arXiv subjects

Z. Toroczkai

Publications and source records attributed to Z. Toroczkai.

27 records · Page 2Linked to original sources

arXiv1999

Mound formation in nonequilibrium surface growth morphology does not necessarily imply a Schwoebel instability

We demonstrate, using well-established nonequilibrium growth models, that mound formation in the dynamical surface growth morphology does not necessarily imply a surface edge diffusion bias (the Schwoebel barrier) as has been almost universally accepted in the literature. We find mounded morphologies in several nonequilibrium growth models which incorporate no Schwoebel barrier. Our work should lead to a critical re-evaluation of recent experimental observations of mounded morphologies which have been theoretically interpreted in terms of Schwoebel barrier effects.

cond-mat.stat-mech↗

arXiv1998

Random Walk with a Hop-Over Site: A Novel Approach to Tagged Diffusion and Its Applications

We study, on a $d$ dimensional hypercubic lattice, a random walk which is homogeneous except for one site. Instead of visiting this site, the walker hops over it with arbitrary rates. The probability distribution of this walk and the statistics associated with the hop-overs are found exactly. This analysis provides a simple approach to the problem of tagged diffusion, i.e., the movements of a tracer particle due to the diffusion of a vacancy. Applications to vacancy mediated disordering are given through two examples.

cond-mat.stat-mech↗

arXiv1998

Sign-time distributions for interface growth

We apply the recently introduced distribution of sign-times (DST) to non-equilibrium interface growth dynamics. We are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear growth processes, and prove the existence of a non-trivial scaling relation. A new critical dimension is found, relating to the persistence properties of these systems. We also illustrate, by means of numerical simulations, the different types of DST to be expected in both linear and non-linear growth mechanisms.

cond-mat.stat-mech↗

arXiv1998

Chemical or Biological Activity in Open Chaotic Flows

We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B --> 2B and A+B --> 2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von Kármán vortex street, a time periodic two-dimensional flow of a viscous fluid around a cylinder. We show that a fractal unstable manifold acts as a catalyst for the process, and the products cover fattened-up copies of this manifold. This may account for the observed filamental intensification of activity in environmental flows. The reaction equations valid in the wake are derived either in the form of dissipative maps or differential equations depending on the regime under consideration. They contain terms that are not present in the traditional reaction equations of the same active process: the decay of the products is slower while the productivity is much faster than in homogeneous flows. Both effects appear as a consequence of underlying fractal structures. In the long time limit, the system locks itself in a dynamic equilibrium state synchronized to the flow for both types of reactions. For particles of finite size an emptying transition might also occur leading to no products left in the wake.

chao-dyn↗

arXiv1998

Diffusive persistence and the `sign-time' distribution

We present a new method for extracting the persistence exponent theta for the diffusion equation, based on the distribution P of `sign-times'. With the aid of a numerically verified Ansatz for P we derive an exact formula for theta in arbitrary spatial dimension d. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d ~ 36, signalling the existence of a sharp change in the ergodic properties of the diffusion field.

cond-mat.stat-mech↗

arXiv1998

The Brownian Vacancy Driven Walk

We investigate the lattice walk performed by a tagged member of an infinite `sea' of particles filling a d-dimensional lattice, in the presence of a Brownian vacancy. Particle-particle exchange is forbidden; the only interaction between them being hard core exclusion. The tagged particle, differing from the others only by its tag, moves only when it exchanges places with the hole. In this sense, it is a lattice walk ``driven'' by the Brownian vacancy. The probability distributions for its displacement and for the number of steps taken, after $n$-steps of the vacancy, are derived. Surprisingly, none of them is a Gaussian! It is shown that the only nontrivial dimension where the walk is recurrent is d=2.

cond-mat.stat-mech↗

arXiv1997

Brownian-Vacancy Mediated Disordering Dynamics

The disordering of an initially phase segregated system of finite size, induced by the presence of highly mobile vacancies, is shown to exhibit dynamic scaling in its late stages. A set of characteristic exponents is introduced and computed analytically, in excellent agreement with Monte Carlo data. In particular, the characteristic time scale, controlling the crossover between increasing disorder and saturation, is found to depend on the exponent scaling the number of vacancies in the sample.

cond-mat.stat-mech↗

arXiv1996

Stabilizing chaotic vortex trajectories: an example of high-dimensional control

A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General conditions for controllability are discussed. The algorithm is applied to the Hamiltonian problem of point vortices inside a circular cylinder with applications to an experimental plasma system.

chao-dyn↗

arXiv1996

Periodic One-Dimensional Hopping Model with one Mobile Directional Impurity

Analytic solution is given in the steady state limit for the system of Master equations describing a random walk on one-dimensional periodic lattices with arbitrary hopping rates containing one mobile, directional impurity (defect bond). Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of Master equations lead naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasi-walker. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasi-particle through physically meaningful equations. Applications in driven diffusive systems are shown, and connections with the Duke-Rubinstein reptation models for gel electrophoresis are discussed.

cond-mat.stat-mech↗