On stability of discontinuous systems via vector Lyapunov functions

This paper deals with the stability of systems with discontinuous right- hand side(with solutions in Filippov's sense)via locally Lipschitz continuous and regular vector Lyapunov functions.A new type of"set-valued derivative"of vector Lyapunov functions is introduced,some generalized comparison principles on discontinuous systems are shown.Furthermore,Lyapunov stability theory is developed for a class of discontinu- ous systems based on locally Lipschitz continuous and regular vector Lyapunov functions.     

Rigid finite element and limit analysis

According to the lower bound theorem of limit analysis the Rigid Finite Element Method (RFEM) is applied to structural limit analysis and the linear programmings for limit analysis are deduced in this paper. Moreover, the Thermo-Parameter Method (TPM) and Parametric Variational principles (PVP) are used to reduce the computational effort while maintaining the accuracy of solutions. A better solution is also obtained in this paper. The project supported by National Natural Science Foundation of China     

A Potential Formulation of Non-Linear Models of Flow through Anisotropic Porous Media

A theoretical analysis, based on the search for a normal dissipation potential, is performed in order to generalize the empirical non-Darcy one-dimensional flow models to 3-D flows through anisotropic porous media. In an abstract framework, it is proven that a large number of heuristic non-linear equations governing the multidimensional flow through isotropic porous media can be derived starting from a potential strictly related to the mechanical power dissipated by the fluid. Such a formulation allows to define, for the tensor permeability case, a wide class of filtration models according to the Onsager's generalized theory of dissipative mechanical systems. A consistent generalization to anisotropic permeability case of polynomial flow models is proposed. Both primal and dual mixed variational formulations associated to the proposed quadratic and incomplete cubic flow models are introduced and discussed.     

耦合热弹性动力学的统一变分原理族

对耦合热弹性动力学问题,迄今文献中只建立了Ｇｕｒｔｉｎ型合卷积的统一变分原理,其缺点是只适用于常系数的线性问题,且因含卷积而使实际数值离散和求解复杂化．文中首次成功地建立了耦合热弹性动力学问题经典型（不含卷积）统一变分原理族,其关键是建议了动态差分变换和初终值条件的新处理法．该方法可以推广到各向异性材料以及非线性问题上去,同时在应用有限元法离散和求解上都比较简便．     

On Substitution Principles in Ideal Magneto-Gasdynamics by Means of Lie Group Analysis

The equations governing the flow of an inviscid thermally non-conducting fluid of infinite electrical conductivity in the presence of a magnetic field and subject to no extraneous forces are considered within the framework of Lie group analysis. It is shown how to recover and extend some results, known in literature as substitution principles, by conveniently requiring the invariance of the basic governing equations under a one-parameter Lie group of point transformations. Moreover, a new substitution principle for the equations ruling the plane motion of a fluid with adiabatic index Γ = 2 subjected to a transverse magnetic field is given. Some applications of the results are also given.     

Hybrid organic–inorganic CH3NH3PbI3 perovskite building blocks: Revealing ultra‐strong hydrogen bonding and mulliken inner complexes and their implications in materials design

Methylammonium lead iodide (CH₃NH₃PbI₃) perovskite compound has produced a remarkable breakthrough in the photovoltaic history of solar cell technology because of its outstanding device‐based performance as a light‐harvesting semiconductor. Whereas the experimental and theoretical studies of this system in the solid state have been numerously reported in the last 4 years, its fundamental cluster physics is yet to be exploited. To this end, this study has performed theoretical investigations using DFT‐M06‐2X/ADZP to examine the principal geometrical, electronic, topological, and orbital properties of the CH₃NH₃PbI₃ molecular building block. The intermolecular hydrogen bonded interactions examined for the most important conformers of the system are found to be unusually strong, with binding energies lying between −93.53 and −125.11 kcal mol⁻¹ (beyond the covalent limit, −40 kcal mol⁻¹), enabling us to classify the underlying interactions as ultra‐strong type since their characteristic properties are unidentical with those have already been proposed as very strong, strong, moderate, weak, and van der Waals. Based on this, together with the unusually high charge transfers, strong hyperconjugative interactions, sophisticated topologies of the charge density, and short intermolecular distances of separation, we have characterized the conformers of CH₃NH₃PbI₃ as Mulliken inner complexes. The consequences of these, as well as of the ultra‐strong interactions, in designing novel functional nanomaterials are outlined. © 2017 Wiley Periodicals, Inc.     

立方KCaF_3电子、弹性和光学性质的第一性原理研究

基于密度泛函理论和赝势平面波近似法计算研究了立方钙钛矿KCaF_3的弹性、电子和光学性质.基态时,KCaF_3平衡晶格常数、体积弹性模量和实验及其他计算值一致.根据Hooke定律和Christoffel方程,研究了KCaF_3弹性常数Cij、体积弹性模量B、各向同性波速和弹性各向性异性因子随压力的变化关系.从电子能带理论出发,计算得到了KCaF_3电子能带、态密度和Milliken电荷布居数,并对其电子性质进行了详细分析.结果显示:立方钙钛矿KCaF_3为直接带隙绝缘体材料,其禁带宽度为6.22 e V;电荷主要从Ca和K原子向F原子转移;立方钙钛矿KCaF_3属于纯粹的共价型化合物.同时,本文还计算研究了KCaF_3的光学介电函数、吸收系数、复折射率、能量损失谱和反射系数等光学性质.     

On unbounded solutions of ergodic problems in ℝm for viscous Hamilton–Jacobi equations

In this article, we study ergodic problems in the whole space ?^m for viscous Hamilton–Jacobi equations in the case of locally Lipschitz continuous and coercive right-hand sides. We prove in particular the existence of a critical value λ* for which (i) the ergodic problem has solutions for all λ≤λ*, (ii) bounded from below solutions exist and are associated to λ*, (iii) such solutions are unique (up to an additive constant). We obtain these properties without additional assumptions in the superquadratic case, while, in the subquadratic one, we assume the right-hand side to behave like a power. These results are slight generalizations of analogous results by Ichihara but they are proved in the present paper by partial differential equation (pde) methods, contrarily to Ichihara who is using a combination of pde technics with probabilistic arguments.     

Band gap modulation of transition-metal dichalcogenide MX2 nanosheets by in-plane strain

The electronic properties of quasi-two-dimensional honeycomb structures of MX₂ nanosheets (M=Mo, W and X=S, Se) subjected to in-plane biaxial strain have been investigated using first-principles calculations. We demonstrate that the band gap of MX₂ nanosheets can be widely tuned by applying tensile or compressive strain, and these ultrathin materials undergo a universal reversible semiconductor-metal transition at a critical strain. Compared to WX₂, MoX₂ need a smaller critical tensile strain for the band gap close, and MSe₂ need a smaller critical compressive strain than MS₂. Taking bilayer MoS₂ as an example, the variation of the band structures was studied and the semiconductor-metal transition involves a slightly different physical mechanism between tensile and compressive strain. The ability to tune the band gap of MX₂ nanosheets in a controlled fashion over a wide range of energy opens up the possibility for its usage in a range of application.     

Anisotropic elastic properties of MB (M = Cr,Mo, W) monoborides: a first-principles investigation

First principles calculations were performed to systematically investigate structure properties, phase stability and mechanical properties of MB (M = Cr, Mo, W) monoborides in orthorhombic and tetragonal structures. The results of equilibrium structures are in good agreement with other available theoretical and experimental data. The elastic properties, including bulk modulus B, shear modulus G, Young’s modulus E and Poisson’s ratio ν were calculated by the Voigt-Reuss-Hill approximation. All considered monoborides are mechanically stable. The results of elastic anisotropies show that elastic anisotropy of orthorhombic structure is larger than that of tetragonal structure. Moreover, the minimum thermal conductivities were also estimated using the Cahill’s model, and the results indicate that the minimum thermal conductivities show a dependence on directions.