A method of moments solution to a three-dimensional whisker structure

A method of moments solution to a three-dimensional whisker structure in a rectangular waveguide is presented. Theoretical results are compared with and verified by corresponding experimental measurements. As a result, it is shown that the orientation of the whisker with typical dimensions is not significant for the impedance tuning.     

Scattering by two-dimensional rough surfaces: comparison between the method of moments, Kirchhoff and small-slope approximations

We use a rigorous numerical code based on the method of moments to test the accuracy and validity domains of two popular first-order approximations, namely the Kirchhoff and the small-slope approximation(SSA), in the case of two-dimensional rough surfaces. The experiment is performed on two representative types of surfaces: surfaces with Gaussian spectrum, which are the paradigm of single-scale surfaces, and ocean-like surfaces, which belong to the family of multi-scale surfaces. The main outcome of these computations in the former case is that the SSA is outperformed by the Kirchhoff approximation(KA) outside the near-perturbative domain and in fact is quite unpredictable in that its accuracy does not depend only on the slope. For ocean-like surfaces, however, SSA behaves surprisingly well and is more accurate than the KA.     

Scattering by two-dimensional rough surfaces: comparison between the method of moments,Kirchhoff and small-slope approximations

Abstract

We use a rigorous numerical code based on the method of moments to test the accuracy and validity domains of two popular first-order approximations, namely the Kirchhoff and the small-slope approximation(SSA), in the case of two-dimensional rough surfaces. The experiment is performed on two representative types of surfaces: surfaces with Gaussian spectrum, which are the paradigm of single-scale surfaces, and ocean-like surfaces, which belong to the family of multi-scale surfaces. The main outcome of these computations in the former case is that the SSA is outperformed by the Kirchhoff approximation(KA) outside the near-perturbative domain and in fact is quite unpredictable in that its accuracy does not depend only on the slope. For ocean-like surfaces, however, SSA behaves surprisingly well and is more accurate than the KA.     

The role of excited species in UV-laser materials ablation

The stability of a planar surface upon pulsed UV-laser irradiation is studied with special emphasis on polymer ablation. Here, we consider a two-level system in which the excitation energy is dissipated via stimulated emission, non-radiative transitions, and activated desorption of excited species. With thermal relaxation times t _T10^–10 s the ablation front turns out to become stable. This could explain the smooth surfaces obtained after pulsed UV-laser ablation of pure and stress free organic polymers. The situation is quite different for materials, for example metals, where fast thermal relaxation of the excitation energy within times, typically, t _T<10^–11 s, gives rise to instabilities which result in surface roughening.On leave from the Institute of General Physics, Russian Academy of Sciences, 117942 Moscow, RussiaOn leave from the Institute of Applied Physics, Russian Academy of Sciences, 603600 Nishnii Novgorod, Russia     

The role of excited species in UV-laser materials ablation

UV-laser ablation is described in terms of a two-level system in which the excitation energy is dissipated via stimulated emission, thermal relaxation, and activated desorption of excited species. For thermal relaxation times t _T>10^–9 s and E* E (activation energies for excited-state and ground-state species) the model predicts high ablation rates at moderate surface temperatures, typically below 2000° C.On leave from General Physics Institute, Russian Academy of Sciences, 117942 Moscow, RussiaOn leave from Institute of Applied Physics, Russian Academy of Sciences, 603600 Nizhnii Novgorod, RussiaOn leave from L.D. Landau Theoretical Physics Institute, Russian Academy of Sciences, 142432 Chernogolovka, Moscow region, Russia     

Direct quadrature method of moments solution of the Fokker–Planck equation

The direct quadrature method of moments is presented as an efficient and accurate means of numerically computing solutions of the Fokker–Planck equation corresponding to stochastic nonlinear dynamical systems. The theoretical details of the solution procedure are first presented. The method is then used to solve Fokker–Planck equations for both 1D and 2D (noisy van der Pol oscillator) processes which possess nonlinear stochastic differential equations. Higher-order moments of the stationary solutions are computed and prove to be very accurate when compared to analytic (1D process) and Monte Carlo (2D process) solutions.     

The role of excited species in ultraviolet-laser materials ablation III. Non-stationary ablation of organic polymers

The role of non-stationary effects in nano-second ultraviolet (UV) excimer-laser ablation of organic polymers is discussed. The model includes reversible changes in absorption related to darkening and bleaching effects. Comparison of calculations and experimental data for polyimide demonstrates that the photophysical model describes the ablation kinetics quite well.     

A method of analyzing stability in dielectrics

The displacement-type ferroelectric phase transition is considered from the point of view of a loss in the lattice stability. An attempt is made to analyze the state using the methods of the theory of engineering cybernetics. The results of an analysis of a one-dimensional model of a crystal, and the results of the behavior of the transverse mode of oscillations of the lattice are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 56–60, December, 1972.     

Application of the improved method of moments to the solution of three-body scattering problems

The improved method of moments procedure which was developed in an earlier paper is applied to the solution of the three-body scattering equations for separable two-body interactions. Results of these calculations further support conclusions reached previously that the improved method of moments provides a rapid and accurate calculational procedure for solving scattering problems.     

黏弹介质包裹的充液管道中低频轴对称波传播特性

研究埋地充液管道中低频轴对称波传播特性。将土壤考虑为黏弹介质,结合Kennard薄壳方程和Kelvin-Voigt线性黏弹性模型,引入土壤载荷矩阵,推导出土-管滑移情形下流体主导波和管壁压缩波的相速度表达式。通过数值模拟计算得到流体主导波和管壁压缩波的频散和衰减曲线并进行可靠性验证,分析两种波引起的管壁径向位移之比,讨论厚径比和品质因子对流体主导波传播的影响。结果表明,黏弹介质对流体主导波和管壁压缩波的相速度影响较小,但对衰减影响较大;流体主导波对管壁径向位移有较大的影响,是泄露噪声传播的主要载体;厚径比越大,流体主导波的相速度越大,衰减越小;而品质因子越大,流体主导波的频散和衰减都越小。研究结果可为埋地充液管道的泄漏检测提供一定的理论参考。     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

The relations between the multipole moments in axistationary electrovacuum spacetimes and the N-soliton solution

General Relativity and Gravitation - We investigate the behavior of the deflection of light rays by charged and rotating AdS black holes using the Gauss–Bonnet formalism. Taking weak field...     

The method of moments and the nonequilibrium thermodynamics of rarefied gases

A generalized variant of the nonequilibrium thermodynamics of rarefied gases based on the linearized equations of Grad’s method of moments is studied. It is shown that despite the more complicated form of the thermodynamic forces, which include spatial derivatives of the fluxes, entropy production remains a bilinear combination of generalized thermodynamic fluxes and forces. Using perturbation theory in the small Knudsen number, the expressions obtained can be reduced to the well-known results of the Chapman-Enskog method at the level of the linearized Burnett approximation. Zh. éksp. Teor. Fiz. 113, 2081–2095 (June 1998)     

The fictitious force method for efficient calculation of vibration from a tunnel embedded in a multi-layered half-space

This paper presents an extension of the Pipe-in-Pipe (PiP) model for calculating vibrations from underground railways that allows for the incorporation of a multi-layered half-space geometry. The model is based on the assumption that the tunnel displacement is not influenced by the existence of a free surface or ground layers. The displacement at the tunnel–soil interface is calculated using a model of a tunnel embedded in a full space with soil properties corresponding to the soil in contact with the tunnel. Next, a full space model is used to determine the equivalent loads that produce the same displacements at the tunnel–soil interface. The soil displacements are calculated by multiplying these equivalent loads by Green?s functions for a layered half-space. The results and the computation time of the proposed model are compared with those of an alternative coupled finite element–boundary element model that accounts for a tunnel embedded in a multi-layered half-space. While the overall response of the multi-layered half-space is well predicted, spatial shifts in the interference patterns are observed that result from the superposition of direct waves and waves reflected on the free surface and layer interfaces. The proposed model is much faster and can be run on a personal computer with much less use of memory. Therefore, it is a promising design tool to predict vibration from underground tunnels and to assess the performance of vibration countermeasures in an early design stage.     

Scattering lengths and baryon magnetic moments in a gauge model of strong and electromagnetic interactions

We present a broken SU(3) gauge model of strong and electromagnetic interactions with the usual vector mesons. All particles (9 vectors, 8 baryons and 9 pseudoscalars) have the right masses by means of the Higgs mechanism. We study the consequences of Sakuraï's idea that strong and electromagnetic interactions are mediated by vector mesons universally coupled to nearly conserved currents: one finds encouraging values for scattering lengths except for P-wave parameters in the meson-baryon sector that are too small. The calculation of the baryon anomalous magnetic moments also gives too-small numbers.     

The adsorption integral equation: A new method of solution

A classification of the adsorption integral equation in to finite and infinite limit problems is made. A method of solution based on the theory of finite Hilbert transforms is proposed.     

The dynamic transient analysis of axisymmetric circular plates by the finite element method

The linear elastic, dynamic transient, analysis of some circular plate bending problems is considered by using axisymmetric, parabolic isoparametric, elements with an explicit time marching scheme. The effects of rotatory inertia and transverse shear deformation are included. A special mass lumping scheme and the use of a reduced integration technique allow the treatment of thin as well as thick plates. Several numerical examples are presented and compared with results from other sources.     

Brownian motion of particles embedded in a solution of giant micelles

We have measured the mean-square displacement of colloidal particles embedded in a semi-dilute solution of worm-like micelles, using diffusing wave spectroscopy. This allowed us to describe their rheological properties over a very wide time range. At very short times, the particles diffuse freely in the solvent, and then, they experience the characteristic relaxation times of the living chains. We deduced directly, from the mean-square displacement of the particles, the mechanical properties of the micellar solution, not only in the high-frequency regime, but also in the low-frequency range, in which we compared our results with direct mechanical measurements, and found good agreement. Received 22 March 2002 and Received in final form 5 June 2002