Quantum macroscopic equations from Bohm potential and propagation of waves

Bohm’s interpretation of Quantum Mechanics leads to the derivation of a Quantum Kinetic Equation. In the present work, moments of this kinetic equation are taken, thus deriving conservation equations. These macroscopic equations are then applied to study the propagation of longitudinal density perturbations in neutral gases and plasmas, of either fermions or bosons. The dispersion relation is derived and the effect of the Bohm potential shown; the speed of propagation calculated and the difference between fermions and bosons investigated. Pseudosonic waves in quantum plasmas are obtained including the effect of the Bohm potential.     

Elastic response of a cylinder containing longitudinal stiffeners

This paper develops a three-dimensional analytical model of a cylinder that contains a longitudinal stiffener. The model begins with the equations of motion for a fully elastic solid that produces displacement fields with unknown wave propagation coefficients. These are inserted into stress and displacement equations at the cylinder boundaries and at the location of the stiffener. Orthogonalization of these equations produces an infinite number of indexed algebraic equations that can be truncated and incorporated into a global matrix equation. Solving this equation yields the solution to the wave propagation coefficients and allows the system's displacements and stresses to be calculated. The model is verified by comparison of the results of a plane strain analysis example to a solution generated using finite element theory. A three-dimensional example problem is formulated and the displacement results are illustrated. The inclusion of multiple stiffeners is discussed.     

Effects of initial compression stress on wave propagation in carbon nanotubes

An analytical method to investigate wave propagation in single- and double- walled carbon nanotubes under initial compression stress is presented. The nanotube structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. The governing equations are derived based on Flügge equations of motion. Frequency equations of wave propagation in single and double wall carbon nanotubes are described through the effects of initial compression stress and van der Waals force. To show the effects of Initial compression stress on the wave propagation in nanotubes, the symmetrical mode can be analyzed based on the present elastic continuum model. It is shown that the wave speed are sensitive to the compression stress especially for the lower frequencies.     

The propagation of discontinuities in non-homogeneous thermoviscoelastic media

In this study, the propagation of plane, cylindrical and spherical dilatational waves in non-homogeneous thermoviscoelastic media is investigated by employing the notion of singular surfaces and the method of characteristics. The inhomogeneity of the medium is such that the material properties depend in an arbitrary manner on the co-ordinate coinciding with the direction of the propagation. An integral type constitutive equation is considered for the heat flux which permits a finite propagation speed for thermal disturbances. It is found that the application of a dynamic input on the boundary surface gives rise to two different wave fronts along which mechanical and thermal effects are coupled. The growth and decay equations describing the change of the strength of the discontinuities on these two wave fronts are then obtained. By integrating the growth and decay equations along the rays the solutions valid at the wave fronts are found. The solutions are then reduced to two special cases: in one the heat flux equation is taken as the so-called modified Fourier equation, and in the other as the classical Fourier equation. The effects of inhomogeneity, geometry of the wave front, thermomechanical coupling and material internal friction on the strength of the discontinuity are discussed.     

Pulse propagation of acoustic waves scattered in a channel

When acoustic waves are scattered by random sound-speed fluctuations in a two-dimensional channel the energy is continually transferred between the propagating modes. In the multiple- scattering region the energy flux assumes an asymptotic form in which there is equal energy flux propagating in each mode. Here we shall make use of this well known result to show how to obtain an asymptotic form for a pulse of acoustic energy propagating in the channel. In the multiple-scattering region the speed of the acoustic waves in the pulse continually changes as the energy is transferred between the modes. The process is basically a diffusion process around the mean speed of propagation. We shall first show, using physical arguments, that the diffusion coefficient is proportional to the square root of the propagation distance times the mean free path of scattering. The theory governing the acoustic propagation in the channel is formulated in terms of modal coherence equations and we shall next give a brief review of the definitions of the coherence functions and a discussion of how the equations governing the propagation of the modal coherence functions are derived. We shall then show how the pulse shape and the relevant parameters may be obtained by solving the basic modal coherence equations at large propagation distances.     

Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori–Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton’s principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.     

Generalization of the spherical harmonic method to radiative transfer in multi-dimensional space

The basic radiative transfer equation in three-dimensional space is expressed in terms of three commonly used coordinate systems, namely, Cartesian, cylindrical and spherical coordinates. The concept of a transformation matrix is applied to the transformation processes between the Cartesian system and two other systems. The spherical harmonic method is then applied to decompose the radiative transfer equation into a set of coupled partial differential equations for all three systems in terms of partial differential operators. By truncating the number of partial differential equations into four along with further mathematical analyses, we obtain a modified Helmholtz equation. For each coordinate system, analytical solutions in terms of infinite series are obtained whenever the equation is solvable by the technique of separation of variables with proper boundary conditions. Numerical computations are carried out for one dimensional radiative transfer to illustrate the applicability of the technique developed in the present study.     

A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation

A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.     

Axisymmetric wave propagation of thermoelastic transversely isotropic half-space under buried loading using potential functions

By virtue of a new scalar potential function and Hankel integral transforms, the wave propagation analysis of a thermoelastic transversely isotropic half-space is presented under buried loading and heat flux. The governing equations of the problem are the differential equations of motion and the energy equation of the coupled thermoelasticity theory. Using a scalar potential function, these coupled equations have been uncoupled and a six-order partial differential equation governing the potential function is received. The displacements, temperature, and stress components are obtained in terms of this potential function in cylindrical coordinate system. Applying the Hankel integral transform to suppress the radial variable, the governing equation for potential function is reduced to a six-order ordinary differential equation with respect to z. Solving that equation, the potential function and therefore displacements, temperature, and stresses are derived in the Hankel transformed domain for two regions. Using inversion of Hankel transform, these functions can be obtained in the real domain. The integrals of inversion Hankel transform are calculated numerically via Mathematica software. Our numerical results for displacement and temperature are calculated for surface excitations and compared with the results reported in the literature and a very good agreement is achieved.     

Ion-acoustic solitary waves in a dense pair-ion plasma containing degenerate electrons and positrons

Fully nonlinear propagation of ion-acoustic solitary waves in a collisionless dense/quantum electron–positron–ion plasma is investigated. The electrons and positrons are assumed to follow the Thomas–Fermi density distribution and the ions are described by the hydrodynamic equations. An energy balance-like equation involving a Sagdeev-type pseudo-potential is derived. Finite amplitude solutions are obtained numerically and their characteristics are discussed. The small-but finite-amplitude limit is also considered and an exact analytical solution is obtained. The present studies might be helpful to understand the excitation of nonlinear ion-acoustic solitary waves in a degenerate plasma such as in superdense white dwarfs.     

Stability borders and classification of density perturbation propagations in deDonder-gauge on a cosmological background

We investigate the propagation and the stability borders of density and metric perturbations on a cosmological background in linear perturbation theory in deDonder-gauge. We obtain the algebraic equations for the generally time-dependent stability borders by setting the typical time for perturbation contrasts infinite in the set of differential equations, while all other typical times stay finite. In dD-gauge there are in general three stability borders whereas in synchronous gauge there is only one. In the limiting cases of radiation perturbations and dustlike perturbations we obtain in deDonder-gauge no stability border resp. only one stability border (the ordinary Jeans limit). The first case is in contrast to the synchronous gauge and means that radiation perturbations cannot become unstable. During the recombination there could be three stability borders. We classify the propagation solutions and the systems of differential equations governing them by comparing the characteristic times in the original general system of differential equations, in deDonder-gauge and synchronous gauge. The greatest differences for the propagation of density contrasts arise from the presence of a gravitational wave time scale in deDonder-gauge. This becomes significant if the density perturbations are relativistic with respect to the velocity of sound. Gravitational retardation effects are the origin of the 6-dimensionality of the solution space for density contrasts. This reflects the necessity and physical meaning of gauge solutions.     

Novel heat conduction model for bridging different space and time scales

This exposition describes a novel heat transport model and an underlying unified theory emanating from the physics of the Boltzmann transport equation which acknowledges simultaneously the coexistence of that termed as slow processes (at low energies) and fast processes (at high energies) as heat carriers while describing the evolution of heat transport characteristics spanning both spatial scales (characterizing ballistic to diffusive limits), and also time scales (characterizing finite to infinite heat propagation speeds).     

Elastic response of an orthogonally reinforced plate

This paper develops a three-dimensional fully elastic analytical model of a solid plate that has two sets of embedded, equally spaced stiffeners that are orthogonal to each other. The dynamics of the solid plate are based on the Navier–Cauchy equations of motion of an elastic body. This equation is solved with unknown wave propagation coefficients at two locations, one solution for the volume above the stiffeners and the second solution for the volume below the stiffeners. The forces that the stiffeners exert on the solid body are derived using beam and bar equations of motion. Stress and continuity equations are then written at the boundaries and these include the stiffener forces acting on the solid. A two-dimensional orthognalization procedure is developed and this produces an infinite number of double indexed algebraic equations. These are all written together as a global system matrix. This matrix can be truncated and solved resulting in a solution to the wave propagation coefficients which allows the systems displacements to be determined. The model is verified by comparison to thin plate theory and finite element analysis. An example problem is formulated. Convergence of the series solution is discussed. The frequency limitations of the model are examined.     

Molecular dynamics study of thermal stress and heat propagation in tungsten under thermal shock

Using molecular dynamics （MD） simulation, we study the thermal shock behavior of tungsten （W）, which has been used for the plasma facing material （PFM） of tokamaks. The thermo-elastic stress wave, corresponding to the collective displacement of atoms, is analyzed with the Lagrangian atomic stress method, of which the reliability is also analyzed. The stress wave velocity corresponds to the speed of sound in the material, which is not dependent on the thermal shock energy. The peak pressure of a normal stress wave increases with the increase of thermal shock energy. We analyze the temperature evolution of the thermal shock region according to the Fourier transformation. It can be seen that the “obvious” velocity of heat propagation is less than the velocity of the stress wave; further, that the thermo-elastic stress wave may contribute little to the transport of kinetic energy. The heat propagation can be described properly by the heat conduction equation. These results may be useful for understanding the process of the thermal shock of tungsten.     

Local excitation-lateral inhibition interaction yields oscillatory instabilities in nonlocally interacting systems involving finite propagation delay

The work studies wave activity in spatial systems, which exhibit nonlocal spatial interactions at the presence of a finite propagation speed. We find analytically propagation delay-induced oscillatory instabilities for various local excitatory and lateral inhibitory spatial interactions. Further, the work shows for general nonlocal interactions analytically that the first kernel Fourier moment defines the stability thresholds. The final numerical simulation confirms the analytical results.     

A Hopf-like equation and perturbation theory for differential delay equations

We extend techniques developed for the study of turbulent fluid flows to the statistical study of the dynamics of differential delay equations. Because the phase spaces of differential delay equations are infinite dimensional, phase-space densities for these systems are functionals. We derive a Hopf-like functional differential equation governing the evolution of these densities. The functional differential equation is reduced to an infinite chain of linear partial differential equations using perturbation theory. A necessary condition for a measure to be invariant under the action of a nonlinear differential delay equation is given. Finally, we show that the evolution equation for the density functional is the Fourier transform of the infinite-dimensional version of the Kramers-Moyal expansion.     

Charge and Heat Transport in Polycrystalline Metallic Nanostructures

Metals are typically good conductors in which the abilities to transport charge and to transport heat can be related through the Wiedemann-Franz law. Here we report on an abnormal charge and heat transport in polycrystalline metallic nanostructures in which the ability to transport charge is weakened more obviously than that to transport heat. We attribute it to the influence of the internal grain boundaries and have formulated a novel relation to predict the thermal conductivity. The Wiedemann-Franz law is then modified to account for the influence of the grain boundaries on the charge and heat transport with the predictions now agreeing well with the measured results.