On the Appearance of Mixed Dynamics as a Result of Collision of Strange Attractors and Repellers in Reversible Systems

Radiophysics and Quantum Electronics - In this work, we propose a scenario of appearance of mixed dynamics in reversible two-dimensional diffeomorphisms. A jump-like increase in the sizes of the...     

Low-Temperature Dynamics of the Curie-Weiss Model: Periodic Orbits,Multiple Histories,and Loss of Gibbsianness

We consider the Curie-Weiss model at initial temperature 0<β ⁻¹≤∞ in vanishing external field evolving under a Glauber spin-flip dynamics with temperature 0<β′⁻¹≤∞. We study the limiting conditional probabilities and their continuity properties and discuss their set of points of discontinuity (bad points). We provide a complete analysis of the transition between Gibbsian and non-Gibbsian behavior as a function of time, extending earlier work for the case of independent spin-flip dynamics.     

Evidence of Strange Attractors in Class C Amplifier with Single Bipolar Transistor: Polynomial and Piecewise-Linear Case

This paper presents and briefly discusses recent observations of dynamics associated with isolated generalized bipolar transistor cells. A mathematical model of this simple system is considered on the highest level of abstraction such that it comprises many different network topologies. The key property of the analyzed structure is its bias point since the transistor is modeled via two-port admittance parameters. A necessary but not sufficient condition for the evolution of autonomous complex behavior is the nonlinear bilateral nature of the transistor with arbitrary reason that causes this effect. It is proved both by numerical analysis and experimental measurement that chaotic motion is miscellaneous, robust, and it is neither numerical artifact nor long transient motion.     

Coexistence of Charge Order and Antiferromagnetic Order in an Extended Periodic Anderson Model

The competition between the RKKY interaction and the Kondo effect leads to a magnetic phase transition,which occurs ubiquitously in heavy fermion materials.However,there are more and more experimental evidences indicating that the valence fluctuation plays an essential role in the Ce-and Y-based compounds.We study an extended periodic Anderson model(EPAM) which includes the onsite Coulomb repulsion Ucf between the localized electrons and conduction electrons.By employing the density matrix embed...     

On the Region of Existence of a Discrete Lorenz Attractor in the Nonholonomic Model of a Celtic Stone

Radiophysics and Quantum Electronics - In this work, we consider the problem of existence of discrete Lorenz attractors in the nonholonomic model of a Celtic stone. To this end, the main local and...     

具有复合幂函数和共存吸引子的新混沌系统的动力学分析与电路仿真

构造一个具有复合幂函数的三维连续自治混沌系统。系统的状态方程仅有5项,其中一项是指数小于1的复合幂函数。该系统具有结构简单、非双曲平衡点、吸引子共存的性质,展现出了复杂的动力学行为。首先,对系统的动力学行为进行分析,包括李雅普诺夫（Lyapunov）指数谱、分岔图以及庞加莱映射等,结果表明此系统具有混沌特性。然后进行混沌系统的电路设计,电路仿真结果验证了理论分析的正确性。     

Properties of Strange Matter in a Model with Effective lagrangian

The strange hadronic mater with nucleons,Λ-hyperons and Ξ-hyperons is studied by using an effective nuclear model in a mean-field approximation.The density and strangeness fraction dependence of the effective baryon masses as well as the saturation properties and stabilities of the strange hadronic matter are discussed.     

A Model with Darwinian Dynamics on a Rugged Landscape

We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase diagram in terms of the size of the population and the diffusion rate, with a glass phase inside which the dynamics keeps searching for better configurations, and outside which deleterious ‘mutations’ spoil the performance. The phase diagram is analogous to that of dense active matter in terms of temperature and drive.

     

Quantum Mechanical Analysis of the Equilateral Triangle Billiard: Periodic Orbit Theory and Wave Packet Revivals

Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by T_rev=9μa²/4?π where a and μ are the length of one side and the mass of the point particle, respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral (60°-60°-60°) triangle, such as the half equilateral (30°-60°-90°) triangle and other “foldings,” which have related energy spectra and revival structures.     

Dynamical Stability and Attractor of the Variable Generalized Chaplygin Gas Model

For the variable generalized Chaplygin gas （VGCG） as a dynamical system, its stability is analyzed and the related dynamical attractors are investigated. By analysis it is shown that there are two critical points corresponding to the matter-dominated phase and the VGCG dark energy-dominated phase, respectively. Moreover, when the parameters n, a and γ take some fixed values, the phase with ωVGCG = --0.92 is a dynamical attractor and the equation of state of VGCG reaches it from either ωVGCG 〉 --1 or ωVGCG 〈 --1, independent of the initial values of the dynamical system. This shows a satisfactory cosmological model： the early matter-dominated era, followed by the dark energy-dominated era. Meanwhile, the evolutions of density parameters Ωγ and ΩVGCG are quite different from each other. For different initial values of x and y, Ωγ decreases and ωVGCG increases as the time grows, they will eventually approach Ωγ = 0 and ωVGCG ---- 1. Furthermore, since different values of n or a may lead to different equation-of-state parameters ωVGCG, we also discuss the constraints on the parameters n and by the observation data.     

Kerr介质中J-C模型的色散近似耗散动力学

应用全量子论研究了含Kerr介质的Jaynes-Cummings模型在色散近似下系统和子系统的相干性丢失及纠缠特性,在输入场为相干场假设下计算了线性熵.结果表明,原子相干性丢失与Kerr效应无关,场和原子-场系统的相干性丢失因Kerr介质的存在而增强,原子与场之间的纠缠因Kerr效应而受到压制,场的相干性时间演化规律在定性和定量两方面都受到腔耗的影响.Kerr介质对场线性熵的作用要通过腔耗才能展现出来.     

Dynamics of Hopfield-Type Neural Networks with Modulo Periodic Unpredictable Synaptic Connections,Rates and Inputs

In this paper, we rigorously prove that unpredictable oscillations take place in the dynamics of Hopfield-type neural networks (HNNs) when synaptic connections, rates and external inputs are modulo periodic unpredictable. The synaptic connections, rates and inputs are synchronized to obtain the convergence of outputs on the compact subsets of the real axis. The existence, uniqueness, and exponential stability of such motions are discussed. The method of included intervals and the contraction mapping principle are applied to attain the theoretical results. In addition to the analysis, we have provided strong simulation arguments, considering that all the assumed conditions are satisfied. It is shown how a new parameter, degree of periodicity, affects the dynamics of the neural network.     

Index and Stability of Symmetric Periodic Orbits in Hamiltonian Systems with Application to Figure-Eight Orbit

In this paper, using the Maslov index theory in symplectic geometry, we build up some stability criteria for symmetric periodic orbits in a Hamiltonian system, which is motivated by the recent discoveries in the n-body problem. The key ingredient is a generalized Bott-type iteration formula for periodic solution in the presence of finite group action on the orbit. For second order system, we prove, under general boundary conditions, the close formula for the relationship between the Morse index of an orbit in a Lagrangian system and the Maslov index of the fundamental solution for the corresponding orbit in its Hamiltonian system counterpart, and the boundary conditions cover the cases which appeared in the n-body problem. As an application we consider the stability problem of the celebrated figure-eight orbit due to Chenciner and Montgomery in the planar three-body problem with equal masses, and we clarify the relationship between linear stability and its variational nature on various loop spaces. The basic idea is as follows: the variational characterization of the figure-eight orbit provides information about its Morse index; based on its relation to the Maslov index, our stability criteria come into play. Partially supported by NSFC (No.10801127) and the knowledge innovation program of the Chinese Academy of Science. Partially supported by NSFC (No.s 10401025, 10571123 and 10731080) and NSFB-FBEC (No. KZ20 0610028015).     

相对论夸克模型中底奇异介子的辐射衰变(英文)

系统地研究了相对论夸克模型框架下的底奇异介子的辐射衰变。给出了底奇异介子E1 和M1 辐射衰变分宽度。这些结果表明,大多数电偶极辐射衰变宽带能达到数个keV,大多数磁偶极辐射衰变宽度小于1 个keV,这为实验上通过辐射衰变寻找底奇异介子提供了理论依据。建设中的Belle II 上的实验可以进一步验证我们的结果。We systematically study the radiative transitions of bottom-strange mesons in the framework of the relativistic constituent quark model. The partial widths of the E1 and M1 decays are predicted. The results predict that most of E1 decay widths are several keV and most of M1 decay widths are less than 1 keV,which give a roadmap of searching for the higher bottom-strange mesons via radiative decays. The experimental searches by the forthcoming Belle II can in turn provide further tests to our result in the present work.     

Protrusion of a Virtual Model Lamellipodium by Actin Polymerization: A Coarse-Grained Langevin Dynamics Model

We report the development of a coarse-grained Langevin dynamics model of a lamellipodium featuring growing F-actin filaments in order to study the effect of stiffness of the F-actin filament, the G-actin monomer concentration, and the number of polymerization sites on lamellipodium protrusion. The virtual lamellipodium is modeled as a low-aspect-ratio doubly capped cylinder formed by triangulated particles on its surface. It is assumed that F-actin filaments are firmly attached to a lamellipodium surface where polymerization sites are located, and actin polymerization takes place by connecting a G-actin particle to a polymerization site and to the first particle of a growing F-actin filament. It is found that there is an optimal number of polymerization sites for rapid lamellipodium protrusion. The maximum speed of lamellipodium protrusion is related to competition between the number of polymerization sites and the number of available G-actin particles, and the degree of pulling and holding of the lamellipodium surface by non-polymerizing actin filaments. The lamellipodium protrusion by actin polymerization displays saltatory motion exhibiting pseudo-thermal equilibrium: the lamellipodium speed distribution is Maxwellian in two dimensions but the lamellipodium motion is biased so that the lamellipodium speed in the direction of the lamellipodium motion is much larger than that normal to the lamellipodium motion.     

A Model of Subdiffusive Interface Dynamics with a Local Conservation of Minimum Height

We define a new model of interface roughening in one dimension which has the property that the minimum of interface height is conserved locally during the evolution. This model corresponds to the limit q of the q-color dimer deposition-evaporation model introduced by us earlier [Hari Menon and Dhar, J. Phys. A: Math. Gen. 28:6517 (1995)]. We present numerical evidence from Monte Carlo simulations and the exact diagonalization of the evolution operator on finite rings that growth of correlations in this model is subdiffusive with dynamical exponent z2.5. For periodic boundary conditions, the variation of the gap in the relaxation spectrum with system size appears to involve a logarithmic correction term. Some generalizations of the model are briefly discussed.