Dynamics of an elastic cylindrical shell with a gas–liquid medium subject to two-frequency vibrational excitation

The paper presents experimental results on nonlinear dynamic processes such as the deformation of the elastic wall of a cylindrical shell filled with a fluid and the formation and clustering of gas bubbles, which interact under two-frequency excitation Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 112–122, November 2008.     

Homogenization of a stationary navier-stokes flow in porous medium with thin film

The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition.At the end of the article,＂Darcy＇s law＂is rigorously derived from this model as the parameter ε tends to zero,which is independent of the coordinates towards the thickness.     

Opposing mixed convection and its interaction with radiation inside eccentric horizontal cylindrical annulus

In the present investigation, the coupled phenomenon of opposing mixed convection and radiation within differentially heated eccentric horizontal cylindrical annulus has been numerically simulated. The radiation transfer contributed from the participating medium is obtained by solving the nonlinear integro‐differential radiative transfer equation using discrete ordinate method. The participating gray medium is considered to be emitting, absorbing and isotropically scattering. The walls of the annulus are considered to be opaque, diffuse and gray. In the study it has been observed that the Richardson number ‘Ri’ has a small effect on the total Nusselt number ‘Nu’ in mixed convection heat transfer with or without radiation. From the present investigation it is found that substantial changes occur in isotherms as well as in flow patterns, when the Richardson number is allowed to vary in the range of 0.01–1. The influence of radiative parameters on the interaction phenomenon has been delineated through isotherm and streamline pattern. Copyright © 2008 John Wiley & Sons, Ltd.     

An alternative procedure for approximating hyperbolic systems of conservation laws

This work presents an alternative numerical procedure for simulating a class of nonlinear hyperbolic systems, using Glimm's method for advancing in time. The standard procedure to implement this methodology suffers from the disadvantage of requiring a complete solution of the associated Riemann problem—a task, in general, not easily reached. The alternative procedure introduced in this article consists in approximating the solution of the associated Riemann problem by piecewise constant functions always satisfying the jump condition—thus circumventing the difficulty of solving the Riemann problem and giving rise to an approximation easier to implement with lower computational cost. In order to illustrate the good performance of the alternative methodology proposed, two problems are considered—namely the transport of a pollutant in the atmosphere and the dynamics of the filling up of a rigid porous medium, modeled under a mixture theory viewpoint. Comparison with the standard procedure, employing the complete solution of the associated Riemann problem for implementing Glimm's scheme, has shown good agreement.     

Transient response of SH waves in a layered half-space with sub-surface and interface cracks

The transient scattering of SH waves by sub-surface and interface cracks parallel to the free surface in a layered elastic solid is investigated. The problem in frequency domain is solved by using a hybrid method which combines the finite element method of the near field with the boundary integral representation of the far field. The transient responses are then obtained by inverting the spectra via fast Fourier transform with the incident pulse Ricker of wavelet. Numerical results are presented for the surface displacements, dynamic stress intensity factors and wave motion in the layered half-space. Furthermore, the propagations of reflected, diffracted, and direct impact waves at any instant are clearly identified by the present method. To understand the mechanism of elastic wave interaction is very important in the field of ultrasonic non-destructive evaluation (NDE) and fracture mechanics studies.     

The influence of the electromagnetic radiation of low intensity on toxicity of an aqueous medium

The toxicity of solutions of phenol in combination with cadmium and cobalt for a culture of micro-seaweed and the opportunity of decreasing their toxicity by the influence of electromagnetic radiation in the range of the highest frequencies (UHF irradiation) are studied. The synergism between phenol and metals and a decrease in their toxicity under the influence of electromagnetic radiation are revealed.     

Inverse problem method in laser physics

Applications of the method of ill-posed inverse problems in laser physics are considered. Means of calculating the level cross sections of physical-chemical reactions with subsequent calculation of the reaction rate constants are developed. Mathematical and numerical aspects for the realization of ill-posed inverse problem are considered in detail using the concrete example of level cross sections of dissociation.     

Elastic properties and mechanical relaxation behaviors of PVDF (poly (vinylidene fluoride)) at temperatures between −20 and 100 °C and at 2 MHz ultrasonic frequency

The elastic properties of PVDF have been investigated as a function of temperature. The propagation velocity and absorption of longitudinal and transverse ultrasonic waves have been measured at a constant frequency of 2 MHz and temperatures between –20 and 100 °C. Hence, the temperature dependences of storage and loss elastic constants have been obtained for temperatures between –20 and 100 °C. It has been seen that the relaxation behavior is affected from the form of mechanical disturbance. For the longitudinal mode, only one relaxation peak at 42 °C, but for transverse mode three relaxation peaks at 28 °C, 60 °C, and 94 °C have been observed. The results have been compared with the literature values obtained previously for PVDF. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2862–2873, 2005     

Collision of optical solitons with Kerr law nonlinearity

The intra-channel collision of optical solitons, with Kerr law nonlinearity, is studied by the aid of quasi-particle theory. The perturbation terms considered in this paper are all of Hamiltonian type. It is shown that the soliton–soliton interaction can be suppressed in the presence of these perturbations, namely, the self-steepening, the third-order dispersion, the fourth-order dispersion and the frequency separation between the soliton carrier and the gain-center frequency. The prediction of quasi-particle theory are fully confirmed by direct numerical simulations.     

Explicit analytical solutions of the anisotropic Brinkman model for the natural convection in porous media (II)

Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model—an improved Darcy model—describing the natural convection in porous media. Besides their important theoretical meaning (for example, in analyzing the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer. Some solutions considering the anisotropic effect of permeability have been given previously by the authors, and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.