Determination of the vapor–liquid transition of square-well particles using a novel generalized-canonical-ensemble-based method

The square-well（SW） potential is one of the simplest pair potential models and its phase behavior has been clearly revealed, therefore it has become a benchmark for checking new theories or numerical methods. We introduce the generalized canonical ensemble（GCE） into the isobaric replica exchange Monte Carlo（REMC） algorithm to form a novel isobaric GCE-REMC method, and apply it to the study of vapor–liquid transition of SW particles. It is validated that this method can reproduce the vapor–liquid diagram of SW particles by comparing the estimated vapor–liquid binodals and the critical point with those from the literature. The notable advantage of this method is that the unstable vapor–liquid coexisting states,which cannot be detected using conventional sampling techniques, are accessed with a high sampling efficiency. Besides,the isobaric GCE-REMC method can visit all the possible states, including stable, metastable or unstable states during the phase transition over a wide pressure range, providing an effective pathway to understand complex phase transitions during the nucleation or crystallization process in physical or biological systems.

Phase structures and transitions of quintessence surrounding RN black holes in a grand canonical ensemble

Considering a grand canonical ensemble,we study the phase structures and transitions of RN black holes surrounded by quintessence dark energy on two different boundary conditions,namely AdS space and a Dirichlet wall.For AdS space,under the condition of fixed temperature and potential,as the temperature increases for lower potential,the black hole undergoes a first-order phase transition,while for higher potential,no phase transition occurs.There are two different regions in the parameter space.For the Dirichlet wall,on which the temperature and potential are fixed,the state parameter of quintessenceω=-2/3 is analyzed in detail.Then,three different physically allowed regions in the parameter space of the black hole are well studied.As the temperature rises,first-order and second-order phase transitions may occur.In this case,there are nine regions in the parameter space,which is evidently distinct from the case of AdS space.

Parallel Tempering Simulation on Generalized Canonical Ensemble

Parallel tempering simulation is widely used in enhanced sampling of systems with complex energy surfaces.We hereby introduce generalized canonical ensemble(GCE)instead of the usual canonical ensemble into the parallel tempering to further improve abilities of the simulation technique.GCE utilizes an adapted weight function to obtain a unimodal energy distribution even in phase-coexisting region and then the parallel tempering on GCE yields the steady swap acceptance rates(SARs)instead of the fluctuated SARs in that on canonical ensemble.With the steady SARs,we can facilitate assign the parameters of the parallel tempering simulation to more efficiently reach equilibrium among different phases.We illustrate the parallel tempering simulation on GCE in the phase-coexisting region of 2-dimensional Potts model,a benchmark system for new simulation method developing.The result indicates that the new parallel tempering method is more efficient to estimate statistical quantities(i.e.,to sample the conformational space)than the normal parallel tempering,specially in phase-coexisting regions of larger systems.

Concrete quantum tunneling spectrum of Schwarzschild black holes

In this paper,a canonical ensemble model for black hole quantum tunneling radiation is introduced.We find that the probability distribution function is the same as the emission rate of a spherical shell in the Parikh-Wilczek tunneling framework.With this model,the probability distribution function corresponding to the emission shell system is calculated.Therefore,the concrete quantum tunneling spectrum of the Schwarzschild black hole is obtained.

ALow-order Model of Two-dimensional Fluid Dynamics on the Surface of a Sphere

Without any other approximations apart from the spectral method which is employed,the energy spectra corresponding to two kinds of'negative temperatures'are simulated with a symmetric trapezium truncation.The simulated results with either of the two negative temperatures are reasonably consistent with those from the statistical theory of turbulence.The more usual case for two positive temperatures evolves differently from the theoretical prediction.The viscosity influence on the ergodicity is discussed. It is shown that two--dimensional(2D)ideal flows on thesphere have a less pronounced tendency to be ergodic than those on planar geometry due to the curvature of thespherical surface that weakens the interaction between different parts of the flow,enabling these parts to behave inmore relative isolation. The expressions for the standard deviations from a canonical ensemble for the two differentoptions of coefficients are shown to be proportional to in(N is the total number of independent modes in the system),independent of the initial conditions of the system.