Nonextensive entropies derived from Gauss? principle

Gauss? principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles.     

超细长弹性杆动力学的Gauss原理

研究基于Gauss 变分的超细长弹性杆动力学建模的分析力学方法.分别在弧坐标和时间的广义加速度空间定义虚位移,给出了非完整约束加在虚位移上的限制方程;建立了弹性杆动力学的Gauss原理,由此导出Kirchhoff方程、Lagrange方程、Nielsen方程以及Appell方程;对于受有非完整约束的弹性杆,导出了带乘子的Lagrange方程;建立了弹性杆截面动力学的Gauss最小拘束原理并说明其物理意义. 关键词： 超细长弹性杆动力学 分析力学 Gauss变分 最小拘束原理     

On Generalized Non-holonomic Systems

Generalized non-holonomic mechanical systems are analyzed from a geometric point of view. The existence and uniqueness of solutions, D’Alembert principle, Gauss principle of minimal constraint, the non-holonomic momentum and Gibbs–Appell equations for such systems are studied in an invariant Lagrangian framework.      

A Langevin approach to the Log–Gauss–Pareto composite statistical structure

The distribution of wealth in human populations displays a Log–Gauss–Pareto composite statistical structure: its density is Log–Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log–Gauss–Pareto composite statistical structure. This equilibrium Langevin explanation is universal — as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.     

事件空间中力学系统的微分变分原理

研究事件空间中力学系统的微分变分原理.基于D'Alembert原理，建立了事件空间中力学系统的D'Alembert-Lagrange原理、Jourdain原理、Gauss原理和万有D'Alembert原理，给出了这些原理的Euler-Lagrange参数形式、Nielsen参数形式和Appell参数形式，并导出了万有D'Alembert原理的Mangeron-Deleanu参数形式. 关键词： 分析力学 事件空间 微分变分原理     

有导体存在时的唯一性定理的一种证明方法

提出一种用积分形式的高斯定理、环路定理（电场线的主要性质是它们的具体体现）和叠加原理来有有导体存在时的唯一性定理的方法。     

超小金属微粒超导电性的能级统计

用平均场理论的自洽方程计算了随机矩阵理论中三种系综(Gauss Orthogonal Ensemble;Gauss Unitary Ensemble;Gauss Symplectic Ensemble)所对应的电子能级的奇/偶电子数分布对临界电子能级间距的影响,得到了在不同的自旋-轨道耦合和磁场中奇/偶电子数分布的临界电子能级间距的定量关系以及奇电子数的Δ((0)随平均能间距o>的变化. 关键词：     

Embedding adaptive arithmetic coder in chaos-based cryptography

In this study an adaptive arithmetic coder is embedded in the Baptista-type chaotic cryptosystem for implementing secure data compression.To build the multiple lookup tables of secure data compression,the phase space of chaos map with a uniform distribution in the search mode is divided non-uniformly according to the dynamic probability estimation of plaintext symbols.As a result,more probable symbols are selected according to the local statistical characters of plaintext and the required number of iterations is small since the more probable symbols have a higher chance to be visited by the chaotic search trajectory.By exploiting non-uniformity in the probabilities under which a number of iteration to be coded takes on its possible values,the compression capability is achieved by adaptive arithmetic code.Therefore,the system offers both compression and security.Compared with original arithmetic coding,simulation results on Calgary Corpus files show that the proposed scheme suffers from a reduction in compression performance less than 12% and is not susceptible to previously carried out attacks on arithmetic coding algorithms.     

一维随机粗糙面后向增强效应的蒙特-卡罗方法研究

根据基尔霍夫近似方法,用蒙特－卡罗方法模拟随机粗糙面,观测到了随机粗糙面的后向增强效应。分别研究了高斯粗糙面及分形粗糙面,讨论了统计特性相同的粗糙面在不同小波尺度的电磁（光）波散射特性。所得结果与实验事实相当吻合     

Mean field and the confined single homopolymer

We develop a statistical model for a confined homopolymeric chain molecule based on a monomer grand ensemble representation. The molecule is subject to a confining external field, a backbone interaction, and an attractive interaction between any pair of monomers. An exact minimum principle for the thermodynamics of the backbone in an external field is obtained, and a controlled mean field approximation results in a modified minimum principle from which relevant physical quantities such as monomer density can be found. We explore the limit in which the chain is subject to tight confinement, and make a preliminary investigation of a prototypical system.