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At least 1,081 records · Page 60Linked to original sources
PubMed2002

Multicomponent binary spreading process.

I investigate numerically the phase transitions of two-component generalizations of binary spreading processes in one dimension. In these models pair annihilation AA --> emptyset, BB --> emptyset, explicit particle diffusion, and binary pair production processes compete with each other. Several versions with spatially different production are explored, and it is shown that for the cases 2A --> 3A, 2B--> 3B and 2A --> 2AB, 2B--> 2BA a phase transition occurs at zero production rate (sigma=0), which belongs to the class of N-component, asymmetric branching and annihilating random walks, characterized by the order parameter exponent beta=2. In the model with particle production AB --> ABA, BA --> BAB a phase transition point can be located at sigma(c)=0.3253 which belongs to the class of one-component binary spreading processes.

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PubMed2002

Spatial behavior of anomalous transport.

We present a general derivation of one-dimensional spatial concentration distributions for anomalous transport regimes. Such transport can be captured in the framework of a continuous time random walk with a broad transition time distribution. This general theory includes a Fokker-Planck equation as a particular limiting case. All of the concentration profiles, as well as the associated temporal first passage time distributions, can be written in terms of a single special function (that belongs to the class of Fox functions). In addition, we consider the first two moments of the spatial concentration distributions, and determine not only their scaling behavior with time but also the coefficients and correction terms.

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PubMed2002

Granular polymer solution.

We have measured the spectrum of fluctuations in the size of a granular polymer in a granular solvent. The system consists of a linear chain of plastic spheres immersed in a planar fluid of self-propelled balls. The time average of the end-to-end length r of the chain scales with the number of links N according to approximately N2nu, with nu=0.75+/-0.01. This provides an experimental test of the theoretical value nu=3 / 4 of the critical exponent for a self-avoiding random walk in two dimensions. The measured probability distribution P(r) is compared with the universal function of the scaling theory.

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PubMed2002

Stretched polymers in a poor solvent.

Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest-neighbor attraction. The bias corresponds to opposite forces applied to the first and last monomers. We show that both in d=2 and d=3 a phase transition occurs as this force is increased beyond a critical value, where the polymer changes from a collapsed globule to a stretched configuration. This transition is second order in d=2 and first order in d=3. For d=2 we predict the transition point quantitatively from properties of the unstretched polymer. This is not possible in d=3, but even there we can estimate the transition point precisely, and we can study the scaling at temperatures slightly below the collapse temperature of the unstretched polymer. We find very large finite size corrections that would make very difficult the estimate of the transition point from straightforward simulations.

Journal Article↗
PubMed2002

Phase transitions in nonequilibrium d-dimensional models with q absorbing states.

A nonequilibrium Potts-like model with q absorbing states is studied using Monte Carlo simulations. In two dimensions and q=3 the model exhibits a discontinuous transition. For the three-dimensional case and q=2 the model exhibits a continuous transition with beta=1 (mean field). Simulations are inconclusive, however, in the two-dimensional case for q=2. We suggest that in this case the model is close to or at the crossing point of lines separating three different types of phase transitions. The proposed phase diagram in the (q,d) plane is very similar to that of the equilibrium Potts model. In addition, our simulations confirm the field-theory prediction that in two dimensions a branching-annihilating random walk model without parity conservation belongs to the directed percolation universality class.

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PubMed2002

Combination of improved multibondic method and the Wang-Landau method.

We propose a method for Monte Carlo simulation of statistical physical models with discretized energy. The method is based on several ideas including the cluster algorithm, the multicanonical Monte Carlo method and its acceleration proposed recently by Wang and Landau. As in the multibondic ensemble method proposed by Janke and Kappler, the present algorithm performs a random walk in the space of the bond population to yield the state density as a function of the bond number. A test on the Ising model shows that the number of Monte Carlo sweeps required of the present method for obtaining the density of state with a given accuracy is proportional to the system size, whereas it is proportional to the system size squared for other conventional methods. In addition, the method shows a better performance than the original Wang-Landau method in measurement of physical quantities.

Journal Article↗
PubMed2002

Time and length scales for diffusion in liquids.

The first six even moments of the displacement of a molecule in water and an atom in liquid argon are found by molecular dynamics simulations and compared with the moments predicted by diffusion theory. We find a noticeable difference between the moments higher than the second. The ratio between predicted and calculated moments approaches unity as 1/t for times larger than 10 ps. Continuous time random walk is used to explain this slow approach of the moments to their diffusion limit.

Argon↗
PubMed2002

Number of distinct sites visited by a random walker trapped by an absorbing boundary.

The number of distinct sites visited by a lattice random walker is a subject of continuing interest in both mathematics and physics. All previous investigations have used the assumption that the lattice is unbounded. An assessment of the amount of tissue interrogated by a photon in reflectance measurements for diagnostic purposes suggests analyzing properties of the average number of distinct sites visited by a random walker trapped by an absorbing plane at time t. We show that for sufficiently large t this number is the same as the average number of distinct sites visited for this time when the surface is not present. A more complete analysis is possible for a random walk on a line terminated by an absorbing point.

Absorption↗
PubMed2002

Dynamics-dependent criticality in models with q absorbing states.

We study a one-dimensional, nonequilibrium Potts-like model that has q symmetric absorbing states. For q=2, as expected, the model belongs to the parity-conserving universality class. For q=3 the critical behavior depends on the dynamics of the model. Under a certain dynamics it remains generically in the active phase, which is also the feature of some other models with three absorbing states. However, a modified dynamics induces a parity-conserving phase transition. Relations with branching-annihilating random walk models are discussed in order to explain such a behavior.

Journal Article↗
PubMed2002

Solitons in the noisy Burgers equation.

We investigate numerically the coupled diffusion-advective type field equations originating from the canonical phase space approach to the noisy Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial dimension. The equations support stable right hand and left hand solitons and in the low viscosity limit a long-lived soliton pair excitation. We find that two identical pair excitations scatter transparently subject to a size-dependent phase shift and that identical solitons scatter on a static soliton transparently without a phase shift. The soliton pair excitation and the scattering configurations are interpreted in terms of growing step and nucleation events in the interface growth profile. Finally, we show that growing steps perform an anomalous random walk with dynamic exponent z=3/2.

Journal Article↗
PubMed2002

Comment on "Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map".

Rajagopalan and Sabir [Phys. Rev. E 63, 057201 (2001)] recently discussed deterministic diffusion in a piecewise linear map using an approach developed by Fujisaka et al. We first show that they rederived the random walk formula for the diffusion coefficient, which is known to be the exact result for maps of Bernoulli-type since the work of Fujisaka and Grossmann [Z. Phys. B: Condens. Matter 48, 261 (1982)]. However, this correct solution is at variance to the diffusion coefficient curve presented in their paper. Referring to another existing approach based on Markov partitions, we answer the question posed by the authors regarding solutions for more general parameter values by recalling the finding of a fractal diffusion coefficient. We finally argue that their model is not suitable for studying intermittent behavior, in contrast to what was suggested in their paper.

Comment↗
PubMed2002

Anisotropic diffusion and correlation analysis.

A method of statistical analysis of the correlation between two given scale invariant sequences is proposed. The relation between the fractal dimension of a two-dimensional random walk, generated with jumps derived from the signals, and the scaling exponents of the sequences is investigated, and a well-defined relation is found in the case of statistically independent signals. The method of analysis, whose performance is described for the case of an intermittent map, might represent a new tool for the study of the correlation between coupled complex systems.

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PubMed2002

Survival and residence times in disordered chains with bias.

We present a unified framework for first-passage time and residence time of random walks in finite one-dimensional disordered biased systems. The derivation is based on the exact expansion of the backward master equation in cumulants. The dependence on the initial condition, system size, and bias strength is explicitly studied for models with weak and strong disorders. Application to thermally activated processes is also developed.

Journal Article↗
PubMed2002

Effects of biased diffusions on dynamical surface structures for the A+B-->0 reaction.

The dynamical scaling property of surface eroded by a chemical reaction A+B-->0 is studied by the simulation. To consider the effect of interactions between an A particle and the material which consists of B particles, the A particle is assumed to undergo a drifted-diffusive motion or a biased random walk before it touches the material. The surface of the material is eroded by the chemical reaction with a B particle which the A particle first encounters. In dimension d=2, we found three regimes in the dynamical surface structure. When there is attractive bias to the material, the dynamical scaling property belongs to the universality class with the dynamic exponent z=2. When there is no bias or relatively small repulsive bias, the scaling property belongs to the class with z=1. The surface roughening behavior disappears when repulsive bias becomes quite large. We also discuss the properties of the crossover between the existing regimes.

Journal Article↗
PubMed2002

Process of irreversible nucleation in multilayer growth. I. Failure of the mean-field approach.

The formation of stable dimers on top of terraces during epitaxial growth is investigated in detail. In this paper we focus on mean-field theory, the standard approach to study nucleation. Such theory is shown to be unsuitable for the present problem, because it is equivalent to considering adatoms as independent diffusing particles. This leads to an overestimate of the correct nucleation rate by a factor N, which has a direct physical meaning: on average, a visited lattice site is visited N times by a diffusing adatom. The dependence of N on the size of the terrace and on the strength of step-edge barriers is derived from well-known results for random walks. The spatial distribution of nucleation events is shown to be different from the mean-field prediction, for the same physical reason. In the following paper we develop an exact treatment of the problem.

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PubMed2002

Intracellular signal propagation in a two-dimensional autocatalytic reaction model.

We study a simple reaction scheme in a two-dimensional lattice of particles or molecules with a refractory state. We analyze the dynamics of the propagating front as a function of physical-chemical properties of the host medium. The anisotropy of the medium significantly affects the smoothness of the wave front. Similarly, if particles or molecules may diffuse slowly to neighboring sites, then the front wave is more likely to be irregular. Both situations affect the ability of the whole system to relax to the original state, which is a required feature in the biological cells. Attempts to map this simple reaction scheme to reactions involved in the intracellular pathways suggest that, in some cases, signal transduction might take both connotation of a random walk and a propagating wave, depending on the local density of the medium. In particular, a sufficient condition for the appearance of waves in high-density regions of the media, is the existence of at least one autocatalytic reaction in the chain of reactions characterizing the pathway.

Biophysical Phenomena↗
PubMed2002

Fluctuations of self-flattening surfaces.

We study the scaling properties of self-flattening surfaces under global suppression on surface fluctuations. Evolution of self-flattening surfaces is described by restricted solid-on-solid type monomer deposition-evaporation model with reduced deposition (evaporation) at the globally highest (lowest) site. We find numerically that equilibrium surface fluctuations are anomalous with roughness exponent alpha approximately equal to 1/3 and dynamic exponent z(W) approximately equal to 3/2 in one dimension (1D) and alpha=0 (log) and z(W) approximately 5/2 in 2D. Stationary roughness can be understood analytically by relating our model to the static self-attracting random walk model and the dissociative dimer-type deposition-evaporation model. In case of nonequilibrium growing-eroding surfaces, self-flattening dynamics turns out to be irrelevant and the normal Kardar-Parisi-Zhang universality is recovered in all dimensions.

Journal Article↗
PubMed2002

Electrophoresis of an end-labeled polymer chain: a molecular dynamics study.

We study the conformational and the dynamic properties of an end-labeled (telechelic) polymer chain embedded in a porous medium made of randomly distributed immobile spherical obstacles using a stochastic molecular dynamics (MD) simulation method for several obstacle densities rho(imp) and for various field intensities Fx applied only to one end of the chain. For F(x)=0, the chain initially shrinks with increasing density of the obstacles rho(imp). In general, for small Fx and low rho(imp), the chain elongates along the direction of the force and shrinks in the transverse direction whereby this effect becomes more pronounced at larger chain lengths. However, we notice that for moderate values of rho(imp) and Fx, the conformational properties exhibit extrema before reaching a saturation at larger values of rho(imp) and Fx. Likewise, we also find that the drift velocity V(d) of the center of mass of the chain is a nonmonotonic function of the field intensity in the sense that V(d) also exhibits a maximum at a critical value of the field intensity F(crit)(x) beyond which it decreases. Our MD results indicate that for large rho(imp) the chain still can be described by a self-avoiding random walk, which contradicts the prediction of variational calculation using the replica trick, but supports a more recent analytical result using the optimal fluctuation method, as well as a Monte Carlo simulation result for a slightly different disordered medium.

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