On the theory of divergence-measure fields and its applications

Divergence-measure fields are extended vector fields, including vector fields inL ^p and vector-valued Radon measures, whose divergences are Radon measures. Such fields arise naturally in the study of entropy solutions of nonlinear conservation laws and other areas. In this paper, a theory of divergence-measure fields is presented and analyzed, in which normal traces, a generalized Gauss-Green theorem, and product rules, among others, are established. Some applications of this theory to several nonlinear problems in conservation laws and related areas are discussed. In particular, with the aid of this theory, we prove the stability of Riemann solutions, which may contain rarefaction waves, contact discontinuities, and/or vacuum states, in the class of entropy solutions of the Euler equations for gas dynamics.Dedicated to Constantine Dafermos on his 60^th birthday     

LARGE MAGNETIC ENTROPY CHANGE NEAR CHARGE-ORDERED TRANSITION TEMPERATURE IN PEROVSKITE-TYPE MANGANITE

The magnetocaloric effect in polycrystalline of Pr_1-xSr_xMnO₃ (x=0.33, 0.43, 0.50) has been investigated. A large magnetic entropy change (7.1J/kgK) was discovered in Pr_0.5Sr_0.5MnO₃ under a low magnetic field of 1T at charge-ordered state transition temperature (161K). The physical mechanism is related to a drastic magnetization change at a temperature where the field-induced magnetic, electron and structural phase transitions occur (from the antiferromagnetic charge-ordered state to the ferromagnetic charge-disordered state).     

STATISTICAL ENTROPIES OF THE TAUB－NUT/BOLT AdS SPACES FROM THE HORIZON CONFORMAL FIELD THEORY

The covariant phase technique is used to compute the constraint algebra of the four-dimensional space-times which are asymptotic to anti-de Sitter (AdS), such as the planar Taub－NUT AdS and Taub－bolt AdS spaces, and the hyperbolic Taub－bolt AdS space. The standard Virasoro subalgebrae with corresponding central charges for these objects are constructed and the resulting densities of states yield the expected Bekenstein－Hawking entropies.     

Exponential convergence rate in Boltzmann-Shannon entropy

This paper deals with the optimal exponential convergence rate β to the equilibrium state in Boltzmann-Shannon entropy for general Markov semigroups. We prove a variational formula of β, and then discuss the relation among β, spectral gap λ and logarithmic Sobolev constant α, which is read as λ≥β≥α.     

基于熵条件二阶差分格式的嵌套网格分区算法

以带熵条件的二阶TVD格式为基本格式,设计了三维曲线坐标下的Euler方程数值计算方法.对多个物体使用分区嵌套网格设计了相应的分区算法.所建立的算法适用于处理物体相互分离以及相互接触的定常与非定常流动问题.给出了绕两圆柱的超声速流动在两圆柱处于不同位置时的详细结果,并模拟了装配鸭舵火箭弹在超声速旋转飞行时的气动特性.     

Influence of second sideband excitation on the dynamics of trapped ions in a cavity

We study the dynamics of a trapped ion placed at an antinode of the standing wave inside a high finesse cavitywith consideration of the second sideband excitation between the ionic internal levels and the light field. We investigatethe entanglement of the three subsystems embodying the ionic internal levels, the vibrational mode of the ion and thecavity field.     

低密度溶液中溶剂的重组织性质

分析了溶液的微观结构,结果表明,单个溶质粒子影响其周围的溶剂的结构,溶质粒子间的相互作用也将影响溶剂的结构,溶质对溶剂结构的影响称作溶剂的重组织.提出了二阶重组织能及二阶重组织熵等概念,可以描述在两个溶质粒子发生碰撞时对其周围溶剂结构的影响.利用二元系的集团展开理论,给出了溶剂的一阶、二阶重组织能和重组织熵的表达式.统计热力学分析给出了溶剂-溶剂径向分布函数与溶质和溶剂化学势之间的关系,给出了无限稀溶液模型是否成立的宏观判据.提出的理论可用于低密度的二元溶液.     

Thermodynamics of alternating copolymer of styrene and CO in the 0—600 K region

The temperature dependence of heat capacity and the temperatures and enthalpies of physical transitions of the alternating copolymer of styrene and CO were studied in the 5—600 K region by the adiabatic vacuum and dynamic calorimetric techniques. The heat of combustion of the copolymer was measured at 298.15 K in a calorimeter with a static bomb and an isothermal shield. The thermodynamic parameters of glass transition and fusion were determined. The thermodynamic functions in the 0—550 K region and thermodynamic characteristics of the formation of the copolymer from simple substances at T = 298.15 K and p = 101.325 kPa were calculated. The thermodynamic parameters of alternating copolymerization in the bulk of styrene and CO were calculated in the 0—350 K region at a standard pressure.     

等离子体热解煤及模型化合物的热力学分析

在等离子体反应器中煤及石墨热解生成乙炔研究的基础上,选取了与挥发物相类似的气态脂肪族及液态芳香族模型化合物以及设计了与这些模型化合物生成乙炔有关的反应,通过计算这些热解反应在不同温度下的Gibbs函数变化ΔG°,对其进行了热力学分析。根据上述实验和理论研究,更进一步证实了煤释放出的挥发分是生成乙炔的主要来源,同时也得出了乙炔在高温时易生成是由于熵效应。这些研究为探索煤在等离子体热解反应器中生成乙炔的机理提供了有用的信息。     

CALCULATION OF CONFORMATIONAL ENTROPY AND FREE ENERGY OF POLYSILANE CHAIN

The conformational entropy S and free energy F were calculated by exact enumeration of polysilane chain up to 23segments with excluded volume (EV) and long-range van der Waals (VW) interaction. A nonlinear relation between S_(EV+VW)and chain length n was found though S_(EV) was found to vary linearly with n. We found that the second-order transitiontemperature of polysilane chain with VW interaction increases with the increase of chain length, while that of polysilanechain without VW interaction is chain length independent Moreover, the free energies F_(EV+VW) and FEv are both linearlyrelated with n, and F_(EV+VW) 相似文献