Random Walk Formalism Research Articles

Random walks and generalized master equations with internal degrees of freedom

We present an extension of the continuous-time random walk formalism to include internal states and to establish the connection to generalized master equations with internal states. The theory allows us to calculate physical observables from which we can extract the characteristic parameters of the internal states of the system under study.

Random-walk theory and the decay of pair correlations in Ornstein-Zernike lattice systems

Abstract A random-walk formalism is applied to some general Ornstein-Zernike lattice systems to obtain information as to the asymptotic form of the total correlation function. Calculations in terms of the Percus-Yevick approximation are then presented for certain lattice gases with interactions extending over a few orders of neighbours, illustrating the circumstances in which the decay of the total correlation function may be monotonic or oscillatory.

Random-walk theory and ordered phases in lattice-gas systems

The random-walk formalism that describes correlation functions in a homogenous system is here extended to cover correlations in ordered phases of a lattice gas. The general method is illustrated by application to certain lattice gases on linear, square and honeycomb lattices, treated under the Percus-Yevick approximation.

Random-walk theory and correlation functions in classical statistical mechanics

Abstract As a step towards a random-process formulation for classical fluids which ivolve many-body correlations, a random-walk formulation is presented wherein, for both lattice-gas and continuum models, the Green function and weight function describing the random walk are related to the total pair-correlation function of the model and to either the direct pair-correlation function or the first element of the direct correlation matrix.

Theory of ac Conductivity Based on Random Walks

It is shown that a simple random-walk formalism is not sufficient to derive ac conductivities when the influence of the first-waiting-time distribution is considered.

Singlet exciton migration and energy transfer in pyrene doped naphthalene

Time resolved spectroscopy measurements of the fluorescence intensities of pyrene doped naphthalene crystals were used to investigate host sensitized energy transfer in this system. A time dependent energy transfer rate is observed and these results are interpreted in terms of a generalized random walk formulation for the migration of singlet excitons. This leads to a value of about 1.5× 10−10sec for the exciton hopping time at room temperature. The results also imply the existence of extended trapping regions surrounding each activator and indicate the importance of including greater than nearest neighbor steps in the random walk. These results are compared to similar ones obtained on anthracene and tetracene doped naphthalene crystals. The temperature dependence of the energy transfer rate in pyrene doped naphthalene is consistent with thermal defect scattering and trapping effects similar to those seen in other doped naphthalene crystals.

Stream length and elevation for the model of Leopold and Langbein

A random walk formulation is given for a simple model of stream profile. The basic assumptions of the model are that in a unit of distance the elevation of the stream remains constant or drops by a unit of elevation and that the probability of each event depends upon elevation. This model is analyzed to obtain the frequency functions, means, and variances for length of stream from its origin to ‘sea‐level’ and for elevation of the stream at each unit distance from its origin.