Search results for "Canonical ensemble"
showing 10 items of 58 documents
Critical end point behaviour in a binary fluid mixture
1997
We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particula…
A note on the uniqueness result for the inverse Henderson problem
2019
The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974, Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here, we provide a rigorous proof of a slightly more …
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.