Magnetic stochasticity in gyrokinetic simulations of plasma microturbulence

Analysis of the magnetic field structure from electromagnetic simulations of tokamak ion temperature gradient turbulence demonstrates that the magnetic field can be stochastic even at very low plasma pressure. The degree of magnetic stochasticity is quantified by evaluating the magnetic diffusion coefficient. We find that the magnetic stochasticity fails to produce a dramatic increase in the electron heat conductivity because the magnetic diffusion coefficient remains small.     

The dissipative effects on stochasticity of the nonlinear oscillator

The effects of dissipation on the stochasticity of a nonlinear oscillator in the presence of a perturbing field are studied analytically. It is shown that the dissipation has two different and opposite effects on the stochasticity depending on the external frequency in the non time asymptotic domain. In the low frequency regime the stochasticity is enhanced while high frequency diminishes the stochasticity. These results may be related to some aspects of recent numerical studies.     

统计物理的微观动力学基础

统计的基本出发点是研究系统具有的随机性,不同系统在不同情形下的宏观热力学性质起源于系统内部随机性的差异,通过对宏观热力学系统的微观非线性动力学进行研究探索，我们可以进一步更为深入地理解物态方程、相变等诸多的宏观热力学现象。本文通过哈密顿系统的非线性动力学研究，以及遍历性理论的动力学随机性研究对此问题进行了分析，研究表明，动力学系统的全局性混沌是系统统计成立的根本要素，系统的无限大自由度（热力学极限）已不是决定性的因素，人们可以在此基础上建立少自由度系统的统计力学及热力学。     

Noise-driven intermittency in tidal dynamics

Summary The tide nonstationarity in the Adriatic Sea is described. We show how this phenomenon can be related to the stochasticity of sea fetch by a nonlinear noise-forced oscillator model. The experimental series correlation dimension reveals a strong lifting with respect to the astronomic tide. The lifting is related to space-time intermittency.     

Radiation-induced robust oscillation [2mm]and non-Gaussian fluctuation

There have been many recent studies devoted to the consequences of stochasticity in protein circuitry. Stress conditions, including DNA damage, hypoxia, heat shock, nutrient deprivation, and oncogene activation, can result in the activation and accumulation of p53. Several experimental studies show that oscillations can be induced by DNA damage following nuclear irradiation. To explore the underlying dynamical features and the role of stochasticity, we discuss the oscillatory dynamics in the well-studied regulatory network motif. The fluctuations around the fixed point of a delayed system are Gaussian in the limit of sufficiently weak delayed feedback, and remain Gaussian along a limit cycle when viewed tangential to the trajectory. The experimental results are recapitulated in this study. We illustrate several features of the p53 activities, which are robust when the parameters change. Furthermore, the distribution in protein abundance can be characterized by its non-Gaussian nature.     

Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002     

Stochasticity in many-dimensional nonlinear oscillating systems

Qualitative analytic estimates of the stochasticity limit of one- and many-dimensional nonlinear oscillating systems are derived using the overlapping of first-order resonances as a criterion for stochasticity. Computational results obtained with several very simple transformations are compared with the analytic estimates. Numerical studies significantly below the stochasticity limit of a many-dimensional nonlinear system reveal an example of a very slow instability, the first, to the best of our knowledge.     

Dynamically orthogonal field equations for continuous stochastic dynamical systems

In this work we derive an exact, closed set of evolution equations for general continuous stochastic fields described by a Stochastic Partial Differential Equation (SPDE). By hypothesizing a decomposition of the solution field into a mean and stochastic dynamical component, we derive a system of field equations consisting of a Partial Differential Equation (PDE) for the mean field, a family of PDEs for the orthonormal basis that describe the stochastic subspace where the stochasticity ‘lives’ as well as a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new evolution equations are derived directly from the original SPDE, using nothing more than a dynamically orthogonal condition on the representation of the solution. If additional restrictions are assumed on the form of the representation, we recover both the Proper Orthogonal Decomposition equations and the generalized Polynomial Chaos equations. We apply this novel methodology to two cases of two-dimensional viscous fluid flows described by the Navier–Stokes equations and we compare our results with Monte Carlo simulations.     

Phase slip phenomena in superconductors: from ordered to chaotic dynamics

We consider flux penetration to a 2D superconducting cylinder. We show that in the low field limit the kinetics is deterministic. In the strong field limit the dynamics becomes stochastic. Surprisingly the inhomogeneity in the cylinder reduces the level of stochasticity because of the predominance of Kelvin-Helmholtz vortices.     

On the vortex flow in bounded domains

We consider the motion ofN vortices in bounded domains in IR². We prove that the set of initial positions which lead to a collapse of two or more vortices has Lebesgue measure zero. We extend this result to the stochastic motion of the vortices, where the stochasticity comes from a Wiener-noise term, which is added to the deterministic equation of motion.On leave of the Fachbereich Mathematik, RUB, 4630 Bochum, Federal Republic of Germany. Supported by a DFG-fellowshipPartially supported by Italian CNR     

Stochastic Nature in Cellular Processes

The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.     

Nonlinear coupling of waves in a plasma in a strong dissipation limit

We study the nonlinear resonant coupling of two waves in a plasma for strong dissipation. We show that the corresponding system of differential equations has a saddle-focus fixed point and study its stable and unstable manifolds. The results we obtain suggest that the stochasticity which is numerically observed might be due to the existence of a spiral-type strange attractor.     

Stochastic Collisional Quantum Thermometry

We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows us to significantly extend the parameter range for which an advantage over the thermal Fisher information is attained. These results are explicitly demonstrated for dephasing interactions and also hold for partial swap interactions. Furthermore, we show that the optimal measurements can be performed locally, thus implying that genuine quantum correlations do not play a role in achieving this advantage. We explicitly confirm this by examining the correlation properties for the deterministic collisional model.     

Equipartition and rate of energy exchanges in a model of a radiant cavity

Results of calculations on a model of a radiant cavity, performed in order to explore the relation between stochasticity and geometrical structure of phase space, are presented. The rate of energy exchanges, as indicator of stochasticity, is found to be quite effective. Furthermore, a trend to equipartition for such a quantity is observed at increasing energy, and this implies an increasing rigidity of high harmonic modes also in the stochastic regime of motion. Such a feature may be correlated to the shape of the spectrum which characterizes the radiant cavity with respect to nonlinear chains.     

动力学系统中非线性项的跳跃随机性

计算机计算和实验的结果表明:动力学系统中非线性函数有一种特殊性质,即跳跃随机性。这种性质使确定的非线性函数中产生了许多不同于自身曲线的跳跃随机曲线。 关键词：     

Stochastic Skellam model

We consider the dynamics of a biological population described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the case where the spatial domain consists of alternating favorable and adverse patches whose sizes are distributed randomly. For the one-dimensional case we define a stochastic analogue of the classical critical patch size. We address the issue of persistence of a population and we show that the minimum fraction of the length of favorable segments to the total length is always smaller in the stochastic case than in a periodic arrangement. In this sense, spatial stochasticity favors viability of a population.     

Stochastic behaviour in presence of an electrostatic wave due to the crossing of multiple cyclotron resonances in an inhomogeneous magnetic field

The criterion for the occurence of stochastic behaviour of particle trajectories in the field of an electrostatic wave is obtained taking into account the longitudinal inhomogeneity of the ambient magnetic field. The origin of the stochasticity is explained. The optimum conditions for particle heating are obtained at a wave amplitude below the threshold of stochasticity in a homogeneous plasma.     

Leading pollicott-ruelle resonances and transport in area-preserving maps

The leading Pollicott-Ruelle resonance is calculated analytically for a general class of two-dimensional area-preserving maps. Its wave number dependence determines the normal transport coefficients. In particular, a general exact formula for the diffusion coefficient D is derived without any high stochasticity approximation, and a new effect emerges: The angular evolution can induce fast or slow modes of diffusion even in the high stochasticity regime. The behavior of D is examined for three particular cases: (i) the standard map, (ii) a sawtooth map, and (iii) a Harper map as an example of a map with a nonlinear rotation number. Numerical simulations support this formula.     

梯度磁场中静电波引起的粒子随机运动

本文讨论了一般非均匀梯度磁场下任意方向传播的静电波引起粒子随机运动的非线性效应。用正则久期扰动理论给出包含粒子周期运动和波振荡之间非线性共振的哈密顿量。根据Chirikov岛重叠条件给出一般梯度磁场下粒子进入随机态的临界波幅值。分析表明,相对均匀磁场,在弱非均匀情形下,该临界值降低,意味着粒子更易进入随机态。 关键词：