Search results for " Statistical Mechanics"
showing 10 items of 557 documents
Levy flights in confining environments: Random paths and their statistics
2013
We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental inhomogeneities), the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Since there is no Langevin representation of the dynamics in question, our main goal here is to establish the appropriate path-wise description of the underlying jump-type process and next infer the $\rho (x,t)$ dynamics directly from the random paths statistics. A pr…
Modeling of biomolecular machines in non-equilibrium steady states
2021
Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling--even if often this step is not made explicit--and any model has to neglect details while still being physically accurate. Equilibrium statistical mechanics guides both the development of models and numerical methods for dynamics obeying detailed balance. For systems driven away from thermal equilibrium such a universal theoretical framework is missing. For a restricted class of driven systems governed by Markov dynamics and local detailed balance, stochastic thermodynamics has evolved to fill this gap and to provide fundamental constraints and guiding principles. The next step…
Aggregation and sedimentation of active Brownian particles at constant affinity.
2019
We study the motility-induced phase separation of active particles driven through the interconversion of two chemical species controlled by ideal reservoirs (chemiostats). As a consequence, the propulsion speed is non-constant and depends on the actual inter-particle forces, enhancing the positive feedback between increased density and reduced motility that is responsible for the observed inhomogeneous density. For hard discs, we find that this effect is negligible and that the phase separation is controlled by the average propulsion speed. For soft particles and large propulsion speeds, however, we predict an observable impact on the collective behavior. We briefly comment on the reentrant…
Escape transition of a polymer chain from a nanotube: How to avoid spurious results by use of the force-biased pruned-enriched Rosenbluth algorithm
2008
A polymer chain containing $N$ monomers confined in a finite cylindrical tube of diameter $D$ grafted at a distance $L$ from the open end of the tube may undergo a rather abrupt transition, where part of the chain escapes from the tube to form a "crown-like" coil outside of the tube. When this problem is studied by Monte Carlo simulation of self-avoiding walks on the simple cubic lattice applying a cylindrical confinement and using the standard pruned-enriched Rosenbluth method (PERM), one obtains spurious results, however: with increasing chain length the transition gets weaker and weaker, due to insufficient sampling of the "escaped" states, as a detailed analysis shows. In order to solve…
Moment equations in a Lotka-Volterra extended system with time correlated noise
2007
A spatially extended Lotka-Volterra system of two competing species in the presence of two correlated noise sources is analyzed: (i) an external multiplicative time correlated noise, which mimics the interaction between the system and the environment; (ii) a dichotomous stochastic process, whose jump rate is a periodic function, which represents the interaction parameter between the species. The moment equations for the species densities are derived in Gaussian approximation, using a mean field approach. Within this formalism we study the effect of the external time correlated noise on the ecosystem dynamics. We find that the time behavior of the $1^{st}$ order moments are independent on th…
Non-equilibrium Markov state modeling of periodically driven biomolecules
2019
Molecular dynamics simulations allow to study the structure and dynamics of single biomolecules in microscopic detail. However, many processes occur on time scales beyond the reach of fully atomistic simulations and require coarse-grained multiscale models. While systematic approaches to construct such models have become available, these typically rely on microscopic dynamics that obey detailed balance. In vivo, however, biomolecules are constantly driven away from equilibrium in order to perform specific functions and thus break detailed balance. Here we introduce a method to construct Markov state models for systems that are driven through periodically changing one (or several) external p…
Magnetic order in 2D antiferromagnets revealed by spontaneous anisotropic magnetostriction
2023
The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. Here, we show that its temperature dependence in AF MPS$_{3}$ (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetiza…
Quantum rescaling, domain metastability and hybrid domain-walls in two-dimensional CrI3 magnets
2020
Higher-order exchange interactions and quantum effects are widely known to play an important role in describing the properties of low-dimensional magnetic compounds. Here we identify the recently discovered two-dimensional (2D) van der Waals (vdW) CrI3 as a quantum non-Heisenberg material with properties far beyond an Ising magnet as initially assumed. We find that biquadratic exchange interactions are essential to quantitatively describe the magnetism of CrI3 but requiring quantum rescaling corrections to reproduce its thermal properties. The quantum nature of the heat bath represented by discrete electron-spin and phonon-spin scattering processes induced the formation of spin fluctuations…
Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands
2015
We report a fast, efficient and credible statistical reconstruction of any two-phase patterns of islands of miscellaneous shapes and poly-dispersed in sizes. In the proposed multi-scale approach called a weighted doubly-hybrid, two different pairs of hybrid descriptors are used. As the first pair, we employ entropic quantifiers, while correlation functions are the second pair. Their competition allows considering a wider spectrum of morphological features. Instead of a standard random initial configuration, a synthetic one with the same number of islands as that of the target is created by a cellular automaton. This is the key point for speeding-up of microstructure reconstruction, making u…
Enhanced structural correlations accelerate diffusion in charge-stabilized colloidal suspensions
1999
Theoretical calculations for colloidal charge-stabilized and hard sphere suspensions show that hydrodynamic interactions yield a qualitatively different particle concentration dependence of the short-time self-diffusion coefficient. The effect, however, is numerically small and hardly accessible by conventional light scattering experiments. Applying multiple-scattering decorrelation equipment and a careful data analysis we show that the theoretical prediction for charged particles is in agreement with our experimental results from aqueous polystyrene latex suspensions.