Search results for "Condensed Matter - Statistical Mechanics"
showing 10 items of 508 documents
Coexistence of active Brownian disks: van der Waals theory and analytical results
2020
At thermal equilibrium, intensive quantities like temperature and pressure have to be uniform throughout the system, restricting inhomogeneous systems composed of different phases. The paradigmatic example is the coexistence of vapor and liquid, a state that can also be observed for active Brownian particles steadily driven away from equilibrium. Recently, a strategy has been proposed that allows to predict phase equilibria of active particles [Solon et al., Phys. Rev. E 97, 020602(R) (2018)2470-004510.1103/PhysRevE.97.020602]. Here we elaborate on this strategy and formulate it in the framework of a van der Waals theory for active disks. For a given equation of state, we derive the effecti…
Microcanonical Determination of the Interface Tension of Flat and Curved Interfaces from Monte Carlo Simulations
2012
The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed, and as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q=30) on LxL square lattices (40<=L<=100) are presented. It is shown that the microcanonical ensemble is well-suited both to find the precise location of the first order phase transition and to obtain an accurate estimate for the interfacial free energy between coexisting ordered and disordered phases. For this purpose, a microcanonical version of the heatbath algorithm is implemented. The finite size behaviour of the loop in the curve describing the inverse temperature vers…
Critical behavior of a tumor growth model: directed percolation with a mean-field flavor.
2012
We examine the critical behaviour of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report (Ferreira et al., Phys. Rev. E 85, 010901 (2012)), which suggested that the critical behaviour of the model differs from the expected Directed Percolation (DP) universality class. Surprisingly, only some of the critical exponents (beta, alpha, nu_perp, and z) take non-DP values while some others (beta', nu_||, and spreading-dynamics exponents Theta, delta, z') remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations beta=alpha*nu_||, beta'=delta*nu_||, and the general…
Lévy flights in confining potentials.
2009
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are considered: those driven by Langevin equation with L\'{e}vy noise and those, named by us topological L\'{e}vy processes (occurring in systems with topological complexity like folded polymers or complex networks and generically in inhomogeneous media), whose Langevin representation is unknown and possibly nonexistent. Our major finding is that both above classes of processes stay in affinity and may share common stationary (eventually asymptotic) probability densit…
Aging Effects in a Lennard-Jones Glass
1997
Using molecular dynamics simulations we study the out of equilibrium dynamic correlations in a model glass-forming liquid. The system is quenched from a high temperature to a temperature below its glass transition temperature and the decay of the two-time intermediate scattering function C(t_w,t+t_w) is monitored for several values of the waiting time t_w after the quench. We find that C(t_w,t+t_w) shows a strong dependence on the waiting time, i.e. aging, depends on the temperature before the quench and, similar to the case of spin glasses, can be scaled onto a master curve.
Collective behaviours: from biochemical kinetics to electronic circuits
2013
In this work we aim to highlight a close analogy between cooperative behaviors in chemical kinetics and cybernetics; this is realized by using a common language for their description, that is mean-field statistical mechanics. First, we perform a one-to-one mapping between paradigmatic behaviors in chemical kinetics (i.e., non-cooperative, cooperative, ultra-sensitive, anti-cooperative) and in mean-field statistical mechanics (i.e., paramagnetic, high and low temperature ferromagnetic, anti-ferromagnetic). Interestingly, the statistical mechanics approach allows a unified, broad theory for all scenarios and, in particular, Michaelis-Menten, Hill and Adair equations are consistently recovered…
Phase separation of an asymmetric binary fluid mixture confined in a nanoscopic slit pore: Molecular-dynamics simulations
2008
As a generic model system of an asymmetric binary fluid mixture, hexadecane dissolved in carbon dioxide is considered, using a coarse-grained bead-spring model for the short polymer, and a simple spherical particle with Lennard-Jones interactions for the carbon dioxide molecules. In previous work, it has been shown that this model reproduces the real phase diagram reasonable well, and also the initial stages of spinodal decomposition in the bulk following a sudden expansion of the system could be studied. Using the parallelized simulation package ESPResSo on a multiprocessor supercomputer, phase separation of thin fluid films confined between parallel walls that are repulsive for both types…
Zero-range model of traffic flow.
2005
A multi--cluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is directly mapped to the mathematically well-studied zero-range process. Knowledge of the asymptotic behaviour of the transition rates for large clusters allows us to apply an established criterion for phase separation in one-dimensional driven systems. The distribution over cluster sizes in our zero-range model is given by a one--step master equation in one dimension. It provides an approximate mean--field dynamics, which, however, leads to the exact stationary s…
Characteristics of the polymer transport in ratchet systems
2010
Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency and non-uniform charge distributions. We also use currents in the non-equilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The domina…
Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension
2018
Combining three numerical methods (forward flux sampling, seeding of droplets, and finite-size droplets), we probe the crystallization of hard spheres over the full range from close to coexistence to the spinodal regime. We show that all three methods allow us to sample different regimes and agree perfectly in the ranges where they overlap. By combining the nucleation work calculated from forward flux sampling of small droplets and the nucleation theorem, we show how to compute the nucleation work spanning three orders of magnitude. Using a variation of the nucleation theorem, we show how to extract the pressure difference between the solid droplet and ambient liquid. Moreover, combining th…