Accurate Monte Carlo Simulations Research Articles

Quantifying transmission reliability margin

In bulk electric power transfer capability computations, the transmission reliability margin accounts for uncertainties related to the transmission system conditions, contingencies, and parameter values. We propose a formula which quantifies transmission reliability margin based on transfer capability sensitivities and a probabilistic characterization of the various uncertainties. The formula is verified by comparison with results from two systems small enough to permit accurate Monte Carlo simulations. The formula contributes to more accurate and defensible transfer capability calculations.

Quantifying transmission reliability margin

In bulk electric power transfer capability computations, the transmission reliability margin accounts for uncertainties related to the transmission system conditions, contingencies, and parameter values. We propose a formula which quantifies transmission reliability margin based on transfer capability sensitivities and a probabilistic characterization of the various uncertainties. The formula is verified by comparison with results from two systems small enough to permit accurate Monte Carlo simulations. The formula contributes to more accurate and defensible transfer capability calculations.

Monte Carlo Simulation of Electron Transport and X-Ray Generation. I. Electron Elastic and Inelastic Scattering

We present different theoretical approaches to determine differential cross sections for elastic and inelastic interactions of electrons. These cross sections are the basic ingredients for accurate Monte Carlo simulation of electron transport in matter. The considered models range from simple analytical approximations employed in early calculations to purely numerical differential cross sections described by large databases calculated with state-of-the-art theory.

Accurate Monte Carlo Simulation of Ion Implantation into Arbitrary 1D/2D/3D Structures for Silicon Technology

ABSTRACTWe present an integrated Monte Carlo implant simulator which is capable of accurately simulating ion implantation into any amorphous materials and crystalline Si for 1D/2D/3D structures with arbitrary geometry and topography. With this simulator, we investigate some practical examples which reveal interesting 2D/3D effects, and demonstrate the importance of <110> channeling for sub-100nm silicon technology.

Accurate Monte Carlo simulation of fluorine and BF 2 ion implantation into crystalline silicon

Fluorine and molecular boron difluoride (BF 2) ion implantation into crystalline silicon are simulated with binary-collision-approximation (BCA) based Monte Carlo (MC) model and an extensive comparison with experimental data is made. It is shown that with the optimized parameters for boron and fluorine, BF 2 implantation can be accurately predicted without further calibration. It is found that for BF 2 implants, in agreement with experiments, while boron and fluorine have approximately the same projected ranges, fluorine has much deeper channeling tails than boron. It is demonstrated that for deeply channeled implant species fluorine, the Monte Carlo model based on amorphous target assumption could result in gross errors even under the implant conditions which minimize the channeling effect. Based on the accurate Monte Carlo simulation results of fluorine implants, an earlier positron annihilation spectroscopy (PAS) experiment is examined, and it is suggested that the deep vacancy concentration detected by PAS could be a direct consequence of deep channeling behavior of fluorine ions.

The rotational motion and electronic relaxation of the Gd(III) aqua complex in water revisited through a full proton relaxivity study of a probe solute

Recent advances in the design of fast field cycling (FFC) relaxometers make it now possible to explore the nuclear magnetic relaxation dispersion (NMRD) of semidilute nuclei with short relaxation times. The paramagnetic relaxation rate enhancement of the protons of the tetramethylammonium (CH3)4N+ cation due to the intermolecular magnetic dipolar coupling with the electronic spin S=7/2 of [Gd(D2O)8]3+ in heavy water has been measured between 10 kHz and 800 MHz by combining FFC and standard relaxation techniques. In order to interpret the complete paramagnetic NMRD profile, particularly in the low field region, two previously neglected features are taken into account: (i) The evolution beyond the Redfield limit of the electronic relaxation of the spin S is obtained from accurate Monte Carlo simulations. (ii) The time fluctuation of the static zero field splitting (ZFS) is attributed not only to the usual global Brownian rotational diffusion of the complex, but also to the rearrangement of the water molecules in the first hydration shell of the Gd3+ ion via 90° pseudorotations [Th. Kowall et al., J. Phys. Chem. 99, 13078 (1995)]. To calculate the longitudinal electronic relaxation function G∥(t) of the Gd3+ ion, its static and transient ZFS parameters in the aqua complex as well as the correlation times of the Brownian rotation and vibrations of this complex are needed. We use the values of these parameters derived from an independent multiple frequency and temperature study of the full electronic paramagnetic resonance spectra of Gd3+ in light water H2O, for magnetic fields where the Redfield limit applies. The predicted NMRD profile is in excellent global agreement with experiment over the whole proton frequency range, especially if the correlation times governing the rotational dynamics of the aqua complex are slightly increased to account for the higher viscosity of D2O with respect to H2O.

The bridge function of hard spheres by direct inversion of computer simulation data

The bridge function of the hard sphere fluid has been calculated from our new highly accurate Monte Carlo and molecular dynamics simulation data on the radial distribution function using the (inverted) Ornstein-Zernike equation. Both the systematic errors (finite size, grid size, tail) and statistical errors are analysed in detail and ways to suppress them are proposed. Uncertainties in the resulting values of B(r) are about 0.001. In contrast with many previous findings the bridge function is both positive and negative.

Study of the electron kinetics in the anode region of a glow discharge by a multiterm approach and Monte Carlo simulations

A recently developed method for the solution of thespace-dependent electron Boltzmann equation in higher-orderaccuracy has been adopted to study the behaviour of the electronsin the anode region of a dc glow discharge. This method is basedupon a multiterm approximation of the Legendre polynomialexpansion of the electron velocity distribution function.Generalizing the boundary conditions, in particular for thepartially absorbing anode, the impact of the anode fall and theinfluence of the electron absorption at the anode on the spatialbehaviour of the electron kinetic properties have beeninvestigated in various approximation orders. The analysis hasshown that the simplified treatment of the kinetic equation usingonly the first two terms of the velocity distribution expansioncan lead to considerable falsifications of the convergentbehaviour. In general, the convergent solution of the significantcomponents of the electron velocity distribution and all importantmacroscopic quantities is obtained by a multiterm approximationincluding six to eight terms of that expansion. The discrepanciesbetween the two-term and convergent results are found to dependsensitively on the parameters of the anode fall. In addition, themultiterm results are compared with corresponding ones obtained by accurate Monte Carlo simulations. Very good agreement between the convergent eight-term Boltzmann and Monte Carlo simulations isfound.

EFFECTIVE ORBITAL INTERACTION: SPIN AND ORBITAL ORDERING IN UNDOPED MANGANITES

Including strong on-site interorbital Coulomb interaction and Jahn–Teller (J-T) coupling, we derive an effective spin and orbital (isospin) interaction from the two-band double-exchange model by using projection operator method. For the resulting Hamiltonian, anisotropic A-type antiferromagnetic (A-AF) state emerges naturally from a simple mean-field approximation in certain parameter region. We predict that the alternatingly occupied eg orbitals in the A-AF state should be (d3z2-r2-dx2-y2)/(d3z2-r2+dx2-y2) not d3x2-r2/d3y2-r2 as suggested in some other works. These results are in good agreement with experimental observations in undoped manganites. More accurate Monte Carlo simulations are performed to verify the mean-field ground-state phase diagram and study the finite-temperature spin and isospin disordering phase transitions. The main effect of the J-T coupling is to alter the effective coupling strength, quantitatively.

The Application of Quantitative Risk Assessment to Microbial Food Safety

Quantitative risk assessment (QRA) is rapidly accumulating recognition as the most practical method for assessing the risks associated with microbial contamination of foodstuffs. These risk analyses are most commonly developed in commercial Computer spreadsheet applications, combined with Monte Carlo simulation add-ins that enable probability distributions to be inserted into a spreadsheet. If a suitable model structure can be defined and all of the variables within that model reasonably quantified, a QRA will demonstrate the sensitivity of the severity of the risk to each stage in the risk-assessment model. It can therefore provide guidance for the selection of appropriate risk-reduction measures and a quantitative assessment of the benefits and costs of these proposed measures. However, very few reports explaining QRA models have been submitted for publication in this area. There is, therefore, little guidance available to those who intend to embark on a full microbial QRA. This paper looks at a number of modeling techniques that can help produce more realistic and accurate Monte Carlo simulation models. The use and limitations of several distributions important to microbial risk assessment are explained. Some simple techniques specific to Monte Carlo simulation modelling of microbial risks using spreadsheets are also offered which will help the analyst more realistically reflect the uncertain nature of the scenarios being modeled. simulation, food safety

Time ‐ Dependent Multi ‐ Term Treatment of Plasma Electrons Acted upon by RF Electric Fields

AbstractUsing a new method for solving the time‐dependent electron Boltzmann equation in higher order accuracy, studies of the temporal behaviour of electrons in weakly ionized, collision‐dominated plasmas under the action of rf fields have been performed. The method is based upon a multi‐term approximation of the Legendre polynomial expansion of electron velocity distribution function and is applied to investigate the established periodic behaviour of the electron velocity distribution in helium, argon and CO plasmas.The results obtained in various approximation orders are discussed. The analysis has shown that the simplified treatment using only two terms of the velocity distribution expansion can fail in several conditions. In general, the four‐term approximation gives already a good representation of the convergent solution of the electron Boltzmann equation at each instant of the rf period. The discrepancies between two‐term and convergent results are found to depend sensitively on the specific atomic data, in particular on the magnitude of the various electron collision cross sections involved.Furthermore, the results obtained in the multi‐term approximation are compared with corresponding ones obtained by accurate Monte Carlo simulations. Very good agreement between convergent eight‐term Boltzmann and Monte Carlo calculations is found.

Light Distributions from Point, Line and Plane Sources for Photochemical Reactions and Fluorescence in Turbid Biological Tissues

Light distributions in biological tissues are summarized in simple expressions for spherical, cylindrical and planar geometries due to point sources, line sources and planar sources. The goal is to provide workable tools for computing light distributions that govern the amount and distribution of photochemical reactions in experimental solutions, films and biological tissues. Diffusion theory expressions are compared with Monte Carlo simulations. Analytic expressions that mimic accurate Monte Carlo simulations are presented. Application to fluorescence measurements and prediction of necrotic zones in photodynamic therapy are outlined.

Light Distributions from Point, Line and Plane Sources for Photochemical Reactions and Fluorescence in Turbid Biological Tissues

Light distributions in biological tissues are summarized in simple expressions for sphewrical, cylindrical and planar geometries due to point sources, line sources and planar sources. The goal is to provide workable tools for computing light distributions that govern the amount and distribution of photochemical reactions in experimental solutions, films and biological tissues. Diffusion theory expressions are compared with Monte Carlo simulations. Analytic expressions that mimic accurate Monte Carlo simulations are presented. Application to fluorescence measurements and prediction of necrotic zones in photodynamic therapy are outlined.

Comparison of Signal-to-Noise Ratios

The probability distribution (density) function for the experimental signal-to-noise ratio (SNR) defined as x/s, where x is the sample mean and s is the customary sample standard deviation, has been derived and found to be in excellent agreement with accurate Monte Carlo simulation results. The SNR probability distribution function is a hypergeometric function which has no closed-form expression in elementary functions. The same applies to the probability distribution function for the relative standard deviation. In contrast, the probability distribution function for the approximate SNR defined by μ/s‘, where μ is the population mean parameter and s‘ ≡ s[(N − 1)/N]1/2, has a closed-form expression but is inaccurate for small numbers of measurements. The experimental SNR is a biased estimator of the true SNR, but the bias is easily correctable. Monte Carlo simulation methods were used to derive critical value tables for comparison of experimental SNRs and relative standard deviations. The critical value ...

TOTAL AND TRANSPORT CROSS SECTIONS FOR ELASTIC SCATTERING OF ELECTRONS BY ATOMS

Tables are given of total cross sections as well as first and second transport cross sections for elastic scattering of electrons with kinetic energies from 100 eV to 1 GeV by neutral atoms with atomic numberZ= 1 to 92. With the information given in the present tables, accurate Monte Carlo simulations of electron multiple elastic scattering can be easily performed. The tabulated cross sections have been calculated by using the Dirac partial wave method with screened potentials obtained from Dirac–Hartree–Fock atomic electron densities. Exchange effects are introduced by means of the local approximation of Furness and McCarthy. Nuclear size effects are accounted for in the Born approximation by using Helm's nuclear form factor.

An Improved First-Order Perturbation Theory of Simple Fluids Using High Temperature Approximation and Random Phase Approximation

In this paper, we have examined accuracy of an improved form of the first-order perturbation theory of simple fluids. Theory consists of the first-order perturbation theory of high temperature approximation and the random phase approximation. Inclusion of the random phase approximation enhances applicability of the perturbation theory to much wider ranges of temperatures and densities, especially to low densities. Comparisons are made between theoretical predictions and accurate computer simulation results for pressure, residual Helmholtz free energy, residual internal energy and vapor/liquid phase equilibria of Lennard-Jones fluids. In general, theoretical predictions are in very good agreement with simulation results. The random phase approximation is responsible for predicting accurate Gibbs ensemble Monte Carlo simulation results for vapor/liquid phase equilibria using the same theory in both vapor and liquid phases.

Local field factor and effective potentials in liquid metals

The authors recently evaluated the local field factor, G(q) of the electron gas by accurate fixed-node diffusion Monte Carlo (DMC) simulations. Here, the G(q) obtained from a simple fit to the DMC results and from several approximations available in the literature is used to derive the effective pair potential (r) in simple metals within second-order perturbation theory. Using a local electron-ion pseudopotential, it is found that is determined mostly by the behavior of G(q) at q ča. 2 q F, where the DMC data are well reproduced by the local field within local density approximation, G LDA( c) = A(q /q F) 2 with A related to the compressibility of the uniform electron gas.

The simple-cubic lattice gas with nearest-neighbour exclusion: Ising universality

The lattice gas with nearest neighbour-exclusion on the simple cubic lattice is studied by means of statistically accurate Monte Carlo simulations with an efficient cluster algorithm. Our results for critical exponents are y h = 2.47(1) and y t = 1.60(2). These results agree well with the three-dimensional Ising universality class. We explain the discrepancy with an earlier study. The critical activity is z c = 1.0559 (1). The size distribution of the clusters indicates that the percolation threshold of the cluster formation process of the Monte Carlo algorithm coincides with the critical point.

Two-Term and multi-term approximation of the nonstationary electron velocity distribution in an electric field in a gas

A very efficient, strict nonstationary multi-term approach has been developed as a generalization of the conventional and the strict nonstationary two-term approximations used for solving the nonstationary , electron Boltzmann equation. As a first application the temporal relaxation of electrons in a model plasma acted upon by a de electric field has been investigated. The results are compared with corresponding ones obtained by the conventional and the strict nonstationary two-term approach as well as with very accurate Monte Carlo simulations. Perfect agreement between nonstationary eight-term Boltzmann and Monte Carlo calculations is found.

Diffusion Monte Carlo Study of Electrons in Two-dimensional Layers

We investigate the phase diagram of electrons in two dimensions at T = 0 by means of accurate diffusion Monte Carlo simulations within the fixed-node approximation. At variance with previous studies, we find that in an isolated layer Slater-Jastrow nodes yield stability of the fully polarised fluid at intermediate coupling, before freezing into a triangular crystal sets in. We have also studied coupled layers of electrons and of electrons and holes. Preliminary results show that at large coupling, as two layers are brought together from infinity, inter-layer correlation first stabilises the crystalline phase at distances of the order of the in-plane inter-particle spacing. As the distance is further decreased the effect of correlation, as expected, turns into an enhanced screening, which disrupts the crystalline order in favour of liquid phases.