Search results for "statistical mechanics"
showing 10 items of 706 documents
Relaxation of the order-parameter statistics and dynamical confinement
2020
We study the relaxation of the local ferromagnetic order in the quantum Ising chain in a slant field with both longitudinal and transverse components. After preparing the system in a fully polarised state, we analyse the time evolution of the entire probability distribution function (PDF) of the magnetisation within a block of $\ell$ spins. We first analyse the effect of confinement on the gaussification of the PDF for large $\ell$, showing that the melting of initial order is suppressed when the longitudinal field is aligned to initial magnetisation while it is sped up when it is in the opposite direction. Then we study the thermalisation dynamics. In the paramagnetic region, the PDF quick…
Noise Induced Phenomena in Lotka-Volterra Systems
2003
We study the time evolution of two ecosystems in the presence of external noise and climatic periodical forcing by a generalized Lotka-Volterra (LV) model. In the first ecosystem, composed by two competing species, we find noise induced phenomena such as: (i) quasi deterministic oscillations, (ii) stochastic resonance, (iii) noise delayed extinction and (iv) spatial patterns. In the second ecosystem, composed by three interacting species (one predator and two preys), using a discrete model of the LV equations we find that the time evolution of the spatial patterns is strongly dependent on the initial conditions of the three species.
Lévy-type diffusion on one-dimensional directed Cantor graphs.
2009
L\'evy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard random walk on the sets but is also allowed to move ballistically throughout the empty regions. Using scaling relations and the mapping onto the electric network problem, we obtain the exact values of the scaling exponents for the asymptotic return probability, the resistivity and the mean square displacement as a function of the topological parameters of the sets. Interestingly, the systems undergoes a transition from superdiffusive to diffusive behavior a…
Low-cost approximate reconstructing of heterogeneous microstructures
2016
We propose an approximate reconstruction of random heterogeneous microstructures using the two-exponent power-law (TEPL). This rule originates from the entropic descriptor (ED) that is a multi-scale measure of spatial inhomogeneity for a given microstructure. A digitized target sample is a cube of linear size L in voxels. Then, a number of trial configurations can be generated by a model of overlapping spheres of a fixed radius, which are randomly distributed on a regular lattice. The TEPL describes the averaged maximum of the ED as a function of the phase concentration and the radius. Thus, it can be used to determine the radius. The suggested approach is tested on surrogate samples of cer…
The $p\lambda n$ fractal decomposition: Nontrivial partitions of conserved physical quantities
2015
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal everywhere to the original function. Thus, the method is specially suited for constructing families of fractal objects arising from a conserved physical quantity, the decomposition yielding an exact partition of the quantity in question. Most prominent classes of examples are provided by Hamiltonians and partition functions of statistical ensembles: By using this method, any such function can be decomposed in the ordinary sum of a specified number of terms (g…
Calcium binding and ionic conduction in single conical nanopores with polyacid chains: model and experiments.
2012
Calcium binding to fixed charge groups confined over nanoscale regions is relevant to ion equilibrium and transport in the ionic channels of the cell membranes and artificial nanopores. We present an experimental and theoretical description of the dissociation equilibrium and transport in a single conical nanopore functionalized with pH-sensitive carboxylic acid groups and phosphonic acid chains. Different phenomena are simultaneously present in this basic problem of physical and biophysical chemistry: (i) the divalent nature of the phosphonic acid groups fixed to the pore walls and the influence of the pH and calcium on the reversible dissociation equilibrium of these groups; (ii) the asym…
Statistical physics: Some basic principles of fluctuation and noise theory
1983
Abstract Models have traditionally played a significant role in statistical mechanics. In view of the complexity of the system which statistical mechanics attempt to describe, this is not at all surprising. The study of simplified models has frequently revealed the underlying mathematical structure of many physical questions and in so doing the study of models has contributed directly to a clarification of several paradoxes which beset statistical mechanics. In this paper some of the models which appear to be useful for the discussion of non-equilibrium phenomena are examined in some detail. As usual these models are extremely simplified versions of the actual situations. It is, finally, as…
Inverted Repeats in Viral Genomes
2004
We investigate 738 complete genomes of viruses to detect the presence of short inverted repeats. The number of inverted repeats found is compared with the prediction obtained for a Bernoullian and for a Markovian control model. We find as a statistical regularity that the number of observed inverted repeats is often greater than the one expected in terms of a Bernoullian or Markovian model in several of the viruses and in almost all those with a genome longer than 30,000 bp.
Happy Aged People Are All Alike, While Every Unhappy Aged Person Is Unhappy in Its Own Way
2011
Aging of the world’s population represents one of the most remarkable success stories of medicine and of humankind, but it is also a source of various challenges. The aim of the collaborative cross-cultural European study of adult well being (ESAW) is to frame the concept of aging successfully within a causal model that embraces physical health and functional status, cognitive efficacy, material security, social support resources, and life activity. Within the framework of this project, we show here that the degree of heterogeneity among people who view aging in a positive light is significantly lower than the degree of heterogeneity of those who hold a negative perception of aging. We base…
Enhanced sampling in simulations of dense systems
2002
In the simulations of a variety of systems we encounter the problem of large relaxation times due to the dense packing of the systems constituents. We propose an algorithm to overcome this slowing down by temporarily allowing the constituents of a 3d systems to escape into a 4th space coordinate. The idea will be exemplified for the problem of a homopolymer collapse.