Photon transport in thin disordered slabs

We examine using Monte Carlo simulations, photon transport in optically ‘thin’ slabs whose thickness L is only a few times the transport mean free path l*, with particles of different scattering anisotropies. The confined geometry causes an auto-selection of only photons with looping paths to remain within the slab. The results of the Monte Carlo simulations are borne out by our analytical treatment that incorporates directional persistence by the use of the Ornstein-Uhlenbeck process, which interpolates between the short time ballistic and long time diffusive regimes.     

Condensation in the Zero Range Process: Stationary and Dynamical Properties

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.     

Study of inclusive baryon-antibaryon pair production of p or Λ in two-photon processes

Inclusive baryon-antibaryon pair production was studied in two-photon events which were collected at the e ⁺ e ^? collider TRISTAN, and correspond to an integrated luminosity of 303 pb^t?1. Correlations between a baryon and an antibaryon were studied for their flavors (p or Λ) and their momentum vectors. The experimental results were compared with the expectations from a jet-fragmentation Monte Carlo simulation. We have found that although the ratios of the cross sections of different baryon-flavor combinations are consistent with the Monte Carlo expectations, the cross section shows an excess over the Monte Carlo expectation in a low invariant-mass region of final-state particles at large angles, that indicates a significant contribution from higher-order QCD or non-perturbative effects. The experimental data show no narrow azimuthal-angle correlation, which is expected from a jet-fragmentation Monte Carlo. A search for exclusive Λ pair production has also been made. We have no candidates and have obtained the upper limit for the cross section.     

Phase coexistence and critical point determination in polydisperse fluids

Phase equilibria of fluids with variable size polydispersity have been investigated by means of Monte Carlo simulations. In the models, spherical particles of different additive diameters interact through Lennard-Jones and hard sphere Yukawa intermolecular potentials and the underlying distribution of particle sizes is a Gaussian. The Gibbs ensemble Monte Carlo technique has been applied to determine the phase coexistence far below the critical temperature. Critical points have been estimated by finite-size scaling analysis using histogram reweighting for NpT simulation data. In order to achieve efficient sampling in the vicinity of the critical points, the hyper-parallel tempering scheme has been utilized.     

Schloegl’s Second Model for Autocatalysis on a Cubic Lattice: Mean-Field-Type Discrete Reaction-Diffusion Equation Analysis

Schloegl’s second model for autocatalysis on a hypercubic lattice of dimension d≥2 involves: (i) spontaneous annihilation of particles at lattice sites with rate p; and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of diagonal pairs of particles on neighboring sites. Kinetic Monte Carlo simulations for a d=3 cubic lattice reveal a discontinuous transition from a populated state to a vacuum state as p increases above p=p _e . However, stationary points, p=p _eq (≤p _e ), for planar interfaces separating these states depend on interface orientation. Our focus is on analysis of interface dynamics via discrete reaction-diffusion equations (dRDE’s) obtained from mean-field type approximations to the exact master equations for spatially inhomogeneous states. These dRDE can display propagation failure absent due to fluctuations in the stochastic model. However, accounting for this anomaly, dRDE analysis elucidates exact behavior with quantitative accuracy for higher-level approximations.     

Phase equilibra in binary Lennard-Jones mixtures: phase diagram simulation

A three-box version of the Gibbs ensemble Monte Carlo method was used to determine the phase diagram type of several binary mixtures of one-centre Lennard-Jones particles. The method can be used to establish a direct link between the intermolecular potential modelling the interactions in a given system and its fluid phase diagram, without the knowledge of the corresponding equation of state governing its ρVT behaviour. As an example of the application of the method, closed-loop behaviour in an isotropic system could be found using a set of Lennard-Jones parameters exhibiting a cross-interaction diameter with a negative deviation from the Lorentz—Berthelot combination rule.     

Simulation of sextet diquark production

We present a method for simulating the production and decay of particles in the sextet representation of SU(3) _C including the simulation of QCD radiation. Results from the Monte Carlo simulation of sextet diquark production at the LHC including both resonant and pair production are presented. We include limits on resonant diquark production from recent ATLAS results and perform the first simulation studies of the less model dependent pair production mechanism.     

Mesoscopic Two‐Dimensional Electron Crystals in Single and Double Layers

We present results of Monte‐Carlo simulations for finite 2D single and bilayer systems. Strong Coulomb correlations lead to arrangement of particles in configurations resembling a crystal lattice. For binary layers there exists a particularly rich variety of lattice symmetries which depend on the interlayer separation d. We demonstrate that in these mesoscopic lattices there exist two fundamental types of ordering: radial and orientational. The dependence of the melting temperature on d is analyzed and a stabilization of the crystal compared to a single layer is found.     

Critical exponents for two-dimensional tracer diffusion through a changing background at concentrationc=c p

We study the diffusion of a particle on the sites of a triangular lattice of which half the sites are occupied by a background of other particles. No two particles may occupy the same site. We carry out Monte Carlo simulations for the following model: At each Monte Carlo step the tracer attempts to move to a neighboring site, which it does if the site is unoccupied. At each step, each background particle attempts to desorb with probability. If a background particle desorbs, it is replaced at a randomly chosen site on the lattice. We define R _tr ² (t)/t=D _tr. For the case=0, we calculateD ₀t ^k and findk=0.71±0.01, wheret is the number of Monte Carlo steps. When0, we calculateD _tr ~ ^– w ₁ and findw _ad=0.24±0.02. We compare this to the model in which the background particles are constrained to move to nearest neighbor sites and findD _tr ^– w ₁ withw ₁=0.28±0.03.     

A first-principles study aided with Monte Carlo simulations of carbon doped iron-manganese alloys

We have investigated the complex magnetic properties of Fe_1?x Mn _x C _y alloys by using an iterative combination of ab initio calculations and Monte Carlo simulations. The latter gives insight into finite temperature magnetism and allows to determine the critical temperature of magnetic phase transitions. We restrict the investigation to ordered systems with 25, 50 and 75% manganese and study the influence of carbon at octahedral interstitial sites on the magnetic properties. The combination of ab initio calculations with Monte Carlo simulations turns out to be a powerful tool to determine the complex magnetic structures, which originate from the competition of ferro- and antiferromagnetic interactions in the FeMn alloys.     

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     

N-body study of anisotropic membrane inclusions: Membrane mediated interactions and ordered aggregation

We study the collective behavior of inclusions inducing local anisotropic curvatures in a flexible fluid membrane. The N-body interaction energy for general anisotropic inclusions is calculated explicitly, including multi-body interactions. Long-range attractive interactions between inclusions are found to be sufficiently strong to induce aggregation. Monte Carlo simulations show a transition from compact clusters to aggregation on lines or circles. These results might be relevant to proteins in biological membranes or colloidal particles bound to surfactant membranes. Received 30 July 1999 and Received in final form 8 September 1999     

A new Monte Carlo power method for the eigenvalue problem of transfer matrices

We propose a new Monte Carlo method for calculating eigenvalues of transfer matrices leading to free energies and to correlation lengths of classical and quantum many-body systems. Generally, this method can be applied to the calculation of the maximum eigenvalue of a nonnegative matrix  such that all the matrix elements of Â^k are strictly positive for an integerk. This method is based on a new representation of the maximum eigenvalue of the matrix  as the thermal average of a certain observable of a many-body system. Therefore one can easily calculate the maximum eigenvalue of a transfer matrix leading to the free energy in the standard Monte Carlo simulations, such as the Metropolis algorithm. As test cases, we calculate the free energies of the square-lattice Ising model and of the spin-1/2XY Heisenberg chain. We also prove two useful theorems on the ergodicity in quantum Monte Carlo algorithms, or more generally, on the ergodicity of Monte Carlo algorithms using our new representation of the maximum eigenvalue of the matrixÂ.     

Successive defects asymmetric simple exclusion processes with particles of arbitrary size

This paper uses various mean-field approaches and the Monte Carlo simulation to calculate asymmetric simple exclusion processes with particles of arbitrary size in the successive defects system. In this system, the hopping probability p (p<1) and the size d of particles are not constant. Through theoretical calculation and computer simulation, it obtains the exact theoretical results and finds that the theoretical results are in agreement with the computer simulation. These results are helpful in analysing the effect of traffic with different hopping probabilities p and sizes d of particle.     

Computation of partial molar properties using continuous fractional component Monte Carlo

ABSTRACT

An alternative method for calculating partial molar excess enthalpies and partial molar volumes of components in Monte Carlo (MC) simulations is developed. This method combines the original idea of Frenkel, Ciccotti, and co-workers with the recent continuous fractional component Monte Carlo (CFCMC) technique. The method is tested for a system of Lennard–Jones particles at different densities. As an example of a realistic system, partial molar properties of a [NH₃, N₂, H₂] mixture at chemical equilibrium are computed at different pressures ranging from P = 10 to 80 MPa. Results obtained from MC simulations are compared to those obtained from the PC-SAFT Equation of State (EoS) and the Peng–Robinson EoS. Excellent agreement is found between the results obtained from MC simulations and PC-SAFT EoS, and significant differences were found for PR EoS modelling. We find that the reaction is much more exothermic at higher pressures.     

Saddle-point energies and Monte Carlo simulation of the long-range order relaxation in CoPt

We present atomic-scale computer simulations in equiatomic L1₀-CoPt where Molecular Dynamics and Monte Carlo techniques have both been applied to study the vacancy-atom exchange and kinetics relaxation. The atomic potential is determined using a Tight-Binding formalism within the Second-Moment Approximation. It is used to evaluate the different saddle-point energies involved in a vacancy-atom exchange between nearest-neighbour sites. The potential and the saddle-point energies have been used to simulate the relaxation of the long-range order in CoPt using a Monte Carlo technique. A vacancy migration energy of 0.73±0.15 eV and an order-disorder transition temperature of 935 K have been found.     

Monte Carlo evaluation of trial wavefunctions for the fractional quantized Hall effect: Spherical geometry

Monte Carlo methods have been employed to evaluate trial wave-functions for quantized Hall states and excitations using up to 92 electrons on a sphere. Results are presented for the energy of quasiparticle and quasihole excitations at filling factorv=1/3. These are consistent with extrapolations of exact small system calculations and earlier Monte Carlo results. A trial wavefunction for neutral excitations atv=1/m (m odd integer) is proposed. Results for its excitation energy in the long wavelength limit, atv=1/3, are consistent with those based on the single mode approximation. We have also studied a trial wavefunction representing a quasiparticle excitation involving an electron with reversed spin. Results are presented for the effects on excitation energies of the finite extent of the electron wave function perpendicular to the surface. We have also evaluated the energy of a microscopic trial wave-function for the ground state atv=2/5.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Evaluation of the SSC/LHNC,SSCF and PY approximations for short ranged,anisotropic potentials

Three approximations for the orientational correlation function of molecular fluids—the single super chain/linearized hypernetted chain (SSC/LHNC), single super chain f-expansion (SSCF) and Percus-Yevick (PY) approximation—are evaluated in the dense liquid state for a fluid inter-acting with short ranged anisotropic interactions. These interactions are prototypical of the forces that determine the non-spherical shape of symmetric linear molecules. We find that SSC/LHNC is very poor, failing to predict many of the structural features present in the Monte Carlo (MC) simulation results. The PY and SSCF approximations produce much better results; however, neither approximation is completely satisfactory.     

Simulation on the response of new phosphate glass RPC for <Emphasis Type="Italic">γ</Emphasis>-rays and e<Superscript>+</Superscript>/e<Superscript>−</Superscript> particles using GEANT3

The influence of phosphate glass electrode in the configuration of resistive plate chamber has been studied using GEANT3.21 Monte Carlo code. Bakelite electrodes were replaced by phosphate glass electrodes, as these glass materials have low bulk resistivity, are portable and easy to handle. These types of RPCs in their compact form of all materials are suitable for high rate background environment. We find that these new types of RPCs give little higher response to γ-rays and e⁺/e⁻ particles, both for single-and double gap RPCs. The results of simulation are discussed.      

Monte Carlo methods for yrast spectroscopy

We discuss the details of the recently proposed Monte Carlo method to evaluate the exact energies of yrast levels. Energy levels are evaluated up to J = 18 with small statistical errors using the Metropolis method for the case of ¹⁶⁶Er using the pairing plus quadrupole model within one major shell. We also discuss the evaluation of the probabilities of the Hartree-Fock-Bogoliubov wave functions in the corresponding yrast eigenstates and they are found to be large. The model displays a too strong backbending behaviour not seen experimentally.Received: 29 September 2003, Published online: 24 August 2004PACS: 21.60.-n Nuclear-structure models and methods - 02.70.Ss Quantum Monte Carlo methods - 21.60.Ka Monte Carlo models - 21.10.Re Collective levels