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Dynamic information theory and information description of dynamic systems

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Science china(Physics,Mechanics & Astronomy) 2010年第4期53卷 607-627页

作者： XING XiuSan department of Physics, beijing {2. of technology, beijing 100081, china 1. department of Physics Beijing Institute of Technology Beijing 100081 China

In this paper, we develop dynamic statistical information theory established by the author. Starting from the ideas that the state variable evolution equations of stochastic dynamic systems, classical and quantum nonequilibrium statistical physical systems and special electromagnetic field systems can be regarded as their information symbol evolution equations and the definitions of dynamic information and dynamic entropy, we derive the evolution equations of dynamic information and dynamic entropy that describe the evolution laws of dynamic information. These four kinds of evolution equations are of the same mathematical type. They show in unison when information transmits in coordinate space outside the systems that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes, and that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes. When space noise can be neglected, an information wave will appear. If we only consider the information change inside the systems, dynamic information evolution equations reduce to information equations corresponding to the dynamic equations which describe evolution laws of the above dynamic systems. This reveals that the evolution laws of respective dynamic systems can be described by information equations in a unified fashion. Hence, the evolution processes of these dynamic systems can be abstracted as the evolution processes of information. Furthermore, we present the formulas for information flow, information dissipation rate, and entropy production rate. We prove that the information production probably emerges in a dynamic system with internal attractive interaction between the elements, and derive a formula for this information production

关键词： dynamic information evolution equation informationization of dynamic equation information wave information flow and force information dissipation and production degradation and evolution

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

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Science china(Physics,Mechanics & Astronomy) 2010年第12期53卷 2194-2215页

作者： XING XiuSan department of Physics, beijing {2. of technology, beijing 100081, china 1. department of Physics Beijing Institute of Technology Beijing 100081 China

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or anothe

关键词： stochastic velocity type’s Langevin equation in 6N dimensional phase space drift-diffusion duality nonequilibrium entropy evolution equation entropy diffusion formula for entropy production rate entropy change from internal interaction a

Nontrivial homoclinic orbits for second-order singular and periodic Hamiltonian systems

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Chinese Science Bulletin 1999年第2期44卷 123-129页

作者： LI Chengyue , FAN Tianyou TONG MingshengResearch Center of Materials Science, beijing institute of {2., beijing 100081, china department of Mathematics, Central University for Nationalities, beijing 100081, china computer Center, beijing institute of {2., beijing 100081, china Research Center of Materials Science Beijing Institute of Technology Beijing China department of Mathematics Central University for Nationalities Beijing China computer Center Beijing Institute of Technology Beijing China

The existence of nontrivial homoclinic orbits of periodic Hamiltonian systems: is proved, where q=（q1,q2.’',qn）, n>2. V（t, q）:R1×Rn\{e}→R1 is a potential With a singularity, i.e. -V（t, q）→+∞, as q→e. The m... 详细信息

The existence of nontrivial homoclinic orbits of periodic Hamiltonian systems: is proved, where q=（q1,q2./sub>,’',qn）, n>2. V（t, q）:R1×Rn\{e}→R1 is a potential With a singularity, i.e. -V（t, q）→+∞, as q→e. The main assumptions are Gordon-strong force condion and the uniqueness of a global maximum of V（t, q）.

关键词： Hamiltonian systems strong force condition homoclinic orbit.

Chaotic attitude and reorientation maneuver for completely liquid-filled spacecraft with flexible appendage

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Acta Mechanica Sinica 2009年第2期25卷 271-277页

作者： B. Yue department of Mechanics, School of Science,beijing {2. of technology, 100081 beijing, china department of Mechanics School of Science Beijing Institute of Technology 100081 Beijing China

The present paper investigates the chaotic attitude dynamics and reorientation maneuver for completely viscous liquid-filled spacecraft with flexible appendage. All of the equations of motion are derived by using Lagrangian mechanics and then transformed into a form consisting of an unperturbed part plus perturbed terms so that the system＇s nonlinear characteristics can be exploited in phase space. Emphases are laid on the chaotic attitude dynamics produced from certain sets of physical parameter values of the spacecraft when energy dissipation acts to derive the body from minor to major axis spin. Numerical solutions of these equations show that the attitude dynamics of liquid-filled flexible spacecraft possesses characteristics common to random, non- periodic solutions and chaos, and it is demonstrated that the desired reorientation maneuver is guaranteed by using a pair of thruster impulses. The control strategy for reorientation maneuver is designed and the numerical simulation results are presented for both the uncontrolled and controlled spins transition.

关键词： Nonlinear attitude dynamics Attitude reorientation maneuver Control strategyLiquid-filled spacecraft

A note on n-edge chromatic number

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Chinese Science Bulletin 1997年第23期42卷 1952-1954页

作者： SUN Liang and ZHANG Zhongfu1. department of Applied Mathematics, beijing {2. of technology, beijing 100081, china 2. {2. of Applied Mathematics, Lanzhou {2. of Railway, Lanzhou 730070, china department of Applied Mathematics Beijing Institute of Technology Beijing 100081 China

ALL graphs appearing in this note are simple. A graph with p vertices and q edges will becalled a (p, q )-graph. The maximum degree of G is denoted by Δ(G).Let n≥2.be an integer. The n-edge chromatic number X_n (G) of a simple graph G is theminimum cardinality of a set of colors with which one can assign the colors to the edges of Gsuch that the edges on a path of length less than or equal to n receive different *** aim of this note is to explore the bounds for X’_n (G) and X’_n (G) + X’_n (G). It is

关键词： graph complement n-edge chromatic number.

Feller property and exponential ergodicity of diffusion processes with state-dependent switching

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Science china Mathematics 2008年第3期51卷 329-342页

作者： XI FuBao department of Mathematics, beijing {2. of technology, beijing 100081, china 1. department of Mathematics Beijing Institute of Technology Beijing 100081 China

In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions.

关键词： Feller continuity Radon-Nikodym derivative strong Feller continuity exponential ergodicity state-dependent switching 60J60 34D2.

On the fluorescence of C_60 at room temperature

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Science china(Physics,Mechanics & Astronomy) 2010年第1期53卷 95-99页

作者： ZHANG Fang & ZHANG XiaoLing department of Chemistry, beijing {2. of technology, beijing 100081, china 1. department of Chemistry Beijing Institute of Technology Beijing 100081 China

The fluorescence properties of C 60 in different organic solvents have been investigated at room temperature. Three fluorescence emission centers are discovered and ascribed to different aggregations of C 60 in solvent. A series of blue fluorescence peaks centered at 440 nm derive from C 60 nanoparticles; a distinctive yellow-green fluorescence band in 575 nm region arises from the aggregates of C 60 nanoparticles; a more informative salmon fluorescence band around 700 nm originates from C 60 microcrystals. And the distinct configurations of C 60 aggregations are closely associated with the characteristic interaction between C 60 and solvent molecules.

关键词： C 60 fluorescence TEM confocal fluorescence spectroscopy

Research progress in synthesis and catalysis of polyoxometalates

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Progress in Natural Science:Materials International 2005年第5期15卷 385-394页

作者： GONG Yun1, HU Changwen1* and LIANG Hong2.1. department of Chemistry, School of Science, the institute for Chemical Physics, {2. institute of technology, beijing 100081, china 2. Chemical Industry Press, {2. 10002., china) department of Chemistry School of Science the Institute for Chemical Physics Beijing Institute of Technology Beijing 100081 China Chemical Industry Press Beijing 100029 China

Recent progress in the synthetic chemistry and catalysis of polyoxometalates (POMs) is reviewed. The novel POMs and their derivatives emerging in nearly three years (2.02.2.04) are introduced, including POMs with novel structure, POMs-organic hybrid compounds and host-guest complexes. Our review is focused on the elaboration of POMs' supramolecular chemistry.

关键词： polyoxometalates hybrid host-guest structure supramolecule catalysis.

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2.and YU Yuanhong 3 1. department of Applied Mathematics, beijing {2. of technology, beijing 100081, china 2. department of Mathematics, Yunnan University, Kunming 650091, china 3. {2. of Applied Mathematics, C department of Applied Mathematics Beijing Institute of Technology Beijing China department of Mathematics Yunnan University Kunming China institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.