Tricriticality in generalized Schloegl models for autocatalysis: Lattice-gas realization with particle diffusion

We analyze lattice-gas reaction-diffusion models which include spontaneous annihilation, autocatalytic creation, and diffusion of particles, and which incorporate the particle creation mechanisms of both Schloegl’s first and second models. For fixed particle diffusion or hop rate, adjusting the relative strength of these creation mechanisms induces a crossover between continuous and discontinuous transitions to a “poisoned” vacuum state. Kinetic Monte Carlo simulations are performed to map out the corresponding tricritical line as a function of hop rate. An analysis is also provided of the tricritical “epidemic exponent” for the case of no hopping. The phase diagram is also recovered qualitatively by applying mean-field and pair-approximations to the exact hierarchical form of the master equation for these models.     

Late-stage coarsening of adlayers by dynamic cluster coalescence

We consider the late stages of adlayer coarsening when this process is dominated by cluster diffusion and coalescence. The growth rate of the average cluster size can be directly related to the cluster diffusion coefficient of individual clusters. The distribution of cluster sizes and the spatial correlations between clusters are examined as a function of coverage and cluster diffusion rate using Monte Carlo simulations. We also show how the Smoluchowski equation can give an approximate closed-form solution for the cluster size distribution during coarsening by coalescence. The coarsening of adlayers by cluster coalescence in a model that includes local inter-cluster interactions is also examined.     

Influence of the magnetic state on the chemical order-disorder transition temperature in Fe-Ni permalloy

In magnetic alloys, the effect of finite temperature magnetic excitations on phase stability below the Curie temperature is poorly investigated, although many systems undergo phase transitions in this temperature range. We consider random Ni-rich Fe-Ni alloys, which undergo chemical order-disorder transition approximately 100 K below their Curie temperature, to demonstrate from ab initio calculations that deviations of the global magnetic state from ideal ferromagnetic order due to temperature induced magnetization reduction have a crucial effect on the chemical transition temperature. We propose a scheme where the magnetic state is described by partially disordered local magnetic moments, which in combination with Heisenberg Monte Carlo simulations of the magnetization allows us to reproduce the transition temperature in good agreement with experimental data.     

蒙特卡罗模拟主方程的一般技巧

本文描述了主方程的蒙特卡罗模拟的一般技巧,考虑了在一般跃迁率情况下主方程差分解的蒙特卡罗模拟,建立了与主方程初值问题等价的具有瞬时源的积分方程,从而提供了直接模拟主方程的更一般的技巧。     

Superfluid-insulator transition in commensurate disordered bosonic systems: large-scale worm algorithm simulations

We report results of large-scale Monte Carlo simulations of superfluid-insulator transitions in disordered commensurate 2D bosonic systems. In the off-diagonal disorder case, we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is z=1.5(2). In the diagonal-disorder case, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in crossover to the generic universality class (apparently with z=2). However, even at strong disorder, the universal behavior sets in only at very large space-time distances. This explains why previous studies of smaller clusters mimicked a direct superfluid-Mott-insulator transition.     

Proton Crystallization in a Dense Hydrogen Plasma

We perform a first‐principle analysis of Coulomb crystallization in neutral two‐component mass asymmetric plasmas by large‐scale path integral Monte Carlo simulations for a dense hydrogen plasma in a broad density range. We observe two large jumps in the relative distance fluctuations of protons that are connected with qualitative changes in the behavior of the proton pair distribution function and are attributed to the formation of a spatially ordered state. A third smaller jump inside the ordered phase indicates a structural transition (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Order-disorder transition in the solid phase of a charged hard sphere model

We investigate the solid phases of the restricted primitive model (RPM). Monte Carlo simulations show the existence of an order-disorder transition from a substitutionally disordered face centered cubic lattice (fcc) to a new ordered fcc structure which is proposed as the ground state of the RPM at the close packing density. Our results suggest that the new phase might turn out in a new triple point in the RPM phase diagram involving three solid phases: CsCl, fcc ordered and fcc disordered structures. The order-disorder transition is also studied using the cell theory. The theory shows good agreement with the simulation results and suggests that the transition is weakly first order.     

金属团簇在单晶表面的稳定性和扩散行为的Monte Carlo研究

采用MonteCarlo方法,研究了正二十面体结构的Cu、Ni、Pd和Pt等金属团簇在Pd(001)表面的稳定性和扩散行为.研究表明,载体对负载型金属团簇的稳定性和扩散性质有明显的影响.由于载体表面和金属团簇的振动偶合,金属团簇结构变化的温度要低于自由团簇的结构转化温度.负载型金属团簇的稳定性不仅取决于团簇内部原子之间的相互作用而且取决于团簇与载体之间的相互作用.对金属团簇扩散的研究表明,金属团簇的扩散常数与单金属原子的扩散常数相差不大,通过比较金属团簇的结构变化温度和扩散常数发现,团簇的稳定性和扩散行为有密切的联系.     

Collisional effects on the collective laser cooling . of trapped bosonic gases

We analyse the effects of atom–atom collisions on a collective laser cooling scheme. We derive a quantum master equation which describes the laser cooling in presence of atom–atom collisions in the weak-condensation regime. Using such equation, we perform Monte Carlo simulations of the population dynamics in one and three dimensions. We observe that the ground-state laser-induced condensation is maintained in the presence of collisions. Laser cooling causes a transition from a Bose–Einstein distribution describing collisionally induced equilibrium, to a distribution with an effective zero temperature. We analyse also the effects of atom–atom collisions on the cooling into an excited state of the trap. Received: 18 June 1999 / Revised version: 24 September 1999 / Published online: 10 November 1999     

The three-dimensional three-state Potts ferromagnet exposed to random fields: evidence for a second order transition

Using large scale Monte Carlo simulations, the ordering of the three-dimensional three state Potts ferromagnet exposed to random fields is investigated. Studies of the order parameter probability distribution and of various of its moments suggest that the order of the transition depends on the strength of the random field: i.e., the first order transition of the pure ferromagnetic model persists for weak random fields, but turns into a second order transition for a range of random fields of medium strength. For large random fields the transition seems to be first order again. In this range large domains of strongly aligned Potts spins occur already in the disordered phase and the associated slow relaxation hampers significantly the Monte Carlo study of thermodynamic equilibrium phenomena. These results are discussed in the light of current theoretical concepts. Possible applications to experiments on diluted anisotropic molecular crystals and orientational glasses are briefly mentioned.     

Phase transition to bundles of flexible supramolecular polymers

We report Monte Carlo simulations of the self-assembly of supramolecular polymers based on a model of patchy particles. We find a first-order phase transition, characterized by hysteresis and nucleation, toward a solid bundle of polymers, of length much greater than the average gas phase length. We argue that the bundling transition is the supramolecular equivalent of the sublimation transition, which results from a weak chain-chain interaction. We provide a qualitative equation of state that gives physical insight beyond the specific values of the parameters used in our simulations.     

The three-dimensional three-state Potts ferromagnet exposed to random fields: evidence for a second order transition

Using large scale Monte Carlo simulations, the ordering of the three-dimensional three state Potts ferromagnet exposed to random fields is investigated. Studies of the order parameter probability distribution and of various of its moments suggest that the order of the transition depends on the strength of the random field: i.e., the first order transition of the pure ferromagnetic model persists for weak random fields, but turns into a second order transition for a range of random fields of medium strength. For large random fields the transition seems to be first order again. In this range large domains of strongly aligned Potts spins occur already in the disordered phase and the associated slow relaxation hampers significantly the Monte Carlo study of thermodynamic equilibrium phenomena. These results are discussed in the light of current theoretical concepts. Possible applications to experiments on diluted anisotropic molecular crystals and orientational glasses are briefly mentioned.     

Phase diagram of the commensurate two-dimensional disordered Bose-Hubbard model

We establish the full ground state phase diagram of the disordered Bose-Hubbard model in two dimensions at a unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions persisting up to extremely large values of disorder and interaction strength which, however, have small superfluid fractions and thus low transition temperatures. In the vicinity of the superfluid-insulator transition of the pure system, we observe an unexpectedly weak--almost not resolvable--sensitivity of the critical interaction to the strength of (weak) disorder.     

Phase transition of compartmentalized surface models

Two types of surface models have been investigated by Monte Carlo simulations on triangulated spheres with compartmentalized domains. Both models are found to undergo a first-order collapsing transition and a first-order surface fluctuation transition. The first model is a fluid surface one. The vertices can freely diffuse only inside the compartments, and they are prohibited from the free diffusion over the surface due to the domain boundaries. The second is a skeleton model. The surface shape of the skeleton model is maintained only by the domain boundaries, which are linear chains with rigid junctions. Therefore, we can conclude that the first-order transitions occur independent of whether the shape of surface is mechanically maintained by the skeleton (=the domain boundary) or by the surface itself.     

A new equation of state for associating Lennard–Jones fluids with two sites: small bond angle

ABSTRACT

We developed a new equation of state for Lennard–Jones spheres with two short-ranged, directional association sites. The theory is novel in that association is dependent on bond angle between the two sites, and formation of self-assembled linear and cyclic clusters is predicted in the model. The competition between ring and chain formations at various densities and temperatures is predicted by the theory and verified by Monte Carlo simulations. It was found that closed-loop structures become important at low temperatures and densities. Also, at fixed association energy, intensifying the Lennard–Jones energy reduces the extent of association in the fluid. The theory and simulation are in excellent agreement.     

A study of non-linear autoregressive processes: Differential theory

Summary It is shown how the general analytical expression of an autoregression, whose stationary solution has an arbitrary given form, can be obtained. The central-limit theorem is used to state a correspondence between autoregression and relevant diffusion equation which not only permits to give analytical form to the stationary distribution of a given autoregression, but also to obtain appropriate series expansions of its fundamental solution and the exact relaxation constants. The interest of the analysis in the context of Monte Carlo simulations of relaxation and steady-state processes is discussed. The procedure is illustrated by two examples of interest in the field of ionized gases.     

A hybrid transport-diffusion Monte Carlo method for frequency-dependent radiative-transfer simulations

Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations in optically thick media. In DDMC, particles take discrete steps between spatial cells according to a discretized diffusion equation. Each discrete step replaces many smaller Monte Carlo steps, thus improving the efficiency of the simulation. In this paper, we present an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold, as optical thickness is typically a decreasing function of frequency. Above this threshold we employ standard Monte Carlo, which results in a hybrid transport-diffusion scheme. With a set of frequency-dependent test problems, we confirm the accuracy and increased efficiency of our new DDMC method.     

Dissipative dynamics for hard spheres

The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated binary scattering operators are defined as the generators for time evolution in phase space. The BBGKY hierarchy for reduced distribution functions is given, and an approximate kinetic equation is obtained that extends the revised Enskog theory to dissipative dynamics. A Monte Carlo simulation method to solve this equation is described, extending the Bird method to the dense, dissipative hard-sphere system. A practical kinetic model for theoretical analysis of this equation also is proposed. As an illustration of these results, the kinetic theory and the Monte Carlo simulations are applied to the homogeneous cooling state of rapid granular flow.