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Dynamic information theory and information description of dynamic systems

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

作者： XING XiuSan department of Physics, beijing institute of technology, beijing 100081, china department of Physics Beijing Institute of Technology Beijing 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

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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 institute of technology, beijing 100081, china department of Physics Beijing Institute of Technology Beijing 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

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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 institute of technology, {4. beijing, china department of Mechanics School of Science Beijing Institute of Technology 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

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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 institute of technology, beijing 100081, china department of Mathematics Beijing Institute of Technology Beijing 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 34.25

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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 institute of technology, beijing 100081, china department of Chemistry Beijing Institute of Technology Beijing 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 4.0 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

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The effects of relative density of metal foams on the stresses and deformation of beam under bending

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Acta Mechanica Sinica 2007年第4期23卷 409-414页

作者： Aiyu Zhu Tianyou Fan department of Mathematics,School of Science,beijing institute of technology,P.O.Box 327,beijing 100081,china department of Physics,School of Science,beijing institute of technology,P.O.Box 327,beijing 100081,china department of Mathematics School of Science Beijing Institute of Technology Beijing China department of Physics School of Science Beijing Institute of Technology Beijing China

The exact analytic solution of the pure bending beam of metallic foams is given. The effects of relative density of the material on stresses and deformation are revealed with the Triantafillou and Gibson constitutive law （TG model） taken as the analysis basis. Several examples for individual foams are discussed, showing the importance of compressibility of the cellular materials. One of the objects of this study is to generalize Hill＇s solution for incompressible plasticity to the case of compressible plasticity, and a kinematics parameter is brought into the analysis so that the velocity field can be determined.

关键词： Metal foams - Relative density Compressible plasticity Constitutive law - TG model

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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 technology, beijing 100081, china department of Mathematics, Central University for Nationalities, beijing 100081, china Computer Center, beijing institute of technology, 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

关键词： Hamiltonian systems strong force condition homoclinic orbit.

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The discrete multiple-parameter fractional Fourier transform

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Science china(Information Sciences) 2010年第11期53卷 2287-2299页

作者： LANG Jun, TAO Ran& WANG Yue department of electronic Engineering, beijing institute of technology, beijing 100081,{4. department of electronic Engineering Beijing Institute of Technology Beijing China

As a generalization of the Fourier transform (FT), the fractional Fourier transform (FRFT) has many applications in the areas of optics, signal processing, information security, etc. Therefore, the efficient discrete computational method is the vital fundament for the application of the fractional Fourier transform. The multiple-parameter fractional Fourier transform (MPFRFT) is a generalized fractional Fourier transform, which not only includes FRFT as special cases, but also provides a unified framework for the study of FRFT. In this paper, we present in detail the discretization method of the MPFRFT and define the discrete multiple-parameter fractional Fourier transform (DMPFRFT). Then, we utilize the tensor product to define two-dimensional multiple-parameter fractional Fourier transform (2D-MPFRFT) and the corresponding two-dimensional discrete multiple-parameter fractional Fourier transform (2D-DMPFRFT). Finally, as an application, a novel image encryption method based on 2D-DMPFRFT is proposed. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.

关键词： multiple-parameter fractional Fourier transform fractional Fourier transform image encryption information security

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Research on distributed intrusion detection system based on multi-living agent

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Science china(Information Sciences) 2010年第5期53卷 1067-1077页

作者： WANG Yue, TAO Ran & ZHANG Hao department of Information and electronic Engineering, beijing institute of technology, beijing 100081,{4. department of Information and electronic Engineering Beijing Institute of Technology Beijing China

In this paper, we propose a novel distributed intrusion detection system based on multi-living agent inspired by the research method of multi-living agent complex information system for improving the security of distributed intrusion detection system using mobile agent. The previous two-layer distributed intrusion detection system has been expanded into a three-layer structure, the new layer of which can monitor the livelihood of each detection agent and utilize the negotiation-coordination mechanism to adjust the working way of each agent for protecting the security of system. In this paper, we propose a quantitative analysis method of agent livelihood in distributed intrusion detection system and further present the design method of living agent. Finally, through the analysis of system working flow and the detection effect of distributed denial of service attack, we have shown that the security and stability of the novel distributed intrusion detection system is effectively enhanced and the agent can work normally in strict restraint strong countermeasure environment.

关键词： multi-living mobile agent living agent lifecycle

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ON THE EXISTENCE OF SOLUTIONS TO A TYPE OF NONLINEAR DIFFERENTIAL-ITERATIVE EQUATIONS

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 217-224页

作者： GE WEIGAO(department of Applied Mathematics, beijing institute of technology, beijing 100081, china.) LI CUIZHE(department of Applied Mathematics, beijing institute of technology, beijing 100081, china.) YU YUANHONG(Inditute of Applied Mathematics, Acad department of Applied Mathematics Beijing Institute of Technology Beijing 100081 China institute of Applied Mathematics Academia Sinica Beijing 100080 China

Under the assumption that h(z) is strictly monotone the existence of solutions to a type of nonlinear differential-iterative equations in the form of x’(t) = g(x(t)) -h(x(x(t))) is discussed according to the behavior... 详细信息

关键词： Differential-iterative equation Quasi-isoclinic curve Fixed point

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