Rarefaction

About: Rarefaction is a research topic. Over the lifetime, 1852 publications have been published within this topic receiving 26943 citations.

Directional dependence of nonlinear surface acoustic waves in the (001) plane of cubic crystals.

Abstract: Spectral evolution equations are used to perform analytical and numerical studies of nonlinear surface acoustic waves in the (001) plane of a variety of nonpiezoelectric cubic crystals. The basic theory underlying the model equations is outlined, and quasilinear solutions of the equations are presented. Expressions are also developed for a characteristic length scale for nonlinear distortion and a nonlinearity coefficient. A time-domain equation corresponding to the spectral equations is derived. Numerical calculations based on measured second- and third-order elastic constants taken from the literature are performed to predict the evolution of initially monofrequency surface waves. Nonlinearity matrix elements that indicate the coupling strength of harmonic interactions are shown to provide a useful tool for characterizing waveform distortion. The formation of compression or rarefaction shocks can be strongly dependent on the direction of propagation, and harmonic generation is suppressed or increased in certain directions.

Interaction of strong converging shock wave with SF 6 gas bubble

Abstract: Interaction of a strong converging shock wave with an SF6 gas bubble is studied, focusing on the effects of shock intensity and shock shape on interface evolution. Experimentally, the converging shock wave is generated by shock dynamics theory and the gas bubble is created by soap film technique. The post-shock flow field is captured by a schlieren photography combined with a high-speed video camera. Besides, a three-dimensional program is adopted to provide more details of flow field. After the strong converging shock wave impact, a wide and pronged outward jet, which differs from that in planar shock or weak converging shock condition, is derived from the downstream interface pole. This specific phenomenon is considered to be closely associated with shock intensity and shock curvature. Disturbed by the gas bubble, the converging shocks approaching the convergence center have polygonal shapes, and the relationship between shock intensity and shock radius verifies the applicability of polygonal converging shock theory. Subsequently, the motion of upstream point is discussed, and a modified nonlinear theory considering rarefaction wave and high amplitude effects is proposed. In addition, the effects of shock shape on interface morphology and interface scales are elucidated. These results indicate that the shape as well as shock strength plays an important role in interface evolution.

Oblique shock waves incident on an interface between two materials for general equations of state

Abstract: Numerical schemes have been devised to solve the problem of an oblique shock scattering off the interface between two solid materials. The problem of a steady three-shock structure is first solved analytically using equations of state (EOS) where the shock speed and particle speed are related through a linear function. The formulation is then generalized to accept general EOS, which requires the incorporation of a more general algorithm to explore possible shock configurations based on the mechanical and thermodynamic parameters in the EOS. The correct configuration is found from the equality of pressure behind the reflected and transmitted waves as well as the equality of boundary deflection due to flow in the upper and lower halves of the three-shock structure. For the case of a reflected rarefaction in material described by general EOS, numerical integration over the release is used for accuracy where the rarefaction has a finite thickness as opposed to a discontinuous “expansion” shock. The results of...

Asymptotic decay toward rarefaction wave for a hyperbolic-elliptic coupled system on half space

Abstract: We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R+ = (0,∞), ut + uux + qx = 0, −qxx + q + ux = 0, with the Dirichlet boundary condition u(0, t) = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58(2004), 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u − < u+. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution (u, q) is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L-energy method and L-estimate. It decays much lower than that of the corresponding Cauchy problem.

Universal distribution of fluctuations at the edge of the rarefaction fan

Abstract: We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with $\rho_-<\rho_+$ so that macroscopically one has a rarefaction fan. We study the fluctuations of the process observed along slopes in the fan, which are given by the Hopf--Cole solution of the Kardar-Parisi-Zhang (KPZ) equation, with appropriate initial data. For slopes strictly inside the fan, the initial data is a Dirac delta function and the one point distribution functions have been computed in [Comm. Pure Appl. Math. 64 (2011) 466-537] and [Nuclear Phys. B 834 (2010) 523-542]. At the edge of the rarefaction fan, the initial data is one-sided Brownian. We obtain a new family of crossover distributions giving the exact one-point distributions of this process, which converge, as $T earrow\infty$ to those of the Airy $\mathcal{A}_{2\to \mathrm{BM}}$ process. As an application, we prove moment and large deviation estimates for the equilibrium Hopf-Cole solution of KPZ. These bounds rely on the apparently new observation that the FKG inequality holds for the stochastic heat equation. Finally, via a Feynman-Kac path integral, the KPZ equation also governs the free energy of the continuum directed polymer, and thus our formula may also be interpreted in those terms.