International Journal of Modern Physics B

Using the maximum-entropy method, the end-to-end distance distribution of the force stretched chain is calculated from the moments of the distribution, which can be obtained from the extension-force curves recorded in single-molecule experiments. If one knows force expansion of the extension through the (n-1)th power of force, it is enough information to calculate the n moments of the distribution. The method is examined with force stretched chain models, Gaussian chain and excluded-volume chain on two-dimension lattice. The method reconstructs all distributions precisely. The method also is applied to force stretched complex chain molecules: the hairpin and secondary structure conformations. We find that the distributions of homogeneous chains of two conformations are very different: there are two independent peaks in hairpin distribution; while only one peak is observed in the distribution of secondary structure conformations. Our discussion also shows that the end-to-end distance distribution may discover more critical physical information than the simpler extension-force curves can give.

No matter how commonly the term innovation has been used in economics, a concrete analytical or computational model of innovation is not yet available. This paper argues that a breakthrough can be made with genetic programming, and proposes a functional-modularity approach to an agent-based computational economic model of innovation.

Based on the general adiabatic theory for the evolutionary minority game (EMG) that we proposed earlier,¹ we perform a detail analysis of the EMG limited to three groups of agents. We derive a formula for the critical point of the transition from segregation (into opposing groups) to clustering (towards cautious behaviors). Particular to the three-group EMG, the strategy switching in the "extreme" group does not occur at every losing step and is strongly intermittent. This leads to an correction to the critical value of the number of agents at the transition, N_c. Our expression for N_c is in agreement with the results obtained from our numerical simulations.

Through the study of US airport network, we find that the network displays a high degree of error tolerance and an extreme vulnerability to attacks. The topological properties, including average degree, clustering coefficient, diameter and efficiency, are slightly affected when a few least connected airports are removed. Such properties change drastically with the removal of a few most connected ones. The degree distribution and the weight distribution under errors behave similarly to those of the original network. Under attacks, the degree distribution changes from a two-segment power-law to a monotonic one. While the under-attacked weight distribution still displays a power-law tail, with the exponent changing from 1.50 to 1.24.

Following an alternative version of Grover's algorithm, we propose a scheme to read- in information in Mn₁₂ molecular magnets with the help of multi-frequency magnetic pulses in two separate steps: first to realize an intermediate state |Ψ(T₁)> and then to reach the state |Ψ(T₂)> to encode information. All controllable parameters are calculated to implement read-in of information, and the durations of magnetic pulses are less than the dephasing time of quantum states in Mn₁₂. It is also shown that all the states of information can be initialized back to the intermediate state.

A one-way coupled chaotic map lattice is used for generating pseudo-random numbers. It is shown that with suitable cooperative applications of both chaotic and conventional approaches, the output of the spatiotemporally chaotic system can easily meet the practical requirements of random numbers, i.e., excellent random statistical properties, long periodicity of computer realizations, and fast speed of random number generations. This pseudo-random number generator system can be used as ideal synchronous and self-synchronizing stream cipher systems for secure communications.

The ultimate state of projective synchronization is usually considered to be hardly controllable due to its close dependence on the initial conditions of both drive and response systems. In this letter, we show that the scaling factor of projective synchronization can be controlled to be proportional to a given scalar function with respect to time even without the knowledge of the initial conditions of response system. Further, we apply it to the chaotic encryption. Comparing with some existing implementations, it is found that the present scheme owns several remarkable advantages. To our knowledge, it is for the first time that the projective synchronization is applied to chaos-based encryption.

We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be plagued by the maladaptive behavior of the players, we find that diversity among the players improves the system efficiency, though it slows the convergence to the steady state. Diversity causes a mild spread of resources at the transient state, but reduces the uneven distribution of resources in the steady state.

Why the classical mechanics and quantum mechanics are reversible while the macroscopic thermodynamic processes are irreversible? Is it because both of the two are different fundamental laws? If yes, what is the difference between them? What is the fundamental equation of nonequilibrium statistical physics? Can it provide a unified framework of statistical physics including nonequilibrium states and equilibrium states? How can we derive rigorously the hydrodynamic equations from microscopic kinetics? Does nonequilibrium entropy obey any evolution equation? What is the form of this equation if it exist? What is the microscopic physical basis of entropy production rate namely the law of entropy increase? Can it be described by a quantitative concise formula? What mechanism is responsible for the processes of approach to equlibrium? How to quantitatively describe it? In this paper we try to solve all these problems from a new fundamental equation of statistical physics in a unified fasion.

In this paper we report our experimental study of dilute-dense transition in a 2-dimensional granular flow of particle size d₀ and channel width D with confined exit of width d. It is found that a maximum inflow rate Q_c exists, above which the outflow changes from dilute to dense and the outflow rate Q(t) drops abruptly from Q_c to a dense flow rate Q_d. The re-scaled critical rate q_c(≡Q_c/(D/d0)) is found to be a function of a scaling variable λ only, i.e. q_c~F(λ), and . The form of this new variable λ suggests that the dilute-to-dense transition is a global property of the flow; unlike the jamming transition, which depends only on . It is also found that this transition occurs when the area fraction of particles near the exit reaches a critical value 0.65±0.03.

Statistical analysis of frequency occurrence of short words in complete genomes reveals the existence of a set of universal lengths common to all extant complete microbial genomes. This phenomenon is consistent with a model for genome growth in which primitive genomes grew mainly by maximally stochastic duplications of short segments from an initial length of about 200 nucleotides. The relevance of these results to the so-called RNA world in which life began and evolved before the rise of proteins is discussed.

Control of beam halo-chaos with complex space-time pattern in proton linacs has become one of key issues for future many important applications. This article offers a brief review for statistical physical model and advances in control methods. However, it is still an open challenging issue.

A set of theorems about the evolutionary properties of the automaton networks are presented in this article, which includes the theorems that, for an additive automaton network, the tree structures are identical, and that the geometric entropy equals to its topological entropy. The exact analytical formula for the entropy of the additive automaton networks is introduced, and applied to investigate the evolutionary properties of the elementary cellular automata of number 90 and number 150.

Combining Edwards' self-consistent-field (SCF) theory and numerical techniques borrowed from fluid dynamics, I have developed a SCF theory for spherical polymeric assemblies. The theory is being used to determine the equilibrium structure of a polymer layer formed by immiscible polymers end-grafted onto a spherical nanoparticle. Here I report some of the preliminary results.

The current-driven three-dimensional frustrated anisotropic XY model with strong disorder is simulated to model the moving vortex matter in layered superconductors. The equilibrium disordered state can be driven to a moving Bragg glass (BrG) by applying an external current. As the pinning strength increases, the moving BrG can melt into a moving smectic via a first-order phase transition.

Using the kinetic equation of subdynamics and the suitable time ordering rule we present a type of irreversible Liouville equation and nonlinear Liouville equation for open quantum systems. We also found a spectral relation for obtaining the non-equilibrium statistical distribution based on the boundary conditions which consistent with H theorem. Furthermore, a formalism of non-equilibrium project Green functions is given, and a non-perturbative method to solve the irreversible Liouville equation is studied. Finally, we give a model of spin-based quantum computing to show that the decoherence free states can be constructed using the non-perturbative approach.

The recently discovered two-phase phenomenon in financial markets [Nature421 (2003) 130] is examined with the German financial index DAX. Based on a realistic assumption, we introduce a dynamic feedback interaction to the Eguiluz–Zimmermann model [Phys. Rev. Lett.85 (2000) 5659]. Such an interaction generates a time correlation of volatility, and correctly produces the two-phase phenomenon.

Recent progresses on collective directional transport in coupled systems are overviewed. By considering the mutual interactions among elements, the directed ratchet motion exhibits complicated and novel cooperative dynamics. The directional transport can be induced not only by breaking the spatial symmetry of the substrate potential, but also by breaking the coupling symmetry and the spatiotemporal symmetries.

The development of Econophysics is studied from the perspective of scientific communication networks. Papers in Econophysics published from 1992 to 2003 are collected. Then a weighted and directed network of scientific communication, including collaboration, citation and personal discussion, is constructed. Its static geometrical properties, including degree distribution, weight distribution, weight per degree, and betweenness centrality, give a nice overall description of the research works. The way we introduced here to measure the weight of connections can be used as a general one to construct weighted network.

Recently the mechanism of the damage caused by invasion of Apis mellifera capensis honeybee into the normal A. M. Scutellata colonies became interesting for scientists due to the fact that the mechanism may resemble those of cancer vicious hyperplasia, spreading of some epidemic, and turbulence of society induced by some bad society groups. We suggest a new guess that losing control of self-reproduction disturbs and throws information structure of the society into confuse. We simulate the damage process with a cellular automata based on the guess. The simulation shows that the process is equivalent to a non-equilibrium percolation phase transition. This discussion remind us that the management and monitor on the information network between society members may be a more effective way for avoiding the overflow of the destructor sub-colonies.

Spider silk exhibits excellent mechanical features in both toughness and extensibility. In recent years considerable investigations have focused on it. The understanding of spider silk protein is important for the development bionic silk. In this paper, we study by Monte Carlo simulation the force-of-extension property of spider silk proteins as a function of the residue composition for major and minor ampullate glands of typical Araneid orb weaver as well as that for one artificial spider silk. The results are also compared with those from a designed protein whose amino acid composition is uniform. The results clearly show that the major and minor ampullate gland proteins are much tougher than the designed protein, whereas the artificial protein, as a model of a nature spider silk, does have good mechanical properties. Our simulation reveals that mechanical property of a spider silk protein is dependent on its amino acid composition and that an excellent result of natural evolution is manifest in the composition of the spider silk protein.

The scaling relations for the fluid permeability in percolation structures are numerically studied using both of the coarse numerical grid and the refined numerical grid. We suggest that the permeability for viscous fluid flows in two-dimensional lattice percolation porous media be equivalent to the conductivity problem in percolation theory, independent of the simulation refinements. The refined numerical grid does not lead to the new universality.

In this paper,the ground state energies of hydrogen-like impurity in a lens-shaped quantum dot (GaAs/In_1-xGa_xAs) under vertical magnetic field have been discussed by using effective mass approximation and variational method. It gives that for a lens-shaped quantum dot, due to the asymmetry of the vertical and lateral bound potentials, the electronic ground state energies are related not only with the deviation distance but also with the deviation direction; for the spherical quantum dot, the ground state energy is only related with the distance of the impurity deviation, neither with vertical nor lateral deviation. And with the increasing of the magnetic field, the ground state energy is increasing.

We study the combined effects of aging and links removal on epidemic dynamics in the Barabási–Albert scale-free networks. The epidemic is described by a susceptible-infected-refractory (SIR) model. The aging effect of a node introduced at time t_i is described by an aging factor of the form (t-t_i)^-β in the probability of being connected to newly added nodes in a growing network under the preferential attachment scheme based on popularity of the existing nodes. SIR dynamics is studied in networks with a fraction 1-p of the links removed. Extensive numerical simulations reveal that there exists a threshold p_c such that for p≥p_c, epidemic breaks out in the network. For p<p_c, only a local spread results. The dependence of p_c on β is studied in detail. The function p_c(β) separates the space formed by β and p into regions corresponding to local and global spreads, respectively.

In this paper, a new model of evolving networks is proposed based on the dynamical behaviors of nodes in the network. The probability that an existing node in the current network receives a new link from the newly added node is proportional to the defined "activity" of that particular node, which is equivalent to the energy signal of the system from a control theory point of view. This network is found to have the scale-free feature with the degree distribution in a power-law form. This model provides another explanation for the emergence of scale-free networks in many real-world examples.

The chaotic synchronization between two unidirectionally coupled single-mode semiconductor lasers is investigated when the lasers are subjected to external feedback. The dynamics of lasers is described by Lang–Kobayashi equation. Through numerical simulations, it is found that the lag and anticipating synchronization coexist in the system, and the transition occurs between two kinds of synchronization. Further discussion shows that the coexistence and transition process is based on the continuous similarity relation in bifilar helix structure.

In this paper we propose an interesting scheme for quantum games. It is found that, for the particular case of the famous Prisoners' Dilemma game, the superiority of the quantum game over its classical counterpart is interconnected to the non-classical quantum correlation between the two players.

SARS onsets within different municipalities/provinces/autonomous regions of the Chinese mainland around April 20, 2003, when normalized by population, obeys a piece-wise Zipf distribution, implying that there are three main modes in the propagation of SARS. Extrapolation of the scaling relation gives that the range of the expected final cumulative SARS cases in Beijing would be 2170-2540. The real situation is 2522 at the end of June 2003.

By using the concurrence, the entanglement of a quantum Ising chain is studied numerically. It is found that there is a gap in the concurrence of the nearest-neighbor spins at the quantum phase transition point for the chain with even spins. The gap disappears as the number of the spins goes to infinite. Except for the critical point, the derivatives of the concurrence display the similar scaling behavior as that of the odd-spin chain.

Some parameters are introduced to evaluate the completeness of a partial multifractal spectrum with the shape of a bell or a hook, calculated using a statistical method due to a finite range of moment q. From the results of two kinds of Cantor sets, p/0/1-p and p/1-2p/p, and some examples of random fractals, it shows that the more homogeneous the probability distribution of the quantity studied is, the larger the range of q in the partial multifractal spectrum with the same evaluation parameters.

The properties of 2D Ising model on a small world network are investigated. It is found that Curie temperature increases with the increase of small world links. The relations between the Curie temperature and the concentration of small world links are found. The possibility of using Ising model to describe real network is discussed.

A transiently chaotic neural network (TCNN) is an approximation method for combinatorial optimization problems. The evolution function of self-back connect weight, called annealing function, influences the accurate and search speed of TCNN model. This paper analyzes two common annealing schemes. Furthermore we proposed a new subsection exponential annealing function. Finally, we compared these annealing schemes in TSP problem.

In this paper, by introducing the collision model of the K ion channel, the maximum value of ions inward the channel per second, the average velocity of ions in the channels and the average time of every ion passing through the channel are obtained. Moreover they are reconciled with the experimental data. Base on the experimental data, the empiristic potential function is deduced. With the Monte–Carlo simulation, the curve of average velocity versus time and average displacement versus time are calculated by resolving the over-damping Langevin equation with Gaussian-white noise. They are according with the experimental dada well.

The energies, radiative and Auger rates of the doubly excited states of Be-like Ar¹⁴⁺ ion are studied by using the multi-configuration-interaction method and model potential method. The doubly excited states of Be-like Ar¹⁴⁺ are labeled by the quantum numbers K, T and A to show the systematic regularity. The results show that the spectroscopy of Be-like ions is different from that of He-like ions because of the polarization and core penetration effects from the 1s² core electrons.

Chinese skyway network is investigated. Nodes are defined as the Airports. Edges are defined as skyways. The statistical properties of the network in 2002, 1998 and 1978 are obtained. A simple dynamical model, which may reproduce the developing process of the network, is suggested. The simulation results show a good agreement with the statistical results.

This article reports a statistical investigation on Chinese power grid. A new statistical parameter, averaged ratio of cycles, is suggested for describing the stratum structure of the grid. A dynamical model, which may reproduce the developing process of Chinese power grid, is also presented.

We suggest a self-adaptive model for a description of actor-collaboration. Suppose that the numbers of actors and directors increase as time progresses (with different velocity). Each of the people is randomly given a style coefficient and a famousness coefficient, which vary on time according to his achievements in every year. A director can conduct more films and an actor can be invited to perform in more films in condition they have a higher famousness coefficient. Our numerical simulation results show that the actor-collaboration network described by this model is both small-world network and scaling-free network. All the important statistical parameters obtained by the simulation are in a good agreement with the statistical results. We also suggest a new parameter, which is addressed as "degree of connexity". Its distribution shows a new power law.

A new kind of crisis is defined as a sudden change of a strange repeller. It can be observed in some non-smooth systems, such as a tent map, a "hole map", an electronic relaxation oscillator, and a discontinuous kicked rotor.

In the transition to chaos via type V intermittency, when a periodic motion loses stability, there may be no intermediate higher-period orbits displayed before chaos or a sequential such orbits that form a staircase. The staircase may take a form of a conventional devil's staircase, a multiple devil's staircase or a seemingly irregular form. This article briefly presents typical examples for these situations.

Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical power law relations of the period and transient iterations with the computation precisions and the sizes of coupled systems are obtained. For each computation we always find, by randomly choosing initial conditions, a single dominant periodic trajectory which is realized with major portion of probability. These understandings are useful for possible applications of chaos, e.g., chaotic cryptography in secure communication.

A direct correlation between the stretched exponent, β(T), of relaxation functions and configurational entropy of the Adam–Gibbs's theory on cooperatively rearranging region (CRR) in glass-forming liquids is investigated. One important result is that β(T) is equal to the relative configurational entropy per molecule. Another significant prediction is that β(T) is inversely proportional to the critical molecule number z*, of a CRR in the transformation. Further, a factor f(T) is proposed to express the temperature dependence of viscosity and configurational entropy. A modified Vogel-Fulcher–Tammann (VFT) equation is obtained by adding a small non-linear term to f(T). The above theoretic investigations coincide precisely with the calorimetric experimental results of 3-bromopentane.

We study kinetic behavior of the growth of A aggregates through reversible migrations between the B intermediaries and the A aggregates. In a model with the migration rate kernels K(k;j)=K'(k;j)∝k^uj^v (u,v≥0) at which monomers migrate from the aggregates A_k of size k to the B intermediaries of size j, we find that for all cases with 0≤u<2 and v>0, the size distribution of A aggregates always obeys the conventional scaling form. When v=0, A aggregates may scale according to a logarithm-correction form. Moreover, the typical aggregate size of A aggregates grows as t^v/(2-u) in the v>0 case and as (lnt)^1/(2-u) in the v=0 case.

An algorithm of constructing the polynomial type conservation laws of nonlinear evolution equations (either parameterized or non-parameterized) is described and a Maple package to automate the computation is presented. For parameterized equation(s), can determine the parameters constraints automatically such that a sequence of conservation laws exist.

The melting of elemental solids is modelled as a dislocation pair-mediated transition on a lattice. Statistical mechanics of linear defects is used to obtain the relation between melting temperature and shear modulus. It is derived theoretically that the phase transition is the first order and the formula for latent heat is also derived.

It has become widely accepted that ventricular fibrillation, the most dangerous cardiac arrhythmias, is a major cause of death in the industrialized world. Alternans and conduction block have recently been related to the progression from ventricular tachycardia to ventricular fibrillation. From the point of view in cellular electrophysiology, ventricular tachycardia is the formation of reentrant wave in cardiac tissue. And ventricular fibrillation arises from subsequent breakdown of reentrant wave into multiple drifting and meandering spiral waves. In this paper, we numerically study pulse and vortex dynamics in cardiac tissue. Our numerical results include 1:1 normal sinus rhythm, 2:1 conduction block, complete conduction block, spiral wave, and spiral breakup. All of our numerical findings can be corresponding to clinical measurements in electrocardiogram. Various electrical activities in cardiac tissue will be discussed in detail in the present manuscript.

We develop a 2-D discrete model to simulate malignant cells growing in healthy tissues using a thermodynamic method on the basis of Potts model. After introducing a malignant seed in a healthy tissue, we use a set of adjustment factors, including the interaction between cells and nutrient, to simulate the growth of malignant cells under different environments. This allows us to investigate the effects of environment on malignant cell growth and the formation of cancer.

A cellular automaton model with open boundary condition for a crossroad system controlled by a traffic light is presented. The traffic flow and speed of the first part of the road are quite different from those of the second part behind the crossing. The impact of turning probabilities and the cycle times of traffic light on the flow are investigated.

When a reactive fluid flows through a porous rock it can dissolve some minerals and increase the porosity and permeability. The positive feedback between fluid flow and mineral dissolution can lead to the complexity of the propagation of dissolution front and the formation of finger flow-focusing reaction area. As an example for in situ leaching Uranium mining, the simulation results indicate that the propagation of dissolution front is complex such as finger and more complicated reaction front morphologies. The nonlinearity of flow-reaction coupling and instability of dissolution front morphologies can lead to unleaching area and affect the rate of recovery of mineral resource.

The phenomenon of tunneling is well-known in quantum theory, however, many novel characteristics appear when the corresponding classical dynamics of the underlying system is chaotic. In this paper, the chaos-assisted tunneling is found in a triple-well potential under an external periodic driving field. We make use of the Husimi distribution to illustrate this characteristic in the quantum phase-space.

In this paper, hyperchaotic synchronization in a network of continuous-time dynamical systems with small-world connections is investigated. The small-world network is obtained by selecting a part of nodes to be hubs and then using a globally coupled network to interconnect these hubs in an originally nearest-neighbor coupled network. We show that, the deterministic small-world dynamical network will also synchronize when the maximal Lyapunov exponent of the self-feedback system of single node is equated to, even great than zero. This explains why many real-world complex networks exhibit strong tendency toward synchronization even with a relatively weak coupling. Our study may shed some new light on synchronization phenomena in real complex networks.

The method of controlling chaos by occasional nonlinear time-delayed feedback is proposed. Through the numerical analysis of bifurcation diagram and Lyapunov exponent, we found that the systematic chaos can be controlled effectively by the nonlinear time-delayed feedback as the form of u(x_n,x_n-k)=cx_nx_n-k. Under the proper feedback coefficient c, time-delayed coefficient k and occasional feedback period N, the system could be controlled from chaos to the steady periodic orbit, and also the steady period is the integral multiple of the occasional feedback period N.

In this paper, a new strategy is developed for controlling chaos and hyperchaos in a nonlinear system via switching modulation of systems parameters. The control method is illustrated by examples of the third-order chaotic Chua's circuit and a sixth-order coupled hyperchaotic Chua's circuit. Numerical simulations show that this method is very effective.

An evolutionary multiple-choice minority game is investigated. In the model, each agent chooses one option out of Nc options. Each agent is assigned a single parameter p (0≤p≤1) that he chooses his best performing strategy of his s strategies for decision. With probability 1-p he chooses his worst performing strategy. If the agent's wealth falls below a value d(d<0), his p value is allowed to modify by picking a new value with a range of R of the old p value. Numerical results reveal that the evolution can considerably enhance the system's coordination.

An artificial stock market is established with the modeling method and ideas of cellular automata. Cells are used to represent stockholders, who have the capability of self-teaching and are affected by the investing history of the neighboring ones. The neighborhood relationship among the stockholders is the expanded Von Neumann relationship, and the interaction among them is realized through selection operator and crossover operator. Experiment shows that the large events are frequent in the fluctuations of the stock price generated by the artificial stock market when compared with a normal process and the price returns distribution is a Lévy distribution in the central part followed by an approximately exponential truncation.

Traffic flow at an uncontrolled T-shaped intersection is modelled by a cellular automaton model. A priority probability of the through car is introduced. The phase diagram of the system and the effect of the turning car on the whole traffic situation are investigated. Our simulation results suggest that priority should be given to either through cars or to turning cars according to the ratio of the turning cars in order to obtain the optimization of the system.

The low frequency vibration energy absorption properties of granular materials have been investigated on an Invert Torsion Pendulum (ITP). The energy absorption rate of granular material changes nonlinearly with amplitude under low frequency vibration. The frequency of ITP system increases a little with granular materials in the holding cup. The vibration frequency of ITP system does not change with time.

By using the method of multiple-scale and the continuum approximation, we study the nonlinear properties of a monoatomic chain with Kac–Baker-like long-range harmonic interaction. It is shown that the dispersion relation, the group velocity and the amplitude of solitons exhibit some new characters different from that of the nonlinear chain without Kac–Baker-like long-range harmonic interaction.

In this paper, we apply IAAFT to generate surrogate time series of measured multivariate time series. A quantitative method to detect nonlinearity in multivariate time series is proposed using the generalized redundancy and linear redundancy as the significance test statistic. The null hypothesis of a multivariate linear Gaussian random process is tested using the multivariate surrogate data. The validity of this method is demonstrated using two types models (linear and nonlinear) and applied to Shanghai stock market.

We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mechanism to ensure the robustness of power-law distributions.

A new powerful tool, chaotic theory, has been used to study mineralization through chaotic analysis for space series of gold grade in this paper. Both of the most important chaotic measures, Largest Lyapunov exponent (LLE) and fractal dimensional, for space series of gold grade in one gold deposit are computed. The positive LLE suggests that the space series of gold grade are chaotic series. When the phase space dimension approach 8~10, a chaotic attractor appears and their fractal dimension values vary from 1.94 to 3.99. It indicates that the evolution of ore-forming fluid and the enrichment and deposition of gold element are chaotic dynamic process.

The spreading of SARS will destruct the initial network structure to a new phase, and in turn the spreading process will be weakened effectively and finally halted by this evolution of network structure. This mechanism is called immunity of contact network in this paper. What we can do is to accelerate effectively this process only.

In this paper, the quantum system with two particles is analyzed and the energy level spacing statistics distribution and Δ₃-statistic are given. The results show that hard quantum chaos appear in the system with a certain potential. Tunnelling effect develops quantum chaos.

Softening of the phase transition and critical phenomena for the 2D random-bond Potts ferromagnet is investigated by using the density-of-states Monte Carlo method to calculate the thermodynamic properties with a variety of the quenched bond-randomness characterized by a disorder amplitude r=K_s/K_w. The numerical results show that the crossover from the 1st- to 2nd-order transition was induced at finite lattices for the self-dual bimodal distribution.

In this paper, the dynamical behavior of a non-symmetric double potential well in a tilted magnetic field is studied. The classical Poincare section is given to exhibit the chaotic behavior of the system, and non-linear resonant lead to chaos. The paper has also given the energy spectral statistics which satisfies Brody's distribution, tunnelling effect develops quantum chaos and also holds back the development of chaos.

A two-dimensional dynamics model of an elliptic cylinder is derived by using the lattice Boltzmann method. With the present model, we have simulated the sedimentation of a single charged elliptic cylinder in a two-dimensional tube in a Newtonian fluid. Due to the polarizing effects and non-axial symmetry shape, there are the Coulomb force and the Coulomb torque on the elliptic cylinder during the sedimentation, which change its ordinary motion significantly. Comparing with the sedimentation of an un-charged elliptic cylinder under the same initial condition, we have further discussed the dynamics characteristics of the charged elliptic cylinder, and obtained some interesting results.

The biochemical process for coupling between hydrolysis of ATP and the performance of mechanical work involves a sequence of events. Here we present a two-dimensional ratchet model with a non-conservative impulsive force field. The non-conservative impulsive force that represents the chemical energy consumed in the conformation changing process provides a source of non-equilibrium fluctuation, which is a crucial factor for the Brownian motors and can lead to macroscopic motion.

Based on the vacancy-assisted diffusion mechanism, the impure atomic moving processes on the close-packed layer of a Cu(001) surface are studied by kinetic Monte Carlo simulations. Our simulation results show that the diffusivity of the Indium atom agrees quite well with the exact lattice solution. In addition, it is found that in the case of muti-impure atoms, there exist a critical point near the value of ∊=0, and the diffusivity of In atom depends on the number of impure atoms only when ∊ is positive.