Asymptotic estimates for two-dimensional area-preserving mappings

We consider the perturbation series for the formal integral of two-dimensional area-preserving mappings and obtain asymptotic formulas for large order terms of this expansion.     

Thermodynamic properties of two-dimensional Yukawa systems

The simple analytical approximation for the energy densities in two-dimensional Yukawa systems is proposed for the wide range of parameters of non-ideal fluids. The use of this approach allows determining all thermodynamic functions and characteristics on the base of general thermodynamic relationships. The comparisons of obtained results with the numerical study of thermodynamic properties are presented. Simulations were performed for parameters typical for the laboratory dusty plasma experiments.     

连续时间系统二维不稳定流形的异构算法

非线性系统的二维流形通常具有复杂几何结构和丰富动力学信息,因此在流形计算与可视化时存在大量的不可避免的数值计算.因此,如何高效地完成这些计算就成了关键问题.鉴于当今计算机的异构发展趋势(包含多核CPU和通用GPU),本文在兼顾精度和通用性的基础上,提出了适用于新一代计算平台的快速流形计算方法.本算法将计算任务分为轨道延伸和三角形生成两部分,前者运算量大而单一适合GPU完成,后者运算量小而复杂适合CPU执行.通过对Lorenz系统原点稳定流形的计算,表明本算法能充分发挥异构平台的综合性能,可大幅度提高计算速 关键词： 不稳定流形 流形计算 异构计算 Lorenz系统     

Ensemble properties and molecular dynamics of unstable systems

The Hertel-Thirring cell model for unstable systems (of purely attractive particles) is solved in the canonical ensemble for arbitrary dimensions. The differences between the phase transitions found in the canonical and in the microcanonical ensemble are discussed. The cluster phase (with a complete collapse in the ground state) exhibits the nonextensive character of the cell model. The results of the cell model are compared with molecular-dynamics simulations of a one-dimensional model with a rectangular-well pair potential. The simulations support the relevance of the cell model to characterize basic properties of gravitational systems.     

Magnetic properties of two-dimensional and layered systems

We consider two-dimensional magnetic systems and compare our results with experimental data on (C₂H₅NH₃)₂CuCl₄.     

Collective effects in the transport properties of two-dimensional electron systems

The results of the experimental study of the nontraditional manifestations of collective effects in the transport properties of two-dimensional electron systems are reported.     

Computer studies of dislocation properties using two-dimensional model systems

The physical properties of dislocations are investigated by means of a two-dimensional Lennard-Jones solid. Using a self consistent linear theory for the elastic properties of two-dimensional systems, analytic expressions for the energy and entropy of a dislocation in the center of a circular finite model are derived. The energy and entropy formulas are compared with the results of molecular dynamics calculations on the model. The resulting atomic structure of the dislocation core is compared with the structure of bubble raft dislocations and with the results of earlier computer calculations.     

Two remarks on the computer study of differentiable dynamical systems

In the first part of this note we find conditions under which the frequency spectrum of a transformation exhibits delta functions. In the second part we show that if an ergodic flow on anm-dimensional manifold hasm–1 strictly negative characteristic exponents, then the measure is concentrated either on a fixed point or on a closed attracting orbit.     

Some dynamical properties of Einstein space-times admitting a Gaussian foliation

We investigate the behavior of curves in the space of Riemannian metrics which corresponds to Einstein space-times admitting a Gaussian foliation. Different types of variational principles are formulated and some global dynamical properties of these space-times are obtained.Alexander-von-Humboldt-Fellow.     

Structural properties of the condensate in two-dimensional mesoscopic systems of strongly correlated excitons

A two-dimensional mesoscopic Bose system of dipoles in a 2D trap is considered using computer simulation by the quantum path-integral Monte Carlo method. The model describes a rarefied system of spatially indirect excitons in a confining potential. Bose condensation in the system and its superfluid and structural properties are studied over a wide range of interparticle spatial correlations, from an almost ideal Bose gas to the regime of a strongly correlated system. It is found that, at strong interparticle spatial correlations, particles in the condensate form a crystal-like structure. In this case, the spatial correlations of particles in the condensate are less pronounced than the correlations of noncondensed particles. The effect of recurrent crystallization is observed in the regime of strong interparticle correlations.     

The mermin-wagner phenomenon and cluster properties of one- and two-dimensional systems

We give optimal conditions concerning the range of interactions for the absence of spontaneous breakdown of continuous symmetries for one- and two-dimensional quantum and classical lattice and continuum systems. For a class of models verifying infrared bounds our conditions are necessary and sufficient. Using the same techniques we obtain a priori bounds on clustering for systems with continuous symmetry, improving results of Jasnow and Fisher.Partially supported by CAPES-PICD.Partially supported by the CNP_q.Partially supported by N.S.F. under grant MCS 7801433.     

Externally perturbed unstable systems

We discuss computer solutions of Newton's equations of motion for unstable systems in a container with time-dependent walls. An expansion leads to the formation of a cluster and a significant increase of the temperature. The question of entropy increase for expansion and compression of the system and the related problem of the feasibility of a perpetum mobile of the second kind are investigated.     

Melting properties of two-dimensional multi-species colloidal systems in a parabolic trap

The angular and radial melting properties of two-dimensional classical systems consisting of different types of particles confined in a parabolic trap are studied through modified Monte Carlo simulations. A universal behavior of the angular melting process is found, which occurs in multiple steps due to shell depended melting temperatures. The melting sequence of the different shells is determined by two major factors: (1) the confinement strength which each shell is subjected to, and (2) the specific structure of each shell. Further, a continuous radial disordering of the particle types forming a single circular shell is found and analyzed. This phenomenon has never been observed before in two-dimensional mono-dispersive systems. This continuous radial disordering results from the high energy barrier between different particle types in multi-species systems.     

On the short-time behaviour of quantum unstable systems

We consider the survival amplitudeA(t) for a normalized decaying state whose energy spectral density vanishes asymptotically as an inverse power. By using simple calculus a Taylor expansion ofA(t) is derived aroundt=0, the form of the remainder term identified, and a physical significance given to the other coefficients. It is shown that the Taylor remainder may contain logarithms oft besides powers.     

Lyapunov exponents in unstable systems

We investigate the dynamical behavior of unstable systems in the vicinity of the critical point associated with a liquid-gas phase transition. By considering a mean-field treatment, we first perform a linear analysis and discuss the instability growth times. Then, coming to complete Vlasov simulations, we investigate the role of nonlinear effects and calculate the Lyapunov exponents. As a main result, we find that near the critical point, the Lyapunov exponents exhibit a power-law behavior, with a critical exponent beta=0.5. This suggests that in thermodynamical systems the Lyapunov exponent behaves as an order parameter to signal the transition from the liquid to the gas phase.