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M Mobilia

Publications and source records attributed to M Mobilia.

8 recordsLinked to original sources
PubMed2005

Exact dynamics of a reaction-diffusion model with spatially alternating rates.

We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative "temperatures" have a perfectly natural interpretation. Observables of interest include the magnetization, the particle density, and all correlation functions for both models. Two generic types of time dependence are found: if both temperatures are positive, the magnetization, density, and correlation functions decay exponentially to their steady-state values. In contrast, if one of the temperatures is negative, damped oscillations are observed in all quantities. They can be traced to a subtle competition of pair creation and annihilation on the two sublattices. We comment on the limitations of mean-field theory and propose an experimental realization of our model in certain conjugated polymers and linear chain compounds.

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PubMed2003

Majority versus minority dynamics: phase transition in an interacting two-state spin system.

We introduce a simple model of opinion dynamics in which binary-state agents evolve due to the influence of agents in a local neighborhood. In a single update step, a fixed-size group is defined and all agents in the group adopt the state of the local majority with probability p or that of the local minority with probability 1-p. For group size G=3, there is a phase transition at p(c)=2/3 in all spatial dimensions. For p>p(c), the global majority quickly predominates, while for p<p(c), the system is driven to a mixed state in which the densities of agents in each state are equal. For p=p(c), the average magnetization (the difference in the density of agents in the two states) is conserved and the system obeys classical voter model dynamics. In one dimension and within a Kirkwood decoupling scheme, the final magnetization in a finite-length system has a nontrivial dependence on the initial magnetization for all p not equal p(c), in agreement with numerical results. At p(c), the exact two-spin correlation functions decay algebraically toward the value 1 and the system coarsens as in the classical voter model.

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PubMed2001

Two-species D-dimensional diffusive model and its mapping onto a growth model.

In this work, we consider a diffusive two-species d-dimensional model and study it in great detail. Two types of particles, with hard core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density, the instantaneous, as well as noninstantaneous, two-point correlation functions for various initial conditions. We study the impact of correlations in the initial state on the dynamics. Finally, we map the one-dimensional version of the model under consideration onto a restricted solid-on-solid growth model with three states and solve its dynamics.

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PubMed2001

Generalized empty-interval method applied to a class of one-dimensional stochastic models.

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models that cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called interparticle distribution function (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model that cannot be solved directly by the conventional IPDF method and that can be viewed as a generalization of the voter model and/or as an epidemic model. We also consider the reversible diffusion-coagulation model with input of particles and determine other reaction-diffusion models that can be mapped onto the latter via suitable similarity transformations. Finally we study the problem of the propagation of a wave front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.

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PubMed2001

Solution of a one-dimensional stochastic model with branching and coagulation reactions.

We solve a one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions; they can also appear on an empty site and disappear spontaneously. This model, which can be viewed as an epidemic model and/or as a generalization of the voter model, is treated analytically beyond the conventional solvable situations. With help of a suitably chosen string function, which is simply related to the density and the noninstantaneous two-point correlation functions of the particles, exact expressions of the density and of the noninstantaneous two-point correlation functions, as well as the relaxation spectrum are obtained on a finite and periodic lattice.

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PubMed2001

Exact solution of a class of one-dimensional nonequilibrium stochastic models.

We consider various one-dimensional nonequilibrium models, namely, the diffusion-limited pair-annihilation and creation model (DPAC) and its unbiased version (the Lushnikov model), the DPAC model with particle injection, as well as (biased) diffusion-limited coagulation model (DC). We study the DPAC model using an approach based on a duality transformation and the generating function of the dual model. We are able to compute exactly the density and correlation functions in the general case with arbitrary initial states. Further, we assume that a source injects particles in the system. Solving, via the duality transformation, the equations of motion of the density, and the noninstantaneous two-point correlation functions, we see how the source affects the dynamics. Finally we extend the previous results to the DC model with help of a similarity transformation.

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PubMed2001

Soluble two-species diffusion-limited models in arbitrary dimensions.

A class of two-species (three-states) bimolecular diffusion-limited models of classical particles with hard-core reacting and diffusing in a hypercubic lattice of arbitrary dimension is investigated. The manifolds on which the equations of motion of the correlation functions close, are determined explicitly. This property allows to solve for the density and the two-point (two-time) correlation functions in arbitrary dimension for both, a translation invariant class and another one where translation invariance is broken. Systems with correlated as well as uncorrelated, yet random initial states can also be treated exactly by this approach. We discuss the asymptotic behavior of density and correlation functions in the various cases. The dynamics studied is very rich.

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