4

Au = \frac {{{\partial ^4}u}}{{\partial {x^4}}}

\]
is established and examined in this paper. Some dual properties determined by the dual boundary conditions are also considered.
On stiffness maximization of variable thickness sheet with unilateral contact
Authors: Petersson J.
Published: December 2016

The problem of maximizing the stiffness of a linearly elastic sheet, in unilateral contact with a rigid frictionless support, is considered. The design variable is the thickness distribution, which is subject to an isoperimetric volume constraint and upper and lower bounds. The bounds may vary over the domain of the sheet, and the lower one is allowed to be zero, hence giving the possibility of obtaining topology information about an optimal design.
Derivative of a function of a nonsymmetric second-order tensor
Authors: Balendran B. , Nemat-Nasser Sia
Published: December 2016

Exact explicit expressions are obtained for an isotropic tensor-valued function of a nonsymmetric second-order tensor, and its derivative, without resort to eigenvector calculations. These are then used to derive explicit expressions for the material time derivative of the general strain measures in terms of the deformation rate tensor.
On existence of periodic orbits for the FitzHugh nerve system
Authors: Treskov S. A. , Volokitin E. P.
Published: December 2016

Applying bifurcation theory, we construct various phase portraits of the FitzHugh differential system and describe the set of parameters for which this system has periodic solutions.
Stability of a linear integro-differential equation with periodic coefficients
Authors: Drozdov Aleksey D. , Gil Michael I.
Published: December 2016

Stability of a linear integro-differential equation with periodic coefficients is studied. Such an equation arises in the dynamics of thin-walled viscoelastic elements of structures under periodic compressive loading. The equation under consideration has a specific peculiarity which makes its analysis difficult: in the absence of the integral term it is only stable, but not asymptotically stable. Therefore, in order to derive stability conditions we have to introduce some specific restrictions on the behavior of the kernel of the integral operator. These restrictions are taken from the analysis of the relaxation measures for a linear viscoelastic material.
The initial-value problem for the Kelvin-Helmholtz instabilities of high-velocity and magnetized shear layers
Authors: Choudhury S. Roy
Published: December 2016

The general initial-value problem for the linear Kelvin-Helmholtz instability of arbitrarily compressible velocity shear layers is considered for both the unmagnetized and magnetized cases. The time evolution of the physical quantities characterizing the layer is treated using Laplace transform techniques. Singularity analysis of the resulting equations using Fuchs-Frobenius theory yields the large-time asymptotic solutions. The instability is found to remain, within the linear theory, of the translationally convective or shear type. No onset of rotational or vortex motion, i.e., formation of “coherent structures” occurs.
Mapping flat cracks onto penny-shaped cracks, with application to somewhat circular tensile cracks
Authors: Martin P. A.
Published: December 2016

Consider a three-dimensional homogeneous isotropic elastic solid containing a flat pressurized crack,

Ω
\Omega

. The problem of finding the resulting stress distribution can be reduced to a hypersingular integral equation over

Ω
\Omega

for the crack-opening displacement. Here, this equation is transformed into a similar equation over a circular region

D
D

, using a conformal mapping between

Ω
\Omega

and

D
D

. This new equation is then regularized analytically by using an appropriate expansion method (Fourier series in the azimuthal direction and series of orthogonal polynomials in the radial direction). Analytical results for regions that are approximately circular are also obtained. The method will generalize to other scalar problems and to vector problems (such as shear loading of the crack).
Symmetric and unsymmetric buckling of circular arches
Authors: Dickey R. W. , Roseman Joseph J.
Published: December 2016

A nonlinear geometrically exact inextensible elastica theory is used to derive a mathematical system which models a clamped circular arch of central angle

2
α

2\alpha

under the action of a vertical force field of amplitude

P
P

(e.g., gravity). The equilibria of the arch are studied for various values of

α
,
0
>
α
>
π

\alpha , 0 > \alpha > \pi

. The existence of a solution of symmetric form for all fixed values of

P
P

and

α
\alpha

is proved analytically by arguments based on variational principles. Numerical solutions are calculated for a variety of choices of

α
\alpha

, and in each case buckling (nonuniqueness) is shown to occur when

P
P

is sufficiently large. In some cases, both symmetric and unsymmetric configurations are found, but each unsymmetric configuration obtained is found to be an unstable equilibrium, having energy greater than that of the symmetric configuration. Implications concerning the relative strengths and weaknesses of the various arches are discussed.
Stochastic Radon operators in porous media hydrodynamics
Authors: Christakos George , Hristopulos Dionissios T.
Published: December 2016

A space transformation approach is established to study partial differential equations with space-dependent coefficients modelling porous media hydrodynamics. The approach reduces the original multi-dimensional problem to the one-dimensional space and is developed on the basis of Radon and Hilbert operators and generalized functions. In particular, the approach involves a generalized spectral decomposition that allows the derivation of space transformations of random field products. A Plancherel representation highlights the fact that the space transformation of the product of random fields inherently contains integration over a “dummy” hyperplane. Space transformation is first examined by means of a test problem, where the results are compared with the exact solutions obtained by a standard partial differential equation method. Then, exact solutions for the flow head potential in a heterogeneous porous medium are derived. The stochastic partial differential equation describing three-dimensional porous media hydrodynamics is reduced into a one-dimensional integro-differential equation involving the generalized space transformation of the head potential. Under certain conditions the latter can be further simplified to yield a first-order ordinary differential equation. Space transformation solutions for the head potential are compared with local solutions in the neighborhood of an expansion point which are derived by using finite-order Taylor series expansions of the hydraulic log-conductivity.
On the existence of steady convex solutions to the regularized evolution problem of interfaces in the plane
Authors: Rosati M. , Vergara Caffarelli G.
Published: December 2016

In this paper we study some questions arising in the area of multiphase thermomechanics with interfacial structure. In particular, we prove existence and uniqueness results for steady convex solutions to the regularized problem of interfaces in the plane.
Unsteady perturbed flow at low Mach number of a viscous compressible fluid
Authors: Ferrari Carlo
Published: December 2016

The problem of the unsteady perturbed two-dimensional flow at low Mach number of a viscous compressible fluid is studied taking the relation between the stress and deformation rates tensors that was obtained and applied in [1] and [3]. It is shown that the system of equations describing the phenomenon is totally hyperbolic and therefore the perturbations in any point

P
P

of the field are propagated by means of waves corresponding to four characteristic surfaces passing through

P
P

. The displacement and propagation velocities of these waves are determined as well as their dependence on the orientation of their front in

P
P

; it is shown besides that the discontinuity vector across the waves has components both longitudinal and transversal. The variation laws of the fluid velocities both on the characteristic surfaces and along their bicharacteristics are determined, which allows us to solve the Cauchy problem with a “step-by-step” method.
Constructing asymptotic series for probability distributions of Markov chains with weak and strong interactions
Authors: Khasminskii R. Z. , Yin G. , Zhang Q.
Published: December 2016

Many applications arise in manufacturing systems, and queueing network problems involve Markov chains having slow and fast components. These components are coupled through weak and strong interactions. The main goal of this work is to study asymptotic properties for the probability distribution of the aforementioned Markov chains. Explicit construction of series expansions, consisting of regular part and boundary layer part or singular part, are developed by means of singular perturbation methods. The regular part is obtained by solving algebraic-differential equations, and the singular part is derived via solution of differential equations. One of the key points in the constructions is to select appropriate initial conditions. This is done by taking into consideration the regular part and the singular part together with their interactions. It is shown that the singular part decays exponentially fast. Analysis of residue is carried out, and the error bound for the remainder terms is ascertained.
The volume-preserving motion by mean curvature as an asymptotic limit of reaction-diffusion equations
Authors: Golovaty Dmitry
Published: December 2016

The asymptotic behavior of a nonlocal Ginzburg-Landau equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Subscript t Superscript epsilon Baseline equals normal upper Delta u Superscript epsilon Baseline minus StartFraction 1 Over epsilon squared EndFraction upper W prime left-parenthesis u Superscript epsilon Baseline right-parenthesis plus StartFraction 1 Over epsilon EndFraction g left-parenthesis u Superscript epsilon Baseline right-parenthesis lamda Superscript epsilon">

u
t
ε

=
Δ

u
ε

−

1

ε
2

W
′

(

u
ε

)

+

1
ε

g

(

u
ε

)

λ
ε

u_t^\varepsilon = \Delta {u^\varepsilon } - \frac {1}{{{\varepsilon ^2}}}W’\left ( {{u^\varepsilon }} \right ) + \frac {1}{\varepsilon }g\left ( {{u^\varepsilon }} \right ){\lambda ^\varepsilon }

\]
is studied when the small parameter

ε
\varepsilon

tends to zero. Here a Lagrange multiplier

λ
ε

{\lambda ^\varepsilon }

is introduced into the equation to enforce the conservation of mass. An energy-estimates approach is used to show that a limiting solution can be characterized by moving interfaces. It is further shown that the asymptotic limit of solutions of the nonlocal Ginzburg-Landau equation is a weak solution of the nonlocal, mass-preserving mean curvature flow. The weak solutions are constructed within a framework of the theory of viscosity solutions. In addition, the results describing interactions between the interfaces are obtained.
On the classification of solutions to the zero-surface-tension model for Hele-Shaw free boundary flows
Authors: Richardson S.
Published: December 2016

We add a possibility to the catalogue of scenarios given by Hohlov and Howison for the behavior of Hele-Shaw free boundary flows when surface tension is assumed to be absent: suction from an initially connected blob of fluid can result in regions of fluid being left marooned some distance from the suction point.
Flows through nonhomogeneous porous media in an isolated environment
Authors: Yin Jingxue , Gao Wenjie
Published: December 2016

The nonhomogeneous gas or fluid flowing through a nonhomogeneous porous medium is studied. An interesting phenomenon is discussed which shows that the state of the flow is not affected by the surrounding environment if some hypotheses are made on the porosity of the gas, the viscosity, and the permeability of the medium. Such a state is called an isolated environment. The conditions under which the state of the gas depends on the surrounding environment are also discussed.
An existence theorem for the multi-fluid Stokes problem
Authors: Nouri A. , Poupaud F. , Demay Y.
Published: December 2016

Time-dependent flows of viscous incompressible immiscible fluids are studied in the limit of vanishing Reynolds numbers. The velocity fields associated to each fluid solve Stokes equations in a time-dependent domain. Classical immiscibility conditions on the varying fluids interfaces are taken into account by a new formulation of the problem: the viscosity solves a transport equation and the velocity field solves a Stokes problem with this nonconstant viscosity. This formulation, based on the use of a pseudoconcentration function, has already been used for numerical computations (see [9] and [4]). For this nonlinear system of equations, existence of solutions is proved, using the Schauder fixed point theorem and the concept of renormalized solutions introduced recently by R. J. DiPerna and P. L. Lions.
The singular limit of a hyperbolic system and the incompressible limit of solutions with shocks and singularities in nonlinear elasticity
Authors: Choksi Rustum
Published: December 2016

Discontinuous solutions with shocks for a family of almost incompressible hyperelastic materials are studied. An almost incompressible material is one whose deformations are not a priori constrained but whose stress response reacts strongly (of order

ε

−
1

{\varepsilon ^{ - 1}}

) to deformations that change volume. The material class considered is isotropic and admits motions that are self-similar, exhibit cavitation, and are energy minimizing. For the initial-value problem when considering the entire material, the solutions converge (as

ε
\varepsilon

tends to zero) to an isochoric solution of the limit (incompressible) system with the corresponding arbitrary hydrostatic pressure being the singular limit of the pressures in the almost incompressible materials. The shocks, if they exist, disappear: their speed tends to infinity and their strength tends to zero.
The evaluation of certain infinite integrals involving products of Bessel functions: a correlation of formula
Authors: Hanson Mark T. , Puja Igusti W.
Published: December 2016

This analysis evaluates certain infinite integrals continuing products of Bessel functions of integer order, an exponential and a power. The integrals considered here have been previously evaluated in the literature in two different forms. In one instance they have been written in terms of complete elliptic integrals of the first, second, and third kind. Some of these integrals have also been evaluated in terms of a Legendre function of the second kind and a complete elliptic integral of the third kind. A recent result in elasticity obtained by the authors has led to a new form for the evaluations of these integrals. The integrals are still evaluated in terms of complete elliptic integrals; however, a new modulus (and parameter for the complete elliptic integral of the third kind) is used. The new form used for the complete elliptic integral of the third kind allows the integral evaluations to be written in a more convenient form than previously given. The new form for the complete elliptic integral of the third kind is also utilized in the evaluations using the Legendre function of the second kind. The new forms to the integral evaluations derived presently are correlated with existing results in the literature.
Electrically charged conducting drops revisited
Authors: Feng James Q.
Published: December 2016

Since its publication in 1882, Rayleigh’s work on electrically charged conducting drops has been widely quoted, but its rigorous derivation has not been given in the literature. By means of the domain perturbation technique, this work presents a rigorous derivation of Rayleigh’s results, following his approach with Lagrange’s equation. With the systematic procedure, it becomes explicit that the first-order surface deformations result in a deviation of the drop surface potential of only second-order significance. Besides providing mathematical details, this work also reveals an apparent error in Rayleigh’s original result for two-dimensional (cylindrical) drops.
Circularly symmetric deformation of shallow elastic membrane caps
Authors: Johnson Kurt N.
Published: December 2016

We consider shallow elastic membrane caps that are rotationally symmetric in their undeformed state, and investigate their deformation under small uniform vertical pressure and a given boundary stress or boundary displacement. To do this we use the small-strain theory developed by Bromberg and Stoker, Reissner, and Dickey. We deal with the two-parameter family of membranes whose undeformed configuration is given in cylindrical coordinates as
\[

z

(
x
)

=
C

(

1
−

x
γ

)

,

(
1
)

z\left ( x \right ) = C\left ( {1 - {x^\gamma }} \right ), \qquad \left ( 1 \right )

\]
which includes the spherical cap as a special case (

γ
=
2

\gamma = 2

and

C
C

small). We show that if

γ
>
4

/

3

\gamma > 4/3

then a circularly symmetric deformation is possible for any positive boundary stress (or any boundary displacement) and any positive pressure, but if

1
>
γ
>
4

/

3

1 > \gamma > 4/3

then no circularly symmetric deformation is possible if the stress and pressure are positive and small (or for non-positive boundary displacement and small positive pressure).
Exponential stability of the Kirchhoff plate with thermal or viscoelastic damping
Authors: Liu Zhuangyi , Zheng Songmu
Published: December 2016

The exponential stability of the semigroup associated with the Kirchhoff plate with thermal or viscoelastic damping and various boundary conditions is proved. This improves the corresponding results by Lagnese by showing that the semigroup is still exponentially stable even without feedback control on the boundary. The proof is essentially based on PDE techniques and the method is remarkable in the sense that it also throws light on applications to other higher-dimensional problems.
Stokes flow around a bend
Authors: Khuri S. A. , Wang C. Y.
Published: December 2016

The matched eigenfunction expansion method is used for solving Stokes flow around a channel bend. The flow region is decomposed into rectangular and cylindrical subregions. This enables the stream function to be represented by means of an expansion of Papkovich-Fadle eigenfunctions in each of these two subregions. The coefficients in these expansions are determined by imposing weak

C

3

C^{3}

continuity of the stream function across subregion interfaces and then taking advantage of the biorthogonality conditions in both cylindrical and rectangular coordinates.
On the computation of zeroes of 𝐽_{𝑛}(𝑧)-𝑖𝐽_{𝑛+1}(𝑧)=0
Authors: MacDonald D. A.
Published: December 2016

The roots of the equation
\[

J
n
2

(
z
)
+

J

n
+
1

2

(
z
)
=
0

J_n^2(z) + J_{n + 1}^2(z) = 0

\]
, in which

n
n

is a positive integer or zero, are of interest to the specialist in wave reflection from multi-sloped beaches [1]. This note shows how to obtain accurate roots of the equation when

n
n

is not large.
On the stability for linear viscoelastic solids
Authors: Giorgi C. , Lazzari B.
Published: December 2016

The stability and asymptotic behaviour of solutions to the dynamical initial past-history problem within the theory of linear viscoelasticity is investigated. First, a family of free energies is introduced as a Liapunov functional via the energy method. Then, emphasizing the role of thermodynamic inequalities, the asymptotic stability property is derived by means of some original a priori integral estimates of the solution.
Analysis of hysteretic reaction-diffusion systems
Authors: Chiu Chichia , Walkington Noel
Published: December 2016

In this paper, we consider a mathematical model motivated by patterned growth of bacteria. The model is a system of differential equations that consists of two sub-systems. One is a system of ordinary differential equations and the other one is a reaction-diffusion system. Pattern formation in this model is caused by an initial instability of the ordinary differential equations. However, nonlinear coupling to the reaction-diffusion system stabilizes the ordinary differential equations resulting in stationary long-time behavior. We establish existence, uniqueness, and characterize long-time behavior of the solutions.
Some boundary value problems and models for coupled elastic bodies
Authors: Arango J. A. , Lebedev L. P. , Vorovich I. I.
Published: December 2016

A new class of boundary value problems is presented. These problems are described by related equations of different nature and possess such properties as the appearance of highest derivatives in boundary conditions. Such problems appear to model common engineering constructions composed of elements of different mechanical natures like plates, shells, membranes, or three-dimensional elastic bodies. Two problems are considered in detail, namely a three-dimensional elastic body with flat elements taken as a plate or a membrane, and a plate-membrane system. The existence-uniqueness theorems for the corresponding boundary value problems are established and an application of a conforming FEM is justified.
Nuclei of strain at three-dimensional bimaterial interfaces
Authors: Markenscoff X. , Ye W.
Published: December 2016

When nuclei of strain approach the interface of two materials, the displacement fields may not be unique and may depend on the direction from which the interface is approached. For example, the displacement fields of a center of dilatation at the interface of two materials are not unique and depend on the direction of approach to the interface. To avoid misunderstanding, it can be stressed that each of the two fields is continuous at the interface. In this paper, we show that there are 12 independent displacement functions of second-order singularities uniquely defined at an interface. The limits of all other nuclei of strain at the interface are linear combinations of these 12 independent displacement functions.
The complete classification of asymptotic behavior for bounded cooperative Lotka-Volterra systems with the assumption (SM)
Authors: Jiang J. F.
Published: December 2016

Assume that the

n
n

-dimensional Lotka-Volterra system is cooperative with the assumption

(
S
M
)

:

a

i
i

>
0
,

a

i
j

>
0

\left ( SM \right ) : {a_{ii}} > 0, {a_{ij}} > 0

for all

i
≠
j

i \ne j

, and all solutions of the system are bounded. Then we give a complete classification of the behavior of the solutions. This classification does not require any restriction on the auto-increase coefficients.
On the feasibility of determining light-source direction from an image
Authors: Chojnacki Wojciech , Brooks Michael J. , Gibbins Daniel
Published: December 2016

Various computational techniques have been developed that perform reasonably well in inferring shape from shading. However, these techniques typically require substantial prerequisite information if they are to evolve an estimate of surface shape. It is therefore interesting to consider how depth might be inferred from shading information without prior knowledge of various scene conditions. One approach has been to undertake a pre-processing step of estimating the light-source direction, thereby providing input to the computation of shape from shading. In this paper, we present evidence that a versatile light-source-direction estimator is unattainable.
A regularizing effect of nonlinear transport equations
Authors: Otto Felix
Published: December 2016

We consider the semigroup on

L
1

(

R

n

)

{L^1}\left ( {\mathbb {R}^n} \right )

defined by the nonlinear transport equation for the scalar

s
s

,
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="partial-differential Subscript t Baseline s plus d i v left-parenthesis f left-parenthesis s right-parenthesis u right-parenthesis equals 0 i n left-parenthesis 0 comma normal infinity right-parenthesis times double-struck upper R Superscript n">

∂
t

s
+
d
i
v

(
f

(
s
)

u
)

=
0

i
n

(
0
,
∞
)

×

R

n

{\partial _t}s + div\left ( f\left ( s \right )u \right ) = 0 \qquad in \left ( 0, \infty \right ) \times {\mathbb {R}^n}

\]
for given velocity field

u
u

. We show that this nonlinear semigroup is Hölder continuous for

t
>
0

t > 0

in the uniform operator topology, provided the graph of

f
f

has no linear segments. This continuity property—which expresses a regularizing effect of the nonlinearity in the transport equation—is robust with respect to the spatial behaviour of the time-independent velocity field

u
u

.
Asymptotic methods for magnetohydrodynamic instability
Authors: Vishik Misha , Friedlander Susan
Published: December 2016

A sufficient condition for instability is obtained for the linearized equations of ideal magnetohydrodynamics. The results are proved by studying the full asymptotic expansion for the evolution operator using oscillatory integrals. It is shown that the growth rate of the evolution operator is bounded from below by the growth rate of an operator given by a system of local hyperbolic PDEs.
Asymptotic stability and global existence in thermoelasticity with symmetry
Authors: Jiang S. , Muñoz Rivera J. E. , Racke R.
Published: December 2016

First we prove an exponential decay result for solutions of the equations of linear, homogeneous, isotropic thermoelasticity in bounded regions in two or three space dimensions if the rotation of the displacement vanishes. As a consequence, we describe the decay in radially symmetrical situations, and in a cylinder in

R

3

{\mathbb {R}^{3}}

. Then we establish the global existence of solutions to the corresponding nonlinear equations for small smooth initial data and a certain class of nonlinearities.
Equilibrium vortex configurations in domains with boundary
Authors: Miller Kenneth G.
Published: December 2016

Given a stable configuration of point vortices for steady two-dimensional inviscid, incompressible fluid flow in a domain

D
D

, it is shown that there is another stable configuration of stationary vortices in

D
D

with vortices near the original vortices plus additional vortices near any points on the boundary where the speed of the original flow is a nonzero relative minimum.
Variational problems on flows of diffeomorphisms for image matching
Authors: Dupuis Paul , Grenander Ulf , Miller Michael I.
Published: December 2016

This paper studies a variational formulation of the image matching problem. We consider a scenario in which a canonical representative image

T
T

is to be carried via a smooth change of variable into an image that is intended to provide a good fit to the observed data. The images are all defined on an open bounded set

G
⊂

R
3

G \subset {R^3}

. The changes of variable are determined as solutions of the nonlinear Eulerian transport equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartFraction d eta left-parenthesis s semicolon x right-parenthesis Over d s EndFraction equals v left-parenthesis eta left-parenthesis s semicolon x right-parenthesis comma s right-parenthesis comma eta left-parenthesis tau semicolon x right-parenthesis equals x comma left-parenthesis 0.1 right-parenthesis">

d
η

(
s
;
x
)

d
s

=
v

(
η

(
s
;
x
)

,
s
)

,

η

(
τ
;
x
)

=
x
,

(
0.1
)

\frac {{d\eta \left ( s; x \right )}}{{ds}} = v\left ( \eta \left ( s; x \right ),s \right ), \qquad \eta \left ( \tau ; x \right ) = x, \qquad \left ( 0.1 \right )

\]
with the location

η

(
0
;
x
)

\eta \left ( 0; x \right )

in the canonical image carried to the location

x
x

in the deformed image. The variational problem then takes the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="arg min Underscript v Endscripts left-bracket double-vertical-bar v double-vertical-bar squared plus integral Underscript upper G Endscripts StartAbsoluteValue upper T o eta left-parenthesis 0 semicolon x right-parenthesis minus upper D left-parenthesis x right-parenthesis EndAbsoluteValue squared d x right-bracket comma left-parenthesis 0.2 right-parenthesis">

arg
⁡

min
v

[

‖
v
‖

2

+

∫
G

|

T
o
η

(

0
;
x

)

−
D

(
x
)

|

2

d
x

]

,

(

0.2

)

\arg \min \limits _v {\kern -0.1pt} \left [ {{{\left \| v \right \|}^2} + \int _G {{{\left | {T o \eta \left ( {0; x} \right ) - D\left ( x \right )} \right |}^2}dx} } \right ], \qquad \left ( {0.2} \right )

\]
where

‖
v
‖

\left \| v \right \|

is an appropriate norm on the velocity field

v
(
⋅
,
⋅
)

v( \cdot , \cdot )

, and the second term attempts to enforce fidelity to the data.
Gauss-Chebyshev quadrature formulae for strongly singular integrals
Authors: Korsunsky Alexander M.
Published: December 2016

This paper presents some explicit results concerning an extension of the mechanical quadrature technique, namely, the Gauss-Jacobi numerical integration scheme, to the class of integrals whose kernels exhibit second order of singularity (i.e., one degree more singular than Cauchy). In order to ascribe numerical values to these integrals they must be understood in Hadamard’s finite-part sense. The quadrature formulae are derived from those for Cauchy singular integrals.
A nonlinear elliptic boundary value problem related to corrosion modeling
Authors: Vogelius Michael , Xu Jian-Ming
Published: December 2016

We study a nonlinear boundary value problem arising from electrochemistry. The essential difficulties are due to the strong nonlinear nature of part of the boundary condition. This part of the boundary condition is of an exponential type and is normally in the corrosion literature associated with the names of Butler and Volmer. We examine the questions of existence and uniqueness of solutions to this boundary value problem. In a numerical example we compare the behaviour of the solutions to the nonlinear problem with the behaviour of the solutions to a corresponding linearized problem. In contrast to earlier studies we put a major emphasis on studying parameter values that may be relevant for the case in which part of the boundary is in a transition to passivity—in practice most likely because it is nearly covered by an oxide layer.
Stochastic methods for the prediction of complex multiscale phenomena
Authors: Glimm James , Sharp David
Published: December 2016

The purpose of this paper is to develop a general framework for the prediction of complex multiscale phenomena and to illustrate this framework through comparison to two examples of current interest to the authors. Prediction involves a two-step process of inverse prediction to describe the system, given observations of its behavior, and forward prediction, to specify system behavior, given its description.
New perspectives in turbulence
Authors: Chorin Alexandre J.
Published: December 2016

An analysis of the mean velocity profile in the intermediate region of wall-bounded turbulence shows that the well-known von Kármán-Prandtl logarithmic law of the wall must be jettisoned in favor of a power law. An analogous analysis of the local structure of turbulence shows that the Kolmogorov-Obukhov scaling of the second and third structure functions is exact in the limit of vanishing viscosity while, in the same limit, higher-order moments fail to exist. These results rely on advanced similarity methods and on vanishing-viscosity asymptotics, and are consistent with a near-equilibrium theory of turbulence of which a new version is presented.
Decay rates of solutions to a von Kármán system for viscoelastic plates with memory
Authors: Muñoz Rivera Jaime E. , Perla Menzala Gustavo
Published: December 2016

We consider the dynamical von Kármán equations for viscoelastic plates under the presence of a long-range memory. We find uniform rates of decay (in time) of the energy, provided that suitable assumptions on the relaxation functions are given. Namely, if the relaxation decays exponentially, then the first-order energy also decays exponentially, When the relaxation

g
g

satisfies
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="minus c 1 g Superscript 1 plus StartFraction 1 Over p EndFraction Baseline left-parenthesis t right-parenthesis less-than-or-equal-to g prime left-parenthesis t right-parenthesis less-than-or-equal-to minus c 0 g left-parenthesis t right-parenthesis Superscript 1 plus StartFraction 1 Over p EndFraction Baseline comma 0 less-than-or-equal-to g left-parenthesis t right-parenthesis less-than-or-equal-to c 2 g Superscript 1 plus StartFraction 1 Over p EndFraction Baseline left-parenthesis t right-parenthesis comma and">

−

c
1

g

1
+

1
p

(
t
)

≤

g
′

(
t
)

≤
−

c
0

g

(
t
)

1
+

1
p

,

0
≤
g

(
t
)

≤

c
2

g

1
+

1
p

(
t
)

,

and

- {c_1}{g^{1 + \frac {1}{p}}}\left ( t \right ) \le g’\left ( t \right ) \le - {c_0}g{\left ( t \right )^{1 + \frac {1}{p}}}, \qquad 0 \le g\left ( t \right ) \le {c_2}{g^{1 + \frac {1}{p}}}\left ( t \right ) , \: \textrm {and}

\]

\[

g
,

g

1
+

1
p

∈

L
1

(

R

)

with

p
>
2
,

g, {g^{1 + \frac {1}{p}}} \in {L^1}\left ( \mathbb {R} \right ) \textrm {with} \: p > 2 ,

\]
then the energy decays as

1

(
1
+
t
)

p

\frac {1}{\left ( 1 +t \right )^{p}}

. A new Liapunov functional is built for this problem.
On the periodic boundary value problem for impulsive parabolic equations
Authors: Bainov Drumi , Minchev Emil , Okoroafor Ikechukwu E.
Published: December 2016

This paper deals with the periodic boundary value problem for impulsive parabolic equations. A comparison result for impulsive differential inequalities is obtained. This result is applied to get a uniqueness criterion for the solutions of impulsive parabolic equations.
Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation
Authors: Toscani G.
Published: December 2016

We reckon the rate of exponential convergence to equilibrium both in relative entropy and in relative Fisher information, for the solution to the spatially homogeneous Fokker-Planck equation. The result follows by lower bounds of the entropy production which are explicitly computable. Second, we show that the Gross’s logarithmic Sobolev inequality is a direct consequence of the lower bound for the entropy production relative to Fisher information. The entropy production arguments are finally applied to reckon the rate of convergence of the solution to the heat equation towards the fundamental one in various norms.
Oscillations in one-dimensional elasticity with surface energy
Authors: Fonseca Irene , Schaeffer Jack , Shvartsman Mikhail M.
Published: December 2016

The characterization of the oscillatory behavior of solutions of a semilinear equation in one space dimension is obtained. In this work the model equation for a material undergoing a phase transition encompasses a surface energy term and first-order memory effects.
A class of inverse problems for viscoelastic material with dominating Newtonian viscosity
Authors: Janno Jaan , von Wolfersdorf Lothar
Published: December 2016

Memory kernels in linear stress-strain relations involving a Newtonian viscosity are identified by solving a class of inverse problems. The inverse problems are reduced to nonlinear Volterra integral equations of the first kind which in turn lead to corresponding Volterra equations of the second kind by differentiation. Applying the contraction principle with weighted norms we derive global (in time) existence, uniqueness and stability of the solution to the inverse problems under similar assumptions as for related inverse problems in heat flow.
Conservative energy discretization of Boltzmann collision operator
Authors: Preziosi L. , Rondoni L.
Published: December 2016

The paper deduces a kinetic model obtained introducing a discretization of the Boltzmann equation based on an equispaced distribution of allowed particle energies. The model obtained is a system of integro-differential equations with integration over suitable angular variables: one over the portion of the unit sphere between two parallels symmetric with respect to the equatorial plane perpendicular to the velocity of the field particle, and one over a unit circle. The model preserves mass, momentum and energy. Furthermore, there exists an

H
H

-functional describing trend toward an equilibrium state described by a Gaussian distribution. Particular attention is paid to the identification of a criterion which indicates the values of the discretization parameters.