共查询到20条相似文献,搜索用时 15 毫秒
1.
L. A. Molotkov 《Journal of Mathematical Sciences》2006,132(1):83-90
The propagation of seismic waves in block two- and three-dimensional media is investigated. These media are composed of identical
cells in which there are several fluid blocks and one elastic block. For these media, effective models, which are anisotropic
fluids, are established. Formulas for the velocities of propagation in these fluids are derived and investigated. A special
investigation is carried out in the cases where the elastic block occupies almost the entire cell or where the relative volume
of the elastic block is very small. Bibliography: 9 titles.
Dedicated to P. V. Krauklis on the occasion of his seventieth birthday
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 147–160. 相似文献
2.
L. A. Molotkov 《Journal of Mathematical Sciences》2005,127(6):2482-2491
A two-dimensional medium consisting of alternating elastic and fluid blocks along the x and z axes is considered. For this block medium, an effective model described by a system of equations is constructed by the method of matrix averaging. An investigation of the equations of this model enables one to separate two body waves from the wave field, to construct their fronts, and to obtain expressions for their velocities along the axes. The effective model is considered in the cases where the block medium is converted to a layered elastic-fluid medium, where all the blocks are of the same size, and where an elastic or a fluid medium occupies the entire volume. Bibliography: 7 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 254–271. 相似文献
3.
L. A. Molotkov 《Journal of Mathematical Sciences》2006,132(1):69-82
The propagation of seismic waves in block two- and three-dimensional fluid media is investigated. For these media, effective
models, which are anisotropic fluids, are established. Formulas for the velocities of wave propagation in these fluid media
are derived and analyzed. Special investigation is conducted in the cases where blocks with different fluids alternate along
the coordinate axes or where blocks filled with a fluid are surrounded by blocks with another fluid. In both cases, the dependence
of the wave velocities in the entire medium on the differences of the densities and the wave velocities in fluid blocks is
studied. Bibliography: 9 titles.
Dedicated to P. V. Krauklis on the occasion of his seventieth birthday
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 124–146. 相似文献
4.
We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations. 相似文献
5.
Doklady Mathematics - The problem of seismic wave propagation in a heterogeneous geological medium is considered. The dynamic behavior of the medium is described by the linear elastic system of... 相似文献
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G. I. Petrashen 《Journal of Mathematical Sciences》2003,117(1):3805-3872
Part II is a continuation of Part I published in Zapiski Nauchnykh Seminarov POMI, Vol. 273 (JOurnal of Mathematical Sciences, Vol. 116, No. 2, 2003). 相似文献
8.
The paper deals with finite–difference (f-d) approach to simulation of elastic waves' propagation in anisotropic elastic media with general symmetry. Any implementation of this approach claims resolution of two key problems:
- construction of an effective f-d scheme itself; we propose to use the Lebedev's scheme (LS) being a natural generalization of Virieux staggered grid scheme (VS) widely used for isotropy; we prove that LS possesses better dispersion properties in comparison with well known Rotated Staggered Grids Scheme (RSGS).
- stable domain distension. The Perfectly Matched Layers(PML) useful for isotropic problems can be unstable in the case of anisotropy. Lebedev scheme allows one to use Optimal Grids (OG) which gives a possibility to implement efficient and low cost domain distension.
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10.
Z. A. Yanson 《Journal of Mathematical Sciences》2003,117(2):4049-4063
The Love waves concentrated near the surface of an anisotropic elastic body are studied. A uniform asymptotics of the wave field is constructed with the use of the nonstationary caustic expansion (Yu. A. Kravtsov's ansatz) in the form of a space-time ray series. Using three types of waves, which propagate along any direction in an elastic medium, as a vector basis, sufficient conditions for the existence of a nonzero asymptotic solution of the problem under study are obtained. The procedure for constructing asymptotic series is illustrated with the model of a transversely isotropic medium. Bibliography: 9 titles. 相似文献
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Computational Mathematics and Mathematical Physics - A nonlinear Sturm–Liouville-type eigenvalue problem on an interval with the boundary conditions of the third kind and an additional... 相似文献
13.
Mariana Haragus 《偏微分方程通讯》2013,38(5):791-815
We investigate corners and steps of interfaces in anisotropic systems. Starting from a stable planar front in a general reaction-diffusion-convection system, we show existence of almost planar interior and exterior corners. When the interface propagation is unstable in some directions, we show that small steps in the interface may persist. Our assumptions are based on physical properties of interfaces such as linear and nonlinear dispersion, rather than properties of the modeling equations such as variational or comparison principles. We also give geometric criteria based on the Cahn–Hoffman vector, that distinguish between the formation of interior and exterior corners. 相似文献
14.
The problem of asymptotic features of front propagation in stirred media is addressed for laminar and turbulent velocity fields. In particular we consider the problem in two dimensional steady and unsteady cellular flows in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. In the steady case we provide an analytical approximation for the front speed, v f, as a function of the stirring intensity, U, in good agreement with the numerical results. In the unsteady (time-periodic) case, albeit the Lagrangian dynamics is chaotic, chaos in the front dynamics is relevant only for a transient. Asymptotically the front evolves periodically and chaos manifests only in the spatially wrinkled structure of the front. In addition we study front propagation of reactive fields in systems whose diffusive behavior is anomalous. The features of the front propagation depend, not only on the scaling exponent ν, which characterizes the diffusion properties, \({( \langle (x(t) - x(0))^2 \rangle \sim t^{2\nu} )}\) , but also on the detailed shape of the probability distribution of the diffusive process. 相似文献
15.
Bettina Albers 《PAMM》2008,8(1):10667-10668
We investigate the propagation of sound waves by means of a newly constructed model in a sandstone filled with two immiscible fluids. The speeds and attenuations of the four emerging waves (one transversal, three longitudinal) are illustrated in dependence on frequency and initial saturation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
饱和土中弹性波的传播速度 总被引:2,自引:0,他引:2
根据所建立的波动方程分析了饱和土中弹性波的弥散特性,并且用室内超声波和现场地震波试验结果进行验证.本文为由弹性波(尤其是P波)速度测得合理的饱和土物理力学参数提供了理论依据. 相似文献
17.
Andrej Zlatoš 《纯数学与应用数学通讯》2017,70(5):884-949
Consider reaction‐diffusion equation u t =Δ u + f (x,u ) with and general inhomogeneous ignition reaction f ≥ 0 vanishing at u = 0,1. Typical solutions 0 ≤ u ≤ 1 transition from 0 to 1 as time progresses, and we study them in the region where this transition occurs. Under fairly general qualitative hypotheses on f we show that in dimensions d ≤ 3, the Hausdorff distance of the superlevel sets {u ≥ ε } and {u ≥ 1‐ε} remains uniformly bounded in time for each ε ? (0,1). Thus, u remains uniformly in time close to the characteristic function of in the sense of Hausdorff distance of superlevel sets. We also show that each {u ≥ ε} expands with average speed (over any long enough time interval) between the two spreading speeds corresponding to any x ‐independent lower and upper bounds on f . On the other hand, these results turn out to be false in dimensions d ≥ 4, at least without further quantitative hypotheses on f . The proof for d ≤ 3 is based on showing that as the solution propagates, small values of u cannot escape far ahead of values close to 1. The proof for d ≥ 4 is via construction of a counterexample for which this fails. Such results were before known for d =1 but are new for general non‐periodic media in dimensions d ≥ 2 (some are also new for homogeneous and periodic media). They extend in a somewhat weaker sense to monostable, bistable, and mixed reaction types, as well as to transitions between general equilibria of the PDE and to solutions not necessarily satisfying . © 2016 Wiley Periodicals, Inc. 相似文献
18.
An asymptotic theory is presented for the analysis of surfacewave propagation at high frequencies. The theory is developedfor scalar surface waves satisfying an impedance boundary conditionon a surface, which may be curved and, whose impedance may bevariable. A surface eikonal equation is derived for the phaseof the surface wave field, and it is shown that the wave fieldpropagates over the surface along the surface rays, which arethe characteristics of the surface eikonal equation. The wavefield in space is found by solving certain eikonal and transportequations with the aid of complex rays. The theory is then appliedto several examples: axial waves on a circular cylinder, sphericallysymmetric waves on a sphere, waves on a circular cone with avariable impedance, and waves on the plane boundary of an inhomogeneousmedium. In each case it is found that the asymptotic expansionof the exact solution agrees with the asymptotic solution. 相似文献
19.
Many wave propagation phenomena in classical physics are governed by equations that can be recast in Schrödinger form. In this approach the classical wave equation (e.g., Maxwell's equations, acoustic equation, elastic equation) is rewritten in Schrödinger form, leading to the study of the spectral theory of its classical wave operator, a self-adjoint, partial differential operator on a Hilbert space of vector-valued, square integrable functions. Physically interesting inhomogeneous media give rise to nonsmooth coefficients. We construct a generalized eigenfunction expansion for classical wave operators with nonsmooth coefficients. Our construction yields polynomially bounded generalized eigenfunctions, the set of generalized eigenvalues forming a subset of the operator's spectrum with full spectral measure. 相似文献
20.
Instability of Solitary Waves in Nonlinear Composite Media 总被引:1,自引:0,他引:1
Ye Zhao 《应用数学学报(英文版)》2007,23(2):311-318
In this paper,we investigate a class of Hamiltonian systems arising in nonlinear composite media.By detailed analysis and computation we obtain a decaying estimates on the semigroup and prove the orbitalinstability of two families of explicit solitary wave solutions (slow family in anisotropic case and solitary wavesin isotropic case),which theoretically verify the related guess and numerical results. 相似文献