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.     

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.     

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 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 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.     

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.     

Benchmark calculations for Monte Carlo simulations of electrontransport

Benchmark calculations have been performed for electron transport coefficients with an aim to produce a body of data required to verify the codes used in plasma modeling. The present code for the time resolved Monte Carlo simulation (MCS) was shown to represent properly DC transport coefficients in a purely electric field, in crossed electric and magnetic fields, and in the presence of nonconservative collisions, ionization, and attachment. In addition, we have suggested tests of the time dependent solutions. Relaxation of the initial transport coefficient may serve as an accurate test of the code as well as the input data for some fluid codes. In this paper, we show only one example, but several different sets of conditions and cross sections should be used as well. Finally, we propose application of the quasi-steady state results in RF fields. As an example we suggest calculation of the components of diffusion tensor showing anomalous longitudinal diffusion and calculations made with nonconservative collisions (ionization in this case). We also check the application of approximate formulas to determine drift velocity on the basis of total collision frequency and to determine a diffusion coefficient by using the Einstein relation. Other tests required to verify the transport data calculations are discussed as well     

Monte Carlo simulations of CO2-expanded acetonitrile

The structure and phase-equilibrium properties of CO₂-expanded acetonitrile (MeCN) were examined using Gibbs Ensemble Monte Carlo simulations. The results showed that the mole fraction of the CO₂ in the binary system increased linearly with pressure and the predicted volume expansion of the liquid phase with pressure is nonlinear and in agreement with experiment. The site–site radial distribution functions (RDFs) were determined for this binary mixture, which show that the homomolecular CO₂–CO₂ and heteromolecular CO₂–MeCN do not exhibit a significant dependence on CO₂ mole fraction. The only major structural change that is seen to occur as the CO₂ mole fraction is increased in the mixture is a decrease in the fraction of nearest neighbour MeCN molecules with parallel dipole orientations.     

Parallel cluster labeling for large-scale Monte Carlo simulations

We present an optimized version of a cluster labeling algorithm previously introduced by the authors. This algorithm is well suited for large-scale Monte Carlo simulations of spin models using cluster dynamics on parallel computers with large numbers of processors. The algorithm divides physical space into rectangular cells which are assigned to processors and combines a serial local labeling procedure with a relaxation process across nearest-neighbor processors. By controlling overhead and reducing inter-processor communication this method attains good computational speed-up and efficiency. Large systems of up to 65536² spins have been simulated at updating speeds of 11 nanosecs/site (90.7 × 10⁶ spin updates/sec) using state-of-the-art supercomputers. In the second part of the article we use the cluster algorithm to study the relaxation of magnetization and energy on large Ising models using Swendsen-Wang dynamics. We found evidence that exponential and power law factors are present in the relaxation process as has been proposed by Hackl et al. The variation of the power-law exponent λ_M taken at face value indicates that the value of Z_M falls in the interval 0.31–0.49 for the time interval analysed and appears to vanish asymptotically.     

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.     

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.     

Variational quantum Monte Carlo simulations with tensor-network states

We show that the formalism of tensor-network states, such as the matrix-product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D x D matrices with D up to 48. The computational cost of our scheme formally scales as ND3, whereas standard MPS approaches and the related density matrix renormalization group method scale as ND5 and ND6, respectively, for periodic systems.