Analytical solution of a multidimensional Langevin equation at high friction limits and probability passing over a two-dimensional saddle

The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.     

用三角级数和Maple软件求Burgers方程的精确解

用三角级数试探求解Burgers方程,得到关于待定系数的非线性代数方程组,利用Maple软件求解此非线性代数方程组,进而求得Burgers方程的精确解.     

Effects of pressure and temperature on the solubility of monosodium L-glutamate monohydrate in water

Abstract

The solubility of monosodium L-glutamate monohydrate (MSG.H₂O) in water was measured at pressures in the range of 0.10-300MPa and 298.15K. The density of MSG solution at high concentrations and heat of solution at saturated concentration were also measured at atmospheric pressure. The solubility, m_s, increased with increasing pressure and the pressure coefficient, Θ_p, [?(? In m_s,? p)_T] at 0.10 MPa was (2.0 ± 0.1) × 10-¹⁰Pa-1. It agrees well with (2.1 ±0.2)× 10-¹⁰ Pa-¹ thermodynamically estimated using the partial molar volume, the activity coefficient of the solute in solution, and the molar volume of the crystal. The excellent agreement at 0.10MPa gives us confidence in the solubility data at higher pressures. The heat of solution data and other pertinent values were used to calculate the temperature coefficient of solubility, Θ_T [? (? In m_s/?(1/T))_p], by a thermodynamic equality. The resulting Θ_T compares well with the data directly measured by Ogawa.     

Alternative difference analysis scheme combining R‐space EXAFS fit with global optimization XANES fit for X‐ray transient absorption spectroscopy

Time‐resolved X‐ray absorption spectroscopy (TR‐XAS), based on the laser‐pump/X‐ray‐probe method, is powerful in capturing the change of the geometrical and electronic structure of the absorbing atom upon excitation. TR‐XAS data analysis is generally performed on the laser‐on minus laser‐off difference spectrum. Here, a new analysis scheme is presented for the TR‐XAS difference fitting in both the extended X‐ray absorption fine‐structure (EXAFS) and the X‐ray absorption near‐edge structure (XANES) regions. R‐space EXAFS difference fitting could quickly provide the main quantitative structure change of the first shell. The XANES fitting part introduces a global non‐derivative optimization algorithm and optimizes the local structure change in a flexible way where both the core XAS calculation package and the search method in the fitting shell are changeable. The scheme was applied to the TR‐XAS difference analysis of Fe(phen)₃ spin crossover complex and yielded reliable distance change and excitation population.     

Numerical solution for curved crack problem in elastic half-plane using hypersingular integral equation

A hypersingular integral equation for the curved crack problems of an elastic half-plane is introduced. Formulation of the equation is based on the usage of a modified complex potential. The potential is generally expressed in the form of a Cauchy-type integral. The modified complex potential is composed of the principal part and the complementary part. The principal part of the complex potential is actually equivalent to the original complex potential for the curved crack in an infinite plate. The role of the complementary part is to eliminate the boundary traction along the boundary of the half-plane caused by the principal part. From the assumed boundary traction condition, a hypersingular integral equation is obtained for the curved crack problems of an elastic half-plane. The curve length coordinate method is used to obtain a final solution. Several numerical examples are presented that prove the efficiency of the suggested method.     

Analytical expressions for partial wave two-body Coulomb transition matrices at ground-state energy

Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann–Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p$p$-, d$d$- and f$f$-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states.     

Effect of hemp surface modification on the morphological and tensile properties of linear medium density polyethylene (LMDPE) composites

This work investigates different hemp surface modifications (mercerization, maleated polyethylene (MAPE) addition in solution or in melt blending) to improve the properties of linear medium density polyethylene (LMDPE). From the composites produced, a complete morphological and tensile characterization was performed for a fixed hemp content (30% wt.). The morphological analysis showed that both the direct (melt blending) and solution modifications were able to significantly improve the composites interface quality and therefore the tensile properties (151% increase in modulus and 36% increase in strength over the neat matrix) within the range of conditions tested.     

基于模糊博弈视角的企业联盟“双循环”合作对策研究

企业合作在“双循环”新发展格局下呈现出更多的模糊特征,能否形成稳定的模糊合作格局及持续合作的收益再分配策略成为合作联盟的关注点。将广义模糊超量博弈和模糊凸博弈及其广义解集应用到“双循环”新发展格局下企业联盟合作与收益再分配中,提出最大广义模糊超量博弈模型及其广义模糊谈判集,并基于最大广义模糊超量博弈均衡性的视角,对模糊凸博弈下广义模糊谈判集与核心的等价性质进行论证。研究结果不仅满足了“双循环”新发展格局下合作企业以部分资源参与合作的意愿,及企业联盟模糊凸合作博弈下再分配方案等价性证明需求,而且实现了保留部分收益用于联盟再发展的策略。     

Global Weak Solutions for Compressible Navier-Stokes-Vlasov-Fokker-Planck System

The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients isinvestigated in the present paper. The existence, uniqueness, and regularityof global weak solution to the initial value problem for general initial data areestablished in spatial periodic domain. Moreover, the long time behavior ofthe weak solution is analyzed. It is shown that as the time grows, the distribution function of the particles converges to the global Maxwellian, and boththe fluid velocity and the macroscopic velocity of the particles converge to thesame speed.