Brownian motion of 2D vacancy islands by adatom terrace diffusion.

We have studied the Brownian motion of two-dimensional (2D) vacancy islands on Ag(110) at temperatures between 175 and 215 K. While the detachment of adatoms from the island and their diffusion on the terrace are permitted in this temperature range, the periphery diffusion of single adatoms is prohibited. The present scanning tunneling microscopy results provide the first direct experimental proof that the Brownian motion of the islands follows a simple scaling law with terrace diffusion being the rate limiting process. The activation energy of the vacancy island motion is determined to 0.41 eV.     

Path-integral Monte Carlo simulations of electron localization in water clusters

Path-integral Monte Carlo simulations are used to investigate the possibility of binding of an excess electron to water clusters. Model potentials are used to characterize the interaction between the excess electron and a water monomer and between two water molecules. The simulations reveal that two water molecules can bind an electron. In addition, it is found that the excess electron can be trapped in the field of three water molecules arranged in a linear configuration. The results are used to comment on recent molecular beam experiments.     

Dielectric properties and compensation behaviors of a monolayer naphthalene-like nanoisland: Monte Carlo simulations

In this paper, we propose a model to study the thermal and dielectric properties of a monolayer naphthalene-like nanoisland. The ferrielectric mixed spin (1, 7/2) Blume-Capel Ising model has been studied, using Monte Carlo simulations under the Metropolis algorithm. The ground state phase diagrams, in the absence of temperature, are investigated. Moreover, we illustrated the thermal and dielectric properties as a function of temperature, for fixed values of the other parameters. On the other hand, we examine the effects of the exchange coupling interactions on the compensation and blocking temperatures. In addition, we explore the effects of crystal and external longitudinal electric fields on total polarizations.     

Monte Carlo simulations on a rigid-rod model for a langmuir monolayer

A monolayer of amphiphilic molecules on water surface (Langmuir monolayer) at the so-called “solid” phase is studied using Monte Carlo simulations. Each molecule is considered to be a rigid rod, one end (the hydrophilic “head”) of which is assumed to be fixed on a two-dimensional lattice, while the other end (the hydrophobic “tail”) interacts with its nearest and next-nearest neighbours through the Lennard-Jones potential. With increase in temperature, the system undergoes a first-order transition from a low-tilt to a high-tilt phase. With increase in tail-length, the two-phase coexistence region decreases and the transition becomes sharper.     

T2 relaxation induced by clusters of superparamagnetic nanoparticles: Monte Carlo simulations

Clustering strongly affects the transverse (T2) relaxation induced by superparamagnetic nanoparticles in magnetic resonance experiments. In this study, we used Monte Carlo simulations to investigate systematically the relationship between T2 values and the geometric parameters of nanoparticle clusters. We computed relaxation as a function of particle size, number of particles per cluster, interparticle distance, and cluster shape (compact vs. linear). We found that compact clusters induced relaxation equivalent to similarly sized single particles. For small particles, the shape and density of clusters had a significant effect on T2. In contrast, for larger particles, T2 relaxation was relatively independent of cluster geometry until interparticle distances within a cluster exceeded ten times the particle diameter. Results from our simulations suggest principles for the design of nanoparticle aggregation-based sensors for MRI.     

Time evolution of adatom and vacancy clusters on Ag(110)

The time evolution of adatom and vacancy islands on an Ag(110) surface is studied by using a variable-temperature ultrahigh vacuum scanning tunneling microscope. The islands are created by Ar⁺ ion sputtering at low temperatures and at very low fluxes (0.004 ML s⁻¹). The area of both kinds of island decreases linearly as a function of time, at least for small islands. The experimental results are compared with kinetic Monte Carlo simulations.     

Brownian motion of spins; generalized spin Langevin equation

We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concommitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature.     

Influence of the Brownian step size in off-lattice Monte Carlo simulations of irreversible particle aggregation

The influence of the Brownian step size in off-lattice Monte Carlo simulations of the aggregation and gelation of spheres is studied. It is found that the kinetics are strongly influenced if the step size is larger than the mean smallest distance between the sphere surfaces. The structure of the clusters and the gels is influenced, but only over length scales smaller than the step size. Using large step sizes leads to a narrower size distribution of the clusters. Implications of the present results are discussed for simulations reported in the literature in which the Brownian step size was chosen equal to the sphere diameter.     

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.     

Mapping the Monte Carlo scheme to Langevin dynamics: a Fokker-Planck approach

We propose a general method of using the Fokker-Planck equation (FPE) to link the Monte Carlo (MC) and the Langevin micromagnetic schemes. We derive the drift and diffusion FPE terms corresponding to the MC method and show that it is analytically equivalent to the stochastic Landau-Lifshitz-Gilbert (LLG) equation of Langevin-based micromagnetics. Subsequent results such as the time-quantification factor for the Metropolis MC method can be rigorously derived from this mapping equivalence. The validity of the mapping is shown by the close numerical convergence between the MC method and the LLG equation for the case of a single magnetic particle as well as interacting arrays of particles. We also find that our Metropolis MC method is accurate for a large range of damping factors alpha, unlike previous time-quantified MC methods which break down at low alpha, where precessional motion dominates.     

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 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.     

Nano-graphene monolayer with higher-order exchange couplings: Monte Carlo study

We have used the Monte Carlo simulation to study the phase diagrams and the magnetic properties of a single nano-graphene layer with next-nearest neighbors coupling $J_2$ and four-spin interaction $J_4$. Interesting behaviors have been found. In particular, the nanographene can present tricritical and triple points for appropriate system parameters.     

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