Monte Carlo simulations of the <Emphasis Type="Italic">μ</Emphasis>CF processes kinetics in deuterium gas

The kinetics of muon-catalyzed-fusion processes (μCF) in pure D₂ gas have been studied by means of Monte Carlo simulations for various target temperatures and densities. In particular, the role of resonant and non-resonant ddμ formation in μCF has been investigated. It has been shown that non-resonant formation can be directly observed at very short times in the neutron time spectra from μCF for low-density D₂ targets. The time spectra of neutrons from the low-temperature ortho-D₂ and para-D₂ gas targets have been calculated. These spectra display a strong ortho-para effect, which agrees with experimental results for the dilute-gas D₂ targets.     

On the spontaneous creation of chromomagnetic fields at high temperature

The spontaneous generation of the chromomagnetic field at high temperature is investigated in a lattice formulation of the SU(2) gluodynamics. The procedure of studying this phenomenon is developed. Monte Carlo simulations of the free energy on the lattices 2 × 8³, 2 × 16³, and 4 × 8³ at various temperatures are carried out. The creation of the field is indicated by means of the χ ² analysis of the data set accumulating (5–10) × 10⁶ Monte Carlo configurations. A comparison with the results of other approaches is done. The text was submitted by the authors in English.     

The Effect of the Number of Simulations on the Exponents Obtained by Finite-Size Scaling Relations of the Order Parameter and the Magnetic Susceptibility for the Four-Dimensional Ising Model on the Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4≤L≤8. The exponents in the finite-size scaling relations for the order parameter and the magnetic susceptibility at the finite-lattice critical temperature are computed to be β=0.49(7), β=0.49(5), β=0.50(1) and γ=1.04(4), γ=1.03(4), γ=1.02(4) for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are consistent with the renormalization group predictions of β=0.5 and γ=1. The values for the critical temperature of the infinite lattice T _c (∞)=6.6788(65), T _c (∞)=6.6798(69), T _c (∞)=6.6802(70) are obtained from the straight-line fit of the magnetic susceptibility maxima using 4≤L≤8 for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the obtained results are in very good agreement with the series expansion results of T _c (∞)=6.6817(15), T _c (∞)=6.6802(2), the dynamic Monte Carlo result of T _c (∞)=6.6803(1), the cluster Monte Carlo result of T _c (∞)=6.680(1) and the Monte Carlo using Metropolis and Wolff-cluster algorithm result of T _c (∞)=6.6802632±5×10⁻⁵.     

Neutron- and muon-induced background in underground physics experiments

Background induced by neutrons in deep underground laboratories is a critical issue for all experiments looking for rare events, such as dark matter interactions or neutrinoless ββ decay. Neutrons can be produced either by natural radioactivity, via spontaneous fission or (α, n) reactions, or by interactions initiated by high-energy cosmic rays. In all underground experiments, Monte Carlo simulations of neutron background play a crucial role for the evaluation of the total background rate and for the optimization of rejection strategies. The Monte Carlo methods that are commonly employed to evaluate neutron-induced background and to optimize the experimental setup, are reviewed and discussed. Focus is given to the issue of reliability of Monte Carlo background estimates. We dedicate this work to the memory of our friend and colleague Nicola Ferrari, who prematurely passed away in July 2006.     

Quantum statistical monte carlo methods and applications to spin systems

A short review is given concerning the quantum statistical Monte Carlo method based on the equivalence theorem⁽¹⁾ thatd-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems. The convergence property of this approximate tansformation is discussed in detail. Some applications of this geneal appoach to quantum spin systems are reviewed. A new Monte Carlo method, “thermo field Monte Carlo method,” is presented, which is an extension of the projection Monte Carlo method at zero temperature to that at finite temperatures. Invited talk presented at “Frontiers of Quantum Monte Carlo,” Los Alamos National Laboratory, September 3–6, 1985.     

Intervalley scattering in GaAs: ab initio calculation of the effective parameters for Monte Carlo simulations

Interactions between excited electrons and short-wavelength (intervalley) phonons in GaAs are studied using density functional theory for the conduction bands, and density functional perturbation theory for phonon frequencies and matrix elements of the electron–phonon interaction. We have calculated the deformation potentials (DPs) and the average intervalley scattering time 〈τ〉. The integration of the scattering probabilities over all possible final states in the Brillouin zone has been performed without any ad hoc assumption about the behavior of the electron–phonon matrix elements nor the topology of the conduction band. For transitions from the L point to Γ valley (within the first conduction band), we find 〈τ〉_L to be 1.5 ps at 300 K, in good agreement with time-resolved photoluminescence experiment. We discuss the difference between our calculated DPs, and effective parameters used in Monte Carlo simulations of optical and transport properties of semiconductors. The latter are based on Conwell’s model, in which electron–phonon interaction is described by one single constant and a parabolic model is used for conduction bands. We deduce the effective DP from our 〈τ〉, and compare it to our calculated DPs. We conclude that only effective DPs obtained from a full calculation of 〈τ〉 are relevant parameters for Monte Carlo simulations. PACS 71.10-w; 72.10.Di; 71.55.Eq     

Statistical mechanics of hydrogen bond networks

The static and dynamic properties of several hydrogen bond network models, based on thesquare ice model of Lieb [Phys. Rev.162, 162 (1967)] are studied. The two dimensionalsquare water (SW) model and the three-dimensioaalbrick water (BW) model were analyzed by means of Monte Carlo simulations. A simplified vesion of SW (simplified square water, SSW) can be solved exactly. All models yield similar thermodynamic results which can be derived-alternatively-from an independent bond approach due to Angell [J. Chem. Phys.75, 3698 (1971)]. We suggest the existence of a universality class of hydrogen bond networks that can be described by this theory, and which may include the liquid state of water. The mean lifetime of a hydrogen bond exhibits an Arrhenius temperature dependence. Comparison with experimental data on water provides an absolute time scale for the Monte Carlo simulations. The possible use of these models in simulations of protein-solvent systems is discussed.     

Transitions between secondary structures in isolated polyalanines

Monte Carlo simulations of gas-phase polyalanine peptides have been carried out with the Amber ff96 force field. A low-temperature structural transition takes place between the α-helix stable conformation and β-sheet structures, followed by the unfolding phase change. The transition state ensembles connecting the helix and sheet conformations are investigated by sampling the energy landscape along specific geometric order parameters as putative reaction coordinates, namely the electric dipole μ, the end-to-end distance d, and the gyration radius R_g. By performing series of shooting trajectories, the committor probabilities and their distributions are obtained, revealing that only the electric dipole provides a satisfactory transition coordinate for the α↔β interconversion. The nucleus at the transition is found to have a high helical content.     

Probabilistically induced domain decomposition methods for elliptic boundary-value problems

Monte Carlo as well as quasi-Monte Carlo methods are used to generate only few interfacial values in two-dimensional domains where boundary-value elliptic problems are formulated. This allows for a domain decomposition of the domain. A continuous approximation of the solution is obtained interpolating on such interfaces, and then used as boundary data to split the original problem into fully decoupled subproblems. The numerical treatment can then be continued, implementing any deterministic algorithm on each subdomain. Both, Monte Carlo (or quasi-Monte Carlo) simulations and the domain decomposition strategy allow for exploiting parallel architectures. Scalability and natural fault tolerance are peculiarities of the present algorithm. Examples concern Helmholtz and Poisson equations, whose probabilistic treatment presents additional complications with respect to the case of homogeneous elliptic problems without any potential term and source.     

Analytic results and weighted Monte Carlo simulations for CDO pricing

We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically ∼ 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulas are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.     

Permutation blocking path integral Monte Carlo simulations of degenerate electrons at finite temperature

We analyse the simulation of strongly degenerate electrons at finite temperature using the recently introduced permutation blocking path integral Monte Carlo (PB‐PIMC) method [T. Dornheim et al., New J. Phys. 17 , 073017 (2015)]. As a representative example, we consider electrons in a harmonic confinement and carry out simulations for up to P = 2000 so‐called imaginary‐time propagators – an important convergence parameter within the PIMC formalism. This allows us to study the P‐dependence of different observables of the configuration space in the Monte Carlo simulations and of the fermion sign problem. We find a surprisingly persisting effect of the permutation blocking for large P, which is explained by comparing different length scales. Finally, we touch upon the uniform electron gas in the warm dense matter regime.     

Phase transition properties of three-dimensional systems described by diluted potts model

Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.     

Expected accuracy in a measurement of the CKM angle α using a Dalitz plot analysis of B 0 → ρπ decays in the BTeV project

A precise measurement of the angle α in the CKM triangle is very important for a complete test of the Standard Model. A theoretically clean method to extract α is provided by B ⁰ → ρπ decays. Monte Carlo simulations to obtain the BTeV reconstruction efficiency and to estimate the signal-to-background ratio for these decays were performed. Finally the time-dependent Dalitz plot analysis, using the isospin amplitude formalism for tree and penguin contributions, was carried out. It was shown that, in one year of data taking, BTeV could achieve an accuracy on α better than 5°. The text was submitted by the authors in English     

Real-time icosahedral to fcc structure transition during CoPt nanoparticles formation

Nucleation and growth of supported CoPt nanoparticles were studied in situ and in real time by combined grazing incidence small-angle x-ray scattering (GISAXS) and grazing incidence x-ray diffraction (GIXD). GISAXS provides morphological features of nanoparticles as a function of size, shape and correlation distance between particles, while GIXD allows the determination of the atomic structure. We focus on the formation of ultrasmall CoPt nanoparticles, in the 1–4 nm size range at 500^○C. The structural analysis method based on the Debye equation is coupled with cluster model calculations performed by Monte Carlo simulations using a semi-empirical tight-binding potential to interpret diffraction spectra and structural transitions. Our results show that the cluster structure evolution during the growth is size-dependent and composition-dependent, yielding an icosahedral to fcc structure transition.     

Quantum Monte Carlo calculations of light nuclei

Quantum Monte Carlo calculations using realistic two- and three-nucleon interactions are presented for nuclei with up to ten nucleons. Our Green's function Monte Carlo calculations are accurate to ∼1-2% for the binding energy. We have constructed Hamiltonians using the Argonne v₁₈ NN interaction and reasonable three-nucleon interactions that reproduce the energies of these nuclear states with only ∼500 keV rms error. Other predictions, such as form factors, decay rates, and spectroscopic factors also agree well with data. Some of these results are presented to show that ab initio calculations of light nuclei are now well in hand. Received: 1 May 2001 / Accepted: 4 December 2001     

Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E _c . Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.     

Deterministic methods for numerical simulation of high-energy runaway electron avalanches

The possibilities of two deterministic methods for describing the kinetics of high-energy runaway electrons (REs) are analyzed as alternatives to stochastic methods requiring unrealistically large computing resources in problems of numerical simulation of electric discharges in dense gases involving REs. One of the methods being developed in recent years is based on multigroup equations for the moments of the electron distribution function, while the second method, which is conventionally used to solve problems in gas discharges, is based on the diffusion-drift equation. The modern method of multigroup equations allows one to calculate the RE energy distribution and the spatial RE distribution along the electric force, which are close to these distributions obtained by the Monte Carlo method if the number N of energy groups is chosen properly. The diffusion-drift equation does not give the energy distribution, but its advantage is the possibility of obtaining spatial RE distributions using small computing resources not only along but also perpendicular to the electric force, which are close to those calculated by the Monte Carlo method. To simulate discharges by the method of multigroup equations, it is necessary to know a priori the number N of groups providing good accuracy, the characteristic RE multiplication time t _e , and the energy runaway threshold ɛ_th as functions of the electric-field overvoltage. The diffusion-drift equation requires the specification, along with t _e , of the directed RE velocity and longitudinal and transverse diffusion coefficients calculated by the Monte Carlo method.     

Modeling of light propagation in turbid medium using Monte Carlo simulation technique

The aim of the current study is to simulate the laser photon through biological tissue during PDT therapy using Monte Carlo simulation technique. The model is coded using MATLAB. Interaction of laser light with turbid medium e.g. human tissue depends on the optical properties of the medium i.e. refractive index n, absorption coefficient μ _a , scattering coefficient μ _s and anisotropy factor g. Laser light transport through tissue is governed by the radiative transport equations based on absorption and scattering. Direct sampling is used for step-size generation before interaction via absorption or scattering with the transmitting medium, for deflection and azimuthal angle (θ and ϕ) when the scattering even occurs. The tissue medium considered is divided into radial, axial and angular grid elements and an infinite narrow beam with normal incidence on the tissue is considered. The laser light absorbance inside the tissue, reflectance at the top boundary of the tissue and transmittance at the bottom are estimated and these quantities are shown varying radially and angularly. Results of reflectance, transmittance and fluence are compared with the already published results to confirm the authenticity of our coding and these results are found to lie at only 3–4% error.     

Spin ice in a field: Quasi-phases and pseudo-transitions

Thermodynamics of a short-range model of spin ice magnets in a field is considered in the Bethe-Peierls approximation. The results obtained for [111], [100], and [011] fields agree reasonably well with the existing Monte Carlo simulations and some experiments. In this approximation, all extremely sharp field-induced anomalies are described by analytic functions of temperature and the applied field. In spite of the absence of true phase transitions, the analysis of the entropy and specific heat reliefs over the H-T plane allows discerning “pseudo-phases” with a specific character of spin fluctuations and defining the lines of relatively sharp “pseudo-transitions” between them.     

Heated granular fluids: The random restitution coefficient approach

We introduce the model of inelastic hard spheres with random restitution coefficient α, in order to account for the fact that, in a vertically shaken granular system interacting elastically with the vibrating boundary, the energy injected vertically is transferred to the horizontal degrees of freedom through collisions only, which leads to heating through collisions, i.e. to inelastic horizontal collisions with an effective restitution coefficient that can be larger than 1. This allows the system to reach a non-equilibrium steady state, where we focus, in particular, on the single-particle velocity distribution f (v) in the horizontal plane, and on its deviation from a Maxwellian. Molecular Dynamics simulations and Direct Simulation Monte Carlo (DSMC) show that, depending on the distribution of α, different shapes of f (v) can be obtained, with very different high-energy tails. Moreover, the fourth cumulant of the velocity distribution quantifying the deviations from Gaussian statistics is obtained analytically from the Boltzmann equation and successfully tested against the simulations. Received 24 November 2000 and Received in final form 8 February 2001