Metastability of thed-dimensional contact process

We prove that thed-dimensional supercritical contact process exhibits metastable behavior, in the pathwise sense. This is done by proving the property of thermalization and using Mountford's theorem. We also extend some previous results on the loss of memory of the process.     

重核存活几率的N/Z效应

用Langevin方程计算了重核 194Pb, 200Pb和206Pb的蒸发残余形成几率。结果表明系统中质比(N/Z）影响了该几率大小,并且高的N/Z增加了重核存活几率。这是由于裂变位垒和鞍点前粒子发射依赖于系统N/Z的缘故。     

Analysis of survival probability based on superasymmetric reaction systems

The survival probability of an excited compound nucleus was studied using two different approaches of the washing out of shell effects with excitation energy based on a superasymmetric reaction system. The estimated evaporation residue cross sections based on the two different methods are compared with the available experimental data. Both methods are in agreement with the experimental data to a certain extent for some specific reactions and \begin{document}$ xn$\end{document} emission channels.     

Hydrodynamic limit of a nongradient interacting particle process

A simple example of a nongradient stochastic interacting particle system is analyzed. In this model, symmetric simple exclusion in one dimension in a periodic environment, the dynamical term in the Green-Kubo formula contributes to the bulk diffusion constant. The law of large numbers for the density field and the central limit theorem for the density fluctuation field are proven, and the Green-Kubo expression for the diffusion constant is computed exactly. The hydrodynamic equation for the model turns out to be linear.     

Hydrodynamics of the Zero-Range Process in the Condensation Regime

We argue that the coarse-grained dynamics of the zero-range process in the condensation regime can be described by an extension of the standard hydrodynamic equation obtained from Eulerian scaling even though the system is not locally stationary. Our result is supported by Monte Carlo simulations.     

Effects of N/Z on survival probability of heavy nuclei

The excitation functions of the evaporation residue formation probability of three heavy nuclei 194Pb, 200Pb and 206Pb are calculated by using a Langevin equation coupled with a statistical decay model.The results show that the neutron-to-proton ratio (N/Z) of a compound nucleus has an effect on survival probability and this effect becomes larger with increasing N/Z. This is because the fission barrier and the pre-saddle particle emission depend on the N/Z ratio of the system.     

Rigorous results on mathematical models of catalytic surfaces

Two types of mathematical models of catalytic surfaces are considered. Conditions guaranteeing either convergence to traps with all sites occupied by a single reactant (poisoning) and or coexistence in equilibrium are established.     

Exact Tracer Diffusion Coefficient in the Asymmetric Random Average Process

We study tracer diffusion in the continuous-time asymmetric random average process which is an interacting particle system on generalizing the Hammersley process. From the equations of motion for the particle-position correlations we obtain the exact tracer diffusion coefficient which is in agreement with a recent heuristic result by Krug and Garcia.     

Critical behavior of a one-dimensional contact process with time-uncorrelated disorder

In this work, the critical behavior of the one-dimensional contact process with time-uncorrelated disorder is investigated. We develop simulations on finite chains and explore the finite size scaling hypothesis to obtain estimates for the relevant parameters associated with static and dynamical critical quantities. We use an auto-adaptative technique that has been recently shown to provide reliable results for the standard contact process transition. We compare the main results with those derived from the usual short-time dynamics scaling. We found that, contrary to the behavior of the contact-process with quenched disorder which displays an infinite randomness critical point with activated scaling, the contact process with time-uncorrelated disorder belongs to the usual universality class of directed percolation.     

Systematic study of survival probability of excited superheavy nuclei

The stability of excited superheavy nuclei (SHN) with 100 Z 134 against neutron emission and fission is investigated by using a statistical model. In particular, a systematic study of the survival probability against fission in the 1n-channel of these SHN is made. The present calculations consistently take the neutron separation energies and shell correction energies from the calculated results of the finite range droplet model which predicts an island of stability of SHN around Z = 115 and N = 179. It turn...     

Some Properties of k-Step Exclusion Processes

We introduce k-step exclusion processes as generalizations of the simple exclusion process. We state their main equilibrium properties when the underlying stochastic matrix corresponds to a random walk or is positive recurrent and reversible. Finally, we prove laws of large numbers for tagged and second-class particles     

On the Spread of Drug-Resistant Diseases

We introduce an interacting particle system to model the emergence of drug-resistant diseases, one of the most serious health problems in modern society. We are interested in diseases for which a natural strain may mutate into a drug-resistant strain. This happens, for instance, when antibiotics are misused. The main result of our analysis is that with an efficient drug against the natural strain, if there is even a small chance that the natural strain mutates into the drug-resistant one, then there will eventually be an outbreak of the drug-resistant strain throughout the population. In that case the natural strain disappears and is replaced by the drug-resistant strain. The disturbing part of this is that an efficient treatment of the natural strain gives an edge to the drug-resistant strain.     

Correlations equalities and some upper bounds for the critical temperature for spin one systems

Starting from correlation identities for the Blume–Capel spin 1 systems and using correlation inequalities, we obtain rigorous upper bounds for the critical temperature. The obtained results improve over effective field type results.     

New Upper Bounds for the Connective Constants of Self-Avoiding Walks

Using a novel implementation of the Goulden–Jackson method, we compute new rigorous upper bounds for the connective constants of self-avoiding walks, breaking Alm's previous records for rectangular (hypercubic) lattices. We also give the explicit generating functions for memory 8. We then incorporate a numerical limit which gives bounds that are even better.     

On the Bergman-Milton bounds for the homogenization of dielectric composite materials

The Bergman-Milton bounds provide limits on the effective permittivity of a composite material comprising two isotropic dielectric materials. These provide tight bounds for composites arising from many conventional materials. We reconsider the Bergman-Milton bounds in light of the recent emergence of metamaterials, in which unconventional parameter regimes for relative permittivities are encountered. Specifically, it is demonstrated that: (a) for nondissipative materials the bounds may be unlimited if the constituent materials have relative permittivities of opposite signs; (b) for weakly dissipative materials characterized by relative permittivities with real parts of opposite signs, the bounds may be exceedingly large.     

Exact results for the asymmetric simple exclusion process with a blockage

We present new results for the current as a function of transmission rate in the one-dimensional totally asymmetric simple exclusion process (TASEP) with a blockage that lowers the jump rate at one site from one tor<1. Exact finitevolume results serve to bound the allowed values for the current in the infinite system. This proves the existence of a nonequilibrium phase transition, corresponding to an immiscibility gap in the allowed values of the asymptotic densities which the infinite system can have in a stationary state. A series expansion inr, derived from the finite systems, is proven to be asymptotic for all sufficiently large systems. Padé approximants based on this series, which make specific assumptions about the nature of the singularity atr=1, match numerical data for the infinite system to 1 part in 10⁴.     

Exact Mean-Field Solutions of the Asymmetric Random Average Process

We consider the asymmetric random average process (ARAP) with continuous mass variables and parallel discrete time dynamics studied recently by Krug/Garcia and Rajesh/Majumdar [both J. Statist. Phys. 99 (2000)]. The model is defined by an arbitrary state-independent fraction density function (r) with support on the unit interval. We examine the exactness of mean-field steady-state mass distributions in dependence of and identify as a conjecture based on high order calculations the class of density functions yielding product measure solutions. Additionally the exact form of the associated mass distributions P(m) is derived. Using these results we show examplary the exactness of the mean-field ansatz for monomial fraction densities (r)=(n–1) r ^n–2 with n2. For verification we calculate the mass distributions P(m) explicitly and prove directly that product measure holds. Furthermore we show that even in cases where the steady state is not given by a product measure very accurate approximants can be found in the class .     

Stationary states for a mechanical system with stochastic boundary conditions

We consider a system of Newtonian particles, with a long-range repulsive pair potential, moving in a cavity whose surface temperature is spatially varying. When a particle hits the surface, it is thermalized at the temperature of the collision point. We prove that this system has a unique stationary ensemble, to which any initial distribution converges for large times. We show that this stationary ensemble depends continuously on the surface temperature profile.     

Random composition of two rational maps: Singularity of the invariant measure

We study the invariant measure of a Markov chain obtained by randomly composing two rational maps related to the Anderson model with a Bernoulli potential. For a certain range of the parameters we show that the invariant measure is singular continuous. In certain cases the support turns out to be a Cantor set with a multifractal structure.