The stochastic finite element method (SFEM) is employed for solving stochastic onedimension time-dependent differential equations with random coefficients. SFEM is used to have a fixed form of linear algebraic equations for polynomial chaos coefficients of the solution process. Four fixed forms are obtained in the cases of stochastic heat equation with stochastic heat capacity or heat conductiv...

Introduction: Zircon is a highly refractory and weathering-resistant mineral that has proven useful as an indicator of shock metamorphism in the study of impact structures and formations (e.g., [1-6]). Zircon has advantages compared to quartz or other shockmetamorphosed rock-forming minerals that have been widely used as impact indicators, but are far less refractory than zircon. The purpose of...

It has been observed by various authors [3, 4, 5, 6, 8, 12] that the Riemann problem for certain equations from nonlinear elasticity and gasdynamics cannot be solved for all combinations of piecewise constant initial states with shock waves, rarefaction waves and contact discontinuities only. For that reason, the notion of a delta shock wave and a singular shock wave was introduced and employed...

Exploding gas-filled balloons are common chemistry demonstrations. They also provide an entertaining and educational means to experimentally verify nonlinear acoustical theory as described by the Earnshaw solution to the lossless Burgers equation and weak-shock theory. This article describes the theory, the demonstration, and the results of a propagation experiment carried out to provide typica...

Experiments on free expansion of Bose-Einstein condensate (BEC) have shown [1] that evolution of large and smooth distributions of BEC is described very well by hydrodynamic approximation [2] where dispersion and dissipation effects are neglected. At the same time, it is well known from classical compressible gas dynamics (see, e.g., [3]) that typical initial distributions of density and veloci...

In this paper, we apply a successful combination of three key tools which allows to get a measure of the cost of the approximate controllability for semilinear heat equation. The first tool consists to get enough information about the approximate control for the linear heat equation with a potential depending on space-time variable. Then a fixed point method is applied. The fixed point techniqu...

Compression wave analysis started nearly 50 years ago with Fowles.[1] Coperthwaite and Williams [2] gave a method that helps identify simple and steady waves. We have been developing a method that gives describes the non-isentropic character of compression waves, in general.[3] One result of that work is a simple analysis tool. Our method helps clearly identify when a compression wave is a simp...

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In several merging clusters of galaxies so-called cluster radio relics have been observed. These are extended radio sources which do not seem to be associated with any radio galaxy. Two competing physical mechanisms to accelerate the radio emitting electrons have been proposed: (i) diffusive shock acceleration and (ii) adiabatic compression of fossil radio plasma by merger shock waves. Here the...