On passage through resonances in volume-preserving systems

Resonance processes are common phenomena in multiscale (slow-fast) systems. In the present paper we consider capture into resonance and scattering on resonance in 3D volume-preserving multiscale systems. We propose a general theory of those processes and apply it to a class of kinematic models inspired by viscous Taylor-Couette flows between two counter-rotating cylinders. We describe the phenomena during a single passage through resonance and show that multiple passages lead to the chaotic advection and mixing. We calculate the width of the mixing domain and estimate a characteristic time of mixing. We show that the resultant mixing can be described using a diffusion equation with a diffusion coefficient depending on the averaged effect of the passages through resonances.     

Theory of defects and defect processes

Most studies of imperfect solids concentrate on the properties of individual isolated defects. These include electronic structure, formation energies and diffusion parameters of point defects and point defect aggregates. Many physical phenomena are determined by defect processes, in which defects interact or the defect state of the lattice evolves. Such phenomena include the radiation damage process and subsequent development of microstructure, the matter and charge transport in the growth of oxide films, the recombination—or ionization—assisted diffusion in many systems, and a range of degradation mechanisms. These and other examples are discussed. The emphasis is on those cases where quantitative theory can unravel phenomena which experiment alone cannot easily do, notably those situations where the time scales are inconvenient or the system too complex for easy experimental analysis.     

On Schrödinger's Search for a Stochastic Interpretation of Quantum Mechanics

Following Schrödinger a stochastic interpretation of quantum mechanics is given based on the introduction of an intermediate probability in diffusion processes. The Schrödinger equation is derived following Nelson's approach and following a variational approach. Some problems of the quantum theory of measurement are discussed.     

Bulk mediated surface diffusion: the infinite system case

An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented. The time evolution of the effective probability distribution width on the surface is calculated and analyzed within an anomalous diffusion framework. The asymptotic behavior for large times shows a sub-diffusive regime for the effective surface diffusion but, depending on the observed range of time, other regimes may be obtained. Monte Carlo simulations show excellent agreement with analytical results. As an important byproduct of the indicated approach, we present the evaluation of the time for the first visit to the surface.Received: 2 September 2003, Published online: 8 December 2003PACS: 05.40.Fb Random walks and Levy flights - 02.50.Ey Stochastic processes - 46.65. + g Random phenomena and media     

Non-Markov stochastic processes satisfying equations usually associated with a Markov process

There are non-Markov Ito processes that satisfy the Fokker-Planck, backward time Kolmogorov, and Chapman-Kolmogorov equations. These processes are non-Markov in that they may remember an initial condition formed at the start of the ensemble. Some may even admit 1-point densities that satisfy a nonlinear 1-point diffusion equation. However, these processes are linear, the Fokker-Planck equation for the conditional density (the 2-point density) is linear. The memory may be in the drift coefficient (representing a flow), in the diffusion coefficient, or in both. We illustrate the phenomena via exactly solvable examples. In the last section we show how such memory may appear in cooperative phenomena.     

Dynamics of conformal maps for a class of non-Laplacian growth phenomena

Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electromigration. Both continuous and stochastic dynamics are described by generalizing conformal-mapping techniques for viscous fingering and diffusion-limited aggregation, respectively. The theory is applied to simulations of advection-diffusion-limited aggregation in a background potential flow. A universal crossover in morphology is observed from diffusion-limited to advection-limited fractal patterns with an associated crossover in the growth rate, controlled by a time-dependent effective Péclet number. Remarkably, the fractal dimension is not affected by advection, in spite of dramatic increases in anisotropy and growth rate, due to the persistence of diffusion limitation at small scales.     

First principles study of the diffusional phenomena across the clean and Re-doped γ-Ni/γ'-Ni_3Al interface of Ni-based single crystal superalloy

Density functional theory calculations in conjunction with the climbing images nudged elastic band method are conducted to study the diffusion phenomena of the Ni-based single crystal superalloys.We focus our attention on the diffusion processes of the Ni and Al atoms in the γ and γ ' phases along the direction perpendicular to the interface.The diffusion mechanisms and the expressions of the diffusion coefficients are presented.The vacancy formation energies,the migration energies,and the activation energies for the diffusing Ni and Al atoms are estimated,and these quantities display the expected and clear transition zones in the vicinity of the interface of about 3–7(002) layers.The local density-of-states profiles of atoms in each(002) layer in the γ and γ ' phases and the partial density-of-states curves of Re and some of its nearest-neighbor atoms are also presented to explore the electronic effect of the diffusion behavior.     

Breakdown of wave diffusion in 2D due to loops

The validity of the diffusion approximation for the intensity of multiply scattered waves is tested with numerical simulations in a strongly scattering 2D medium of finite extent. We show that the diffusion equation underestimates the intensity and attribute this to both the neglect of recurrent scattering paths and interference within diffusion theory. We present a theory to quantify this discrepancy based on counting all possible scattering paths between point scatterers. Interference phenomena, due to loop paths, are incorporated in a way similar to coherent backscattering.     

On transient behavior of non-premixed counter-flow diffusion flames within the REDIM based model reduction concept

In the present work non-stationary behavior of the counter-flow diffusion flame is examined in the context of the recently developed approach of model reduction called REaction–DIffusion Manifolds (REDIM) method. It is a natural extension of the ILDM approach which takes into account both the chemical reaction and the diffusion processes. It has been developed to treat both premixed and non-premixed regimes of combustion. In this work we investigate the ability of the concept to describe transient processes of extinction and re-ignition. A very simple flame configuration and transport model are considered in this current study for the sake of transparency because the main focus is on the transient and non-stationary behavior of flames. H₂/O₂/N₂ combustion system is considered in a non-premixed counter-flow diffusion 1D flame configuration. This study shows how the REDIM concept performs in the transient regimes; it interprets the effect of local extinction and reigniting phenomena using detailed and reduced models. It shows how the unstable/transient behavior of a detailed system can be successfully accounted with the help of the REDIM based reduced model.     

Imaging of dynamic processes on surfaces by light

This work focuses on imaging of dynamic processes on surfaces, using light to illuminate the area of interest. The methods discussed here are those in which the photoelectrons emitted from or the light reflected off the surface are measured. While the first approach is well-known since electron microscopy was invented and has been used in surface science applications for a decade, genuine optical microscope methods using polarized light were first developed in 1995 for imaging surface reactions.

The results discussed here are from different fields of surface research. These include the imaging of adsorption phenomena, surface diffusion and growth processes. The main emphasis will be on pattern formation of surface reactions under strictly controlled parameters. The most recent techniques expand the range of observable pressure conditions by many orders of magnitude, thus bridging the pressure gap in imaging surface reactions.     

Optimal control of open quantum systems applied to the photochemistry of surfaces

A quantum system in a condensed phase undergoes strong dissipative processes. The last decades have seen the rise of experimental and theoretical approaches for gaining control over dissipative phenomena. From a theoretical viewpoint it is important to model such processes in a rigorous way. An efficient and accurate method to find control fields is optimal control theory (OCT). In this Letter, a control scheme relying on OCT with time-dependent targets is employed to minimize dissipation, modeled within the surrogate Hamiltonian approach, on adsorbate-surface systems.     

Autocorrelation functions of nonlinear Fokker-Planck equations

We compute autocorrelation functions from nonlinear Fokker-Planck equations that describe nonlinear families of Markov diffusion processes and illustrate this approach for the Plastino-Plastino Fokker-Planck equation related to the Tsallis entropy.Received: 30 October 2003, Published online: 15 March 2004PACS: 05.20.-y Classical statistical mechanics - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion     

The transport of slow ions in gases: Experiment, theory, and applications

This review is concerned with the two most important transport phenomena in involving slow ions in gases, namely their drift and diffusion in an externally applied electric field. The energy range of interest extends from thermal values at low temperatures up to about 10 eV. The transport phenomena are first discussed in physical terms, and experimental techniques for measuring ionic drift velocities and diffusion coefficients are then described. Brief coverage is given to ionic transport theory up to the time of Wannier's landmark contributions in 1951–1952; later theoretical developments are treated in more detail. Special emphasis is placed on aspects of modern theory that permit the determination of interaction potentials and collision frequencies for momentum transfer from experimental transport data. The review ends with a discussion of several applications of transport data to ionospheric problems.     

Phonon heat transport in gallium arsenide

The lifetimes of quantum excitations are directly related to the electron and phonon energy linewidths of a particular scattering event. Using the versatile double time thermodynamic Green’s function approach based on many-body theory, an ab-initio formulation of relaxation times of various contributing processes has been investigated with newer understanding in terms of the linewidths of electrons and phonons. The energy linewidth is found to be an extremely sensitive quantity in the transport phenomena of crystalline solids as a collection of large number of scattering processes, namely, boundary scattering, impurity scattering, multiphonon scattering, interference scattering, electron–phonon processes and resonance scattering. The lattice thermal conductivities of three samples of GaAs have been analysed on the basis of modified Callaway model and a fairly good agreement between theory and experimental observations has been reported.     

Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids

Quantitative predictions of the behavior of many deterministic systems are uncertain due to ubiquitous heterogeneity and insufficient characterization by data. We present a computational approach to quantify predictive uncertainty in complex phenomena, which is modeled by (partial) differential equations with uncertain parameters exhibiting multi-scale variability. The approach is motivated by flow in random composites whose internal architecture (spatial arrangement of constitutive materials) and spatial variability of properties of each material are both uncertain. The proposed two-scale framework combines a random domain decomposition (RDD) and a probabilistic collocation method (PCM) on sparse grids to quantify these two sources of uncertainty, respectively. The use of sparse grid points significantly reduces the overall computational cost, especially for random processes with small correlation lengths. A series of one-, two-, and three-dimensional computational examples demonstrate that the combined RDD–PCM approach yields efficient, robust and non-intrusive approximations for the statistics of diffusion in random composites.     

Atomic quantum diffusion,tunnelling states and some related phenomena in condensed systems

This article presents a review of some basic problems and results in the theory of atomic quantum diffusion, atomic tunnelling states and some related phenomena in condensed systems: crystals and amorphous materials.General concepts, including the defecton concept, are reviewed in the introduction. The first part of this paper considers the principal ideas, results and problems in the quantum diffusion theory for both underbarrier and overbarrier transitions of atomic particles in solids. Much attention is given to the fundamental role of the interactions between a weakly tunnelling particle and its environment, i.e. defects, other tunnelling particles and thermal fluctuations of atomic configurations.The second part of this review deals with the theory of atomic tunnelling states, their peculiar origin and low-temperature effects and, particularly, the origin and effects of the intrinsic atomic low-energy excitations in amorphous materials. The third part of this article discusses some related low-temperature phenomena. Some experimental data associated with the phenomena under consideration are presented. Finally, some actual problems of the theory are discussed in the Concluding Remarks.The review contains a discussion of results mainly coming to our attention by the summer of 1982.     

Identification of Spin Diffusion Pathways in Isotopically Labeled Biomolecules

One-dimensional NOE experiments applicable to labeled macromolecules are presented which allow the manipulation of specific spin diffusion pathways and thus unambiguously identify clandestine spins through which the direct NOE is mediated. A treatment of spin diffusion using average Liouvillian theory is shown to describe adequately these phenomena. Experiments are carried out on an 15N-labeled sample of human ubiquitin.     

强激光场阈上电离理论

本文提出一种统一的阈上电离理论。根据该理论,可以定量描述较真实的原子阈上电离过程并能清楚地阐明实验观测的阈上电离现象。该现象可理解为前后相继的两个过程:(1)先从无场的初态吸收N个光子而到场缀末态的量子跃迁过程。(2)欲定量描述实验测量,还需考虑光电子逃离光场时与光场相互作用的“后作用效应”。该“后作用效应”是由非均匀激光场所形成的无质动力所引起的经典物理过程。 关键词：