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At least 1,063 records · Page 59Linked to original sources
PubMed2000

Critical behavior of the one-dimensional annihilation-fission process 2A-->O, 2A-->3A

Numerical simulations and cluster mean-field approximations with coherent anomaly extrapolation show that the critical line of the 1d annihilation-fission process is separated into two regions. In both the small and high diffusion cases, the critical behavior is different from the well known universality classes of nonequilibrium phase transitions to absorbing states. The high diffusion region seems to be well described by the cyclically coupled directed percolation and annihilating random walk. Spreading exponents show nonuniversal behavior.

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PubMed2001

Pair contact process with diffusion: anew type of nonequilibrium critical behavior?

In the preceding article Carlon et al. investigate the critical behavior of the pair contact process with diffusion. Using density matrix renormalization group methods, they estimate the critical exponents, raising the possibility that the transition might belong to the same universality class as branching annihilating random walks with even numbers of offspring. This is surprising since the model does not have an explicit parity-conserving symmetry. In order to understand this contradiction, we estimate the critical exponents by Monte Carlo simulations. The results suggest that the transition might belong to a different universality class that has not been investigated before.

Journal Article↗
PubMed2001

Kinetics of domain growth in systems with local barriers.

We study domain growth in spin-1 lattice models having nonconserved spin-flip kinetics with local barriers. Our primary motivation is to model the relaxational behavior of physical systems in which molecular motion is impeded by local kinetic barriers. The kinetic constraint is such that a spin from an up (down) state can flip to a down (up) state only via the zero state, which has a higher energy. We examine how the usual curvature-driven domain growth is affected by these local barriers, and whether the single-spin barriers have a collective effect. This paper presents comprehensive numerical results for phase ordering dynamics in this model using Monte Carlo simulations. We demonstrate dynamical scaling for domain-size distribution functions and spatial correlation functions. We also present results for the time dependence of characteristic length scales and autocorrelation functions. The length-scale behavior is interpreted in terms of the random walk of steps on domain boundaries. Furthermore, we present a simple stochastic model to derive an analytic expression for the autocorrelation function, which exhibits a stretched-exponential behavior over an extended regime-in agreement with our numerical simulations.

Journal Article↗
PubMed2001

Fractional Fokker-Planck equation, solution, and application.

Recently, Metzler et al. [Phys. Rev. Lett. 82, 3563 (1999)], introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field, and a Boltzmann thermal heat bath. In this paper we present the solution of the FFPE in terms of an integral transformation. The transformation maps the solution of ordinary Fokker-Planck equation onto the solution of the FFPE, and is based on Lévy's generalized central limit theorem. The meaning of the transformation is explained based on the known asymptotic solution of the continuous time random walk (CTRW). We investigate in detail (i) a force-free particle, (ii) a particle in a uniform field, and (iii) a particle in a harmonic field. We also find an exact solution of the CTRW, and compare the CTRW result with the corresponding solution of the FFPE. The relation between the fractional first passage time problem in an external nonlinear field and the corresponding integer first passage time is given. An example of the one-dimensional fractional first passage time in an external linear field is investigated in detail. The FFPE is shown to be compatible with the Scher-Montroll approach for dispersive transport, and thus is applicable in a large variety of disordered systems. The simple FFPE approach can be used as a practical tool for a phenomenological description of certain types of complicated transport phenomena.

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PubMed2001

Time decay of the remanent magnetization in the +/-J spin glass model at T=0.

Using the zero-temperature Metropolis dynamics, the time decay of the remanent magnetization in the +/-J Edward-Anderson spin glass model with a uniform random distribution of ferromagnetic and antiferromagnetic interactions has been investigated. Starting from the saturation, the magnetization per spin m reveals a slow decrease with time, which can be approximated by a power law: m(t)=m(infinity)+(t/a(0))(a(1)), a(1)<0. Moreover, its relaxation does not lead it into one of the ground states, and therefore the system is trapped in metastable isoenergetic microstates remaining magnetized. Such behavior is discussed in terms of a random walk that the system performs on its available configuration space.

Journal Article↗
PubMed2001

Directed particle diffusion under "burnt bridges" conditions.

We study random walks on a one-dimensional lattice that contains weak connections, so-called "bridges." Each time the walker crosses the bridge from the left or attempts to cross it from the right, the bridge may be destroyed with probability p; this restricts the particle's motion and directs it. Our model, which incorporates asymmetric aspects in an otherwise symmetric hopping mechanism, is very akin to "Brownian ratchets" and to front propagation in autocatalytic A+B-->2A reactions. The analysis of the model and Monte Carlo simulations show that for large p the velocity of the directed motion is extremely sensitive to the distribution of bridges, whereas for small p the velocity can be understood based on a mean-field analysis. The single-particle model advanced by us here allows an almost quantitative understanding of the front's position in the A+B-->2A many-particle reaction.

Biophysics↗
PubMed2001

Model of C60 fullerene, (H2O)60 water, and other similar clusters.

An analytical calculation of the partition function for the lattice gas model of a finite fullerene type cluster and of an infinite nanotube type cluster is presented. The method of calculation is based on the Vdovichenko random walk approach. There appear to be two values of critical temperature, and the heat capacity in their vicinities is proportional to (T-T(c))(-1).

Journal Article↗
PubMed2001

Perturbed on-off intermittency.

A basic requirement for on-off intermittency to occur is that the system possesses an invariant subspace. We address how on-off intermittency manifests itself when a perturbation destroys the invariant subspace. In particular, we distinguish between situations where the threshold for measuring the on-off intermittency in numerical or physical experiments is much larger than or is comparable to the size of the perturbation. Our principal result is that, as the perturbation parameter increases from zero, a metamorphosis in on-off intermittency occurs in the sense that scaling laws associated with physically measurable quantities change abruptly. A geometric analysis, a random-walk model, and numerical computations support the result.

Journal Article↗
PubMed2001

Generalized contact process with n absorbing states.

We investigate the critical properties of a one-dimensional stochastic lattice model with n (permutation symmetric) absorbing states. We analyze the cases with n</=4 by means of the nonhermitian density-matrix renormalization group. For n=1 and n=2 we find that the model is, respectively, in the directed percolation and parity conserving universality class, consistent with previous studies. For n=3 and n=4, the model is in the active phase in the whole parameter space and the critical point is shifted to the limit of one infinite reaction rate. We show that in this limit, the dynamics of the model can be mapped onto that of a zero temperature n-state Potts model. On the basis of our numerical and analytical results, we conjecture that the model is in the same universality class for all n>/=3 with exponents z=nu( ||)/nu( perpendicular)=2, nu( perpendicular)=1, and beta=1. These exponents coincide with those of the multispecies (bosonic) branching annihilating random walks. For n=3 we also show that, upon breaking the symmetry to a lower one (Z2), one gets a transition either in the directed percolation, or in the parity conserving class, depending on the choice of parameters.

Journal Article↗
PubMed2001

Anomalous two-state model for anomalous diffusion.

An anomalous two-state model (ATSM) with the anomalous long-tailed kinetics of transitions between states is proposed to describe the specific features of anomalous diffusion (AD) and AD-assisted transitions (ADAT) in the double-well potential. In the ATSM the system is assumed to undergo the conventional diffusion in both states but with different diffusion coefficients. The anomalous features of diffusion result from the modulation of the diffusion coefficient caused by transitions between ATSM states. The anomalous space-time evolution predicted by the ATSM is treated within the continuous time random walk theory. With the use of the proposed ATSM the transient behavior of the AD and the ADAT is analyzed in detail. We found a large variety of different (and sometimes peculiar) types of the space-time behavior of the free AD and ADAT. The free AD is found to be of subdiffusion or superdiffusion type for fairly long time depending on the relation between the parameters of the ATSM. The kinetics of the ADAT can be either conventional (exponential) or anomalous (of inverse power type) for different parameters of the model and time.

Journal Article↗
PubMed2001

Accurate estimation of the survival probability for trapping in two dimensions.

In this work we study the mean survival probability Phi(n,c) of random walks on a two-dimensional lattice in the presence of traps of concentration c, as a function of the number of steps n. The computation of this quantity is performed indirectly by using the distribution of the number of sites visited S(n). In order to achieve an accurate description of this distribution we use a combination of numerical techniques. The method allows an accurate calculation of Phi down to very small values (of the order of 10(-100), for example), which is not possible via direct simulations. The survival probability is analyzed in terms of an asymptotic expansion, following the results of Donsker and Varadhan [Commun. Pure Appl. Math. 28, 525 (1975); 32, 721 (1979)], and by using the outcome of a scaling ansatz, as described in our earlier work.

Journal Article↗
PubMed2001

Scaling of random spreading in small world networks.

In this study we have carried out computer simulations of random walks on Watts-Strogatz-type small world networks and measured the mean number of visited sites and the return probabilities. These quantities were found to obey scaling behavior with intuitively reasoned exponents as long as the probability p of having a long range bond was sufficiently low.

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PubMed2001

Anomalous diffusion and phase relaxation.

The diffusion and relaxation of a phase are investigated on the basis of several stochastic models. A simple relation between the diffusional behavior of the extended phase and the relaxation of periodic phase observables is found in the case of Gaussian and Lèvy distributed increments. In these cases, an anomalous diffusion gives rise to a stretched exponential relaxation of phase observables. Continuous time random walks may lead, even in the case of normal diffusion, to a slow algebraic relaxation.

Journal Article↗
PubMed2001

Intrinsic viscosity and the electrical polarizability of arbitrarily shaped objects.

The problem of calculating the electric polarizability tensor alpha(e) of objects of arbitrary shape has been reformulated in terms of path integration and implemented computationally. The method simultaneously yields the electrostatic capacity C and the equilibrium charge density. These functionals of particle shape are important in many materials science applications, including the conductivity and viscosity of filled materials and suspensions. The method has been validated through comparison with exact results (for the sphere, the circular disk, touching spheres, and tori), it has been found that 10(6) trajectories yield an accuracy of about four and three significant figures for C and alpha(e), respectively. The method is fast: For simple objects, 10(6) trajectories require about 1 min on a PC. It is also versatile: Switching from one object to another is easy. Predictions have also been made for regular polygons, polyhedra, and right circular cylinders, since these shapes are important in applications and since numerical calculations of high stated accuracy are available. Finally, the path-integration method has been applied to estimate transport properties of both linear flexible polymers (random walk chains of spheres) and lattice model dendrimer molecules. This requires probing of an ensemble of objects. For linear chains, the distribution function of C and of the trace (alpha(e)), are found to be universal in a size coordinate reduced by the chain radius of gyration. For dendrimers, these distribution functions become increasingly sharp with generation number. It has been found that C and alpha(e) provide important information about the distribution of molecular size and shape and that they are important for estimating the Stokes friction and intrinsic viscosity of macromolecules.

Journal Article↗
PubMed2001

Renormalization group analysis of autoregressive processes and fractional noise.

A renormalization group analysis is applied to autoregressive processes with an infinite series of coefficients. A simple fixed point is given by a random walk, and a second class is found that is proportional to the high order coefficients of fractional autoregressive integrated moving average (ARIMA) processes. The approach might be useful to detect nonstationarity in autoregressive processes.

Journal Article↗
PubMed2002

Diffusion on random-site percolation clusters: theory and NMR microscopy experiments with model objects.

Quasi-two-dimensional random-site percolation model objects were fabricated based on computer-generated templates. Samples consisting of two compartments, a reservoir of H2O gel attached to a percolation model object, which was initially filled with D2O, were examined with nuclear magnetic resonance microscopy for rendering proton spin density maps. The propagating proton/deuteron interdiffusion profiles were recorded and evaluated with respect to anomalous diffusion parameters. The deviation of the concentration profiles from those expected for unobstructed diffusion directly reflects the anomaly of the propagator for diffusion on a percolation cluster. The fractal dimension of the random walk d(w) evaluated from the diffusion measurements on the one hand and the fractal dimension d(f) deduced from the spin density map of the percolation object on the other permits one to experimentally compare dynamical and static exponents. Approximate calculations of the propagator are given on the basis of the fractional diffusion equation. Furthermore, the ordinary diffusion equation was solved numerically for the corresponding initial and boundary conditions for comparison. The anomalous diffusion constant was evaluated and is compared to the Brownian case. Some ad hoc correction of the propagator is shown to pay tribute to the finiteness of the system. In this way, anomalous solutions of the fractional diffusion equation could experimentally be verified.

Journal Article↗
PubMed2002

Finite-temperature large acoustic polaron dynamics in quasi-one-dimensional molecular crystals.

We report the results of theoretical examinations of large polaron motion in one-dimensional (1D) molecular crystals under the influence of thermal fluctuations of the host lattice and constant electric field. Such a situation may arise in biological macromolecules such as an alpha helix where charge (electron) transfer may be achieved by a polaron (soliton) mechanism. In that case, the electric field represents the effective endogenous electric field which is always present in realistic conditions. We derive and solve the Fokker-Planck equation for the distribution function of the soliton's center-of-mass position. It is shown that the soliton effectively exhibits a random walk. Moreover, in order to examine statistical properties of the soliton wave function, we calculate the mean value of the soliton probability density: and we find that, for sufficiently large times, thermal fluctuations destruct the soliton, which transforms into the Gaussian packet. These results were used in order to estimate the relevance of the soliton model of charge transfer in polypeptide chains.

Acoustics↗
PubMed2002

Simple model for 1/f(alpha) noise.

We present a simple stochastic mechanism which generates pulse trains exhibiting a power-law distribution of the pulse intervals and a 1/f(alpha) power spectrum over several decades at low frequencies with alpha close to 1. The essential ingredient of our model is a fluctuating threshold which performs a Brownian motion. Whenever an increasing potential V(t) hits the threshold, V(t) is reset to the origin and a pulse is emitted. We show that if V(t) increases linearly in time, the pulse intervals can be approximated by a random walk with multiplicative noise. Our model agrees with recent experiments in neurobiology and explains the high interpulse interval variability and the occurrence of 1/f(alpha) noise observed in cortical neurons and earthquake data.

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