Search results for " statistical mechanics"
showing 7 items of 557 documents
GPU accelerated Monte Carlo simulations of lattice spin models
2011
We consider Monte Carlo simulations of classical spin models of statistical mechanics using the massively parallel architecture provided by graphics processing units (GPUs). We discuss simulations of models with discrete and continuous variables, and using an array of algorithms ranging from single-spin flip Metropolis updates over cluster algorithms to multicanonical and Wang-Landau techniques to judge the scope and limitations of GPU accelerated computation in this field. For most simulations discussed, we find significant speed-ups by two to three orders of magnitude as compared to single-threaded CPU implementations.
Modeling long-range memory with stationary Markovian processes
2009
In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate transformation of a specific power-law correlated additive process x(t), already known in the literature, whose pdf shows power-law tails 1/x^a. We give analytical and numerical evidence that although the new processes (i) are Markovian and (ii) have gaussian or exponential tails their autocorrelation function still shows a power-law decay =1/T^b where b grows with a with a law which is compatible with b=a/2-c, where c is a numerical constant. When a<2(1+c) th…
Autocatalytic reaction-diffusion processes in restricted geometries
2008
We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the system achieves its inert state. By means of both analytical and numerical methods, we are also able to highlight the role of topology in the temporal evolution of the system.
Nonlinear Relaxation in Population Dynamics
2001
We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the i-th population and on the distribution of the population and of the local field.
Equilibrium fluid-crystal interfacial free energy of bcc-crystallizing aqueous suspensions of polydisperse charged spheres
2015
The interfacial free energy is a central quantity in crystallization from the meta-stable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from this data effective non-equilibrium values for the interfacial free energy between the emerging bcc-nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory. A strictly linear increase of the interfacial free energy was observed as a function of increased meta-stability. Here, we further analyze this data for five aqueous suspensions of charg…
On the discreet spectrum of fractional quantum hydrogen atom in two dimensions
2019
We consider a fractional generalization of two-dimensional (2D) quantum-mechanical Kepler problem corresponding to 2D hydrogen atom. Our main finding is that the solution for discreet spectrum exists only for $\mu>1$ (more specifically $1 < \mu \leq 2$, where $\mu=2$ corresponds to "ordinary" 2D hydrogenic problem), where $\mu$ is the L\'evy index. We show also that in fractional 2D hydrogen atom, the orbital momentum degeneracy is lifted so that its energy starts to depend not only on principal quantum number $n$ but also on orbital $m$. To solve the spectral problem, we pass to the momentum representation, where we apply the variational method. This permits to obtain approximate analytica…
Kinetics of phase separation in thin films: Lattice versus continuum models for solid binary mixtures
2008
A description of phase separation kinetics for solid binary (A,B) mixtures in thin film geometry based on the Kawasaki spin-exchange kinetic Ising model is presented in a discrete lattice molecular field formulation. It is shown that the model describes the interplay of wetting layer formation and lateral phase separation, which leads to a characteristic domain size $\ell(t)$ in the directions parallel to the confining walls that grows according to the Lifshitz-Slyozov $t^{1/3}$ law with time $t$ after the quench. Near the critical point of the model, the description is shown to be equivalent to the standard treatments based on Ginzburg-Landau models. Unlike the latter, the present treatmen…