Metastable behavior of stochastic dynamics: A pathwise approach

In this paper a new approach to metastability for stochastic dynamics is proposed. The basic idea is to study the statistics of each path, performing time averages along the evolution. Metastability would be characterized by the fact that the process of these time averages converges, under a suitable rescaling, to a measure valued Markov jump process. Here this convergence is shown for the Curie-Weiss mean field dynamics and also for a model with spatial structure: Harris contact process.Partially supported by CNPq, Grant No. 301301/79.     

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.     

Linear stochastic dynamics with nonlinear fractal properties

Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with multiplicative noise produce intermittency of a special kind, characterized by a power law probability density distribution. We present a review of applications, highlight the common physical mechanism and summarize the main known results. The distribution and statistical properties of the duration of intermittent bursts are also characterized in detail.     

Stochastic dynamics of two-dimensional infinite-particle systems

The time evolution of an open system of infinitely many two-dimensional classical particles is investigated. Particles are interacting by a singular pair potentialU, and each particle is connected to a heat bath of temperatureT. The heat baths are represented by independent white noise forces and Langevin damping terms. Existence of strong solutions to the corresponding infinite system of stochastic differential equations is proved for initial configurations with a logarithmic order of energy fluctuations. Gibbs states forU at temperatureT are invariant under time evolution.     

Relaxation dynamics in a stochastic bosonic Josephson junction

We consider a bosonic Josephson junction in the Bose-Hubbard two-mode approximation where some of the parameters are corrupted by physically meaningful noise processes and study the corresponding relaxation dynamics towards its equilibrium state. We show with numerical simulations that this model can essentially capture all the important features observed in a recent experiment regarding the relaxation dynamics in one-dimensional bosonic Josephson junctions, namely the damped oscillations of the population imbalance and the relative phase, as well as the large final coherence factor. We expect that this work will further motivate research about the origin of relaxation mechanism in these systems.     

A comparative study on the effect of hydrodynamic interactions in the non-sequential deposition of concentrated colloidal dispersions: stochastic rotation dynamics and Brownian dynamics simulations

Irreversible adsorption of particles onto a flat surface as a consequence of sedimentation colloidal suspension has been studied by two simulation techniques: Brownian dynamics (BD) and stochastic rotation dynamics (SRD). The purpose of using both methods is to investigate the effect of hydrodynamic interactions on adsorption kinetics and structure of the first monolayer of sediment obtained from the sedimentation of a concentrated and monodisperse colloidal suspension. Three systems were studied, characterised by the Péclet numbers: 0.1, 1.0 and 10. To physically understand the kinetic behaviour, simulation results were analysed using a kinetic model based on chemical reactions. High values of jamming limit (θ_∞ > 0.61) were obtained for both simulation techniques, with the SRD showing the highest figures (0.631) due to the hydrodynamics effect that takes into account the fluid backflow produced on particle sedimentation. A two-step adsorption mechanism was proposed based on the observed kinetic behaviour.     

Evolutionary dynamics of nationalism and migration

I present a dynamic evolutionary game model to address the relation between nationalism against immigrants and assimilation of the latter into the host country culture. I assume a country composed of two different large polymorphic populations, one of native citizens and the other of immigrants. A native citizen may behave nationalistically or may welcome immigrants. Immigrants may have an interest in learning the host country language or not. Evolution is modeled using replicator dynamics (RD). I also account for the presence of an enclave of immigrants in the host country. In the RD, the latter represents the immigrants’ own population effect, which contribution to fitness is controlled using a parameter ρ$\rho$, 0≤ρ≤1$0\le \rho \le 1$, that represents the enclave size. In line with the empirical literature on migration, the existence of an enclave of immigrants makes assimilation less likely to occur. For large values of ρ$\rho$, complete assimilation may not occur even if immigrants and natives share very close cultures and norms. Government policy regarding nationalism is modeled both exogenously and endogenously. A single or multiple asymptotically stable states exist for all cases studied but one in which the dynamics is similar to that found in the predator–prey model of Lotka–Volterra for competing species.     

A stochastic approach to Wilson loops

Wilson loops exp (i A (x) dx) are investigated in two-dimensional Euclidean space-time. The electromagnetic vector potential A is regarded as a generalized random field given by the stochastic partial differential equation A = F where is a first-order differential operator and F is white noise. We give a rigorous definition of Wilson loops and examine the properties of the N-loop Schwinger functions.     

耦合双稳系统的随机共振控制

两个双稳系统经非线性耦合而成为多稳态系统,该耦合系统与单一双稳系统相比具有较高的理论研究和实际应用价值.解析地分析了耦合系统在含噪弱周期信号作用下的响应特性,给出了耦合系数和双稳系统参数对随机共振的影响,表明耦合系统的随机共振是在带状的双势阱作用下产生的,还构建了反馈耦合控制原理框图.这为在双稳类系统中人为地产生随机共振或使共振效应更加强烈即随机共振的控制及其应用提供了可靠的理论依据.数值仿真结果与理论分析完全符合. 关键词： 耦合双稳系统 随机共振 控制     

利用随机拓扑方法分析系统级高功率微波效应

为研究高功率微波与复杂系统的耦合问题,提出了随机拓扑方法。该方法是一种新的系统级电磁敏感度分析预测方法,它结合电磁拓扑理论和随机耦合模型理论,可对包含多个腔体的复杂系统的短波电磁耦合问题进行统计分析。介绍了随机拓扑方法的理论基础,并利用计算机机箱搭建了双腔体和多腔体实验平台。使用该方法对目标位置处感应电压的统计分布进行了预测,并与其他方法得到的感应电压分布进行了比较,其结果基本一致,从而证明了该方法的可行性和准确性。     

Determination of the activation energy by stochastic analyses of molecular dynamics simulations of dislocation processes

An investigation is reported of the probability and the probability density of thermal activation of stress-driven dislocation processes, as simulated using molecular dynamics (MD). Stochastic analyses of the survival probability are found to lead to simple relationships between the loading history and the distribution of the interaction time and strength. It is shown that the determination of the activation energy associated to a thermally activated event can be achieved by a reduction of the stochastic process to a process obeying the Poisson's distribution, preserving the activation probability at the survival time. The method is applied to the kink-pair mechanism for screw dislocations in iron. Predictions are compared with experimental results and with other methods reported in the literature, which allows the difference in the approximations and in the assumptions considered in these models to be underlined.     

Percolation analysis of stochastic models of galactic evolution

The stochastic star formation model of galactic evolution can be cast as a problem of directed percolation, the time dimension being that along which the directed bonds exist. We study various aspects of this percolation, those of general interest for the percolation phase transition and those of particular importance for the astrophysical application. Both analytical calculations and computer simulations are provided and the results compared. Among the properties are: value of the percolation threshold, critical indices, percolation probability (star density) near and away from the critical point, local density, cluster sizes, effects of rotation (for disk galaxy models) on the percolation threshold. Astrophysical consequences of some of these properties are discussed, in particular the way in which general phase transition behavior contributes to spiral arm morphology. We look at 1 (space) + 1 (time), 2 + 1 and + 1 dimensions, the 2 + 1 case being of interest for disk galaxies.     

A stochastic model for the dynamics of a classical spin

A stochastic model for the dynamics of a macroscopic or classical spin based on a classical generalized Lagrangian formalism is proposed. The model can be used to describe the evolution of the magnetic moment of superparamagnetic particles. In this sense, it is a generalization of the model proposed by Brown, allowing for fluctuations on the magnitudes of the magnetic moments of the particles. The corresponding covariant Fokker-Planck equation is also obtained.     

Electroless formation of silver nanoaggregates: an experimental and molecular dynamics approach

The ability to manipulate matter to create non-conventional structures is one of the key issues of material science. The understanding of assembling mechanism at the nanoscale allows us to engineer new nanomaterials, with physical properties intimately depending on their structure.

This paper describes new strategies to obtain and characterise metal nanostructures via the combination of a top-down method, such as electron beam lithography, and a bottom-up technique, such as the chemical electroless deposition. We realised silver nanoparticle aggregates within well-defined patterned holes created by electron beam lithography on silicon substrates. The quality characteristics of the nanoaggregates were verified by using scanning electron microscopy and atomic force microscopy imaging. Moreover, we compared the experimental findings to molecular dynamics simulations of nanoparticles growth. We observed a very high dependence of the structure characteristics on the pattern nanowell aspect ratio. We found that high-quality metal nanostructures may be obtained in patterns with well aspect ratio close to one, corresponding to a maximum diameter of 50 nm, a limit above which the fabricated structures become less regular and discontinuous. When regular shapes and sizes are necessary, as in nanophotonics, these results suggest the pattern characteristics to obtain isolated, uniform and reproducible metal nanospheres.     

Non-Markovian random unitary qubit dynamics

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates.