On the maximal noise for stochastic and QCD travelling waves

Using the relation of a set of nonlinear Langevin equations to reaction–diffusion processes, we note the existence of a maximal strength of the noise for the stochastic travelling wave solutions of these equations. Its determination is obtained using the field-theoretical analysis of branching-annihilation random walks near the directed percolation transition. We study its consequence for the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation. For the related Langevin equation modeling the quantum chromodynamic nonlinear evolution of gluon density with rapidity, the physical maximal-noise limit may appear before the directed percolation transition, due to a shift in the travelling-wave speed. In this regime, an exact solution is known from a coalescence process. Universality and other open problems and applications are discussed in the outlook.     

The thermodynamic characteristics of multicomponent reaction mixtures in the sub- and supercritical states

The paper presents mathematical models and calculation methods for solving particular research problems related to the thermodynamic characteristics of multicomponent and multiphase mixtures. The special features of chemical and phase equilibria in such mixtures are considered in the ideal gas approximation and taking nonideality into account. The conditions of equilibrium phase stability are studied for multiphase systems. The results of calculations of characteristic phase diagrams and binodal and spinodal are given for model systems with a fixed chemical composition, and a new interpretation of the mathematical model for localizing the critical point of a multicomponent mixture with a given composition is presented. A new interpretation of the well-known classic homotopy method is suggested for solving complex nonlinear systems of equations. Some anomalies of phase portraits and critical curves that are necessary to take into account in selecting (planning) experimental conditions and calculating chemical processes and reaction parameters are considered separately. The possibility of calculating thermodynamic and thermophysical properties (entropy, enthalpy, heat capacity, heat effects of reactions, and adiabatic heating) is demonstrated for the example of particular multicomponent nonideal mixtures. The conclusion is drawn that cubic equations of state can be used for predicting the deviations of these properties from the ideal gas state and their anomalies in the vicinity of the critical points of mixtures.     

Physically self-consistent basis for modern cosmology

Cosmoparticle physics appeared as a natural result of internal development of cosmology seeking physical grounds for inflation, baryosynthesis, and nonbaryonic dark matter and of particle physics going outside the Standard Model of particle interactions. Its aim is to study the foundations of particle physics and cosmology and their fundamental relationship in the combination of respective indirect cosmological, astrophysical, and physical effects. The ideas on new particles and fields predicted by particle theory and on their cosmological impact are discussed, as well as the methods of cosmoparticle physics to probe these ideas, are considered with special analysis of physical mechanisms for inflation, baryosynthesis, and nonbaryonic dark matter. These mechanisms are shown to reflect the main principle of modern cosmology, putting, instead of formal parameters of cosmological models, physical processes governing the evolution of the big-bang universe. Their realization on the basis of particle theory induces additional model-dependent predictions, accessible to various methods of nonaccelerator particle physics. Probes for such predictions, with the use of astrophysical data, are the aim of cosmoarcheology studying astrophysical effects of new physics. The possibility of finding quantitatively definite relationships between cosmological and laboratory effects on the basis of cosmoparticle approach, as well as of obtaining a unique solution to the problem of physical candidates for inflation, mechanisms of baryogenesis, and multicomponent dark matter, is exemplified in terms of gauge model with broken family symmetry, underlying horizontal unification and possessing quantitatively definite physical grounds for inflation, baryosynthesis, and effectively multicomponent dark-matter scenarios.     

Topics in data assimilation: Stochastic processes

Stochastic models with varying degrees of complexity are increasingly widespread in the oceanic and atmospheric sciences. One application is data assimilation, i.e., the combination of model output with observations to form the best picture of the system under study. For any given quantity to be estimated, the relative weights of the model and the data will be adjusted according to estimated model and data error statistics, so implementation of any data assimilation scheme will require some assumption about errors, which are considered to be random. For dynamical models, some assumption about the evolution of errors will be needed. Stochastic models are also applied in studies of predictability.

The formal theory of stochastic processes was well developed in the last half of the twentieth century. One consequence of this theory is that methods of simulation of deterministic processes cannot be applied to random processes without some modification. In some cases the rules of ordinary calculus must be modified.

The formal theory was developed in terms of mathematical formalism that may be unfamiliar to many oceanic and atmospheric scientists. The purpose of this article is to provide an informal introduction to the relevant theory, and to point out those situations in which that theory must be applied in order to model random processes correctly.     

Two-phase filtration of multicomponent mixtures with a retrograde region of the phase diagram

The results of mathematical and physical modeling of an isothermal filtration of multicomponent mixtures with a retrograde region of the phase diagram are presented. By the example of mixtures of hydrocarbons of the methane line, the conditions at which the hydrocarbon-two-phase fluid?porous space system is a self-oscillation system are determined. The data obtained make it possible to explain certain regularities of the filtration of gas-condensate mixtures and can be used to increase the extraction of gas-condensate deposits.     

Analytical methods for modeling of ultrasonic nondestructive testing of anisotropic media

Many modern structural materials exhibit anisotropic elastic behavior leading to complicated wave propagation phenomena. To ensure the reliability of ultrasonic nondestructive testing techniques, these material properties as well as the influence of microstructural inhomogeneities and the effects of interfaces on ultrasonic wave propagation have to be taken into account. In this respect, mathematical modeling provides an efficient method of assisting analysis. Two computationally efficient analytical approaches--a Gaussian beam and a point source superposition technique--are presented, which are well-suited for performing ultrasonic wave propagation and scattering simulations for anisotropic media. Results for homogeneous as well as inhomogeneous anisotropic media like composites and weld material are presented.     

Random quantum states: recent developments and applications

We review the methods and use of random quantum states with particular emphasis on recent theoretical developments and applications in various fields. The guiding principle of the review is the idea that random quantum states can be understood as classical probability distributions in the Hilbert space of the associated quantum system. We show how this central concept connects questions of physical interest that cover different fields such as quantum statistical physics, quantum chaos, mesoscopic systems of both non-interacting and interacting particles, including superconducting and spin–orbit phenomena, and stochastic Schrödinger equations describing open quantum systems.     

Grain Boundary Migration in Ceramics

During ceramic fabrication, densification processes compete with coarsening processes to determine the path of microstructural evolution. Grain growth is a key coarsening process. This paper examines grain boundary migration in ceramics, and discusses the effects of solutes, pores, and liquid phases on grain boundary migration rates. An effort is made to highlight work in the past decade that has contributed to and advanced our understanding of solute drag effects, pore-boundary interactions, and the role of liquid phases in grain growth and microstructural evolution. Anisotropy of the grain boundary mobility, and its role in the development of anisotropic (anisometric) microstructures is discussed as it is a central issue in recent efforts to produce ceramic materials with new combinations of properties and functionality.     

Gaussian random fields

Two results on Gaussian random fields are presented. The first characterizes the unit Gaussian random field by a strong independence property and the second determines Gaussian random fields that are generated by stochastic processes.     

Boundary Mobility and Energy Anisotropy Effects on Microstructural Evolution During Grain Growth

We have performed mesoscopic simulations of microstructural evolution during curvature driven grain growth in two-dimensions using anisotropic grain boundary properties obtained from atomistic simulations. Molecular dynamics simulations were employed to determine the energies and mobilities of grain boundaries as a function of boundary misorientation. The mesoscopic simulations were performed both with the Monte Carlo Potts model and the phase field model. The Monte Carlo Potts model and phase field model simulation predictions are in excellent agreement. While the atomistic simulations demonstrate strong anisotropies in both the boundary energy and mobility, both types of microstructural evolution simulations demonstrate that anisotropy in boundary mobility plays little role in the stochastic evolution of the microstructure (other than perhaps setting the overall rate of the evolution. On the other hand, anisotropy in the grain boundary energy strongly modifies both the topology of the polycrystalline microstructure the kinetic law that describes the temporal evolution of the mean grain size. The underlying reasons behind the strongly differing effects of the two types of anisotropy considered here can be understood based largely on geometric and topological arguments.     

A stochastic approach to open quantum systems

Stochastic methods are ubiquitous to a variety of fields, ranging from physics to economics and mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in contact with a somewhat bigger system, an environment with which it is considered in thermal equilibrium. Any small fluctuation of the environment has some random effect on the system. In physics, stochastic methods have been applied to the investigation of phase transitions, thermal and electrical noise, thermal relaxation, quantum information, Brownian motion and so on. In this review, we will focus on the so-called stochastic Schr?dinger equation. This is useful as a starting point to investigate the dynamics of open quantum systems capable of exchanging energy and momentum with an external environment. We discuss in some detail the general derivation of a stochastic Schr?dinger equation and some of its recent applications to spin thermal transport, thermal relaxation, and Bose-Einstein condensation. We thoroughly discuss the advantages of this formalism with respect to the more common approach in terms of the reduced density matrix. The applications discussed here constitute only a few examples of a much wider range of applicability.     

The three-dimensional three-state Potts ferromagnet exposed to random fields: evidence for a second order transition

Using large scale Monte Carlo simulations, the ordering of the three-dimensional three state Potts ferromagnet exposed to random fields is investigated. Studies of the order parameter probability distribution and of various of its moments suggest that the order of the transition depends on the strength of the random field: i.e., the first order transition of the pure ferromagnetic model persists for weak random fields, but turns into a second order transition for a range of random fields of medium strength. For large random fields the transition seems to be first order again. In this range large domains of strongly aligned Potts spins occur already in the disordered phase and the associated slow relaxation hampers significantly the Monte Carlo study of thermodynamic equilibrium phenomena. These results are discussed in the light of current theoretical concepts. Possible applications to experiments on diluted anisotropic molecular crystals and orientational glasses are briefly mentioned.     

The three-dimensional three-state Potts ferromagnet exposed to random fields: evidence for a second order transition

Using large scale Monte Carlo simulations, the ordering of the three-dimensional three state Potts ferromagnet exposed to random fields is investigated. Studies of the order parameter probability distribution and of various of its moments suggest that the order of the transition depends on the strength of the random field: i.e., the first order transition of the pure ferromagnetic model persists for weak random fields, but turns into a second order transition for a range of random fields of medium strength. For large random fields the transition seems to be first order again. In this range large domains of strongly aligned Potts spins occur already in the disordered phase and the associated slow relaxation hampers significantly the Monte Carlo study of thermodynamic equilibrium phenomena. These results are discussed in the light of current theoretical concepts. Possible applications to experiments on diluted anisotropic molecular crystals and orientational glasses are briefly mentioned.     

A Mathematical Characterization of Quantum Gaussian Stochastic Evolution Schemes

We give a common mathematical characterization of relevant stochastic evolution schemes built up in the literatute to attack the quantum measurement problem. This characterization is based on two hypotheses, namely, (i) the trace conservation with probability one and (ii) the existence of a complex phase determining a linear support for the stochastic process driving the random evolution.This paper is dedicated to Prof. Emilio Santos on the occasion of his 70th birthday.     

QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC PROCESSES BASED ON MEASURED DATA, I: THEORY AND APPLICATIONS TO SYNTHETIC DATA

Analysis of stochastic processes governed by the Langevin equation is discussed. The analysis is based on a general method for non-parametric estimation of deterministic and random terms of the Langevin equation directly from given data. Separate estimation of the terms corresponds to decomposition of process dynamics into deterministic and random components. Such decomposition provides a basis for qualitative and quantitative analysis of process dynamics. In Part I, the following analysis possibilities are described and illustrated using various synthetic datasets: (1) qualitative inspection of the estimated terms presented as fields, (2) reconstruction of the deterministic and stochastic evolution of the process and (3) approximation of the deterministic term by an analytical function and quantitative treatment of the equations obtained. In Part II, these analysis possibilities are applied to experimental datasets from metal cutting and laser-beam welding.     

脉冲激光沉积动力学研究进展

脉冲激光沉积技术是现代常用的先进薄膜材料制备技术之一.文章在简要介绍脉冲激光沉积技术及其进展的基础上,较全面地介绍了脉冲激光沉积动力学的基本物理图像和动力学构架,深入地探讨了激光烧蚀靶材过程、等离子体膨胀过程和薄膜沉积过程的动力学规律,阐述了我国学者在脉冲激光沉积动力学研究方面的贡献,例如包括脉冲激光沉积三个工艺过程自洽的统一模型,等离子体膨胀的冲击波模型,基于局域能量动量守恒定律的新等离子体演化动力学模型,包括热源项、蒸发项、等离子体屏蔽效应和动态物性参数的烧蚀热传导模型,考虑电子碰撞效应和能带结构变化的修正双温模型,能统一描写从纳秒级到飞秒级脉冲激光烧蚀规律的统一双温模型等.     

Two-time scale subordination in physical processes with long-term memory

We describe dynamical processes in continuous media with a long-term memory. Our consideration is based on a stochastic subordination idea and concerns two physical examples in detail. First we study a temporal evolution of the species concentration in a trapping reaction in which a diffusing reactant is surrounded by a sea of randomly moving traps. The analysis uses the random-variable formalism of anomalous diffusive processes. We find that the empirical trapping-reaction law, according to which the reactant concentration decreases in time as a product of an exponential and a stretched exponential function, can be explained by a two-time scale subordination of random processes. Another example is connected with a state equation for continuous media with memory. If the pressure and the density of a medium are subordinated in two different random processes, then the ordinary state equation becomes fractional with two-time scales. This allows one to arrive at the Bagley-Torvik type of state equation.