A model of modulated diffusion. I. Analytical results

We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion.     

Diffusion on the torus for Hamiltonian maps

For a mapping of the torusT ² we propose a definition of the diffusion coefficientD suggested by the solution of the diffusion equation ofT ². The definition ofD, based on the limit of moments of the invariant measure, depends on the set where an initial uniform distribution is assigned. For the algebraic automorphism of the torus the limit is proved to exist and to have the same value for almost all initial sets in the subfamily of parallelograms. Numerical results show that it has the same value for arbitrary polygons and for arbitrary moments.     

Numerical study of aD-dimensional periodic Lorentz gas with universal properties

We give the results of a numerical study of the motion of a point particle in ad-dimensional array of spherical scatterers (Sinai's billiard without horizon). We find a simple universal law for the Lyapounov exponent (as a function ofd) and a stretched exponential decay for the velocity autocorrelation as a function of the number of collisions. The diffusion seems to be anomalous in this problem. Ergodicity is used to predict the shape of the probability distribution of long free paths. Physical interpretations or clues are proposed.     

A stochastic model of tweet diffusion on the Twitter network

We introduce a stochastic model which describes the information diffusion on the network of a popular web service, Twitter. Restricting our attention to the daily diffusion from a popular account, we model the information diffusion as a random multiplicative process. We justify our model by directly observing the statistics of the multiplicative factors in the Twitter data.     

Simple statistical model for predicting thermal atom diffusion on crystal surfaces

A simple model based on the statistics of single atoms is developed to predict the diffusion rate of thermal atoms in （or on） bulk materials without empirical parameters. Compared with vast classical molecular-dynamics simulations for predicting the self-diffusion rate of Pt, Cu, and Ar adatoms on crystal surfaces, the model is proved to be much more accurate than the Arrhenius law and the transition state theory. Applying this model, the theoretical predictions agree well with the experimental values in the presented paper about the self-diffusion of Pt （Cu） adatoms on the surfaces.     

Statistical properties of a nonuniformly hyperbolic map of the interval

We prove a power-law upper bound for the decay of the correlations for Hölder observables in the case of a nonuniformly hyperbolic map of the interval introduced by Gaspard and Wang as a piecewise linear approximation of the intermittent map of Manneville-Pomeau. The result is then applied to compute the Central Limit Theorem for the same class of observables.     

Explicit inertial range renormalization theory in a model for turbulent diffusion

The inertial range for a statistical turbulent velocity field consists of those scales that are larger than the dissipation scale but smaller than the integral scale. Here the complete scale-invariant explicit inertial range renormalization theory for all the higher-order statistics of a diffusing passive scalar is developed in a model which, despite its simplicity, involves turbulent diffusion by statistical velocity fields with arbitrarily many scales, infrared divergence, long-range spatial correlations, and rapid fluctuations in time-such velocity fields retain several characteristic features of those in fully developed turbulence. The main tool in the development of this explicit renormalization theory for the model is an exact quantum mechanical analogy which relates higher-order statistics of the diffusing scalar to the properties of solutions of a family ofN- body parabolic quantum problems. The canonical inertial range renormalized statistical fixed point is developed explicitly here as a function of the velocity spectral parameter, which measures the strength of the infrared divergence: for<2, mean-field behavior in the inertial range occurs with Gaussian statistical behavior for the scalar and standard diffusive scaling laws; for>2 a phase transition occurs to a fixed point with anomalous inertial range scaling laws and a non-Gaussian renormalized statistical fixed point. Several explicit connections between the renormalization theory in the model and intermediate asymptotics are developed explicitly as well as links between anomalous turbulent decay and explicit spectral properties of Schrödinger operators. The differences between this inertial range renormalization theory and the earlier theories for large-scale eddy diffusivity developed by Avellaneda and the author in such models are also discussed here.     

Transverse momentum diffusion and broadening of the back-to-back di-hadron correlation function

We extend the Gyulassy–Levai–Vitev reaction operator approach to multiple elastic scattering of fast partons traversing dense nuclear matter to take into account the leading power corrections due to the medium recoil and to derive the change in the partons' longitudinal momentum. We employ a boost-invariant formalism to generalize previous treatments of the problem, which were specific to the target rest frame. We apply the transverse momentum diffusion results in a simple analytic model to evaluate the broadening of the back-to-back di-hadron correlation function in d+Au reactions.     

Ergodic and statistical properties of piecewise linear hyperbolic automorphisms of the 2-torus

We study generic piecewise linear hyperbolic automorphisms of the 2-torus. We explain why the resulting dynamical system is ergodic and mixing and prove the exponential decay of correlations.     

A unified approach for deriving kinetic equations in nonequilibrium statistical mechanics. II. Approximate results

The exact form for the kinetic equation derived by Mori, Fujisaka, and Shigematsu (MFS) is used to obtain several approximations better suited to be compared with macroscopic transport equations. Three approximations are discussed, namely, those known as the diagonal, the slow process, and the Markovian. The corresponding results are emphasized and their relationship is established. In particular, the Kramers-Moyal expansion for the Markovian kinetic equation is obtained from a microscopic basis.     

Dynamical properties for a mixed Fermi accelerator model

The behavior of the decay of velocity in a semi-dissipative one-dimensional Fermi accelerator model is considered. Two different kinds of dissipative forces were considered: (i) F∝−v$F\propto -v$ and; (ii) F∝−v²$F\propto -v^2$. We prove the decay of velocity is linear for (i) and exponential for (ii). During the decay, the particles move along specific corridors which are constructed by the borders of the stable manifolds of saddle points. These corridors organize themselves in a very complicated way in the phase space leading the basin of attraction of the sinks to be seemingly of fractal type.     

Asymptotic results for a persistent diffusion model of Taylor dispersion of particles

We study Taylor diffusion for the case when the diffusion transverse to the bulk motion is a persistent random walk on a one-dimensional lattice. This is mapped onto a Markovian walk where each lattice site has two internal states. For such a model we find the effective diffusion coefficient which depends on the rate of transition among internal states of the lattice. The Markovian limit is recovered in the limit of infinite rate of transitions among internal states; the initial conditions have no role in the leading-order time-dependent term of the effective dispersion, but a strong effect on the constant term. We derive a continuum limit of the problem presented and study the asymptotic behavior of such limit.     

Time-domain simulation of damped impacted plates. II. Numerical model and results

A time-domain model for the flexural vibrations of damped plates was presented in a companion paper [Part I, J. Acoust. Soc. Am. 109, 1422-1432 (2001)]. In this paper (Part II), the damped-plate model is extended to impact excitation, using Hertz's law of contact, and is solved numerically in order to synthesize sounds. The numerical method is based on the use of a finite-difference scheme of second order in time and fourth order in space. As a consequence of the damping terms, the stability and dispersion properties of this scheme are modified, compared to the undamped case. The numerical model is used for the time-domain simulation of vibrations and sounds produced by impact on isotropic and orthotropic plates made of various materials (aluminum, glass, carbon fiber and wood). The efficiency of the method is validated by comparisons with analytical and experimental data. The sounds produced show a high degree of similarity with real sounds and allow a clear recognition of each constitutive material of the plate without ambiguity.     

A Model with Simultaneous First and Second Order Phase Transitions

We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two “bond ordered phases”, one with local ferromagnetic order and another with local anti-ferromagnetic order. We also prove that at the transition temperature the bond-ordered phases coexist with a disordered phase as predicted by Domany, Schick and Swendsen [1]. This last result generalizes the result of van Enter and Shlosman [2] We argue that these phenomena are quite general and should occur for a large class of potentials. PACS number: 64.60.Cn, 75.10.Hk     

Diffraction from modulated structures II. Quasiperiodic model of the modulated structures

The present model of modulated structure assumes the variation of the number of atomic planes in the inner part of the individual zones in their array. This variation is described by the interzone correlation function. The analytical expression for the diffracted intensity from this aperiodic array of zones is also given.     

Numerical experiments on billiards

We investigate decay properties of correlation functions in a class of chaotic billiards. First we consider the statistics of Poincaré recurrences (induced by a partition of the billiard): the results are in agreement with theoretical bounds by Bunimovich, Sinai, and Bleher, and are consistent with a purely exponential decay of correlations out of marginality. We then turn to the analysis of the velocity-velocity correlation function: except for intermittent situations, the decay is purely exponential, and the decay rates scale in a simple way with the (uniform) curvature of the dispersing arcs. A power-law decay is instead observed when the system is equivalent to an infinite-horizon Lorentz gas. Comments are given on the behaviour of other types of correlation functions, whose decay, during the observed time scale, appears slower than exponential.     

扩散理论对RLA模型中交换作用的研究

以扩散理论为基础，建立以“基本微观过程” 为核心的新模型，引入交换比的概念，对存在表面活化剂时薄膜生长的微观过程进行Kinetic Monte Carlo模拟.模拟发现，活化层原子和沉积原子都会发生跨层间的扩散，跨层扩散主要是单个原子的扩散，层间扩散的原子数目随着温度的升高或沉积厚度的增加而增多.RLA模型中的“交换作用”只是若干个“基本微观过程”的组合，大多数交换不是位置的“完全交换”，交换比也并非恒为1.     

Slow Rates of Mixing for Dynamical Systems with Hyperbolic Structures

We consider invertible discrete-time dynamical systems having a hyperbolic product structure in some region of the phase space with infinitely many branches and variable return time. We show that the decay of correlations of the SRB measure associated to that hyperbolic structure is related to the tail of the recurrence times. We also give sufficient conditions for the validity of the Central Limit Theorem. This extends previous results by Young in (Ann. Math. 147: 585–650, [1998]; Israel J. Math. 110: 153–188, [1999]). Work carried out at the Federal University of Bahia, University of Porto and IMPA. J.F.A. was partially supported by FCT through CMUP and POCI/MAT/61237/2004. V.P. was partially supported by PADCT/CNPq and POCI/MAT/61237/2004.     

扩散理论对RLA模型中交换作用的研究

以扩散理论为基础,建立以“基本微观过程” 为核心的新模型,引入交换比的概念,对存在表面活化剂时薄膜生长的微观过程进行Kinetic Monte Carlo模拟.模拟发现,活化层原子和沉积原子都会发生跨层间的扩散,跨层扩散主要是单个原子的扩散,层间扩散的原子数目随着温度的升高或沉积厚度的增加而增多.RLA模型中的“交换作用”只是若干个“基本微观过程”的组合,大多数交换不是位置的“完全交换”,交换比也并非恒为1. 关键词： 扩散理论 薄膜生长 交换作用 RLA