Cavity-bias sampling in reaction ensemble Monte Carlo simulations

A methodology is presented to sample efficiently configurations of reacting mixtures in the reaction ensemble Monte Carlo simulation technique. A cavity-biasing scheme is used, which more effectively samples configurations than conventional random sampling. Akin to other biasing schemes that are implemented into insertion-based Monte Carlo methods such as Gibbs ensemble Monte Carlo, the method presented here searches for space in the reacting mixture whereby the insertion of a product molecule is energetically favoured. This sampling bias is then corrected in the acceptance criteria. The approach allows for the study of reacting mixtures at high density as well as for polyatomic molecular species. For some cases, the method is shown to increase the efficiency of the reaction steps by a factor greater than 20. The approach is shown to be readily generalized to other biasing schemes such as orientational-biasing of polar molecules and configurational-biasing of chain-like molecules.     

Quantative measure of efficiency of Monte Carlo simulations

An easily applied, physically motivated algorithm for determining the efficiency of Monte Carlo simulations is introduced. The theoretical basis for the algorithm is developed. As an illustration we apply the method to the Lennard-Jones liquid near the triple point. We show that an acceptance ratio of 0.2 is twice as efficient for the purpose of generating a satisfactory sample as is an acceptance ratio of 0.5. There is a strong correlation between the efficiency measure and the diffusion rate of liquid particles during the simulation. We argue that the optimal value of the acceptance ratio is calculable from short Monte Carlo simulations. The method is very general and is applicable to Monte Carlo simulations involving arbitrary potentials.     

Monte Carlo molecular dynamics simulations for two-dimensional magnets

A combined Monte Carlo molecular dynamics simulation technique is used to study thedynamic structure factor on a square lattice for isotropic Heisenberg and planar classical ferromagnetic spin Hamiltonians.     

Monte Carlo simulations including energy from an entropic force

Several experimental techniques have shown that the primary response of many materials comes from a heterogeneous distribution of independently relaxing nanoscale regions; but most Monte Carlo simulations have homogeneous correlations. Resolving this discrepancy may require including the energy needed to change the configurational entropy, which is often used in theoretical treatments of thermal fluctuations, but not in computer simulations. Here the local configurational entropy is shown to give a nonlinear correction to the Metropolis algorithm that restores conservation of energy, maintains maximum entropy, and yields heterogeneous correlations. The nonlinear correction also improves agreement between Monte Carlo simulations of the Ising model and measurements of specific heat and structural correlations from the Jahn–Teller distortion in LaMnO₃.     

Monte Carlo simulations of the Lewis effect

Recent experiments measuring the thick-target yield curve of narrow resonances in (p, γ) reactions on²³Na,²⁶Mg and²⁷Al nuclei clearly show the Lewis effect. We have studied this effect theoretically on the basis of a Monte Carlo simulation of the nuclear and electronic energy loss curve in the target. We are able to reproduce the experimental data qualitatively. We discuss possible implications of precision measurements of the Lewis effect.     

Monte Carlo simulations of sexual reproduction

Modifying the Redfield model of sexual reproduction and the Penna model of biological aging, we compare reproduction with and without recombination in age-structured populations. In constrast to Redfield and in agreement with Bernardes we find sexual reproduction to be preferred to asexual one. In particular, the presence of old but still reproducing males helps the survival of younger females beyond their reproductive age.     

Comparison of molecular dynamics and Monte Carlo computer simulations of spinodal decomposition

The main results of recent computer simulations of spinodal decomposition in various systems are summarized and compared. Both Monte Carlo simulations of the kinetic Ising system and molecular dynamics simulations of phase separation in Lennard-Jones systems yield power law growth for the coarsening of the decomposition pattern and scaling of the spinodal peak of the structure factor. These similarities and also distinct differences of the dynamics of one-and two-component systems and of the different simulation techniques are discussed.     

Monte Carlo simulations of parapatric speciation

Parapatric speciation is studied using an individual-based model with sexual reproduction. We combine the theory of mutation accumulation for biological ageing with an environmental selection pressure that varies according to the individuals geographical positions and phenotypic traits. Fluctuations and genetic diversity of large populations are crucial ingredients to model the features of evolutionary branching and are intrinsic properties of the model. Its implementation on a spatial lattice gives interesting insights into the population dynamics of speciation on a geographical landscape and the disruptive selection that leads to the divergence of phenotypes. Our results suggest that assortative mating is not an obligatory ingredient to obtain speciation in large populations at low gene flow.     

Monte Carlo simulations of nitrogen using an ab initio potential

A new ab initio pair potential for nitrogen has been calculated at CCSD(T) level with aug-cc-pVDZ and -pVTZ correlation consistent basis sets. The results were extrapolated to approximate the basis set limit. This potential was used within Gibbs ensemble Monte Carlo (GEMC) simulations to obtain the densities of the coexisting phases, the vapour pressure and the enthalpy of vaporization from 70 K to close to the critical point. The influence of several 3-body interactions (an approximate anisotropic triple dipole potential derived by Stogryn, the isotropic triple dipole potential by Axilrod and Teller (AT), and a 3-body induction potential on the above mentioned properties was investigated. Satisfactory agreement with experimental data was observed. To determine whether the remaining deviations between experimental and computed data are due to inaccuracies in the 2-body or 3-body potential, the 2-body potential was rescaled to reproduce experimental 2nd virial coefficients accurately, and some of the calculations were repeated with the new potential. It turns out that an accurate 2-body potential only in connection with the AT potential yields accurate results for the thermodynamic properties phase equilibria.     

Comparing the efficiency of Metropolis Monte Carlo and molecular-dynamics methods for configuration space sampling

Summary Computer methods for sampling statistical ensembles generate chains of configurations in which subsequent members differ only slightly. Statistical errors are determined by the number of independent configurations contained in the sample. A quantitative treatment of the persistence of correlation shows how the first two moments of the autocorrelation function of a variablef along the chain are connected with the expected variance of its mean. The variance of the potential energy in the canonical ensemble is shown be to larger than that in the microcanonical one by a factor which is the ratio of the system heat capacity to that of an ideal gas. A comparison has been made of the efficiency of Metropolis Monte Carlo (MC), the usual microcanonical molecular dynamic (MDM) and a modification of molecular dynamics for canonical ensemble sampling (MDC). The analysis is focused on three aspects: the mean square displacement of a representative point in configuration space, the persistence of correlation in the potential energyV and also in a function of interest in free-energy-difference calculations. In MDM simulations of crystalline solids, it was found thatV behaves as an ?oscillatory? variable and that the variance of its mean is reduced by antithetic variations of its values. Work performed under the auspices of the United State Department of Energy, Istituto per la Ricerca Scientifica e Tecnologica, Trento, and Gruppo Nazionale di Struttura della Materia del C.N.R., Italy.     

Supercooled superfluids in Monte Carlo simulations

We perform path integral Monte Carlo simulations to study the imaginary time dynamics of metastable supercooled superfluid states and nearly superglassy states of a one component fluid of spinless bosons square wells. Our study shows that the identity of the particles and the exchange symmetry is crucial for the frustration necessary to obtain metastable states in the quantum regime. Whereas the simulation time has to be chosen to determine whether we are in a metastable state or not, the imaginary time dynamics tells us if we are or not close to an arrested glassy state.     

Monte Carlo simulations of an innovative molecular breast imaging system for the small breast cancer diagnosis using GATE

ABSTRACT

This paper draws attention to the study of performance of a new Molecular Breast Imaging (MBI) device, whose purpose is the early diagnosis of breast cancer, using Monte Carlo simulations. MBI provides functional and specific information that are more appropriated to dense breasts. Two asymmetric heads with different types of collimators, facing each other in anti-parallel viewing direction, characterize the system. Detectors and phantoms, together with the data taking procedure, are shortly reported. Monte Carlo simulations using the GATE (GEANT4 Application for Tomographic Emission) simulation toolkit have been implemented to evaluate the optimal detector configuration, in terms of sensitivity and spatial resolution, and also to reproduce the real experimental data. The device can be used both in spot compression and in Limited Angle Tomography (LAT); in the latter configuration one detector head with pinhole collimator is able to rotate around the breast in order to diagnose and localized the small tumors.     

Monte Carlo simulations of GaN cold cathodes

Ensemble Monte Carlo simulations of electron transport through a new aluminum gallium nitride/gallium nitride (AlGaN/GaN) cold cathode emitter are reported. We analyze the energy spectrum of carriers prior to being injected into a low work function slab of Lanthanum Hexaboride (LaB₆) as a function of the ramp energy of the carriers at the AlGaN/GaN heterojunction. Plasmon scattering is shown to be the major scattering mechanism in the structure leading to substantial shift towards the low kinetic energy end of the energy spectrum of the carriers injected into the low work function Lanthanum Hexaboride thin film. Intervalley scattering is found to dominate in the depletion layer at the GaN/LaB₆interface. Design improvements to increase the efficiency of the cold cathode are suggested.     

Monte Carlo simulations of regularized bosonic strings

The world sheet of the bosonic string is regularized by triangulation. The corresponding statistical theory of triangulated random surfaces is simulated by Monte Carlo methods and the critical exponent γ for the susceptibility determined. A careful analysis of the systematic and statistical errors reveals that we have to wait for the next generation of computers before a high-precision measurement of γ is possible.     

Monte Carlo simulations of star-branched polyelectrolyte micelles

The concentration profiles of monomers and counterions in star-branched polyelectrolyte micelles are calculated through Monte Carlo simulations, using the freely jointed chain model. We have investigated the onset of different regimes corresponding to the spherical and Manning condensation of counterions as a function of the strength of the Coulomb coupling. The Monte Carlo results are in fair agreement with the predictions of Self-Consistent-Field analytical models. We have simulated a real system of diblock copolymer micelles of (sodium-polystyrene-sulfonate)(NaPSS)-(polyethylene-propylene)(PEP) with f = 54 hydrophilic branches of N = 251 monomers at room temperature in salt-free solution. The calculated form factor compares nicely with our neutron scattering data. Received 18 July 2002 and Received in final form 11 October 2002 RID="a" ID="a"e-mail: roger@drecam.saclay.cea.fr     

Monte Carlo simulations for two-dimensional quantum systems

The Trotter-Suzuki transformation has been used to obtain the classical representation ford-dimensional lattice systems with boson and fermion degrees of freedom. A Monte Carlo algorithm for the equivalent (d+1)-dimensional classical system is presented. Numerical results are shown for the Heisenberg-spin-glass, the XY model and the spinless fermion lattice gas in two dimensions.