arXiv subjects
Publications and source records attributed to V. Privman.
We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter evolution with typically one basic irrational frequency. We concentrate on the description of the global temporal properties in terms of second-order difference equations.
We study by Monte Carlo computer simulations random sequential adsorption (RSA) with diffusional relaxation, of lattice hard squares in two dimensions. While for RSA without diffusion the coverage approaches its maximum jamming value (large-time fractional coverage) exponentially, added diffusion allows the deposition process to proceed to the full coverage. The approach to the full coverage is consistent with the t**(-1/2) power law reminiscent of the equilibrium cluster coarsening in models with nonconserved order-parameter dynamics.
We derive an improved mean-field approximation for k-body annihilation reactions kA --> inert, for hard-core diffusing particles on a line, annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping and annihilation processes are correlated to mimic chemical reactions. Our new mean-field theory accounts for hard-core particle properties and has a larger region of applicability than the standard chemical rate equation especially for large k values. Criteria for validity of the mean-field theory and its use in phenomenological data fits are derived. Numerical tests are reported for k=3,4,5,6.
We report numerical simulation of the deposition of spherical particles on a planar surface, by ballistic, straight-line trajectory transport, and assuming irreversible adhesion on contact with the surface or previously deposited particles. Our data indicate that the deposit formed has a loosely layered structure within few diameters from the surface. This structure can be explained by a model of growth via chain formation. Away from the surface we found evidence of a monotonic, power-law approach to the bulk density. Both density and contact-statistics results suggest that the deposit formed is sparse: the space-filling fraction is about 15%, and the average number of contacts is 2. The morphology of the deposit both near the surface and in the bulk seems to be a result of competition of screening and branching; nearly half of all the spheres are either single-contact dangling ends, or branching nodes with more than two contacts.