Thermal self-action effects of acoustic beam in a vibrationally relaxing gas

Thermal self-action of acoustic beam in a molecular gas with excited internal degrees of molecules’ freedom, is studied. This kind of thermal self-action differs from that in a Newtonian fluid. Heating or cooling of a medium takes place due to transfer of internal vibrational energy. Equilibrium and non-equilibrium gases, which may be acoustically active, are considered. A beam in an acoustically active gas is self-focusing unlike a beam in a standard viscous gas. The self-action effects relating to wave beams containing shock fronts, are discussed. Stationary and non-stationary kinds of self-action are considered.     

Modelling and simulation of acoustic pulse interaction with a fluid-filled hollow elastic sphere through numerical Laplace inversion

A detailed study is undertaken to analyze the non-steady interaction of plane progressive pressure pulses with an isotropic, homogeneous, fluid-filled and submerged spherical elastic shell of arbitrary wall thickness within the scope of linear acoustics. The formulation is based on the general three dimensional equations of linear elasticity and the wave equation for the internal and external acoustic domains. The Laplace transform with respect to the time coordinate is invoked, and the classical method of separation of variables is used to obtain the transformed solutions in the form of partial-wave expansions in terms of Legendre polynomials. The inversion of Laplace transforms have been carried out numerically using Durbin’s approach based on Fourier series expansion. Special convergence enhancement techniques are invoked to completely eradicate spurious oscillations (Gibbs’ phenomenon), and obtain uniformly convergent solutions. Detailed numerical results for the transient and vibratory responses of water-submerged steel shells of selected wall thickness parameters with various internal fluid loadings under an exponential wave excitation are presented. Many of the interesting dynamic features in the transient shell–shock interaction such as shock transparency, shell-radiated negative pressure waves, formation of triple points, and focusing of the reflected waves are examined using appropriate 2D images of the internal pressure field. Also, the temporal behavior of the specularly-reflected, the lowest symmetric S₀- and antisymmetric A₀-Lamb waves, as well as appearance of the Franz’s creeping waves are discussed through proper visualization of the external scattered field. Likelihood of cavitation is addressed and regions proned to cavitation are identified. Moreover, the effects of internal fluid impedance in addition to shell wall thickness on the dynamic stress concentrations induced within the shell are analyzed. Limiting cases are considered and fair agreements with well-known solutions are established.     

On the far field patterns for electromagnetic scattering by a chiral obstacle in a chiral environment

A time-harmonic plane electromagnetic wave is scattered by a chiral body in a chiral environment. The body is either a perfect conductor, or a dielectric, or a scatterer with an impedance surface. Using the Huygens's principle, we construct in closed forms both the left-circularly polarized and right-circularly polarized electric far field patterns for such chiral media. We prove reciprocity relations and general scattering theorems for chiral materials which are a generalization of those obtained by Twersky for achiral electromagnetic scattering. In the special case when the directions of incidence and observation are the same we prove the associated forward scattering theorems.     

Applying proper orthogonal decomposition to the computation of particle dispersion in a two-dimensional ventilated cavity

The Lagrangian technique is used to compute particle dispersion in a two-dimensional ventilated cavity. The instantaneous air velocity field at the particle’s location is obtained by proper orthogonal decomposition (POD). The low-dimensional dynamic model is obtained by performing a Galerkin projection of the Navier–Stokes equations onto each POD eigenfunction and it is coupled with the particle’s equation of motion. A substantial decrease in computing time (when comparing with LES computations) is noted. Two different cases of particles’ injection are modelled: the particle source is located in the inlet in the first simulation, and close to the floor in the second simulation.     

An error estimate of the proper orthogonal decomposition in model reduction and data compression

A kind of the proper orthogonal decomposition (POD) is used for data compression of rugged surface and reduction of the Navier–Stokes equations. An error estimate of the POD in model reduction and data compression is discussed. The numerical examples show that the error between the POD approximate solution and reference solution is consistent with theoretical results, and also show that the proposed algorithm is feasible and efficient. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

Model simulation and experiments of flow and mass transport through a nano-material gas filter

A computational model for evaluating the performance of nano-material packed-bed filters was developed. The porous effects of the momentum and mass transport within the filter bed were simulated. For the momentum transport, an extended Ergun-type model was employed and the energy loss (pressure drop) along the packed-bed was simulated and compared with measurement. For the mass transport, a bulk adsorption model was developed to study the adsorption process (breakthrough behavior). Various types of porous materials and gas flows were tested in the filter system where the mathematical models used in the porous substrate were implemented and validated by comparing with experimental data and analytical solutions under similar conditions. Good agreements were obtained between experiments and model predictions.     

Error estimates of proper orthogonal decomposition eigenvectors and Galerkin projection for a general dynamical system arising in fluid models

We study estimates for proper orthogonal decomposition eigenvectors and eigenvalues as well as error estimates between the exact solution of a 2D Navier–Stokes model and the numerical approach when the proper orthogonal decomposition method is considered. These estimates are also extended when bifurcation diagram are calculated using the so called p-POD or SPOD methods with a new cut-off criterion to minimize noisy modes produced by the p-POD method.     

Split fields and direction of propagation for the solution to first-order systems of equations

The standard wave-splitting approach for the wave equation in inhomogeneous media is first reexamined. Next, by analogy with the theory of wave propagation through singular surfaces, a characterization is given for a function in space-time to represent a wave propagating in a direction. The condition is applied in connection with a simple example and found to be quite restrictive. The same problem is then considered in the Fourier-transform domain where the unknown function is an n-tuple satisfying a system of ordinary differential equations. The condition for propagation in a direction is established for the Fourier components. Next, some physical problems are considered which are expressed by partial differential equations or by integro-differential equations. The associated first-order system of equations is examined in terms of the eigenvalues of a matrix. This shows that, for any eigenvalue, the direction of propagation may change with the frequency and that arguments about the dominance of the principal part of the operator may cease to hold.     

Electromagnetic scattering by a homogeneous chiral obstacle: scattering relations and the far‐field operator

Time‐harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle. The reciprocity principle, the basic scattering theorem and an optical theorem are proved. These results are used to prove that if the chirality measure of the obstacle is real, then the far‐field operator is normal. Moreover, it is shown that the eigenvalues of the far‐field operator are the same as the eigenvalues of Waterman's T‐matrix. Copyright © 1999 John Wiley & Sons, Ltd.     

Conservative finite-difference scheme for the problem of propagation of a femtosecond pulse in a photonic crystal with combined nonlinearity

A conservative finite-difference scheme is constructed for the problem of propagation of a light pulse in a one-dimensional nonlinear photonic crystal with combined nonlinearity. The invariants of the corresponding differential problem and their difference analogues are given. The scheme is compared with those based on the widespread splitting method. For combined cubic and quadratic nonlinearity in photonic crystal layers, it is shown that the classical splitting method is ineffective, since it requires time steps that are smaller by one or more orders of magnitude. The finite-difference scheme proposed conserves the propagation invariants, which cannot be achieved for splitting schemes even on considerably finer grids. Nonreflecting conditions substantially improve the efficiency of conservative finite-difference schemes as applied to the simulation of complex nonlinear effects in photonic crystals, which require much smaller steps in space and time than those used in the case of linear propagation. The simulation is based on the approach proposed by the authors for the given class of problems.     

Electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment: solvability and low‐frequency theory

The scattering of plane time‐harmonic electromagnetic waves propagating in a homogeneous isotropic chiral environment by a bounded perfectly conducting obstacle is studied. The unique solvability of the arising exterior boundary value problem is established by a boundary integral method. Integral representations of the total exterior field, as well as of the left and right electric far‐field patterns are derived. A low‐frequency theory for the approximation of the solution to the above problem, and the derivation of the far‐field patterns is also presented. Copyright © 2002 John Wiley & Sons, Ltd.     

Evolution of curves on a surface driven by the geodesic curvature and external force

We study a flow of closed curves on a given graph surface driven by the geodesic curvature and external force. Using vertical projection of surface curves to the plane we show how the geodesic curvature-driven flow can be reduced to a solution of a fully nonlinear system of parabolic differential equations. We show that the flow of surface curves is gradient-like, i.e. there exists a Lyapunov functional nonincreasing along trajectories. Special attention is placed on the analysis of closed stationary surface curves. We present sufficient conditions for their dynamic stability. Several computational examples of evolution of surface curves driven by the geodesic curvature and external force on various surfaces are presented in this article. We also discuss a link between the geodesic flow and the edge detection problem arising from the image segmentation theory.     

A multisymplectic framework for classical field theory and the calculus of variations II: space + time decomposition

In a previous paper I laid the foundations of a covariant Hamiltonian framework for the calculus of variations in general. The purpose of the present work is to demonstrate, in the context of classical field theory, how this covariant Hamiltonian formalism may be space + time decomposed. It turns out that the resulting “instantaneous” Hamiltonian formalism is an infinite- dimensional version of Ostrogradski 's theory and leads to the standard symplectic formulation of the initial value problem. The salient features of the analysis are: (i) the instantaneous Hamiltonian formalism does not depend upon the choice of Lepagean equivalent; (ii) the space + time decomposition can be performed either before or after the covariant Legendre transformation has been carried out, with equivalent results; (iii) the instantaneous Hamiltonian can be recovered in natural way from the multisymplectic structure inherent in the theory; and (iv) the space + time split symplectic structure lives on the space of Cauchy data for the evolution equations, as opposed to the space of solutions thereof.     

Justification of Dipole Approximation in the Problem of Nonlinear Wave Generation by a Submerged Sphere

Some nonlinear dipole approximation is constructed for the nonstationary problem of a solid sphere motion under a free surface. The approximation is justified in the class of analytic functions decaying at infinity.Original Russian Text Copyright © 2005 Pyatkina E. V.The author was supported by the State Maintenance Program for the Leading Scientific Schools (Grant NSh-440.2003.1) and the Russian Foundation for Basic Research (Grant 05-01-00250).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 907–927, July–August, 2005.     

Line source and point source scattering of acoustic waves by the junction of transmissive and soft-hard half planes

Firstly, the analysis of [A. Büyükaksoy, G. Cinar, A.H. Serbest, Scattering of plane waves by the junction of transmissive and soft-hard half planes, ZAMP 55 (2004) 483-499] for the scattering of plane waves by the junction of transmissive and soft-hard half planes is extended to the case of a line source. The introduction of the line source changes the incident field and the method of solution requires a careful analysis in calculating the scattered field. The graphical results are presented using MATHEMATICA. We observe that the graphs of the plane wave situation [A. Büyükaksoy, G. Cinar, A.H. Serbest, Scattering of plane waves by the junction of transmissive and soft-hard half planes, ZAMP 55 (2004) 483-499] can be recovered by shifting the line source to a large distance. Subsequently, the problem is further extended to the case of scattering due to a point source using the results obtained for a line source excitation. The introduction of a point source (three dimensions) involves another variable which then requires the calculation of an additional integral appearing in the inverse transform.     

纳米流体流经热分层线性多孔伸展平面时的MHD自然对流及其Lie对称群变换

就不可压缩粘性纳米流体,流经半无限垂直伸展平面并计及热分层时,研究该流体的MHD自然对流和热交换.通过特定形式的Lie对称群变换,即单参数群变换,将所考虑问题的偏微分控制方程变换为常微分方程组.然后,使用基于打靶法的Runge Kutta Gill法进行数值求解.最后得到结论:流场、温度和纳米颗粒体积率受热分层和磁场的影响很显著.     

Research in the flexural buckling modes of a cylindrical sandwich shell under the action of a temperature field inhomogeneous across its thickness

A solution to the problem on the stability according to the flexural buckling mode is given for a cylindrical sandwich shell with a transversely soft core of arbitrary thickness. The shell is under the action of a temperature field inhomogeneous across the thickness, and its end faces are fastened in such a way (in the axial direction, the face sections of the external layer are fixed, but of the internal one are free) that an inhomogeneous subcritical stress-strain state arises in the shell across the thickness of its layers. It is shown that, under such conditions, the buckling mode of the shell is mixed flexural. To reveal and investigate this mode, equations of subcritical equilibrium and stability of a corresponding degree of accuracy are needed.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 715–730, November–December, 2004.     

On a System of Equations of Evolution with a Non-Symmetrical Parabolic Part Occuring in the Analysis of Moisture and Heat Transfer in Porous Media

Most non-trivial existence and convergence results for systems of partial differential equations of evolution exclude or avoid the case of a non-symmetrical parabolic part. Therefore such systems, generated by the physical analysis of the processes of transfer of heat and moisture in porous media, cannot be analyzed easily using the standard results on the convergence of Rothe sequences (e.g. those of W. Jager and J. Kacur). In this paper the general variational formulation of the corresponding system is presented and its existence and convergence properties are verified; its application to one model problem (preserving the symmetry in the elliptic, but not in the parabolic part) is demonstrated.