A fast discontinuous finite element discretization for the space‐time fractional diffusion‐wave equation

In this article, we study fast discontinuous Galerkin finite element methods to solve a space‐time fractional diffusion‐wave equation. We introduce a piecewise‐constant discontinuous finite element method for solving this problem and derive optimal error estimates. Importantly, a fast solution technique to accelerate Toeplitz matrix‐vector multiplications which arise from discontinuous Galerkin finite element discretization is developed. This fast solution technique is based on fast Fourier transform and it depends on the special structure of coefficient matrices. In each temporal step, it helps to reduce the computational work from required by the traditional methods to log , where is the size of the coefficient matrices (number of spatial grid points). Moreover, the applicability and accuracy of the method are verified by numerical experiments including both continuous and discontinuous examples to support our theoretical analysis.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2043–2061, 2017     

Equality of the homogeneous and the Gabor wave front set

We prove that Hörmander’s global wave front set and Nakamura’s homogeneous wave front set of a tempered distribution coincide. In addition, we construct a tempered distribution with a given wave front set, and we develop a pseudodifferential calculus adapted to Nakamura’s homogeneous wave front set.     

完整Coriolis力作用下带有外源强迫的非线性KdV方程

利用摄动方法,从描写既有Coriolis力垂直分量又含有水平分量的位涡方程出发,给出了近赤道非线性Rossby波所满足的具有外源强迫的非线性KdV方程,并利用Jacobi椭圆函数展开法,求解了改进后的非线性KdV方程的行波解及孤立波解.通过分析KdV方程的行波解,指出Coriolis力的水平分量和外源对Rossby波动的影响.     

自由来流湍流与三维壁面局部粗糙诱导平板边界层不稳定T-S波的数值研究

采用直接数值模拟（DNS）方法,研究了在自由来流湍流与三维壁面局部粗糙作用下平板边界层内诱导产生不稳定T-S波的物理问题.数值结果可知,在平板边界层内发现了二维和三维T-S波组成的波包空间序列以及求得了波包向前传播的群速度大小,从而证明了自由来流湍流与三维壁面局部粗糙作用是激励平板边界层内诱导产生不稳定T-S波的一种机制.随后,建立了平板边界层内被激发的二维和三维T S波的初始幅值与自由来流湍流度,三维壁面局部粗糙的流向长度、展向宽度及法向高度之间的关系.这一问题的深入研究,进一步完善了流动稳定性与湍流理论.     

一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题

依据一维六方准晶压电材料反平面问题的基本方程,利用复变函数方法,通过引入适当的保角映射,研究了一维六方准晶压电材料中幂函数型曲线裂纹的反平面问题,并利用Cauchy积分理论,得到电不可通和电可通边界条件下的应力场和位移场的复表示以及裂纹尖端场强度因子的解析表达式.     

Hyperbolic Yamabe problem

In this paper, we investigate the solutions of the hyperbolic Yamabe problem for the(1 + n)-dimensional Minkowski space-time. More precisely speaking, for the case of n = 1, we derive a general solution of the hyperbolic Yamabe problem; for the case of n = 2, 3, we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem;while for general multi-dimensional case n ≥ 2, we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.     

The effect of external forces on the initial dissociation of RDX (1,3,5‐trinitro‐1,3,5‐triazine): A mechanochemical study

Experimental and theoretical studies have proposed different initiation reactions for the decomposition of hexahydro‐1,3,5‐trinitro‐1,3,5‐triazine (RDX). Three primary reactions are considered to start RDX decomposition: homolytic N? N bond fission, HONO elimination, and concerted fission of C? N bonds. The focus of this article is to study the effect of external forces on the energy barrier and reaction energies of all three mechanisms. We used the Nudged Elastic Band method along with ab initio Density Functional Theory within the framework of a generalized force‐modified potential energy surface (G‐FMPES) to calculate the minimum energy paths at different compressive (corresponding to pressure between approximately 6 and 294 MPa) and expansive force values (between 10 and 264 pN). For all three reactions, the application of an expansive force increases the exothermicity and lowers the energy barriers to different extents, while a compressive force decreases the exothermicity and raises the energy barrier to different extents.     

Quantum reaction dynamics of C(1D) + HD → CH(CD) + D(H) on the ground state potential energy surface

We present accurate quantum dynamic calculations of the reaction C(¹D) + HD on the latest version of the potential energy surface [Zhang et al., J. Chem. Phys. 140, 234301 (2014)]. Using a Chebyshev real wave packet method with full Coriolis coupling, we obtain the initial state‐specified ( ) reaction probabilities, integral cross sections, and rate constants. The resulting probabilities display oscillatory structures due to numerous long‐lived resonances supported by the deep potential well. The calculated rate constants and CD/CH product branching ratio at room temperature are in reasonably good agreement with the experimental measurements.     

Global X2A′ potential energy surface of Li2H and quantum dynamics of H + Li2 (X1Σg+) → Li + LiH (X1Σ+) reaction

A global potential energy surface (PES) for the electronic ground state of Li₂H system is constructed over a large configuration space. About 30 000 ab initio energy points have been calculated by MRCI‐F12 method with aug‐cc‐pVTZ basis set. The neural network method is applied to fit the PES and the root mean square error of the current PES is only 1.296 meV. The reaction dynamics of the title reaction has been carried out by employing time‐dependent wave packet approach with second order split operator on the new PES. The reaction probability, integral cross section and thermal rate constant are obtained from the dynamics calculation. In most of the collision energy regions, the integral cross sections are in well agreement with the results reported by Gao et al. The rate constant calculated from the new PES increases in the temperature range of present investigation.