Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Master equation”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24Linked to original sources
PubMed2004

Critical dynamics of the kinetic Glauber-Ising model on hierarchical lattices.

The critical dynamics of the kinetic Glauber-Ising model is studied on a family of the diamond-type hierarchical lattices with various branches. By carrying out the time-dependent real-space renormalization-group transformation to the master equation of the systems considered, the dynamic exponent is calculated. We find that the dynamic exponent depends on fractal dimension d(f) or the branch number m in a generator, and that it increases with the increase of d(f) or m. We notice that for the case of m=1 (one-dimensional spin chain, d(f)=1) our result z=2 is the same as the exact result obtained by Glauber, and for the case of m=2 (the simplest one in the diamond-type hierarchical lattices, d(f)=2) the exponent z=2.626 is higher than those of the two-dimensional regular lattice and the triangular lattice.

Journal Article↗
PubMed2004

Statistical properties of a discrete version of the Ornstein-Uhlenbeck process.

A discrete version of the Ornstein-Uhlenbeck process is discussed which arises from a simple generalization of the master equation of the random walk. The calculation of the statistical properties of the free propagator for this process can be obtained using essentially the same formalism as for simple random walks. These calculations are carried out in some detail for the one-dimensional case. The usual equation for the evolution of the probability distribution of the Ornstein-Uhlenbeck process is recovered in the continuum limit if the jump distribution has a finite variance. However, the discrete process is also well defined for long tailed jump distributions and, thus, can be used to describe a Lèvy walk under the effect of a harmonic potential. Finally, a brief discussion of the generalization of this process to describe random walks in general potentials is presented and briefly compared with results arising from the fractional diffusion approach.

Journal Article↗
PubMed2004

Molecular traffic control in single-file networks with fast catalysts.

As a model for molecular traffic control we investigate the diffusion of hard core particles in crossed single-file systems. We consider a square lattice of single-files being connected to external reservoirs. The (vertical) alpha channels, carrying only A particles, are connected to reservoirs with constant density rho(A). B particles move along the (horizontal) beta channels, which are connected to reservoirs of density rho(B). We allow the irreversible transition A-->B at intersections. We are interested in the stationary density profile in the alpha and beta channels, which is the distribution of the occupation probabilities over the lattice. We calculate the stationary currents of the system and show that for sufficiently long channels the currents (as a function of the reservoir densities) show in the limit of large transition rates nonanalytic behavior. The results obtained by direct solution of the master equation are verified by kinetic Monte Carlo simulations.

Journal Article↗
PubMed2004

Self-organization in a simple model of adaptive agents playing 2 x 2 games with arbitrary payoff matrices.

We analyze, both analytically and numerically, the self-organization of a system of "selfish" adaptive agents playing an arbitrary iterated pairwise game (defined by a 2 x 2 payoff matrix). Examples of possible games to play are the prisoner's dilemma (PD) game, the chicken game, the hero game, etc. The agents have no memory, use strategies not based on direct reciprocity nor "tags" and are chosen at random, i.e., geographical vicinity is neglected. They can play two possible strategies: cooperate (C) or defect (D). The players measure their success by comparing their utilities with an estimate for the expected benefits and update their strategy following a simple rule. Two versions of the model are studied: (1) the deterministic version (the agents are either in definite states C or D) and (2) the stochastic version (the agents have a probability c of playing C). Using a general master equation we compute the equilibrium states into which the system self-organizes, characterized by their average probability of cooperation c(eq). Depending on the payoff matrix, we show that c(eq) can take five different values. We also consider the mixing of agents using two different payoff matrices and show that any value of c(eq) can be reached by tuning the proportions of agents using each payoff matrix. In particular, this can be used as a way to simulate the effect of a fraction d of "antisocial" individuals--incapable of realizing any value to cooperation--on the cooperative regime hold by a population of neutral or "normal" agents.

Journal Article↗
PubMed2004

Anomalous hydrodynamical dispersion and the transport with multiple families of paths in porous media.

We investigate a family of probability distributions that shows anomalous hydrodynamic dispersion, by solving a particular class of coupled generalized master equations. The Fourier-Laplace solution is obtained analytically in terms of the matrix Green function method; then the Coats-Smith concentration profile is revisited in a particular case. Two models of disorder are worked out explicitly, and the mean current is asymptotically calculated. We present an approximation method to calculate the first passage time distribution for this stochastic transport process, and as an example an exact Markovian result is worked out; scaling results are also shown. We discuss the comparison with other different methods to work out complex diffusion phenomena in the presence of disordered multiple transport paths. Extensions when the models are nondiffusive can also be solved in the Fourier-Laplace representation.

Journal Article↗
PubMed2004

Suppression of the pulsed regimes appearing in free-electron lasers using feedback control of an unstable stationary state.

We show that the pulsed regimes observed in free-electron lasers (FELs) can be suppressed using feedback control. By applying tiny parameter perturbations, the feedback allows to keep the systems onto a stationary state that is naturally existing in phase space, but is usually inaccessible because of its unstable nature. We test this method numerically on a master equation derived from the classical iterative model. Then we present the experimental results obtained on the super-ACO FEL. This method is in principle directly applicable to the other free-electron lasers, whose instabilities have a dynamical (deterministic) origin.

Journal Article↗
PubMed2004

Resonant activation in discrete systems.

The resonant activation phenomenon (RAP) in a discrete system is studied using the master equation formalism. We show that the RAP corresponds to a nonmonotonic behavior of the frequency dependent first passage time probability density function (PDF). An analytical expression for the resonant frequency is introduced, which, together with numerical results, helps understand the RAP behavior in the space spanned by the transition rates for the case of reflecting and absorbing boundary conditions. The limited range of system parameters for which the RAP occurs is discussed. We show that a minimum and a maximum in the mean first passage time can be obtained when both boundaries are absorbing. Relationships to some biological systems are suggested.

Algorithms↗
PubMed2004

Bethe ansatz solution of zero-range process with nonuniform stationary state.

The eigenfunctions and eigenvalues of the master equation for zero-range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe ansatz applicability requires the rates of hopping of particles out of a site to be the q numbers [n](q). This is a generalization of the rates of hopping of noninteracting particles equal to the occupation number n of a site of departure. The noninteracting case can be restored in the limit q-->1. The limiting cases of the model for q=0, infinity correspond to the totally asymmetric exclusion process, and the drop-push model, respectively. We analyze the partition function of the model and apply the Bethe ansatz to evaluate the generating function of the total distance traveled by particles at large time in the scaling limit. In case of nonzero interaction, q not equal 1, the generating function has the universal scaling form specific for the Kardar-Parizi-Zhang universality class.

Journal Article↗
PubMed2004

Random walks of molecular motors arising from diffusional encounters with immobilized filaments.

Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random walks. Effects of detachment and reattachment are calculated by an analytical solution of the master equation in two and three dimensions. Results are obtained for the fraction of bound motors, their average velocity, displacement, and dispersion. The analytical results are in good agreement with results from Monte Carlo simulations and confirm the behavior predicted by scaling arguments. The diffusion coefficient parallel to the filament becomes anomalously large since detachment and subsequent reattachment, in the presence of directed motion of the bound motors, leads to a broadening of the density distribution. The occurrence of protofilaments on a microtubule is modeled by internal states of the binding sites. After a transient time, all protofilaments become equally populated.

Adsorption↗
PubMed2004

Analytic study of the three-urn model for separation of sand.

We present an analytic study of the three-urn model for separation of sand, which can be regarded as a zero-range process. We solve analytically the master equation and the first-passage problem. We find that the stationary probability distribution obeys the detailed balance and is governed by the free energy. We find that the characteristic lifetime of a cluster diverges algebraically with exponent 1/3 at the limit of stability. We also give a general argument that the scaling behavior is robust with respect to different expressions of the flux.

Journal Article↗
PubMed2004

Epidemic spreading in a hierarchical social network.

A model of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The structure of interpersonal connections is based on a scale-free network. Spatial localization of individuals belonging to different social groups, and the mobility of a contemporary community, as well as the effectiveness of different interpersonal interactions, are taken into account. Typical relations characterizing the spreading process, like a range of epidemic and epidemic curves, are discussed. The influence of preventive vaccinations on the spreading process is investigated. The critical value of preventively vaccinated individuals that is sufficient for the suppression of an epidemic is calculated. Our results are compared with solutions of the master equation for the spreading process and good agreement of the character of this process is found.

Animals↗
PubMed2004

Cluster growth in far-from-equilibrium particle models with diffusion, detachment, reattachment, and deposition.

Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for postdeposition coarsening dynamics, contains mechanisms of diffusion, attachment, and slow activated detachment (at rate epsilon<<1 ) of particles on a line. Simulation shows three successive regimes of cluster growth: fast attachment of isolated particles; detachment allowing further ( epsilont )(1/3) coarsening of average cluster size; and t(-1/2) approach to a saturation size varying as epsilon(-1/2) . Model II generalizes the first one in having an additional mechanism of particle deposition into cluster gaps, suppressed for the smallest gaps. This model exhibits early rapid filling, leading to slowing deposition due to the increasing scarcity of deposition sites, and then continued power law [ ( epsilont )(1/2) ] cluster size coarsening through the redistribution allowed by slow detachment. The basic ( epsilont )(1/3) domain growth laws and epsilon(-1/2) saturation in model I are explained by a simple scaling picture involving the time for a particle to detach and diffuse to the next cluster. A second, fuller approach is presented that employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation. This allows, through the steady state solution of the corresponding equation for a cluster probability generating function, quantitative results for the saturation of model I in excellent agreement with the simulation results. For model II, it provides a one-variable scaling function solution for the coarsening probability distribution, and in particular quantitative agreement with the cluster length scaling and its amplitude.

Journal Article↗
PubMed2005

Optimal path to epigenetic switching.

We use large deviation methods to calculate rates of noise-induced transitions between states in multistable genetic networks. We analyze a synthetic biochemical circuit, the toggle switch, and compare the results to those obtained from a numerical solution of the master equation.

Adaptation, Physiological↗
PubMed2005

Non-Markovian dynamics of quantum systems. II. Decay rate, capture, and pure states.

On the basis of a master equation for the reduced density matrix of open quantum systems, we study the influence of time-dependent friction and diffusion coefficients on the decay rate from a potential well and the capture probability into a potential well. Taking into account the mixed diffusion coefficient Dqp, the quasistationary decay rates are compared with the analytically derived Kramers-type formulas for different temperatures and frictions. The diffusion coefficients supplying the purity of states are derived for a non-Markovian dynamics.

Journal Article↗
PubMed2005

Nonuniversal coarsening and universal distributions in far-from-equilibrium systems.

Anomalous coarsening in far-from-equilibrium one-dimensional systems is investigated by applying simulation and analytic techniques to minimal hard-core particle (exclusion) models. They contain mechanisms of aggregated particle diffusion, with rates epsilon<<1 , particle deposition into cluster gaps, but suppressed for the smallest gaps, and breakup of clusters that are adjacent to large gaps. Cluster breakup rates vary with the cluster length x as k x(alpha) . The domain growth law x approximately (epsilont)(z) , with z=1/ (2+alpha) for alpha>0 , is explained by a simple scaling picture involving the time for two particles to coalesce and a new particle to be deposited. The density of double vacancies, at which deposition and cluster breakup are allowed, scales as 1/ [t (epsilont)(z) ] . Numerical simulations for several values of alpha and epsilon confirm these results. A fuller approach is presented which employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation. The equation for a one-variable scaling function explains the above average cluster length scaling. The probability distributions of cluster lengths x scale as P (x) = [1/ (epsilont)(z) ] g (y) , with y identical with x/ (epsilont)(z) , which is confirmed by simulation. However, those distributions show a universal tail with the form g (y) approximately exp (- y(3/2) ) , which is explained by the connection of the vacancy dynamics with the problem of particle trapping in an infinite sea of traps. The high correlation of surviving particle displacement in the latter problem explains the failure of the independent cluster approximation to represent those rare events.

Journal Article↗
PubMed2005

Generating function, path integral representation, and equivalence for stochastic exclusive particle systems.

We present the path integral representation of the generating function for classical exclusive particle systems. By introducing hard-core bosonic creation and annihilation operators and appropriate commutation relations, we construct the Fock space structure. Using the state vector, the generating function is defined and the master equation of the system is transformed into the equation for the generating function. Finally, the solution of the linear equation for the generating function is derived in the form of the path integral. Applying the formalism, the equivalence of reaction-diffusion processes of single species and two species is described.

Journal Article↗
PubMed2005

Evidence on DNA slippage step-length distribution.

A simple model based on a master equation is constructed in order to reveal the details of the mutational events modifying simple sequence repeats in the human genome, A database of simple repeats together with their flanking sequences comprising approximately 10(5) entries from all 24 human chromosomes was constructed. By aligning the pairs of fragments of sequences containing the repeat elements, the matrices that count the number of slippage events were evaluated. The counts were then used as a target to be reproduced by our theoretical model, in which the elongation and shortening of the repeats proceed through a mechanism in which the step lengths exhibit a decaying distribution in the form of an inverse power law rather than through one nucleotide extension or deletion, which was the most frequent supposition in previous studies.

Chromosomes, Human↗
PubMed2005

Coupled dynamics of DNA breathing and of proteins that selectively bind to single-stranded DNA.

We study the size fluctuations of a local denaturation zone in a DNA molecule in the presence of proteins that selectively bind to single-stranded DNA, based on a (2+1)-dimensional master equation. By tuning the physical parameters we can drive the system from undisturbed bubble fluctuations to full, binding-protein-induced denaturation. We determine the effective free-energy landscape of the DNA bubble and explore its relaxation modes.

Binding Sites↗