Representation formulae of general solutions in the theory of hemitropic elasticity

We consider the steady state oscillation equations of the theoryof elasticity of hemitropic materials. We derive general representationformulae for the displacement and microrotation vectors by meansof six scalar metaharmonic functions. These formulae are veryconvenient and useful in many particular problems for domainswith concrete geometry. Here we consider two canonical transmissionproblems for piecewise homogeneous bodies with spherical interfacesand with the help of the representation formulae construct explicitsolutions in the form of absolutely and uniformly convergentseries. The representations can also be applied to multi-layeredbodies with spherical and cylindrical interfaces.     

Domain decomposition methods for the study of the particular behavior of a very thin long structure

The homogenization process of the Poisson equations in a thin structure leads to partial differential equation systems on different subdomains. As a result, it produces artificial interfaces and particular transmission conditions. © 1996 John Wiley & Sons, Inc.     

On the admissibility of stable spherical multivariate tests

This paper deals with correlation tests from the class of spherical tests introduced by Läuter (Biometrics 52 (1996) 964). These methods provide an alternative to classical MANOVA approaches and are particularly useful in small samples. Following a brief introduction of the spherical tests, it is shown that the so-called principal component correlation test is admissible in this class. A Bayesian approach is used to prove this result.     

Generation of interfaces for Lotka-Volterra competition-diffusion system with large interaction rates

We discuss the generation and motion of interfaces for Lotka-Volterra competition-diffusion system with large interaction. An asymptotic analysis of solutions shows that the two competing species are segregated and an interface appears on the common boundary of their habitats. The motion of the interface is governed by a free boundary problem. In this paper we establish a mathematical theory for the formation of interfaces (at the initial stage) by using an upper and lower solutions method. In addition, combining our results and a known result for the motion of interfaces (after the initial stage), we obtain some information on the generation and motion of interfaces for given almost any smooth initial data.     

Almost Everywhere Convergence of Multiple Trigonometric Fourier Series of Functions from Sobolev Classes

Mathematical Notes - In this paper, we study the almost everywhere convergence of spherical partial sums of multiple Fourier series of functions from Sobolev classes. It is proved that almost...     

Orthogonal and Nonorthogonal Multiresolution Analysis, Scale Discrete and Exact Fully Discrete Wavelet Transform on the Sphere

Based on a new definition of dilation a scale discrete version of spherical multiresolution is described, starting from a scale discrete wavelet transform on the sphere. Depending on the type of application, different families of wavelets are chosen. In particular, spherical Shannon wavelets are constructed that form an orthogonal multiresolution analysis. Finally fully discrete wavelet approximation is discussed in the case of band-limited wavelets. June 18, 1996. Date revised: January 14, 1997.     

不变形双滴的热毛细迁移及相互作用

对微重力下不变形双滴的非定常热毛细迁移运动进行了数值模拟,采用了有限差分方法对动量方程和能量方程进行离散,使用波前追踪法捕捉运动的不变形液滴界面．研究显示双滴的排列方式对它们的迁移规律和相互作用影响很大,其中影响任一个液滴运动的最主要的因素是另一个液滴的存在所引起的温度场的扰动．     

A discussion about the homogenization of moving interfaces

There has been considerable interest lately in the homogenization theory for first- and second-order partial differential equations in periodic/almost periodic and random, stationary, ergodic environments. Of special interest is the study of the averaged behavior of moving interfaces. In this note we revisit the last issue. We present several new results concerning interfaces moving by either oscillatory first-order or curvature dependent coupled with oscillatory forcing normal velocity in periodic environments and analyze in detail their behavior. Under sharp assumptions we show that such fronts may homogenize, get trapped or oscillate.     

Marangoni效应对等曲率弯曲界面凝固过程的影响

用渐近方法和相场数值模拟分别研究了球状晶体和柱状晶体凝固过程中,固液界面表面张力随温度的变化对界面运动的影响．结果表明Marangoni效应将增大临界晶核半径,减缓界面运动速度．在静止熔体中,枝晶尖端生长速度随Marangoni数线性下降．渐近展开和相场模拟得到的结果定性是一致的．     

Convergence rate of spherical harmonic expansions of smooth functions

We extend a well-known result of Bonami and Clerc on the almost everywhere (a.e.) convergence of Cesàro means of spherical harmonic expansions. For smooth functions measured in terms of φ-derivatives on the unit sphere, we obtained the sharp a.e. convergence rate of Cesàro means of their spherical harmonic expansions.     

A new class of compact spherical spaces

We describe a class of almost symmetric spherical spaces which is absent in the known classifications made by M. Krämer and I. Mikityuk.     

Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous,incompressible fluids

We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects into account. This leads to a coupled system of Navier–Stokes and Mullins–Sekerka type parts that coincides with the asymptotic limit of a diffuse interface model. We prove the long-time existence of weak solutions, which is an open problem for the classical two-phase model. We show that the phase interfaces have in almost all points a generalized mean curvature.     

Spherical quasi-newtonian stellar pulsations in RTG

It is shown that in the relativistic theory of gravity (RTG), in contrast to the general theory of relativity (GTR), spherical stellar pulsations lead to the appearance of a nonstatic behavior of the external gravitational field.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 320–324, February, 1996.     

Almost disjoint permutation groups

A permutation group on a set of (infinite) cardinality is almost disjoint if no element of except the identity has fixed points, i.e., if is an almost disjoint family of subsets of . We show how almost disjoint permutation groups can be constructed from almost disjoint families of sets.

     

Simulation of mass transfer at free liquid/liquid interfaces

A numerical scheme for the simulation of mass transfer processes at free liquid/liquid interfaces using the interface tracking method is presented. Due to comparable diffusion coefficients in liquid/liquid systems, the mass transfer resistance in both phases is relevant for the entire transient mass transfer process. Exemplary, the extraction process from a free rising spherical droplet of constant shape is used. The presented approach can be used in general for any multiphase steady-state mass transfer system. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

High-frequency projection method for plane problems of wave diffraction on dielectric bodies

A version of the Galerkin incomplete projection method is described for plane problems of wave diffraction on dielectric bodies of arbitrary shape. The proposed method generalizes the Sommerfeld method, which constructs diffraction series rapidly converging at high frequencies for circular and spherical bodies. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 58–67.     

Simplified immersed interface methods for elliptic interface problems with straight interfaces

In this article, we propose simplified immersed interface methods for elliptic partial/ordinary differential equations with discontinuous coefficients across interfaces that are few isolated points in 1D, and straight lines in 2D. For one‐dimensional problems or two‐dimensional problems with circular interfaces, we propose a conservative second‐order finite difference scheme whose coefficient matrix is symmetric and definite. For two‐dimensional problems with straight interfaces, we first propose a conservative first‐order finite difference scheme, then use the Richardson extrapolation technique to get a second‐order method. In both cases, the finite difference coefficients are almost the same as those for regular problems. Error analysis is given along with numerical example. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 188–203, 2012     

Finite element methods and their convergence for elliptic and parabolic interface problems

In this paper, we consider the finite element methods for solving second order elliptic and parabolic interface problems in two-dimensional convex polygonal domains. Nearly the same optimal -norm and energy-norm error estimates as for regular problems are obtained when the interfaces are of arbitrary shape but are smooth, though the regularities of the solutions are low on the whole domain. The assumptions on the finite element triangulation are reasonable and practical. Received July 7, 1996 / Revised version received March 3, 1997     

Steiner Symmetrization is Continuous in W1,p

We study the continuity, smoothing, and convergence properties of Steiner symmetrization in higher space dimensions. Our main result is that Steiner symmetrization is continuous in W ^{1, p} in all dimensions. This implies that spherical symmetrization cannot be approximated in W ^{1, p} by sequences of Steiner symmetrizations. We also give a quantitative version of the standard energy inequalities for spherical symmetrization. Submitted: September 1996     

Almost optimal convergence of the point vortex method for vortex sheets using numerical filtering

Standard numerical methods for the Birkhoff-Rott equation for a vortex sheet are unstable due to the amplification of roundoff error by the Kelvin-Helmholtz instability. A nonlinear filtering method was used by Krasny to eliminate this spurious growth of round-off error and accurately compute the Birkhoff-Rott solution essentially up to the time it becomes singular. In this paper convergence is proved for the discretized Birkhoff-Rott equation with Krasny filtering and simulated roundoff error. The convergence is proved for a time almost up to the singularity time of the continuous solution. The proof is in an analytic function class and uses a discrete form of the abstract Cauchy-Kowalewski theorem. In order for the proof to work almost up to the singularity time, the linear and nonlinear parts of the equation, as well as the effects of Krasny filtering, are precisely estimated. The technique of proof applies directly to other ill-posed problems such as Rayleigh-Taylor unstable interfaces in incompressible, inviscid, and irrotational fluids, as well as to Saffman-Taylor unstable interfaces in Hele-Shaw cells.