Search results for "ENSEMBLE"
showing 10 items of 162 documents
The growth of charged platelets.
2014
Growth models of charged nanoplatelets are investigated with Monte Carlo simulations and simple theory. In a first model, 2-dimensional simulations in the canonical ensemble are used to demonstrate that the growth of a single weakly charged platelet could be limited by its own internal repulsion. The short range attractive interaction in the crystal is modeled with a square well potential while the electrostatic interactions are described with a screened Coulomb potential. The qualitative behavior of this case can also be described by simply balancing the attractive crystal energy with the screened Coulomb repulsion between the crystal sites. This repulsion is a free energy term dominated b…
Monte Carlo Simulations of a Clay Inspired Model Suspension: The Role of Rim Charge
2012
International audience; We present a theoretical investigation of a model clay dispersion in 1-1 salt solutions by varying the particle volume fraction and ionic strength as well as the charge distribution on the clay platelets. The platelets are modeled as discs with charged sites distributed on a hexagonal lattice. The edge sites can be positively charged while the remaining sites are negative giving rise to a strong charge anisotropy. Simulations are carried out using a Monte Carlo method in the canonical ensemble. The interactions between the platelet sites are described with a screened Coulomb potential plus a short range repulsive potential. Simulations show a complex phase behavior. …
Canonical versus microcanonical analysis of first-order phase transitions
1998
Abstract I discuss the relation between canonical and microcanonical analyses of first-order phase transitions. In particular it is shown that the microcanonical Maxwell construction is equivalent to the equal-peak-height criterion often employed in canonical simulations. As a consequence the microcanonical finite-size estimators for the transition point, latent heat and interface tension are identical to standard estimators in the canonical ensemble. Special emphasis is placed on various ways for estimating interface tensions. The theoretical considerations are illustrated with numerical data for the two-dimensional 10-state Potts model.
Quantum Effects and Phase Transitions in Adsorbed Molecular Layers
1998
Phase transitions in adsorbed (two dimensional) fluids and in adsorbed layers of molecules are studied with a combination of path integral Monte Carlo (PIMC), Gibbs ensemble Monte Carlo (GEMC) and finite size scaling techniques. Entropy driven phase transitions in systems with purely repulsive interactions are analyzed as well phase diagrams of fluids with internal quantum states. Adsorbed layers of H 2 molecules at a full monolayer coverage in the \(\sqrt 3 \times \sqrt 3 \) structure have a higher transition temperature to the disordered phase compared to the system with the heavier D 2 molecules, this effect is analyzed by PIMC. Linear N 2 molecules adsorbed on graphite show a transition…
Monte Carlo Simulation of Alloy Phase Diagrams and Short-Range Order
1986
As a prototype model for order-disorder phenomena in binary alloys, a face-centered cubic lattice is considered,the sites of which can be taken by either A-atoms or B-atoms, assuming pair-wise interactions between nearest (J) and next nearest neighbours (J). The phase diagram is constructed from Monte Carlo calculations. Some technical aspects essential for the success of such calculations are briefly mentioned (use of grand-canonical rather than canonical ensemble, how to obtain the free energy needed to locate first-order phase transitions, etc.). It is shown that the topology of the phase diagram changes when the ratio R = Jnnn/Jnn is varied, and this behaviour is discussed in the contex…
Counting statistics for electron capture in a dynamic quantum dot
2012
We report non-invasive single-charge detection of the full probability distribution $P_n$ of the initialization of a quantum dot with $n$ electrons for rapid decoupling from an electron reservoir. We analyze the data in the context of a model for sequential tunneling pinch-off, which has generic solutions corresponding to two opposing mechanisms. One limit considers sequential "freeze out" of an adiabatically evolving grand canonical distribution, the other one is an athermal limit equivalent to the solution of a generalized decay cascade model. We identify the athermal capturing mechanism in our sample, testifying to the high precision of our combined theoretical and experimental methods. …
Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis
1993
The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionPL(ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities . Particular attention is paid to the qu…
Replica-exchange molecular dynamics simulation for supercooled liquids
2000
We investigate to what extend the replica-exchange Monte Carlo method is able to equilibrate a simple liquid in its supercooled state. We find that this method does indeed allow to generate accurately the canonical distribution function even at low temperatures and that its efficiency is about 10-100 times higher than the usual canonical molecular dynamics simulation.
CLASSIFICATION THEORY FOR PHASE TRANSITIONS
1993
A refined classification theory for phase transitions in thermodynamics and statistical mechanics in terms of their orders is introduced and analyzed. The refined thermodynamic classification is based on two independent generalizations of Ehrenfests traditional classification scheme. The statistical mechanical classification theory is based on generalized limit theorems for sums of random variables from probability theory and the newly defined block ensemble limit. The block ensemble limit combines thermodynamic and scaling limits and is similar to the finite size scaling limit. The statistical classification scheme allows for the first time a derivation of finite size scaling without reno…
Temperature concepts for small, isolated systems: 1/t decay and radiative cooling
2003
We report on progress in our investigations of cluster cooling. The analysis of measurements is based on introduction of the microcanonical temperature and a statistical description of the decay of an ensemble with a broad distribution in temperature. The resulting time dependence of the decay rate is a power law close to t �1 , replaced by nearly exponential decay after a characteristic time for quenching by radiative cooling. We focus on results obtained for fullerenes, both anions and cations and recently also neutral C60.