Search results for "Random walk"

PFG n.m.r. study of diffusion anisotropy in oriented ZSM-5 type zeolite crystallites

1991

ZSM-5 zeolite crystallites are oriented by introducing them into a system of parallel capillaries. In this way, by applying pulsed-field gradient (PFG) n.m.r., a direct measurement of the orientation dependence of diffusion in ZSM-5 crystals has become possible. Using methane as a diffusant, the ratio D xy /D z between the diffusivities in the xy plane and in the z direction has been found to be of the order of 4.5. This value is in satisfactory agreement with the behavior expected from both MD calculations and a random walk model of molecular propagation in the two-channel network of ZSM-5-type zeolites.

Using anatomic and metabolic imaging in stereotactic radio neuro-surgery treatments

2016

Scaling and data collapse for the mean exit time of asset prices

2005

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model …

The non-random walk of stock prices: The long-term correlation between signs and sizes

2007

We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-…

A partially reflecting random walk on spheres algorithm for electrical impedance tomography

2015

In this work, we develop a probabilistic estimator for the voltage-to-current map arising in electrical impedance tomography. This novel so-called partially reflecting random walk on spheres estimator enables Monte Carlo methods to compute the voltage-to-current map in an embarrassingly parallel manner, which is an important issue with regard to the corresponding inverse problem. Our method uses the well-known random walk on spheres algorithm inside subdomains where the diffusion coefficient is constant and employs replacement techniques motivated by finite difference discretization to deal with both mixed boundary conditions and interface transmission conditions. We analyze the global bias…

Indefinitely growing self-avoiding walk.

1985

We introduce a new random walk with the property that it is strictly self-avoiding and grows forever. It belongs to a different universality class from the usual self-avoiding walk. By definition the critical exponent $\ensuremath{\gamma}$ is equal to 1. To calculate the exponent $\ensuremath{\nu}$ of the mean square end-to-end distance we have performed exact enumerations on the square lattice up to 22 steps. This gives the value $\ensuremath{\nu}=0.57\ifmmode\pm\else\textpm\fi{}0.01$.

Diffusive thermal dynamics for the spin-S Ising ferromagnet

2008

We introduce an alternative thermal diffusive dynamics for the spin-S Ising ferromagnet realized by means of a random walker. The latter hops across the sites of the lattice and flips the relevant spins according to a probability depending on both the local magnetic arrangement and the temperature. The random walker, intended to model a diffusing excitation, interacts with the lattice so that it is biased towards those sites where it can achieve an energy gain. In order to adapt our algorithm to systems made up of arbitrary spins, some non trivial generalizations are implied. In particular, we will apply the new dynamics to two-dimensional spin-1/2 and spin-1 systems analyzing their relaxat…

One-Dimensional Diffusion

2009

Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction

2010

The role of thermal and non-Gaussian noise on the dynamics of driven short overdamped Josephson junctions is studied. The mean escape time of the junction is investigated considering Gaussian, Cauchy-Lorentz and Levy-Smirnov probability distributions of the noise signals. In these conditions we find resonant activation and the first evidence of noise enhanced stability in a metastable system in the presence of Levy noise. For Cauchy-Lorentz noise source, trapping phenomena and power law dependence on the noise intensity are observed.

The effective diffusion coefficient in a one-dimensional discrete lattice with the inclusions

2015

Abstract The expression for the effective diffusion coefficient in one-dimensional discrete lattice model of random walks in matrix with inclusions and unequal hopping lengths is derived. This allowed us to suggest a physical interpretation to the concentration jump – ad hoc parameter commonly used in extended effective medium theory for accounting particle partial reflection on the boundary matrix–inclusion. The analytical results obtained are in excellent agreement with computer simulations.