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991.
IntroductionInrecentyearsmuchprogresshasbeenmadeonthehigherandinfinitedimensionaldynamicalsystems (see ,e .g .[1 ]~ [1 0 ] ) ,andmainlybasedonreaction_diffusionequations,Kuramoto_SivashinskyequationsNavier_Stokesequations ,etc .Becauseofthefactthattheprincipaloper… 相似文献
992.
A. Berezovski J. Engelbrecht G. A. Maugin 《Archive of Applied Mechanics (Ingenieur Archiv)》2000,70(10):694-706
Summary A novel approach to the modeling of thermoelastic wave propagation is presented, based on the thermodynamics of discrete
systems. The first novelty includes the representation of integral balance laws for thermoelasticity in terms of contact quantities
that describe the nonequilibrium state of elements. The next new aspect is a modification of the recently proposed wave-propagation
algorithm, which is used as a tool for determining the contact quantities in a finite-volume scheme for the numerical simulation
of two-dimensional thermoelastic wave propagation in inhomogeneous media. Such a modification is needed to provide the satisfaction
of the thermodynamic consistency conditions between adjacent discrete elements. Results of computations for certain test problems
show the efficiency and physical consistency of the algorithm.
Received 11 November 1999; accepted for publication 2 May 2000 相似文献
993.
Interest in nonlinear wave equations has been stimulated bynumerous physical applications, such as telecommunication (e.g.nonlinear telegrapher equation), gasdynamics, anisotropic plasticity andnonlinear elasticity, etc. Mathematical models of these phenomena canoften be reduced to particular types of the equation u
tt
= f(x, u
x
) u
xx
+ g(x, u
x
). In this paper, the problem ofclassification of the latter equation with respect to admitted contacttransformation groups is reduced to the investigation of pointtransformation groups of the equivalent system of first-orderquasi-linear equations v
t
=a(x, v)w
x
, w
t
= b(x,v)v
x
. 相似文献
994.
We continue work by the second author and co-workers onsolitary wave solutions of nonlinear beam equations and their stabilityand interaction properties. The equations are partial differentialequations that are fourth-order in space and second-order in time.First, we highlight similarities between the intricate structure ofsolitary wave solutions for two different nonlinearities; apiecewise-linear term versus an exponential approximation to thisnonlinearity which was shown in earlier work to possess remarkablystable solitary waves. Second, we compare two different numericalmethods for solving the time dependent problem. One uses a fixed griddiscretization and the other a moving mesh method. We use these methodsto shed light on the nonlinear dynamics of the solitary waves. Earlywork has reported how even quite complex solitary waves appear stable,and that stable waves appear to interact like solitons. Here we show twofurther effects. The first effect is that large complex waves can, as aresult of roundoff error, spontaneously decompose into two simplerwaves, a process we call fission. The second is the fusion of twostable waves into another plus a small amount of radiation. 相似文献
995.
A speckle photographic technique is used for visualizing the planar distribution of the refractive deflection angles of light
transmitted through a compressible turbulent flow. Double exposure speckle photography is applied for the statistical analysis
of such flows. Quantitative visualization of the planar distribution of the refractive deflection angles of the light transmitted
through the compressible turbulent flow is performed. Turbulent structures are visible in the patterns of the deflection angles
isolines. The 2-D correlation functions of these deflection angles are constructed and analyzed. A mathematical procedure
for solving Erbeck-Merzkirch integral transformation is described and the 3-D density correlation functions are evaluated
using 2-D correlation functions of deflection angles of the light passed through the turbulence.
Received 14 November 1999 / Accepted 3 June 2000 相似文献
996.
Abstract. Numerical modeling of explosive consolidation of powders under two-dimensional conditions has been performed. Various regimes
of flow depending on detonation velocity have been considered. The appearance of “cold” layer during explosive consolidation
of powders has been studied by calculations.
Received 12 July 1999 / Accepted 27 April 2000 相似文献
997.
Dynamic fracture behaviour of crack curving in bent beams has been investigated. In order to understand the propagation mechanism
of such cracks under impact, an experimental method is used that combines dynamic photoelasticity with dynamic caustics to
study the interaction of the flexural waves and the crack. From the state change of the transient stresses in polymer specimen,
the curving fracture in the impulsively loaded beams is analyzed. The dynamic responses of crack tips are evaluated by the
stress intensity factors for the cracks running in varying curvature paths under bending stress wave.
The project supported by the National Natural Science Foundation of China and the Scientific Commission of Yunnan Province
of China 相似文献
998.
给出KdV-Burgers方程的有界行波解的精确级数解,采用Adomian算子分解法分别求行二个区域ζ〈0和ζ〉0的级数解,然后利用对接连续条件构成整体级数解。所得级数解能精确满足对接连续条件,并由此得到确定级数的系数递推公式,无需解非红性高阶代数方程组。与某些精确解及其它方法比较,计算简捷具在对接点处是收剑的。对某些非线性波动现象的研究,可作为计算和分析的数学依据。 相似文献
999.
1000.