摘要:

Here is presented a fragment of the family tree of the Vienna School of statistical physics. Its branches have extended far beyond the Austrian national boundaries into The Netherlands, the United States, and China. Some vignettes from the lives and works of some of the Vienna School’s prominent members are also given.

ISSN:0094-243X    

DOI:10.1063/1.34336

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

The Pearson random walk consists of a sequence of straight lines each at a random angle with respect to the preceding one. This article reviews some of the techniques available for approximating the probability density function for the end‐toddistances and the projection on a given axis. When there is a known upper bound on the maximum extension (i.e., the sum of the step lengths) one can write a Fourier series for the density function whose rate of convergence increases with increasing number of steps. When the step sizes are not too disparate use of the method of steepest descents leads to an approximation that is good to 0(1/n) (wherenis the number of steps) over the entire range. In addition we develop a method for approximating the behavior of the density functions in the neighborhood of maximum extension. In 2‐D this leads to an asymptotic series, derived by the use of a Tauberian theorem. In 3‐D the technique leads to the generalization of an exact solution derived by Rayleigh and Treloar. Finally, some applications of the Pearson walk are reviewed.

ISSN:0094-243X    

DOI:10.1063/1.34331

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

Principles and applications of a direct position space renormalization group for lattice models of polymers—called the Cluster Renormalization (CR)—are reviewed in detail. Particular emphasis is placed on the study of crossover phenomena and determination of universality classes in polymer models. The first part is largely a pedagogical description of the scaling concept and the idea of fractal dimensionality for polymers, and discusses the relation between polymer statistics and critical phenomena. The generalized lattice animal model for polymers is then introduced and it is shown that within a grand canonical ensemble polymers can be described as critical objects. This description enables us to apply CR to polymer models. Next, essentials of the CR are presented. Discussion of the applications begins with a single‐parameter CR study of the scaling properties of models of linear polymers, branched polymers and polymer networks. Finally various applications of two‐parameters CR to crossover phenomena are discussed. These include a study of the crossover from a random walk to a renormalization group approach for random walks, and a discussion of the effects of branches and loops on the universality classes of polymers. It also deals with the effects of screening in solutions of branched polymers and the crossover from lattice animals to percolation.

ISSN:0094-243X    

DOI:10.1063/1.34339

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

It is found that there is a subtle difference between the set of energy‐weighted random walks generated in the discrete random‐walk model of polymer chain adsorption at the critical energy and the corresponding set of random walks generated in the presence of a reflecting boundary. This difference is lost in the continuous random flight model of adsorption.

ISSN:0094-243X    

DOI:10.1063/1.34340

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

A review of the Weierstrassian and Levey random walks and the spherical model of ferromagnetism with long‐range interactions, is given. The three problems share the common features of having an infinite mean square correlation length, and of having a singular structure function at the origin. Questions concerning self‐similar clustering, transience, persistence, phase transition and long‐range correlation are discussed.

ISSN:0094-243X    

DOI:10.1063/1.34341

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

Stochastic Hamiltonian models are often used to describe the behavior of excitons in molecular aggregates. In such descriptions, the exciton‐phonon interactions is modeled as a fluctuating potential. In this paper we show that the equations of motion obtained from stochastic Hamiltonian models lack dissipative terms that must be present if the excitons are to achieve thermal equilibrium. We consider a particular fully dynamical model whose results guide us in the choice of the appropriate dissipative term. We thus show explicitly that the stochastic Hamiltonian models correspond to infinite temperature, and we construct stochastic equations of motion that are applicable at finite temperatures. As a particular application of the model we consider optical lineshapes and compare results in the presence and absence of the dissipative contribution.

ISSN:0094-243X    

DOI:10.1063/1.34342

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

A random‐walk in a random environment is studied in connection with hopping conduction in doped semiconductors and with the dynamical percolation problem. A brief review is given of linear response theory, the continuous time random walk method, multiple scattering theory and the coherent medium approximation. The ac hopping conductivity in doped semiconductors is obtained in the coherent medium approximation and compared with experiment. Critical properties of the ac conductivity of the dynamical percolation problem are discussed with the use of some rigorous arguments and the coherent medium approximation.

ISSN:0094-243X    

DOI:10.1063/1.34332

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

We have developed the first conprehensive model of geminate recombination which depends on molecular parameters and focuses on the competition between the inter‐ and intramolecular rates. The model is random walk on a lattice in a combined Coulomb and external field. The model is solved exactly and is computationally straightforward. The analytic method we have used is quite general and can easily be extended to include a broad class of problems involving large numbers of (correlated) ‘‘special sites’’. The main feature of the computation needed to solve these problems, is the evaluation of the lattice Green’s functions (G) in the presence of E, the electric field. We will show that the computation of the E‐dependent G‐functions are greatly simplified with the use of a newly derived symmetry relation. We will elaborate this approach and discuss our results for the quantum efficiency as a function of external field, temperature and molecular concentration, &eegr; (E,T,c). In general, within this framework, one can study the influence on &eegr; of such factors as dimensionality, lattice structure, disorder, tunnelling transition rates, intramolecular rates and intrinsic energy level differences.

ISSN:0094-243X    

DOI:10.1063/1.34333

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

We present a study of transport and reaction in disordered materials based on the continous time random walk (CTRW) formalism. We focus on the ensemble averaged probability that no transfer occurs during a given amount of time, and derive from this quantity the distribution of stepping times. The distribution of stepping times is then used to mimic the random walk on a disordered system. We derive first in the CTRW framework the diffusion coefficient D(t) for a random system devoid of traps, and make connection to other approximate approaches used to calculate D(t). Then we introduce trapping centers and establish the behaviors obtain for different classes of stepping time distributions. As an example for applications we use our results to analyze electron scavenging in glassy materials.

ISSN:0094-243X    

DOI:10.1063/1.34334

出版商:AIP    

年代:1984

数据来源: AIP

摘要:

Dispersion results from different flow paths and consequent different first passage times available to tracer particles crossing from one plane to another in a porous medium. A continous‐time random walk model of dispersion is proposed and is investigated by means of Monte Carlo simulations in square and cubic networks of random conductances. Dispersion is found to be diffusive and longitudinal dispersion coefficient (i.e., the effective diffusion coefficient in the direction of mean flow) is found to be one order of magnitude larger than transverse dispersion coefficient. As the percolation threshold is approached, dispersivities, i.e., the ratio of dispersion coefficients and the mean flow velocity, increase dramatically. This is attributed to the increase in tortuosity of the backbone of the percolation cluster as the percolation threshold is approached, with the appearance of numerous loops which provide alternate particle paths that are highly effective in dispersing a concentration front of tracer particles. This results in a broad distribution of the first passage times and thus large dispersivities. A possible connection between dispersion process near a percolation threshold and directed percolation is investigated and it is shown how Monte Carlo simulations of dispersion near the percolation threshold yield a great deal of information about the structure of the backbone.

ISSN:0094-243X    

DOI:10.1063/1.34335

出版商:AIP    

年代:1984

数据来源: AIP