Variations of the elastic constants of InSb near the covalent-metallic transition

Abstract

The pulse-echo-overlap method was used to measure the longitudinal and transverse wave velocities in single-crystal (100) and (111) samples of InSb up to 3 GPa at room temperature. The peculiar variations of the elastic constants were observed near the covalent-metallic transition.     

Novel Mittag-Leffler stability of linear fractional delay difference equations with impulse

In this letter we propose a class of linear fractional difference equations with discrete-time delay and impulse effects. The exact solutions are obtained by use of a discrete Mittag-Leffler function with delay and impulse. Besides, we provide comparison principle, stability results and numerical illustration.     

The derivation of the conservation law for defocusing nonlinear Schrödinger equations with non-vanishing initial data at infinity

For nonlinear Schrödinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed.     

Global persistence of geometrical structures for the Boussinesq equation with no diffusion

Our main aim is to investigate the temperature patch problem for the two-dimensional incompressible Boussinesq system with partial viscosity: the initial temperature is the characteristic function of some simply connected domain with 𝒞^1,𝜀 Hölder regularity. Although recent results ensure that the 𝒞¹ regularity of the patch persists for all time, whether higher order regularity is preserved has remained an open question. In the present paper, we give a positive answer to that issue. We also study the higher dimensional case, after prescribing an additional smallness condition involving critical Lebesgue or weak-Lebesgue norms of the data, so as to get a global-in-time statement. All our results stem from general properties of persistence of geometrical structures (of independent interest), that we establish in the first part of the paper.     

参数化连分式拟合方法研究及应用

通过倒差商-连分式算法,提出了一种保端点非线性有理参数化拟合算法,通过选取中间点的参数化,利用连分式插值法,得到的拟合函数具有保端点性,规律性和灵活性.实例表明,算法减少了连分式插值迭代次数,避免插值连分式的不存在性,所得到拟合值具有更好的精度,大大提高了计算效率,拟合的误差更具有平稳性,逼近效果更好,并具有较好的预测等方面的应用.     

A new characteristic approach for incompressible thermo‐flow in Cartesian and non‐Cartesian grids

A virtual‐characteristic approach is developed for thermo‐flow with finite‐volume methodology in which a multidimensional characteristic (MC) scheme is applied along with artificial compressibility. To obtain compatibility equations and pseudo‐characteristics, energy equation is taken into account in the MC scheme. With this inherent upwinding of convective fluxes, no artificial viscosity is required even at high Reynolds numbers. Another remarkable advantage of the MC scheme lies in its faster convergence rate with respect to the averaging scheme that is found to exhibit substantial delays in convergence. As benchmarks, forced and mixed convections in a cavity and in flow over cylinder and between parallel plates are examined for a wide range of Reynolds, Grashof, and Prandtl numbers. The MC and averaging schemes are applied for simulation purposes. Results show the better performance of the MC scheme in forced and mixed convections. Results confirm the robustness of the MC scheme in terms of accuracy and convergence. Copyright © 2015 John Wiley & Sons, Ltd.     

Improvement of multistep WENO scheme and its extension to higher orders of accuracy

This paper presents an efficient procedure for overcoming the deficiency of weighted essentially non‐oscillatory schemes near discontinuities. Through a thorough incorporation of smoothness indicators into the weights definition, up to ninth‐order accurate multistep methods are devised, providing weighted essentially non‐oscillatory schemes with enhanced order of convergence at transition points from smooth regions to a discontinuity, while maintaining stability and the essentially non‐oscillatory behavior. We also provide a detailed analysis of the resolution power and show that the solution enhancements of the new method at smooth regions come from their ability to render smoothness indicators closer to uniformity. The new scheme exhibits similar fidelity as other multistep schemes; however, with superior characteristics in terms of robustness and efficiency, as no logical statements or mapping function is needed. Extensions to higher orders of accuracy present no extra complexity. Numerical solutions of linear advection problems and nonlinear hyperbolic conservation laws are used to demonstrate the scheme's improved behavior for shock‐capturing problems. Copyright © 2016 John Wiley & Sons, Ltd.     

Probabilistic interpretation of a system of quasilinear parabolic PDEs

Using a forward–backward stochastic differential equations (FBSDE) associated to a transmutation process driven by a finite sequence of Poisson processes, we obtain a probabilistic interpretation for a non-degenerate system of quasilinear parabolic partial differential equations (PDEs). The novetly is that the linear second order differential operator is different on each line of the system.     

Peculiarities of wave dynamics in media with oscillating inclusions

The article is concerned with mathematical models for media with oscillating inclusions. These models consist of mutually connected equations, one of which is the wave equation for carrying medium and others are equations of motion for partial oscillators. To close these models, we use cubic and nonlocal equations of state for the carrying medium. Travelling wave solutions to these models are studied in detail. Using qualitative analysis methods, the phase space is shown to contain periodic, homo- and heteroclinic trajectories. Moreover, in the case of nonlocal models we observe the creation of quasiperiodic and chaotic regimes. Bifurcations of localized regimes are studied via the Poincaré section technique.