bluuebunny/crossref_metadata_2025 huggingface dataset:
Asymptotic analysis of stochastic variational inequalities modeling an elasto-plastic problem with vanishing jumps
Authors: Bensoussan Alain , Jasso-Fuentes Héctor , Menozzi Stéphane , Mertz Laurent
Published: November 2019

In a previous work by the first author with J. Turi [Appl. Math. Optim. 58(1) (2008), 1–27], a stochastic variational inequality has been introduced to model an elasto-plastic oscillator with noise. A major advantage of the stochastic variational inequality is to overcome the need to describe the trajectory by phases (elastic or plastic). This is useful, since the sequence of phases cannot be characterized easily. In particular, when a change of regime occurs, there are numerous small elastic phases which may appear as an artefact of the Wiener process. However, it remains important to have informations on both the elastic and plastic phases. In order to reconcile these contradictory issues, we introduce an approximation of stochastic variational inequalities by imposing artificial small jumps between phases allowing a clear separation of the elastic and plastic regimes. In this work, we prove that the approximate solution converges on any finite time interval, when the size of jumps tends to 0.
Pricing perpetual American puts under multi-scale stochastic volatility
Authors: Chen Wen-Ting , Zhu Song-Ping
Published: November 2019

In this paper, we consider the problem of pricing perpetual American put options with volatility driven by two other processes. By using a perturbation approach, we obtain approximate but explicit closed-form pricing formulae for the option and optimal exercise prices, respectively, under a general multi-scale SV (stochastic volatility) model. A key feature of the expansion methodology employed here is to balance the two SV processes, while dealing with the free boundary conditions properly. It turns out that in the current formulae, the fast volatility factor does not play an explicit role, while the slow factor is quite crucial, a phenomenon that is shown to be quite reasonable through our discussions.
Uniform null controllability of a parabolic equation with rapidly oscillating periodic coefficients
Authors: Tebou Louis
Published: November 2019

We consider a parabolic equation with fast oscillating periodic coefficients, and an interior control in a bounded domain. First, we prove sharp convergence estimates depending explicitly on the initial data for the corresponding uncontrolled equation; these estimates are new in a bounded domain, and their proof relies on a judicious smoothing of the initial data. Then we use those estimates to prove that the original equation is uniformly null controllable, provided a carefully chosen extra vanishing interior control is added to that equation. This uniform null controllability result is the first in the multidimensional setting for parabolic equations with oscillating coefficients. Finally, we prove that the sequence of null controls converges to the optimal null control of the homogenized equation when the period tends to zero.
Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator
Authors: Yoshitomi Kazushi
Published: November 2019

We study inverse scattering problems for the singular rank-one perturbations of a selfadjoint operator. We obtain a necessary and sufficient condition for a given function to be the scattering phase shift of a singular rank-one perturbation of the operator.
Ruelle's lemma and Ruelle zeta functions
Authors: Wright Paul
Published: November 2019

In this article we prove an important inequality regarding the Ruelle operator in hyperbolic flows. This was already proven briefly by Mark Pollicott and Richard Sharp in a low dimensional case [Amer. J. Math. 120 (1998), 1019–1042], but we present a clearer proof of the inequality, filling in gaps and explaining the ideas in more detail, and extend the inequality to higher-dimensional flows. This inequality is necessary to prove a proposition about the analyticity of Ruelle zeta functions.
Rate of convergence of a two-scale expansion for some “weakly” stochastic homogenization problems
Authors: Le Bris Claude , Legoll Frédéric , Thomines Florian
Published: November 2019

We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of periodic coefficients.
Sharp asymptotics of the quasimomentum
Authors: Korotyaev Evgeny L.
Published: November 2019

We consider the Schrödinger operator with a periodic potential p on the real line. We assume that p belongs to the real Sobolev space Hm on the circle for some m≥−1. We determine the sharp asymptotics of the quasimomentum and the Titchmarsh–Weyl functions, the Bloch functions at high energy.
On homogenization of nonlinear Robin type boundary conditions for cavities along manifolds and associated spectral problems
Authors: Gómez D. , Pérez E. , Shaposhnikova T.A.
Published: November 2019

Let uε be the solution of the Poisson equation in a domain periodically perforated along a manifold γ=Ω∩{x1=0}, with a nonlinear Robin type boundary condition on the perforations (the flux here being O(ε−κ)σ(x,uε)), and with a Dirichlet condition on ∂Ω. Ω is a domain of Rn with n≥3, the small parameter ε, that we shall make to go to zero, denotes the period, and the size of each cavity is O(εα) with α≥1. The function σ involving the nonlinear process is a C1(Ω¯×R) function and the parameter κ∈R. Depending on the values of α and κ, the effective equations on γ are obtained; we provide a critical relation between both parameters which implies a different average of the process on γ ranging from linear to nonlinear. For each fixed κ a critical size of the cavities which depends on n is found. As ε→0, we show the convergence of uε in the weak topology of H1 and construct correctors which provide estimates for convergence rates of solutions. All this allows us to derive convergence for the eigenelements of the associated spectral problems in the case of σ a linear function.
Quasi-periodic solutions of the 2D Euler equation
Authors: Crouseilles Nicolas , Faou Erwan
Published: November 2019

We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles with compact support propagating over a stationary state depending on only one variable. The direction of propagation is orthogonal to this variable, and the support is concentrated on flat strips of the stationary state. The frequencies of the solution are given by the locally constant velocities associated with the stationary state.
On the time-periodic Stokes problem in domains with cylindrical outlets to infinity
Authors: Skujus M.
Published: November 2019

A time-periodic Stokes problem is studied in the domain with cylindrical outlets to infinity. A basis in the set of solutions to the homogeneous problem is constructed. This basis possesses several properties that are essential for the setting correct asymptotic conditions at infinity.
Asymptotic analysis of nonlinearly elastic shells “mixed approach”
Authors: Chacha Djamal Ahmed , Miloudi Madjda
Published: November 2019

The aim of this paper is to extend the results obtained by Miara [Arch. Ration. Mech. Anal. 142 (1998), 331–353] and Lods and Miara [Arch. Ration. Mech. Anal. 142 (1998), 335–374] on the asymptotic analysis of nonlinearly elastic shells to the nonhomogeneous anisotropic case. To this end, we use the Hellinger–Reissner variational principle.
Homogenization of the Reynolds equation in the radial face seals case
Authors: Nicolescu Bogdan N. , Petrescu Tudor C.
Published: November 2019

In this paper we obtain the Reynolds equation for the case of a Newtonian incompressible fluid with a stationary isothermal motion in a tribological system of radial face seals when one of the contact surfaces (the rotor) has an oscillatory motion around its equilibrium point. Moreover, it is supposed that this surface is rough. We also obtain the homogenized equation whose coefficients are given explicitly. Finally, we present numerical results for the homogenized equation.
Estimates in homogenization of degenerate elliptic equations by spectral method
Authors: Cardone G. , Pastukhova S.E. , Perugia C.
Published: November 2019

We study the homogenization of elliptic equations stated in L2-space with degenerate weight. Both coefficients of the differential operator and the weight are ε-periodic and highly oscillating as ε tends to zero. Under minimal hypotheses on the coefficients and the weight we prove estimates of order ε and ε2 for L2-norm of the difference between the exact solution and its appropriate approximations by L2-norm of the right-side function. The spectral method based on Bloch decomposition is used. In the case of nonunique solution provided that the weight is not regular we consider estimates for any of so-called variational solutions.
The dominant asymptotic term of solution to the Hamer equation
Authors: Soloviev A.A.
Published: November 2019

It is shown that the dominant asymptotic term of solution to the problem

ut+uux=K*u−u, u|t=0=u0,

where K(x)=(1/2)e−|x|, is a function u0(x,t)=2ζ(x,t)(1−∫−∞xζ(s,t) ds)−1

with ζ(x,t)=M0(h)ex2/4t/√4πt, M0(h)=∫−∞∞h(s) ds and h(x)=(1/2)u0(x)exp {−(1/2)∫−∞xu0(s) ds}, and the function u0(x,t) coincides with the principal asymptotic term of solution to the Burgers equation with initial function u0.
On a Vlasov–Euler system for 2D sprays with gyroscopic effects
Authors: Moussa Ayman , Sueur Franck
Published: November 2019

In this paper we introduce a PDE system which aims at describing the dynamics of a dispersed phase of particles moving into an incompressible perfect fluid, in two space dimensions. The system couples a Vlasov-type equation and an Euler-type equation: the fluid acts on the dispersed phase through a gyroscopic force whereas the latter contributes to the vorticity of the former.

First we give a Dobrushin-type derivation of the system as a mean-field limit of a PDE system which describes the dynamics of a finite number of massive pointwise particles moving into an incompressible perfect fluid. This last system is itself inferred from the paper “On the motion of a small body immersed in a two-dimensional incompressible perfect fluid”, accepted for publication in Bulletin de la SMF where the system for one massive pointwise particle was derived as the limit of the motion of a solid body when the body shrinks to a point with fixed mass and circulation.

Then we deal with the well-posedness issues including the existence of weak solutions. Next we exhibit the Hamiltonian structure of the system and finally, we study the behavior of the system in the limit where the mass of the particles vanishes.
Asymptotic equipartition of operator-weighted energies in damped wave equations
Authors: Goldstein Jerome A. , Reyes Guillermo
Published: November 2019

We prove an asymptotic energy equipartition result for abstract damped wave equations of the form

utt+2F(S)ut+S2u=0,

where S is a strictly positive self-adjoint operator and the damping operator F(S) is “small”. This means that under certain assumptions, the ratio of suitably modified kinetic and potential energies, K˜(t)/P˜(t), tends to 1 as t→∞ for all nonzero solutions u(t) of the equation. Here, K˜(t) and P˜(t) are conveniently weighted versions of the usual kinetic and potential energies of the associated undamped equation. Previous results, concerning the undamped case and the scalar-damped one, are particular cases. We propose an extension of the concepts of hyperbolicity and unitarity that allows one to consider the equipartition property in a more general setting. Some examples involving PDEs, as well as pseudo-differential equations, are given.
Spectral analysis and transport of energy density for an hyperbolic system with periodic oscillations
Authors: Petrini Milena
Published: November 2019

We deal with an hyperbolic degenerate system with periodic oscillations in the lower order term and principal part with characteristics of variable multiplicity. In the homogenization limit the effective system does not present a memory term, however it loses the property of energy conservation. A spectral analysis on the Bloch space is worked out for the system in some particular case of oscillating term. Through a decomposition in Bloch waves we determine the transport for the limiting energy density related to the solution a Cauchy problem with oscillatory initial data.
Asymptotic pyroelectricity and pyroelasticity in thermopiezoelectric plates
Authors: Miara Bernadette , Sejje Suárez Julian
Published: November 2019

We consider a three-dimensional body whose energy couples mechanic, electric and thermic effects. By using an asymptotic approach we establish the associated bi-dimensional dynamic model for a thermopiezoelectric plate. The computation of the new constitutive laws shows that pyroelectric effect (coupling of the electric field and the temperature) can appear in the limit 2D model even though the 3D dielectric displacement field does not present any coupling with the temperature. Pyrokinetic effect (coupling of elastic and temperature fields) is exhibited by the same way.
Two-scale convergence of periodic elliptic spectral problems with indefinite density function in perforated domains
Authors: Douanla Hermann
Published: November 2019

Spectral asymptotics of linear periodic elliptic operators with indefinite (sign-changing) density function is investigated in perforated domains with the two-scale convergence method. The limiting behavior of positive and negative eigencouples depends crucially on whether the average of the weight over the solid part is positive, negative or equal to zero. We prove concise homogenization results in all three cases.
Optimization of quasi-normal eigenvalues for 1-D wave equations in inhomogeneous media; description of optimal structures
Authors: Karabash Illya M.
Published: November 2019

The paper is devoted to optimization of resonances associated with 1-D wave equations in inhomogeneous media. The medium's structure is represented by a nonnegative function B. The problem is to design for a given α∈R a medium that generates a resonance on the line α+iR with a minimal possible modulus of the imaginary part. We consider an admissible family of media that arises in a problem of optimal design for photonic crystals. This admissible family is defined by the constraints 0≤b1≤B(x)≤b2 with certain constants b1,2. The paper gives an accurate definition of optimal structures that ensures their existence. We prove that optimal structures are piecewise constant functions taking only two extreme possible values b1 and b2. This result explains an effect recently observed in numerical experiments. Then we show that intervals of constancy of an optimal structure are tied to the phase of the corresponding resonant mode and write this connection as a nonlinear eigenvalue problem.
Asymptotic behavior of a generalization of the Caginalp phase-field system
Authors: Conti Monica , Dell'Oro Filippo , Miranville Alain
Published: November 2019

We discuss the asymptotic behavior of a generalized nonlinear Caginalp phase-field system, based on the theory of heat conduction of type III devised by Green and Naghdi. In the case of two nonlinearities of polynomial critical growth, we prove the existence of global attractors of optimal regularity.
Inverse obstacle problems with backscattering or generalized backscattering data in one or two directions
Authors: Christiansen T.J.
Published: November 2019

This paper is concerned with scattering by a smooth compact obstacle in Rd. The main results are that for certain classes of obstacles knowledge of the scattering amplitude in only one or two pairs of incident and reflected directions suffices to recover the Taylor series of a boundary defining function for the obstacle at a point. Thus certain obstacles with real analytic boundaries can be determined.
Periodic elliptic operators with asymptotically preassigned spectrum
Authors: Khrabustovskyi Andrii
Published: November 2019

We deal with operators in Rn of the form

A=−1/b(x)Σk=1n∂/∂xk(a(x)∂/∂xk),

where a(x),b(x) are positive, bounded and periodic functions. We denote by Lper the set of such operators. The main result of this work is as follows: for an arbitrary L>0 and for arbitrary pairwise disjoint intervals (αj,βj)⊂[0,L], j=1,…,m (m∈N) we construct the family of operators {Aε∈Lper}ε such that the spectrum of Aε has exactly m gaps in [0,L] when ε is small enough, and these gaps tend to the intervals (αj,βj) as ε→0. The idea how to construct the family {Aε}ε is based on methods of the homogenization theory.
Optimal control problem for the time-dependent Kirchhoff–Love plate in a domain with rough boundary
Authors: Prakash Ravi
Published: November 2019

In this paper, we study the asymptotic behavior of an optimal control problem for the time-dependent Kirchhoff–Love plate whose middle surface has a very rough boundary. We identify the limit problem which is an optimal control problem for the limit equation with a different cost functional.
Branching diffusion in inhomogeneous media
Authors: Koralov L.
Published: November 2019

We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the super-critical regime, we describe the asymptotics of the number of particles in a given domain. In the sub-critical and critical regimes, we describe the distribution of the limiting number of particles.
Semi-classical resolvent estimates for Schrödinger operators
Authors: Vodev Georgi
Published: November 2019

We prove optimal resolvent estimates for self-adjoint operators of the form P(h)=(ih∇+b(x,h))2+V(x,h) on L2(Rn), n≥3, where 0<h<<1 is a semi-classical parameter and the coefficients have very little regularity with respect to the radial variable only.
Global asymptotics of the discrete Chebyshev polynomials
Authors: Lin Y. , Wong R.
Published: November 2019

In this paper, we study the asymptotics of the discrete Chebyshev polynomials tn(z,N) as the degree grows to infinity. Global asymptotic formulas are obtained as n→∞, when the ratio of the parameters n/N=c is a constant in the interval (0,1). Our method is based on a modified version of the Riemann–Hilbert approach first introduced by Deift and Zhou.
Eigenvalue estimates for a three-dimensional magnetic Schrödinger operator
Authors: Helffer Bernard , Kordyukov Yuri A.
Published: November 2019

We consider a magnetic Schrödinger operator Hh=(−ih∇−A¯)2 with the Dirichlet boundary conditions in a domain Ω⊂R3, where h>0 is a small parameter. We suppose that the minimal value b0 of the module |B¯| of the vector magnetic field B¯ is strictly positive, and there exists a unique minimum point of |B¯|, which is non-degenerate. The main result of the paper is upper estimates for the low-lying eigenvalues of the operator Hh in the semiclassical limit. We also prove the existence of an arbitrary large number of spectral gaps in the semiclassical limit in the corresponding periodic setting.
Simultaneous study of the diffraction by a 2D-convex obstacle through boundary layer method and microlocal analysis
Authors: Bouche Daniel , Lafitte Olivier
Published: November 2019

In this paper we consider the high frequency diffraction of electromagnetic waves by a strictly convex obstacle. We restrict ourselves to the case of an obstacle in 2D and to the diffraction of a TE or TM wave.

The aim of this paper is to present simultaneously with the same notations, unknowns and special functions the boundary layer analysis of this problem with stretched variables using the intuition of the solutions and the microlocal analysis way of construction of an adapted parametrix. We concentrate on the case of diffraction, i.e. studying the representation of a creeping wave on the boundary, which occurs in the case of the study of a glancing point.

We use both methods to derive the exact solution near a diffractive point, obtaining results in terms of suitable Airy functions.
Free boundary solutions to a log-singular elliptic equation
Authors: Montenegro Marcelo , Lorca Sebastián
Published: November 2019

The aim of this paper is study the equation −Δu=(log (u)+λup)χ{u>0} in Ω with Dirichlet boundary condition, where 0
0 is sufficiently large, the corresponding energy functional to the perturbed equation −Δu+gε(u)=λ(u+)p has nontrivial critical points uε in H01(Ω). Letting ε→0, then uε converges to a solution of the original problem, which is nontrivial and nonnegative. For 1<p<(N+2)/(N−2) there is at least one nontrivial solution. While for 0<p<1, there are at least two nontrivial distinct solutions.
On homogenization problems for fully nonlinear equations with oscillating Dirichlet boundary conditions
Authors: Barles Guy , Mironescu Elisabeth
Published: November 2019

We study two types of asymptotic problems whose common feature – and difficulty – is to exhibit oscillating Dirichlet boundary conditions: the main contribution of this article is to show how to recover the Dirichlet boundary condition for the limiting equation. These two types of problems are (i) periodic homogenization problems for fully nonlinear, second-order elliptic partial differential equations set in a half-space and (ii) parabolic problems with an oscillating in time Dirichlet boundary condition. In order to obtain the Dirichlet boundary condition for the limiting problem, the key step is a blow-up argument near the boundary which leads to the study of Dirichlet problems set on half-space type domains and of the asymptotic behavior of the solutions when the distance to the boundary tends to infinity.
High-frequency limit of the Maxwell–Landau–Lifshitz system in the diffractive optics regime
Authors: Yong Lu
Published: November 2019

We study semilinear Maxwell–Landau–Lifshitz systems in one space dimension. For highly oscillatory and prepared initial data, we construct WKB approximate solutions over long times O(1/ε). The leading terms of the WKB solutions solve cubic Schrödinger equations. We show that the nonlinear normal form method of Joly, Métivier and Rauch [J. Diff. Eq. 166 (2000), 175–250] applies to this context. This implies that the Schrödinger approximation stays close to the exact solution of Maxwell–Landau–Lifshitz over diffractive times. In the context of Maxwell–Landau–Lifshitz, this extends the analysis of Colin and Lannes [Discrete and Continuous Dynamical Systems 11(1) (2004), 83–100] from times O(|ln ε|) up to O(1/ε).
Homogenization via unfolding in periodic elasticity with contact on closed and open cracks
Authors: Cioranescu Doina , Damlamian Alain , Orlik Julia
Published: November 2019

We consider the elasticity problem in a heterogeneous domain with an ε-periodic micro-structure, ε<<1, including multiple micro-contacts between the structural components. These components can be a simply connected matrix domain with open cracks or inclusions completely surrounded by cracks, which do not touch the outer boundary. The contacts are described by the Signorini and Tresca-friction contact conditions. The Signorini condition is described mathematically by a closed convex cone, while the friction condition is a nonlinear convex functional over the interface jump of the solution on the oscillating interface.

The difficulties appear when the inclusions are completely surrounded by cracks and can have rigid displacements. In this case, in order to obtain preliminary estimates for the solution in the ε-domain, the Korn inequality should be modified, first in the fixed context and then for the ε-dependent periodic case. Additionally, for all states of the contact (inclusions can freely move, or are locked/sticked to the interface with the matrix, or the frictional traction is achieved on the inclusion-matrix interface and the inclusions can slide in the tangential to the interface direction) we obtain estimates for the solution in the ε-domain, uniform with respect to ε.

An asymptotic analysis (as ε→0) for the nonlinear functionals over the growing interface is carried out, based on the application of the periodic unfolding method for sequences of jumps of the solution on the oscillating interface. This allows to obtain the homogenized limit as well as a corrector result.
Convergence properties for a generalization of the Caginalp phase field system
Authors: Canevari Giacomo , Colli Pierluigi
Published: November 2019

We are concerned with a phase field system consisting of two partial differential equations in terms of the variables thermal displacement, that is basically the time integration of temperature, and phase parameter. The system is a generalization of the well-known Caginalp model for phase transitions, when including a diffusive term for the thermal displacement in the balance equation and when dealing with an arbitrary maximal monotone graph, along with a smooth anti-monotone function, in the phase equation. A Cauchy–Neumann problem has been studied for such a system in Commun. Pure Appl. Anal. 11 (2012), 1959–1982, by proving well-posedness and regularity results, as well as convergence of the problem as the coefficient of the diffusive term for the thermal displacement tends to zero. The aim of this contribution is rather to investigate the asymptotic behavior of the problem as the coefficient in front of the Laplacian of the temperature goes to 0: this analysis is motivated by the types III and II cases in the thermomechanical theory of Green and Naghdi. Under minimal assumptions on the data of the problems, we show a convergence result. Then, with the help of uniform regularity estimates, we discuss the rate of convergence for the difference of the solutions in suitable norms.
Scale-transformations and homogenization of maximal monotone relations with applications
Authors: Visintin Augusto
Published: November 2019

In homogenization, two-scale models arise, e.g., by applying Nguetseng's notion of two-scale convergence to nonlinear PDEs. A homogenized single-scale problem may then be derived via scale-transformations. A variational formulation due to Fitzpatrick is here used for the scale-integration of two-scale maximal monotone relations, and for the converse operation of scale-disintegration. These results are applied to the periodic homogenization of a quasilinear model of Ohmic electric conduction with Hall effect:

$\lefteqn{\vec{E}\in\vec{\alpha}(\vec{J},x/\varepsilon )+h(x/\varepsilon )\vec{J}\times\vec{B}(x/\varepsilon )+\vec{E}_{a}(x/\varepsilon ),}$

$\lefteqn{\nabla\times\vec{E}=\vec{g}(x/\varepsilon ),\qquad\nabla\cdot\vec{J}=0\quad\mbox{in }\varOmega,}$

with $\vec{\alpha}(\cdot,x/\varepsilon )$ maximal monotone, $\vec{B},\vec{E}_{a},h,\vec{g}$ prescribed fields. (This corresponds to a quasilinear second-order elliptic equation in curl form: $\nabla\times\vec{\beta}(\nabla\times u,x/\varepsilon )=\vec{g}(x/\varepsilon )$ .) This result is also retrieved via De Giorgi's Γ-convergence.
Homogenization of a class of linear partial differential equations
Authors: Waurick Marcus
Published: November 2019

We present a unified Hilbert space perspective to homogenization of a class of evolutionary equations of mathematical physics. We formulate homogenization in a purely operator-theoretic setting. Using “A structural observation for linear material laws in classical mathematical physics” by R. Picard [Mathematical Methods in the Applied Sciences 32 (2009), 1768–1803], we discuss constitutive relations as certain elements of the Hardy space ℋ∞(E;L(H)) of bounded, analytic and operator-valued functions M:E→L(H), where E\subseteqq C open, H Hilbert space. The core idea is to introduce a certain topology on the set of constitutive relations. Given a convergent sequence of constitutive relations, the behavior of solutions to the respective problems is discussed. We apply the results to the equations of acoustics, thermodynamics, elasticity or coupled systems such as thermo-elasticity. The respective equations may also incorporate memory or delay terms and fractional derivatives. In particular, constitutive relations via differential equations can also be treated.
On the global solvability of the Cauchy problem for a quasilinear ultraparabolic equation
Authors: Tersenov Alkis S.
Published: November 2019

In the present paper we study the Cauchy problem as well as the first initial boundary value problem for a class of quasilinear ultraparabolic equations. We show that the presence of the low order term satisfying a certain assumption provides a global solvability of the above problems. The optimality of this assumption is demonstrated.
Asymptotically self-similar global solutions of a damped wave equation with nonlinear memory
Authors: Berbiche Mohamed
Published: November 2019

In this paper we consider the Cauchy problem of semi-linear damped wave equation with nonlinear memory term a∫0t(t−τ)−γ|u|α−1u(τ,x) dτ. We prove global existence and asymptotic behavior of solution for small initial data. Moreover, we show that the global solutions behave asymptotically like self-similar solutions of the semi-linear heat equation with nonlinear memory as t→∞.
Asymptotic profiles of solutions for the isothermal Falk–Konopka system of shape memory alloys with weak damping
Authors: Takeda Hiroshi , Yoshikawa Shuji
Published: November 2019

The aim of this paper is to investigate asymptotic behavior of solutions to the Cauchy problem of certain fourth-order semilinear elastic system with weak damping in three space dimension. The system corresponds to the isothermal case of the thermoelastic system representing the martensitic phase transitions on shape memory alloys. We give several asymptotic profiles of solutions. By considering the second-order expansion of solutions, we obtain more precise information about asymptotic behavior of solutions as t→∞, and observe the contribution of the nonlinear term to solutions. Moreover, we give the third-order expansion formula which enable us to clarify the relation between the fourth- and the second-order derivative term.
On the Laplacean transfer across fractal mixtures
Authors: Capitanelli R. , Vivaldi M.A.
Published: November 2019

Laplacean transport across and towards irregular interfaces have been used to model many phenomena in nature and technology. The peculiar aspect is that these phenomena take place in domains with small bulk and large interfaces in order to produce rapid and efficient transport. In this paper we perform the asymptotic homogenization analysis of Robin problems in domains with a fractal boundary.
High order asymptotics for wave propagation across thin periodic interfaces
Authors: Claeys Xavier , Delourme Bérangère
Published: November 2019

This work deals with the scattering of acoustic waves by a thin ring that contains many regularly-spaced heterogeneities. We provide and justify a complete description of the solution with respect to the period and the thickness of the heterogeneities. Our approach mixes matched asymptotic expansions and homogenization theory.
A Liouville comparison principle for solutions of semilinear parabolic second-order partial differential inequalities
Authors: Kurta Vasilii V.
Published: November 2019

We obtain a new Liouville comparison principle for entire weak solutions (u,v) of semilinear parabolic second-order partial differential inequalities of the form

ut−ℒu−|u|q−1u≥vt−ℒv−|v|q−1v  (*)

in the half-space S=R+×Rn, where n≥1 is a natural number, q>0 is a real number and

ℒ=Σi,j=1n ∂/∂xi [aij(t,x) ∂/∂xj].

We assume that the coefficients aij(t,x), i,j=1,…,n, of the operator ℒ are functions that are defined, measurable and locally bounded in S. We also assume that aij(t,x)=aji(t,x), i,j=1,…,n, for almost all (t,x)∈S and that

Σi,j=1naij(t,x)ξiξj≥0

for almost all (t,x)∈S and all ξ∈Rn. The critical exponents in the Liouville comparison principle obtained, which are responsible for the non-existence of non-trivial (i.e., such that u\not\equiv v) entire weak solutions to (*) in S, depend on the behavior of the coefficients of the operator ℒ at infinity. As direct corollaries we obtain a new Fujita comparison principle for entire weak solutions (u,v) of the Cauchy problem for the inequality (*), as well as new Liouville-type and Fujita-type theorems for non-negative entire weak solutions u of the inequality (*) in the case when v≡0. All the results obtained are new and sharp.
Logarithmic stabilisation of a multidimensional structure by the boundary
Authors: Ouksel Leila
Published: November 2019

We examine the decay of the energy for wave equations on a bounded domain Rn, connected through one point to a rod modelled by a segment of R. It is shown that the energy decreases at least as the inverse logarithm of time. This result is obtained using a dissipative condition of the Neumann type on the boundary of the domain.
Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary
Authors: De Maio U. , Nandakumaran A.K.
Published: November 2019

In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter ε>0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.
A 1-d quasilinear nonuniform parabolic chemotaxis model with volume-filling effect
Authors: Zhang Yanyan , Zheng Songmu
Published: November 2019

In this paper, a 1-d quasilinear nonuniform parabolic chemotaxis model with volume-filling effect is studied. The global existence and uniqueness of classical solution is proved. Furthermore, we prove that the global solution is uniformly bounded in time. With the help of a suitable non-smooth Simon–Łojasiewicz approach, we obtain the results on convergence of the solution to equilibrium and the convergence rate.
Singular limits for thin film superconductors in strong magnetic fields
Authors: Alama Stan , Bronsard Lia , Galvão-Sousa Bernardo
Published: November 2019

We consider singular limits of the three-dimensional Ginzburg–Landau functional for a superconductor with thin-film geometry, in a constant external magnetic field. The superconducting domain has characteristic thickness on the scale ε>0, and we consider the simultaneous limit as the thickness ε→0 and the Ginzburg–Landau parameter κ→∞. We assume that the applied field is strong (on the order of ε−1 in magnitude) in its components tangential to the film domain, and of order log κ in its dependence on κ. We prove that the Ginzburg–Landau energy Γ-converges to an energy associated with a two-obstacle problem, posed on the planar domain which supports the thin film. The same limit is obtained regardless of the relationship between ε and κ in the limit. Two illustrative examples are presented, each of which demonstrating how the curvature of the film can induce the presence of both (positively oriented) vortices and (negatively oriented) antivortices coexisting in a global minimizer of the energy.
Alzheimer’s/Vascular Spectrum Dementia: Classification in Addition to Diagnosis
Authors: Emrani Sheina , Lamar Melissa , Price Catherine C. , Wasserman Victor , Matusz Emily , Au Rhoda , Swenson Rodney , Nagele Robert , Heilman Kenneth M. , Libon David J.
Published: December 2019

Alzheimer’s disease (AD) and vascular dementia (VaD) are the two most common types of dementia. Although the combination of these disorders, called ‘mixed’ dementia, is recognized, the prevailing clinical and research perspective continues to consider AD and VaD as independent disorders. A review of recent neuropathological and neuropsychological literature reveals that these two disorders frequently co-occur and so-called ‘pure’ AD or VaD is comparatively rare. In addition, recent research shows that vascular dysfunction not only potentiates AD pathology, but that pathological changes in AD may subsequently induce vascular disorders. On the basis of these data, we propose that the neurobiological underpinnings underlying AD/VaD dementia and their neuropsychological phenotypes are best understood as existing along a clinical/pathological continuum or spectrum. We further propose that in conjunction with current diagnostic criteria, statistical modeling techniques using neuropsychological test performance should be leveraged to construct a system to classify AD/VaD spectrum dementia in order to test hypotheses regarding how mechanisms related to AD and VaD pathology interact and influence each other.
Circulating Vitamin D Levels and Alzheimer’s Disease: A Mendelian Randomization Study in the IGAP and UK Biobank
Authors: Wang Longcai , Qiao Yanchun , Zhang Haihua , Zhang Yan , Hua Jiao , Jin Shuilin , Liu Guiyou
Published: December 2019

Observational studies strongly supported the association of low levels of circulating 25-hydroxyvitamin D (25OHD) and cognitive impairment or dementia in aging populations. However, randomized controlled trials have not shown clear evidence that vitamin D supplementation could improve cognitive outcomes. In fact, some studies reported the association between vitamin D and cognitive impairment based on individuals aged 60 years and over. However, it is still unclear that whether vitamin D levels are causally associated with Alzheimer’s disease (AD) risk in individuals aged 60 years and over. Here, we performed a Mendelian randomization (MR) study to investigate the causal association between vitamin D levels and AD using a large-scale vitamin D genome-wide association study (GWAS) dataset and two large-scale AD GWAS datasets from the IGAP and UK Biobank with individuals aged 60 years and over. Our results showed that genetically increased 25OHD levels were significantly associated with reduced AD risk in individuals aged 60 years and over. Hence, our findings in combination with previous literature indicate that maintaining adequate vitamin D status in older people especially aged 60 years and over, may contribute to slow down cognitive decline and forestall AD. Long-term randomized controlled trials are required to test whether vitamin D supplementation may prevent AD in older people especially those aged 60 years and may be recommended as preventive agents.
Could Lifetime Lead Exposure Play a Role in Limbic-predominant Age-related TDP-43 Encephalopathy (LATE)?
Authors: Fuller-Thomson Esme , Deng ZhiDi
Published: December 2019

Limbic-predominant Age-related TDP-43 Encephalopathy (LATE) is a disease in which the clinical presentation mimics that of Alzheimer’s disease. TDP-43 proteinopathy associated with LATE has been identified in more than 20% of autopsies of community-dwelling adults over the age of 80. It is believed to contribute significantly toward tau-negative dementia. Heavy metals such as lead has also been linked to TDP-43 proteinopathy. In particular, lead triggers TDP-43 accumulation and disrupts TDP-43 homeostasis. However, the specific relationship between LATE and lead remains unknown. Before leaded gasoline was phased out during the 1970s and 1980s, average blood lead levels were 15 times what they are today. Thus, each successive birth cohort entering old age has had less cumulative lifeime exposure to lead. Lifetime exposure can be tracked in the tibia bone, where the half-life of lead is many decades. We hypothesize that lead plays a role in the development of LATE. There are two ways to explore the validity of this hypothesis. Generational differences in lead exposure should result in a steady decline in the prevalence of LATE among older adults. We propose the use of tibia bone lead levels be examined in conjunction with brain autopsies from different birth cohorts to examine the link between lead exposure and LATE prevalence, holding age constant. Furthermore, individuals with genetic polymorphisms that confer a greater lead absorption phenotype should display a higher degree of TDP-43 accumulation in autopsies. The results of such studies could provide insight into gene by environment interactions relevant to the development of LATE.
A Study on Ganre-Based Approach in Teaching Speaking to Indonesian EFL Learners
Authors: Putra Rangga Mega
Published: December 2019

The implementation of genre-based approach in EFL teaching has been increasingly attracting many EFL teachers’ attention. This study aimed at investigating the implementation of Ganre-Based Approach in teaching and learning process of speaking skill at SMPN 1 Gamping Yogyakarta. This study was descriptive qualitative. The techniques of collecting the data were observation, interviews and documentation. The data was analyzed by referring to theory of the stages of genre-based approach developed by Hammond et al., (1992). The total of the sample of this study was 28 students in the seventh grade of SMPN 1 Gamping Yogyakarta. The findings showed that the English teacher still had some weakness in implementing genre-based approach. Moreover, the students still had many difficulties in generic structure and social function of the text.
Konzepte der Teilhabe: Bedingungsloses Grundeinkommen oder Recht auf Arbeit?
Authors: Kronauer Martin
Published: December 2019

Der Beitrag stellt die Forderung nach einem bedingungslosen Grundeinkommen, die in der Linken großen Zuspruch erfährt, der Forderung nach einem Recht auf Arbeit („lieber weniger arbeiten und besser, Arbeit für alle“) gegenüber, die in der Linken in Vergessenheit geraten zu sein scheint. Er stellt beide Forderungen auf den Prüfstand gesellschaftlicher Teilhabe und sieht eine grundlegende Differenz darin, welcher Stellenwert jeweils der gesellschaftlich notwendigen Arbeit (innerhalb und jenseits kapitalistischer Verhältnisse) beigemessen wird. Daraus folgt ein Plädoyer dafür, die Forderung nach einem Recht auf Arbeit neuerlich und auf neue Weise in die gesellschaftliche Debatte einzubringen.
Determination of Ethanol Content in Fuels with Phononic Crystal Sensor
Authors: Mukhin N. V. , Oseev A. , Kutia M. M. , Borodacheva E. S. , Korolev P. G.
Published: December 2019

Introduction. In-line analysis of ethanol content in gasoline blends is currently one of the urgent needs of fuel industry. Developing safe and secure approaches is critical for real applications. A phononic crystal sensor have been introduced as an innovative approach to high performance gasoline sensing. Distinguishing feature of proposed sensor is the absence of any electrical contact with analysed gasoline blend, which allows the use of sensors directly in pipelines without the risk of explosion in an emergency.

Aim. Investigation of the possibilities of using phononic sensor structures to determine the ethanol content in liquid hydrocarbons.

Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. For measurement, substances of ordinary gasoline and gasoline 63–80 with ethanol concentrations in the range of 1–10 % by volume in increments of 2 % were prepared. The phononic crystal sensor was designed as a stainless steel plate with cylindrical holes and a resonant cavity, formed as a running across the wave propagation path slit between two lattices.

Results. In-line analysis of measuring the concentration of ethanol in alcohol-containing fuels on a phononic crystal structure with a resonant cavity was carried out. Using the Agilent4395A admittance meter, the transmission spectra of longitudinal acoustic waves through the gasoline-filled sensor structure with were obtained. The non-linear correlation between the composition and the speed of sound of the blend is presented in the article is due to the ability to reduce the speed of sound of the mixture with an increase in ethanol concentration in the range of 0–10 % by volume.

Conclusion. A measurement structure on the basis of phononic crystal was created. The measurements of various gasoline-ethanol mixtures show that the sensor has significant sensitivity (0.91 kHz/ms−1 ) with quality factor of 200) to distinguish between regular fuels, gasoline based blends and the presence of additives in standard fuels. The sensor has prospects for in-line analyzes the composition of liquid hydrocarbons.
Wideband Waveguide-to-Microstrip Transition for mm-Wave Applications
Authors: Mozharovskiy Andrey V. , Soykin Oleg V. , Artemenko Aleksey A. , Maslennikov Roman O. , Vendik Irina B.
Published: December 2019

Introduction. Increased data rate in modern communication systems can be achieved by raising the operational frequency to millimeter wave range where wide transmission bands are available. In millimeter wave communication systems, the passive components of the antenna feeding system, which are based on hollow metal waveguides, and active elements of the radiofrequency circuit, which have an interface constructed on planar printed circuit boards (PCB) are interconnected using waveguide-to-microstrip transition.

Aim. To design and investigate a high-performance wideband and low loss waveguide-to-microstrip transition dedicated to the 60 GHz frequency range applications that can provide effective transmission of signals between the active components of the radiofrequency circuit and the passive components of the antenna feeding system

Materials and methods. Full-wave electromagnetic simulations in the CST Microwave Studio software were used to estimate the impact of the substrate material and metal foil on the characteristics of printed structures and to calculate the waveguide-to-microstrip transition characteristics. The results were confirmed via experimental investigation of fabricated wideband transition samples using a vector network analyzer

Results. The probe-type transition consist of a PCB fixed between a standard WR-15 waveguide and a back-short with a simple structure and the same cross-section. The proposed transition also includes two through-holes on the PCB in the center of the transition area on either side of the probe. A significant part of the lossy PCB dielectric is removed from that area, thus providing wideband and low-loss performance of the transition without any additional matching elements. The design of the transition was adapted for implementation on the PCBs made of two popular dielectric materials RO4350B and RT/Duroid 5880. The results of full-wave simulation and experimental investigation of the designed waveguide to microstrip transition are presented. The transmission bandwidth for reflection coefficient S11 < –10 dB is in excess of 50…70 GHz. The measured insertion loss for a single transition is 0.4 and 0.7 dB relatively for transitions based on RO4350B and RT/Duroid 5880.

Conclusion. The proposed method of insertion loss reduction in the waveguide-to-microstrip transition provides effective operation due to reduction of the dielectric substrate portion in the transition region for various high-frequency PCB materials. The designed waveguide-to -microstrip transition can be considered as an effective solution for interconnection between the waveguide and microstrip elements of the various millimeter-wave devices dedicated for the 60 GHz frequency range applications.
A Survey on Internet of Things : Applications and Layered Wise Security Issues
Authors: Sirisha Uppuluri , Eswari G. Lakshme
Published: December 2019

This paper briefly introduces Internet of Things(IOT) as a intellectual connectivity among the physical objects or devices which are gaining massive increase in the fields like efficiency, quality of life and business growth. IOT is a global network which is interconnecting around 46 million smart meters in U.S. alone with 1.1 billion data points per day[1]. The total installation base of IOT connecting devices would increase to 75.44 billion globally by 2025 with a increase in growth in business, productivity, government efficiency, lifestyle, etc., This paper familiarizes the serious concern such as effective security and privacy to ensure exact and accurate confidentiality, integrity, authentication access control among the devices.