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At least 127 records · Page 7Linked to original sources
PubMed2006

Flux reversal in a simple random-walk model on a fluctuating symmetric lattice.

A rather simple random-walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site with respect to each other, and consist of infinite arrays of absorbing sites separated by two nonabsorbing sites. Exact explicit expressions for the long-time velocity and the effective diffusion coefficient are obtained and discussed. In particular, it is shown that the direction of the steady motion can be reversed by conveniently varying the values of either the mean residence times in the lattice states or the transition rates to the absorbing and nonabsorbing sites.

Journal Article↗
PubMed2005

Continuous-time random-walk theory of interfering diffusion and chemical reaction with an application to electrochemical impedance spectra of oxidized Zr-1%Nb.

A microscopic theory is developed for the interplay of diffusion and chemical reaction and the results are compared with electrode impedance measurements on an oxide electrode. The theory is based on the ideas of continuous-time random walk and accounts for the interference of diffusion and recombination of the charge carriers in the oxide. The treatment results in a dispersive diffusivity with two time constants, one of them corresponding to the random walk, the other to the reaction. Combining this diffusivity with the Warburg electrode admittance expression, which refers to cases where the rate-limiting step is diffusion in a semi-infinite medium bounded by a plane, an admittance function is obtained. The phase angle is found to be higher than 45 degrees distinguishing it from the Gerischer impedance which was developed for a related problem. The oxides were produced by hydrothermal oxidation of Zr-l%Nb alloy, a metal used as cladding material for nuclear fuel elements. The electrode impedance spectra of Zr/Zr-oxide electrodes in aqueous SO(3) (2-) solutions were taken at various anodic voltages between 1 Hz and 100 kHz and temperatures between 278 and 333 K. The theoretical admittance functions could be successfully compared with the observed spectra. Both the functional forms and the fitted parameter values support our theory which is also in keeping with Macdonald's point-defect model.

Journal Article↗
PubMed2004

Diffusion at finite speed and random walks.

Diffusion, which occurs with infinite speed, results from a random walk with steps of finite speed. We resolve this paradox and derive a modified diffusion equation with finite speed.

Journal Article↗
PubMed2003

Surface growth models with a random-walk-like nonlocality.

To understand the effects of a random-walk-like nonlocality on the dynamical scaling properties of surface growths, a stochastic growth model in which the height difference triangle up h((i,i+1))=|h(i)-h(i+1)| of a chosen nearest neighbor column pair (i,i+1) is decreased by one unit is introduced and studied by simulations. The probability P((i,i+1)) of choosing a column pair (i,i+1) on a one-dimensional substrate is assigned as P((i,i+1))=e(kappa triangle up h((i,i+1)))/ summation operator (L)(j=1)e(kappa triangle up h((j,j+1))). On a substrate of given size L, the dynamical scaling property satisfies a normal scaling behavior as W=L(alpha)f(t/L(z)), when kappa is very small. If kappa becomes moderately large, the scaling property with the dynamic exponent z=1 as in diffusion-limited erosion appears. If kappa becomes very large, no surface roughening is found.

Journal Article↗
PubMed2002

A tandem random walk model of the SAT paradigm: response times and accumulation of evidence.

The speed-accuracy trade-off (SAT) paradigm forces participants to trade response speed for information accuracy by presenting them with a response signal at variable times after the onset of processing to which they must give an immediate response (within 300 ms). The processes that underlie the paradigm, especially those affecting response times, are not completely understood. Also, the extent to which the paradigm might affect the evidence accumulation process is still unclear. By testing several different sets of assumptions, we present a random walk model for the SAT paradigm that qualitatively explains both accuracy and response time data. The model uses a tandem random walk, with two possible continuations in a second phase which begins after the response signal. If a boundary is not reached during phase one, the walk transfers the current sum (relative to the size of the boundaries) from phase one to phase two in the form of bias, with drift rate equal to zero. If, however, a boundary is reached in phase one, the second phase starts from zero (no bias) with a strong drift rate towards the previously reached boundary. The model also incorporates a psychological refractory period: a delay in the onset of a second task when two tasks are presented in close succession. The model is consistent with the idea that information about the evidence accumulation rate is not contaminated by the paradigm.

Models, Psychological↗
PubMed2003

Feature-sampling and random-walk models of individual-stimulus recognition.

Traditional process models of old-new recognition have not addressed differences in accuracy and response time between individual stimuli. Two new process models of recognition are presented and applied to response time and accuracy data from 3 old-new recognition experiments. The 1st model is derived from a feature-sampling account of the time course of categorization, whereas the 2nd model is a generalization of a random-walk model of categorization. In the experiments, a new technique was used, which yielded reliable individual-stimulus data through repeated presentation of structurally equivalent items. The results from the experiments showed reliable differences in accuracy and response times between stimuli. The random-walk model provided the better account of the results from the 3 experiments. The implications of the results for process models of recognition are discussed.

Adult↗
PubMed1989

Random-walk chemotaxis: trial and error as a control process.

The biased random-walk chemotaxis of the bacterium Escherichia coli is a remarkably effective method of navigation based on random trial-and-error responding rather than steering. Humans restricted to the same mode of responding are able to navigate to target locations, just like the bacterium. This mode of navigation can be modeled as an input control process that selectively retains favorable and rejects unfavorable consequences of the random responses. The selection process is determined by the internal organization of the system rather than the external influence of the environment (as in natural selection or reinforcement).

Adolescent↗
PubMed2001

Duration time of a one-dimensional random walk as a function of the energies of the intermediate states: application for dissociation and relaxation processes in DNA hybrids.

Kinetic parameters of macromolecular systems are important for their function in vitro and in vivo. These parameters describe how fast the system dissociates (the characteristic dissociation time), and how fast the system reaches equilibrium (characteristic relaxation time). For many macromolecular systems, the transitions within the systems are described as a random walk through a number of states with various free energies. The rate of transition between two given states within the system is characterized by the average time which passes between starting the movement from one state, and reaching the other state. This time is referred to as the mean first-passage time between two given states. The characteristic dissociation and relaxation times of the system depend on the first-passages times between the states within the system. Here, for a one-dimensional random walk we derived an equation, which connects the mean first-passage time between two states with the free energies of the states within the system. We also derived the general equation, which is not restricted to one-dimensional systems, connecting the relaxation time of the system with the first-passage times between states. The application of these equations to DNA branch migration, DNA structural transitions and other processes is discussed.

DNA↗
PubMed1995

Random walk calculations for bacterial migration in porous media.

Bacterial migration is important in understanding many practical problems ranging from disease pathogenesis to the bioremediation of hazardous waste in the environment. Our laboratory has been successful in quantifying bacterial migration in fluid media through experiment and the use of population balance equations and cellular level simulations that incorporate parameters based on a fundamental description of the microscopic motion of bacteria. The present work is part of an effort to extend these results to bacterial migration in porous media. Random walk algorithms have been used successfully to date in nonbiological contexts to obtain the diffusion coefficient for disordered continuum problems. This approach has been used here to describe bacterial motility. We have generated model porous media using molecular dynamics simulations applied to a fluid with equal sized spheres. The porosity is varied by allowing different degrees of sphere overlap. A random walk algorithm is applied to simulate bacterial migration, and the Einstein relation is used to calculate the effective bacterial diffusion coefficient. The tortuosity as a function of particle size is calculated and compared with available experimental results of migration of Pseudomonas putida in sand columns. Tortuosity increases with decreasing obstacle diameter, which is in agreement with the experimental results.

Algorithms↗
PubMed1991

Chaotic jets with multifractal space-time random walk.

The problem of normal and anomalous diffusion is examined for the four-dimensional (4-D) map that arises from the problem of particle motion in a constant magnetic field and electrostatic wave packet. This 4-D map consists of two coupled 2-D maps: a standard map and a web map. The case of a weak chaos is considered. It is shown that due to the finite observation time, the particle diffusion possesses strong nonhomogeneous properties. Existence of long-living bundles of orbits with coherent propagation property is checked. These bundles are named "chaotic jets." The same name is used for a part of the trajectory if this part corresponds to long-living trapping or flight. The existence of chaotic jets depends on the topological properties of the phase space and influences the asymptotic law of transport. The particle transport can be considered as a random walk in the multifractal space-time that is produced by flights and trappings of a test particle in some area of its phase space. Levy random walk theory and its generalization for the multifractal space-time situation is considered and asymptotic laws for displacements are derived. Different intermediate asymptotics are discussed.

Journal Article↗
PubMed2000

Critical behavior of the annihilating random walk of two species with exclusion in one dimension

The A+A-->0, B+B-->0 process, with exclusion between the different kinds, is investigated here numerically. Before treating this model explicitly, we study the generalized Domany-Kinzel cellular automaton model of Hinrichsen on the line of parameter space where only compact clusters can grow. The simplest version is treated with two absorbing phases in addition to the active one. The two kinds of kinks which arise in this case do not react, leading to kinetics differing from the standard annihilating random walk of two species. Time dependent simulations are presented here to illustrate differences caused by exclusion in scaling properties of the usually discussed characteristic quantities. The dependence on the density and composition of the initial state is most apparent. Making use of the parallelism between this process and directed percolation limited by a reflecting parabolic surface, we argue that the two kinds of kinks exert marginal perturbation on each other and lead to deviations from standard annihilating random walk behavior.

Journal Article↗
PubMed2002

Centrosome-dependent anisotropic random walk of cytoplasmic vesicles.

We approach the problem of an apparently random movement of small cytoplasmic vesicles and its relationship to centrosome functioning. Motion of small vesicles in the cytoplasm of BSC-1 cells was quantified using computer-assisted microscopy. The vesicles move across the cytoplasm frequently changing their directions with negligible net displacement. The autocorrelation function for consecutive velocities of individual vesicles becomes indistinguishable from zero in 10s. Variance in the displacement is proportional to time. The motion of vesicles is anisotropic: It has diffusivity along the radii drawn from the centrosome several times higher than the tangential diffusivity. This anisotropy is abolished by ultraviolet microbeam irradiation of the centrosome when the microtubule array loses radial structure. We conclude that the motion of the vesicles in the cytoplasm can be described as diffusion-like random walk with centrosome-dependent anisotropy. The present analysis quantitatively corroborates the 'trial and error' model of vesicular transport.

Animals↗
PubMed2001

Trapping of random walks on small-world networks.

We investigate the trapping of random walkers on small-world networks (SWN's), irregular graphs. We derive bounds for the survival probability Phi(SWN)(n) and display its analysis through cumulant expansions. Computer simulations are performed for large SWNs. We show that in the limit of infinite sizes, trapping on SWNs is equivalent to trapping on a certain class of random trees, which are grown during the random walk.

Journal Article↗
PubMed2005

Searching on patch networks using correlated random walks: space usage and optimal foraging predictions using Markov chain models.

We describe a novel representation of a discrete correlated random walk as the transition matrix of a Markov chain with the displacements as the states. Such a representation makes it possible to utilize results from the theory of absorbing Markov chains, to make biologically interesting predictions without having to resort to Monte Carlo simulations. Our motivation for constructing such a representation is to explore the relationship between the movement strategy of an animal searching for resources upon a network of patches, and its consequent utilization of space and foraging success. As an illustrative case study, we have determined the optimal movement strategy and the consequent usage of space for a central place forager utilizing a continuous movement space which is discretized as a hexagonal lattice. The optimal movement strategy determines the size of the optimal home range. In this example, the animal uses mnemokinesis, which is a sinuosity regulating mechanism, to return it to the central place. The movement strategy thus refers to the choice of the intrinsic path sinuosity and the strength of the mnemokinetic mechanism. Although the movement space has been discretized as a regular lattice in this example, the method can be readily applied to naturally compartmentalized movement spaces, such as forest canopy networks. This paper is thus an attempt at incorporating results from the theory of random walk-based animal movements into Foraging Theory.

Animals↗
PubMed2005

Order-disorder phase transition in random-walk networks.

In this paper we study in detail the behavior of random-walk networks (RWN's). These networks are a generalization of the well-known random Boolean networks (RBN's), a classical approach to the study of the genome. RWN's are also discrete networks, but their response is defined by small variations in the state of each gene, thus being a more realistic representation of the genome and a natural bridge between discrete and continuous models. RWN's show a clear transition between order and disorder. Here we explicitly deduce the formula of the critical line for the annealed model and compute numerically the transition points for quenched and annealed models. We show that RBN's and the annealed model of RWN's act as an upper and a lower limit for the quenched model of RWN's. Finally we calculate the limit of the annealed model for the continuous case.

Journal Article↗
PubMed2001

Multifractal random walk.

We introduce a class of multifractal processes, referred to as multifractal random walks (MRWs). To our knowledge, it is the first multifractal process with continuous dilation invariance properties and stationary increments. MRWs are very attractive alternative processes to classical cascadelike multifractal models since they do not involve any particular scale ratio. The MRWs are indexed by four parameters that are shown to control in a very direct way the multifractal spectrum and the correlation structure of the increments. We briefly explain how, in the same way, one can build stationary multifractal processes or positive random measures.

Journal Article↗
PubMed1980

Biased random walk models for chemotaxis and related diffusion approximations.

Stochastic models of biased random walk are discussed, which describe the behavior of chemosensitive cells like bacteria or leukocytes in the gradient of a chemotactic factor. In particular the turning frequency and turn angle distribution are derived from certain biological hypotheses on the background of related experimental observations. Under suitable assumptions it is shown that solutions of the underlying differential-integral equation approximately satisfy the well-known Patlak-Keller-Segel diffusion equation, whose coefficients can be expressed in terms of the microscopic parameters. By an appropriate energy functional a precise error estimation of the diffusion approximation is given within the framework of singular perturbation theory.

Animals↗
PubMed2001

Continuously variable survival exponent for random walks with movable partial reflectors.

We study a one-dimensional lattice random walk with an absorbing boundary at the origin and a movable partial reflector. On encountering the reflector at site x, the walker is reflected (with probability r) to x-1 and the reflector is simultaneously pushed to x+1. Iteration of the transition matrix, and asymptotic analysis of the probability generating function show that the critical exponent delta governing the survival probability varies continuously between 1/2 and 1 as r varies between 0 and 1. Our study suggests a mechanism for nonuniversal kinetic critical behavior, observed in models with an infinite number of absorbing configurations.

Journal Article↗