Thermoelasticity without energy dissipation of materials with microstructure

In this article we propose a model of the thermoelastic theory without energy dissipation for materials with affine microstructure. The equations of the linear theory are also obtained. We obtain as well a uniqueness theorem for materials with a center of symmetry and an existence and uniqueness result in the general linear case.     

Spatial behavior for some non-standard problems in linear thermoelasticity without energy dissipation

In the present paper we consider a prismatic cylinder occupied by an anisotropic and homogeneous compressible linear thermoelastic material within the framework of the linear theory of thermoelasticity without energy dissipation. The cylinder is subject to zero body force and heat supply and zero lateral specific boundary conditions and the motion is induced by a time-dependent displacement and thermal displacement specified pointwise over the base. Further, the motion is constrained such that the displacement, thermal displacement, velocity and temperature variation at points in the cylinder and at a prescribed time are in given proportions to, but not identical with, their respective initial values. It is shown that certain integrals of the solution spatially evolve with respect to the axial variable. Conditions are derived that show the integrals exhibit alternative behavior and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay, provided the elasticity tensor is positive definite or strongly elliptic.     

On the exponential decay in thermoelasticity without energy dissipation and of type III in presence of an absorbing boundary

We study the asymptotic behavior of the solution of a 3D hyperbolic system arising in the Green-Naghdi models of thermoelasticity of type II and III with a dissipative boundary condition for the displacement and prove that the energy exponentially decays in time.     

A numerical investigation of energy dissipation with a shallow depth sloshing absorber

A liquid sloshing absorber consists of a container, partially filled with liquid. The absorber is attached to the structure to be controlled, and relies on the structure’s motion to excite the liquid. Consequently, a sloshing wave is produced at the liquid free surface within the absorber, possessing energy dissipative qualities. The behaviour of liquid sloshing absorbers has been well documented, although their use in structural control applications has attracted considerably less attention.     

Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension

The fundamental equations of the problems of generalized thermoelasticity with one relaxation parameter including heat sources in infinite rotating magneto-thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace transform domain for a one dimensional problem. These equations have been solved by the eigenvalue approach to determine deformations, stress, and temperature. The results have been compared to those available in the existing literature. The graphs have been drawn to show the effect of rotation in the medium.     

Variational and reciprocal principles in thermoelasticity without energy dissipation

In the context of the linear theory of thermoelasticity without energy dissipation for homogeneous and isotropic materials, variational principles of Biot-and Hamilton-types and a reciprocal principle of Betti-Rayleigh-type are presented.     

On the global existence and small dissipation limit for generalized dissipative Zakharov system

This paper deals with the existence and uniqueness of the global solutions to the initial boundary value problem for a generalized Zakharov system with direct self‐interaction of the dispersive waves and weak dissipation in the nondispersive subsystem. We prove the global existence of the generalized solution to the problem by a priori estimates and Galerkin method. We also establish the regularity of the global generalized solution and the existence and uniqueness of the global classical solution. Moreover, we obtain the convergence of the solutions of the generalized Zakharov system with dissipation as the dissipative coefficient approaches zero.     

Reflection of magneto-thermoelastic waves with two relaxation times and temperature dependent elastic moduli

The model of the equations of generalized magneto-thermoelasticity with two relaxation times in an isotropic elastic medium under the effect of reference temperature on the modulus of elasticity is established. The modulus of elasticity is taken as a linear function of reference temperature. Reflection of magneto-thermoelastic waves under generalized thermoelasticity theory is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid in a vacuum. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained. Similarly, the reflection coefficients ratios variations with the angle of incident under different conditions are shown graphically. A comparison is made with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature.     

Rotational and voids effect on the reflection of P waves from stress-free surface of an elastic half-space under magnetic field and initial stress without energy dissipation

The influence of rotation, magnetic field, voids and initial stress on the reflection of P waves in thermoelasticity without energy dissipation are studied. The basic governing equations for isotropic and homogeneous thermoelastic half-space with voids, rotation, are based on Green and Naghdi (GN) theory under the effect of initial stress, where there is an initial magnetic field parallel to the plane boundary of the half-space. The solution of the problem in xz-plane indicates the existence of four plane waves; $P_1\text{;}{P}_2\text{;}{P}_3$ and $P_4$ and an SV waves. The relevant boundary conditions at stress-free insulated surface are satisfied by appropriate solutions in the half-space to obtain the reflection coefficients for the incidence of P waves. The numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effect of the rotation, magnetic field, initial stress and voids parameters.     

On a 1D transport equation with nonlocal velocity and supercritical dissipation

We study a 1D transport equation with nonlocal velocity. First, we prove eventual regularization of the viscous regularization when dissipation is in the supercritical range with non-negative initial data. Next, we will prove global regularity for solutions when dissipation is slightly supercritical. Both results utilize a nonlocal maximum principle.     

Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

Uniform energy and L² decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L²-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L²-norm and the total energy of solutions, respectively, decay like and O(1/t²) as t→+∞ for a kind of the weighted initial data.     

Global existence and blow-up of solutionsfor a higher-order kirchhoff-type equation with nonlinear dissipation

This paper deals with the higher-order Kirchhoff-type equation with nonlinear dissipationu_tt+(∫_Ω׀D^mu׀²dx)^q(−Δ)^mu+u_t׀u_t׀^r=׀u׀^pu,xΩ,t>0,in a bounded domain, where m < 1 is a positive integer, q, p, r < 0 arepositive constants. We obtain that the solution exists globally if p ≤ r, while ifp > max r, 2q , then for any initial data with negative initial energy, the solution blowsup at finite time in L^p+2 norm.     

The Kontorovich-Lebedev integral transformation with a Hankel function kernel in a space of generalized functions of doubly exponential descent

A version of the Kontorovich-Lebedev transformation with the Hankel function of second kind in the kernel is investigated in a space of distributions of doubly exponential descent. The inversion theorem is rigorously established making use in some steps of the proof of a relation of this transform with the Laplace one. Finally, the theory developed is illustrated in solving certain type of partial differential equations.     

Asymptotic behavior of nonlinear waves in elastic media with dispersion and dissipation

In the case of nonlinear elastic quasitransverse waves in composite media described by nonlinear hyperbolic equations, we study the nonuniqueness problem for solutions of a standard self-similar problem such as the problem of the decay of an arbitrary discontinuity. The system of equations is supplemented with terms describing dissipation and dispersion whose influence is manifested in small-scale processes. We construct solutions numerically and consider self-similar asymptotic approximations of the obtained solution of the equations with the initial data in the form of a “spreading” discontinuity for large times. We find the regularities for realizing various self-similar asymptotic approximations depending on the choice of the initial conditions including the dependence on the form of the functions determining the small-scale smoothing of the original discontinuity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 240–256, May, 2006.     

Heat transfer in a visco-elastic fluid past a stretching sheet with viscous dissipation and internal heat generation

This paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of a visco-elastic fluid over a linearly stretching continuous surface with variable wall temperature subjected to suction or blowing. The study considers the effects of frictional heating (viscous dissipation) and internal heat generation or absorption. An analysis has been carried out for two different cases of heating processes namely: (i) Prescribed surface temperature (PST) and (ii) Prescribed wall heat flux (PHF) to get the effect of visco-elastic parameter for various situations. Further increase of visco-elastic parameter is to decrease the skin friction on the sheet. The solutions for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Received: June 16, 2004; revised: February 8, 2005     

Mathematical modelling and analysis of bulk waves in rotating generalized thermoelastic media with voids

The present paper deals with the propagation of body waves in a homogenous isotropic, rotating, generalized thermoelastic solid with voids. The complex quartic secular equation has been solved by employing Descartes’ algorithm and perturbation method to obtain phase velocities, attenuations and specific loss factors of four attenuating and dispersive waves, which are possible to exist in such media. These wave characteristics have been computed numerically for magnesium crystal and presented graphically. Statistical analysis has been performed to compare the obtained computer simulated result in order to have estimate on the suitability of the method to compute various characteristics of the waves. This work may find applications in geophysics and gyroscopic sensors.     

An exact algorithm to minimize the makespan in project scheduling with scarce resources and generalized precedence relations

In this paper we propose an exact algorithm for the Resource Constrained Project Scheduling Problem (RCPSP) with generalized precedence relationships (GPRs) and minimum makespan objective. For the RCPSP with GPRs we give a new mathematical formulation and a branch and bound algorithm exploiting such a formulation. The exact algorithm takes advantage also of a lower bound based on a Lagrangian relaxation of the same mathematical formulation. We provide an extensive experimentation and a comparison with known lower bounds and competing exact algorithms drawn from the state of the art.     

A regularity criterion for 2D MHD flows with horizontal dissipation and horizontal magnetic diffusion

This paper concerns the conditional global regularity of incompressible MHD equations with horizontal dissipation and horizontal magnetic diffusion in two dimension. When only horizontal dissipation and horizontal magnetic diffusion are present, there is no control on the vertical derivatives of velocity field and magnetic field, which is the main difficulty to establish the global regularity. In this paper, we establish a global regularity criterion in terms of one entry of the velocity gradient tensor or one entry of the magnetic field gradient tensor, which extends the recent work (Fan and Ozawa, 2014).     

Finite dimensionality and regularity of attractors for a 2-D semilinear wave equation with nonlinear dissipation

We consider a semilinear wave equation, defined on a two-dimensional bounded domain Ω, with a nonlinear dissipation. Our main result is that the flow generated by the model is attracted by a finite dimensional global attractor. In addition, this attractor has additional regularity properties that depend on regularity properties of nonlinear functions in the equation. To our knowledge this is a first result of this type in the context of higher dimensional wave equations.