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We present a novel Monte Carlo simulation of protein folding, in which all heavy atoms are represented as interacting hard spheres. This model includes all degrees of freedom relevant to folding - all sidechain and backbone torsions - and uses a Go potential. In this study, we focus on the 46 residue alpha-beta protein crambin and two of its structural components, the helix and helix hairpin. For a wide range of temperatures, we have recorded multiple folding events of these three structures from random coils to native conformations that differ by less than 1 A dRMS from their crystal structure coordinates. The thermodynamics and kinetic mechanism of the helix-coil transition obtained from our simulation shows excellent agreement with currently available experimental and molecular dynamics data. Based on insights obtained from folding its smaller structural components, a possible folding mechanism for crambin is proposed. We observe that the folding occurs via a cooperative, first order-like process, and that many folding pathways to the native state exist. One particular sequence of events constitutes a ``fast-folding'' pathway where kinetic traps are avoided. At very low temperatures, a kinetic trap arising from the incorrect packing of sidechains was observed. These results demonstrate that folding to the native state can be observed in a reasonable amount of time on desktop computers even when an all-atom representation is used, provided the energetics sufficiently stabilize the native state.

The coil-globule transition has been studied for A-B copolymer chains both by means of lattice Monte Carlo simulations using bond fluctuation algorithm and by a numerical self-consistent field method. Copolymer chains of fixed length with A and B monomeric units with regular, random and specially designed (protein-like) primary sequences have been investigated. The dependence of the transition temperature on the AB sequence has been analyzed. A protein-like copolymer is more stable than a copolymer with statistically random sequence. The transition is more sharpe for random copolymers. It is found that there exist a temperature below which the chain appears to be in the lowest energy state (ground state). Both for random and protein-like sequences and for regular copolymers with a relatively long repeating block, a molten globule regime is found between the ground state temperature and the transition temperature. For regular block copolymers the transition temperature increases with block size. Qualitatively, the results from both methods are in agreement. Differences between the methods result from approximations in the SCF theory and equilibration problems in MC simulations. The two methods are thus complementary.

The direct simulation Monte Carlo method (DSMC) has evolved over 40 years into a powerful numerical technique for the computation of complex, nonequilibrium gas flows. In this context, nonequilibrium means that the velocity distribution function is not in an equilibrium form due to a low number of intermolecular collisions within a fluid element. In atmospheric entry, nonequilibrium conditions occur at high altitude and in regions of flow fields with small length scales. In this first article of two parts, the theoretical basis of the DSMC technique is discussed. In addition, the methods used in DSMC are described for simulation of high temperature, real gas effects and gas-surface interactions. The current status of the various models is reviewed and areas where further work is required are identified.

This article is from BMC Medical Research Methodology , volume 14 . Abstract Background: In biomedical research, response variables are often encountered which have bounded support on the open unit interval - (0,1). Traditionally, researchers have attempted to estimate covariate effects on these types of response data using linear regression. Alternative modelling strategies may include: beta regression, variable-dispersion beta regression, and fractional logit regression models. This study employs a Monte Carlo simulation design to compare the statistical properties of the linear regression model to that of the more novel beta regression, variable-dispersion beta regression, and fractional logit regression models. Methods: In the Monte Carlo experiment we assume a simple two sample design. We assume observations are realizations of independent draws from their respective probability models. The randomly simulated draws from the various probability models are chosen to emulate average proportion/percentage/rate differences of pre-specified magnitudes. Following simulation of the experimental data we estimate average proportion/percentage/rate differences. We compare the estimators in terms of bias, variance, type-1 error and power. Estimates of Monte Carlo error associated with these quantities are provided. Results: If response data are beta distributed with constant dispersion parameters across the two samples, then all models are unbiased and have reasonable type-1 error rates and power profiles. If the response data in the two samples have different dispersion parameters, then the simple beta regression model is biased. When the sample size is small (N0 = N1 = 25) linear regression has superior type-1 error rates compared to the other models. Small sample type-1 error rates can be improved in beta regression models using bias correction/reduction methods. In the power experiments, variable-dispersion beta regression and fractional logit regression models have slightly elevated power compared to linear regression models. Similar results were observed if the response data are generated from a discrete multinomial distribution with support on (0,1). Conclusions: The linear regression model, the variable-dispersion beta regression model and the fractional logit regression model all perform well across the simulation experiments under consideration. When employing beta regression to estimate covariate effects on (0,1) response data, researchers should ensure their dispersion sub-model is properly specified, else inferential errors could arise.

A Monte Carlo program for the simulation of electromagnetic cascades initiated by high-energy photons and electrons interacting with extragalactic background light (EBL) is presented. Pair production and inverse Compton scattering on EBL photons as well as synchrotron losses and deflections of the charged component in extragalactic magnetic fields (EGMF) are included in the simulation. Weighted sampling of the cascade development is applied to reduce the number of secondary particles and to speed up computations. As final result, the simulation procedure provides the energy, the observation angle, and the time delay of secondary cascade particles at the present epoch. Possible applications are the study of TeV blazars and the influence of the EGMF on their spectra or the calculation of the contribution from ultrahigh energy cosmic rays or dark matter to the diffuse extragalactic gamma-ray background. As an illustration, we present results for deflections and time-delays relevant for the derivation of limits on the EGMF.

Monte Carlo simulation provides a powerful tool for understanding and exploring thermodynamic phase equilibria in many-particle interacting systems. Among the most physically intuitive simulation methods is Gibbs ensemble Monte Carlo (GEMC), which allows direct computation of phase coexistence curves of model fluids by assigning each phase to its own simulation cell. When one or both of the phases can be modeled virtually via an analytic free energy function [M. Mehta and D. A. Kofke, Molecular Physics 79, 39 (1993)], the GEMC method takes on new pedagogical significance as an efficient means of analyzing fluctuations and illuminating the statistical foundation of phase behavior in finite systems. Here we extend this virtual GEMC method to binary fluid mixtures and demonstrate its implementation and instructional value with two applications: (1) a lattice model of simple mixtures and polymer blends and (2) a free-volume model of a complex mixture of colloids and polymers. We present algorithms for performing Monte Carlo trial moves in the virtual Gibbs ensemble, validate the method by computing fluid demixing phase diagrams, and analyze the dependence of fluctuations on system size. Our open-source simulation programs, coded in the platform-independent Java language, are suitable for use in classroom, tutorial, or computational laboratory settings.

The radiation field over a broken stratocumulus cloud deck is simulated by the Monte Carlo method. We conducted four experiments to investigate the main factor for the observed shortwave reflectively over the FIRE flight 2 leg 5, in which reflectivity decreases almost linearly from the cloud center to cloud edge while the cloud top height and the brightness temperature remain almost constant through out the clouds. From our results, the geometry effect, however, did not contribute significantly to what has been observed. We found that the variation of the volume extinction coefficient as a function of its relative position in the cloud affects the reflectivity efficiently. Additional check of the brightness temperature of each experiment also confirms this conclusion. The cloud microphysical data showed some interesting features. We found that the cloud droplet spectrum is nearly log-normal distributed when the clouds were solid. However, whether the shift of cloud droplet spectrum toward the larger end is not certain. The decrease of number density from cloud center to cloud edges seems to have more significant effects on the optical properties.

The radiation field over a broken stratocumulus cloud deck is simulated by the Monte Carlo method. We conducted four experiments to investigate the main factor for the observed shortwave reflectively over the FIRE flight 2 leg 5, in which reflectivity decreases almost linearly from the cloud center to cloud edge while the cloud top height and the brightness temperature remain almost constant through out the clouds. From our results, the geometry effect, however, did not contribute significantly to what has been observed. We found that the variation of the volume extinction coefficient as a function of its relative position in the cloud affects the reflectivity efficiently. Additional check of the brightness temperature of each experiment also confirms this conclusion. The cloud microphysical data showed some interesting features. We found that the cloud droplet spectrum is nearly log-normal distributed when the clouds were solid. However, whether the shift of cloud droplet spectrum toward the larger end is not certain. The decrease of number density from cloud center to cloud edges seems to have more significant effects on the optical properties.

This article is from PLoS ONE , volume 9 . Abstract Purpose: To compare semi-quantitative (SQ) and pharmacokinetic (PK) parameters for analysis of dynamic contrast enhanced MR data (DCE-MRI) and investigate error-propagation in SQ parameters. Methods: Clinical data was collected from five patients with type 2-neurofibromatosis (NF2) receiving anti-angiogenic therapy for rapidly growing vestibular schwannoma (VS). There were 7 VS and 5 meningiomas. Patients were scanned prior to therapy and at days 3 and 90 of treatment. Data was collected using a dual injection technique to permit direct comparison of SQ and PK parameters. Monte Carlo modeling was performed to assess potential measurement errors in SQ parameters in persistent, washout, and weakly enhancing tissues. The simulation predictions for five semi-quantitative parameters were tested using the clinical DCE-MRI data. Results: In VS, SQ parameters and Ktrans showed close correlation and demonstrated similar therapy induced reductions. In meningioma, only the denoised Signal Enhancement Ratio (Rse1/se2(DN)) showed a significant therapy induced reduction (p

The multi-spin coding of the Monte Carlo simulation of the three-state Potts model on the simple cubic lattice is presented. The ferromagnetic (F) model, the antiferromagnetic (AF) model, and the random mixture of the F and AF couplings are treated. The multi-spin coding technique is also applied to the block-spin transformation. The block-spin transformation of the F Potts model is simply realized by the majority rule, whereas the AF three-state Potts model is transformed to the block spin having a six-fold symmetry.

Monte Carlo simulation, lattice dynamics in the harmonic approximation, and solution of the hypernetted chain equation were used to study the classical two-dimensional one component plasma. The system consists of a single species of charged particles immersed in a uniform neutralizing background. The particles interact via a l/r potential, where r is the two dimensional separation. Equations of state were calculated for both the liquid and solid phases. Results of calculation of the thermodynamic functions and one and two particle correlation functions are presented.

This study looked at how Hexa (3-methoxy propan-1,2 diol) cyclotriphosphazene (HMC) can prevent corrosion on carbon steel in a 3% NaCl solution. The team used various techniques, including weight loss measurements, potentiodynamic polarization, and electrochemical impedance spectroscopy, as well as computational methods like Density functional theory and Monte Carlo simulation. They found that the best concentration for HMC was 10-3M, which prevented 99% of corrosion at 298 K, but that the effectiveness decreased at higher temperatures. The team also observed that HMC adhered to the steel surface according to Langmuir isotherm, and that the inhibitor was of the anodic type. Computational studies showed that HMC interacted with the surface through donor-acceptor interactions, with the anionic parts donating electrons and the cationic parts accepting them. Monte Carlo simulation confirmed that HMC adsorbed spontaneously on Fe (110) surface.

This study looked at how Hexa (3-methoxy propan-1,2 diol) cyclotriphosphazene (HMC) can prevent corrosion on carbon steel in a 3% NaCl solution. The team used various techniques, including weight loss measurements, potentiodynamic polarization, and electrochemical impedance spectroscopy, as well as computational methods like Density functional theory and Monte Carlo simulation. They found that the best concentration for HMC was 10-3M, which prevented 99% of corrosion at 298 K, but that the effectiveness decreased at higher temperatures. The team also observed that HMC adhered to the steel surface according to Langmuir isotherm, and that the inhibitor was of the anodic type. Computational studies showed that HMC interacted with the surface through donor-acceptor interactions, with the anionic parts donating electrons and the cationic parts accepting them. Monte Carlo simulation confirmed that HMC adsorbed spontaneously on Fe (110) surface.

We present a path integral Monte Carlo study of the global superfluid fraction and local superfluid density in cylindrically-symmetric reservoirs of liquid $^{4}$He separated by nanoaperture arrays. The superfluid response to both translations along the axis of symmetry (longitudinal response) and rotations about the cylinder axis (transverse response) are computed, together with radial and axial density distributions that reveal the microscopic inhomogeneity arising from the combined effects of the confining external potential and the $^4$He-$^4$He interatomic potentials. We make a microscopic determination of the length-scale of decay of superfluidity at the radial boundaries of the system by analyzing the local superfluid density distribution to extract a displacement length that quantifies the superfluid mass displacement away from the boundary. We find that the longitudinal superfluid response is reduced in reservoirs separated by a septum containing sufficiently small apertures compared to a cylinder with no intervening aperture array, for all temperatures below $T_{\lambda}$. For a single aperture in the septum, a significant drop in the longitudinal superfluid response is seen when the aperture diameter is made smaller than twice the empirical temperature-dependent $^4$He healing length, consistent with the formation of a weak link between the reservoirs. Increasing the diameter of a single aperture or the number of apertures in the array results in an increase of the superfluid density toward the expected bulk value.

Purpose: For Monte Carlo simulation of radiotherapy, x-ray CT number of every system needs to be calibrated and converted to mass density and elemental composition. This study aims to formulate material properties of body tissues for practical two-step conversion from CT number. Methods: We used the latest compilation on body tissues that constitute reference adult male and female. We formulated the relations among mass, electron, and elemental densities into polylines to connect representative tissues, for which we took mass-weighted mean for the tissues in limited density regions. We compared the polyline functions of mass density with a bi-line for electron density and broken lines for elemental densities, which were derived from preceding studies. Results: There was generally high correlation between mass density and the other densities except of C, N, and O for light spongiosa tissues occupying 1% of body mass. The polylines fitted to the dominant tissues and were generally consistent with the bi-line and the broken lines. Conclusions: We have formulated the invariant relations between mass and electron densities and from mass to elemental densities for body tissues. The formulation enables Monte Carlo simulation in treatment planning practice without additional burden with CT-number calibration.

Weinberg (2012) described a constructive algorithm for computing the marginal likelihood, Z, from a Markov chain simulation of the posterior distribution. Its key point is: the choice of an integration subdomain that eliminates subvolumes with poor sampling owing to low tail-values of posterior probability. Conversely, this same idea may be used to choose the subdomain that optimizes the accuracy of Z. Here, we explore using the simulated distribution to define a small region of high posterior probability, followed by a numerical integration of the sample in the selected region using the volume tessellation algorithm described in Weinberg (2012). Even more promising is the resampling of this small region followed by a naive Monte Carlo integration. The new enhanced algorithm is computationally trivial and leads to a dramatic improvement in accuracy. For example, this application of the new algorithm to a four-component mixture with random locations in 16 dimensions yields accurate evaluation of Z with 5% errors. This enables Bayes-factor model selection for real-world problems that have been infeasible with previous methods.

A novel method for simulating the statistical mechanics of molecular systems in which both nuclear and electronic degrees of freedom are treated quantum mechanically is presented. The scheme combines a path integral description of the nuclear variables with a first-principles adiabatic description of the electronic structure. The electronic problem is solved for the ground state within a density functional approach, with the electronic orbitals expanded in a localized (Gaussian) basis set. The discretized path integral is computed by a Metropolis Monte Carlo sampling technique on the normal modes of the isomorphic ring-polymer. An effective short-time action correct to order $\tau^4$ is used. The validity and performance of the method are tested in two small Lithium clusters, namely Li$_4$ and Li$_5^+$. Structural and electronic properties computed within this fully quantum-mechanical scheme are presented and compared to those obtained within the classical nuclei approximation. Quantum delocalization effects are significant but tunneling turns out to be irrelevant at low temperatures.

The direct simulation Monte Carlo method (DSMC) has evolved over 40 years into a powerful numerical technique for the computation of complex, nonequilibrium gas flows. In this context, nonequilibrium means that the velocity distribution function is not in an equilibrium form due to a low number of intermolecular collisions within a fluid element. In atmospheric entry, nonequilibrium conditions occur at high altitude and in regions of flow fields with small length scales. In this second article of two parts, several different implementations of the DSMC technique in various, widely used codes are described. Validation of the DSMC technique for hypersonic flows using data measured in the laboratory is discussed. A review is then provided of the application of the DSMC technique to atmospheric entry flows. Illustrations of DSMC analyses are provided for slender and blunt body vehicles for entry into Earth, followed by examples of DSMC modeling of planetary entry flows.

This Technical Publication (TP) is meant to address a number of topics related to the application of Monte Carlo simulation to launch vehicle design and requirements analysis. Although the focus is on a launch vehicle application, the methods may be applied to other complex systems as well. The TP is organized so that all the important topics are covered in the main text, and detailed derivations are in the appendices. The TP first introduces Monte Carlo simulation and the major topics to be discussed, including discussion of the input distributions for Monte Carlo runs, testing the simulation, how many runs are necessary for verification of requirements, what to do if results are desired for events that happen only rarely, and postprocessing, including analyzing any failed runs, examples of useful output products, and statistical information for generating desired results from the output data. Topics in the appendices include some tables for requirements verification, derivation of the number of runs required and generation of output probabilistic data with consumer risk included, derivation of launch vehicle models to include possible variations of assembled vehicles, minimization of a consumable to achieve a two-dimensional statistical result, recontact probability during staging, ensuring duplicated Monte Carlo random variations, and importance sampling.

The Markov chain Monte Carlo method as a statistical mechanics technique for the study of macroscopic systems has furnished the scientific community with great knowledge and advances in the theory of phase transitions. While a number of Monte Carlo models have been proposed for the study of surface growth, these models have not nearly being studied as exhaustively as in the models of magnetic systems, a paradigm of which is the classical model of Ernest Ising. In particular, studies of phase transitions in surface/interface science are almost non-existent. This article has been written to motivate research in this area of statistical mechanics from the perspective of surface science. In this article we survey the rudiments of the method along with some models of disordered systems such as magnetic systems, material fracture, nano-pattern formation under ion bombardment, and molecular chirality.

Two coarse-grained models for polymer chains in dense glass-forming polymer melts are studied by computer simulation: the bond-fluctuation model on a simple cubic lattice, where a bond-length potential favors long bonds, is treated by dynamic Monte Carlo methods, and a bead-spring model in the continuum with a Lennard-Jones potential between the beads is treated by Molecular Dynamics. While the dynamics of both models differ for short length scales and associated time scales, on mesoscopic spatial and temporal scales both models behave similarly. In particular, the mode coupling theory of the glass transition can be used to interpret the slowing down of the undercooled polymer melt. For the off-lattice model, the approach to the critical point of mode coupling is both studied for constant pressure and for constant volume. The lattice model allows a test of the Gibbs-Di Marzio entropy theory of the glass transition, and our finding is that although the entropy does decrease significantly, there is no ``entropy catastrophe'', where the fluid entropy would turn negative. Finally, an outlook on confinement effects on the glass transition in thin film geometry is given.

We describe the results of object kinetic Monte Carlo (OKMC) simulations of the annealing of primary cascade damage in bulk tungsten using a comprehensive database of cascades obtained from molecular dynamics [1] as a function of primary knock-on atom (PKA) energy and direction, and temperatures of 300, 1025 and 2050 K. An increase in SIA clustering but decrease in vacancy clustering with temperature combined with disparate mobilities of SIAs versus vacancies causes an interesting temperature effect on cascade annealing, which is quite different from what one would expect. The annealing efficiency (ratio of number of defects after and before annealing) exhibits an inverse U-shape curve as a function of temperature. In addition, we will also describe the capabilities of our newly developed OKMC code; KSOME (kinetic simulations of microstructure evolution) used to carryout these simulations

$H_2$ is the most abundant interstellar species. Its deuterated forms ($HD$ and $D_2$) are also significantly abundant. Huge abundances of these molecules could be explained by considering the chemistry occurring on the interstellar dust. Because of its simplicity, Rate equation method is widely used to study the formation of grain-surface species. However, since recombination efficiency of formation of any surface species are heavily dependent on various physical and chemical parameters, Monte Carlo method would be best method suited to take care of randomness of the processes. We perform Monte Carlo simulation to study the formation of $H_2$, $HD$ and $D_2$ on interstellar ices. Adsorption energies of surface species are the key inputs for the formation of any species on interstellar dusts but binding energies of deuterated species are yet to known with certainty. A zero point energy correction exists between hydrogenated and deuterated species which should be considered while modeling the chemistry on the interstellar dusts. Following some earlier studies, we consider various sets of adsorption energies to study the formation of these species in diverse physical circumstances. As expected, noticeable difference in these two approaches (Rate equation method and Monte Carlo method) is observed for production of these simple molecules on interstellar ices. We introduce two factors, namely, $S_f$ and $\beta$ to explain these discrepancies: $S_f$ is a scaling factor, which could be used to correlate discrepancies between Rate equation and Monte Carlo methods. $\beta$ factor indicates the formation efficiency under various circumstances. Higher values of $\beta$ indicates a lower production efficiency. We found that $\beta$ increases with a decrease in rate of accretion from gas phase to grain phase.

The electrical discharges in air are a technology of great interest for certain environmental-related industrial sectors such as water treatment and air sterilization by ozone generators or the depollution by precipitators, when it comes to the removal of industrial particles, dust and/or heavy metals; or by corona discharge reactors with or without DBD depending on the geometries of the electrodes [1,2,3]. The modeling makes it possible to optimize these electric discharges through the knowledge of the physical and chemical phenomena intervening in the discharge dynamic. Generally the model used at atmospheric pressure is the fluid model, the latter is based on the first moments of the Boltzmann equation and requires some average quantities called transport coefficients. The main objective of this work is the calculation of the electron transport coefficients in oxygen, nitrogen, and air. They are calculated by using Monte Carlo method [4,5], and the results obtained are compared to the measurements in order to validate the used data for each gas.

Unidimensionality is fundamental to psychometrics. In the last decade, network analysis in psychology has skyrocketed in popularity. Dimensionality assessment has been a strong focus of network psychometrics yet unidimensionality assessment remains a challenge. Community detection algorithms are the most common approach to estimating dimensionality in networks. Most of these algorithms optimize an objective function called modularity. A limitation of modularity is that it penalizes unidimensional structures and tends to favors two or more communities (dimensions). In this study, I perform a Monte Carlo simulation using one and two factor models to determine what community detection algorithms work best. Based on previous simulation studies, I compare the best performing community detection algorithms: Leading Eigenvalue, Leiden, Louvain, and Walktrap. A grid search is performed on these algorithms parameters to determine the optimal trade-off between unidimensional and bidimensional detection. The best performing parameters for each algorithm are then compared against each other. This study advances undimensionality detection in network psychometrics, further developing the psychometric toolbox of network analysis in psychology.

Summary: The Software Maintenance Group at Hill Air Force Base has created a Quality Model applicable formost software development projects. Quality is modeled by predicting defect injection and removal using historical data. Variation is taken into account by using a MonteCarlo Simulation to adjust estimates, defect injection rates and defect detection ratios. Interim results can be used to guide the project toward a final quality goal. Actual data replaces projected in the model as the project progresses.

Written Kernel Density Estimation Monte Carlo Simulation taken from "Nuclear Science and Engineering: An International Research Journal of the American Nuclear Society Vol. 188 Num 1" in Taylor and Francis Group found in Missouri S&T QC 770.N85. Thanks Internet Archive for storing this for free (unlike many other image hosting sites), and I promise you will become a world causeffectist bank for causing free and openly accessible accurate virtual information like the one I am uploading.

We numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory, a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameter and liquid state correlation functions. This theory has not been subjected to stringent tests against simulation data for ordering across the polymerization transition. We numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results.

Simulations of physicists for the competition between adult languages since 2003 are reviewed. How many languages are spoken by how many people? How many languages are contained in various language families? How do language similarities decay with geographical distance, and what effects do natural boundaries have? New simulations of bilinguality are given in an appendix.

We study, through the diffusion Monte Carlo method, a spin one-half fermion fluid, in the three dimensional Euclidean space, at zero temperature. The point particles, immersed in a uniform "neutralizing" background, interact with a pair-potential which can be continuously changed from zero to the Coulomb potential depending on a parameter $\mu$. We determine the radial distribution functions of the system for various values of density, $\mu$, and polarization. We discuss about the importance, in a computer experiment, of the choice of suitable estimators to measure a physical quantity. The radial distribution function is determined through the usual histrogram estimator and through an estimator determined via the use of the Hellmann and Feynman theorem. In a diffusion Monte Carlo simulation the latter route introduces a new bias to the measure of the radial distribution function due to the choice of the auxiliary function. This bias is independent from the usual one due to the choice of the trial wave function. A brief account of the results from this study were presented in a recent communication [R. Fantoni, Solid State Communications, {\bf 159}, 106 (2013)].

The mass and kinetic energy distribution of nuclear fragments from thermal neutron induced fission of 235U have been studied using a Monte-Carlo simulation. Besides reproducing the pronounced broadening on the standard deviation of the final fragment kinetic energy distribution $\sigma_{e}(m)$ around the mass number m = 109, our simulation also produces a second broadening around m = 125, that is in agreement with the experimental data obtained by Belhafaf et al. These results are consequence of the characteristics of the neutron emission, the variation in the primary fragment mean kinetic energy and the yield as a function of the mass.

We present atomic-scale computer simulations in equiatomic L1$_0$-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 $0.73\pm 0.15 eV$ and an order-disorder transition temperature of 935 K have been found.

We propose a new ensemble for Monte Carlo simulations, in which each state is assigned a statistical weight $1/k$, where $k$ is the number of states with smaller or equal energy. This ensemble has robust ergodicity properties and gives significant weight to the ground state, making it effective for hard optimization problems. It can be used to find free energies at all temperatures and picks up aspects of critical behaviour (if present) without any parameter tuning. We test it on the travelling salesperson problem, the Edwards-Anderson spin glass and the triangular antiferromagnet.

We describe a hybrid Direct Simulation Monte Carlo (DSMC) code for simultaneously solving the collisional Boltzmann equation for gas and the collisionless Boltzmann equation for stars and dark matter for problems important to galaxy evolution. This project is motivated by the need to understand the controlling dynamics at interfaces between gases of widely differing densities and temperature, i.e. multiphase media. While more expensive than hydrodynamics, the kinetic approach does not suffer from discontinuities and it applies when the continuum limit does not, such as in the collapse of galaxy clusters and at the interface between coronal halo gas and a thin neutral gas layer. Finally, the momentum flux is carried, self-consistently, by particles and this approach explicitly resolves and thereby captures shocks. The DSMC method splits the solution into two pieces: 1) the evolution of the phase-space flow without collisions; and 2) the evolution governed the collision term alone without phase-space flow. This splitting approach makes DSMC an ideal match to existing particle-based n-body codes. If the mean free path becomes very small compared to any scale of interest, the method abandons simulated particle collisions and simply adopts the relaxed solution in each interaction cell consistent with the overall energy and momentum fluxes. This is functionally equivalent to solving the Navier-Stokes equations on a mesh. Our implementation is tested using the Sod shock tube problem and the non-linear development of an Kelvin-Helmholtz unstable shear layer.

Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. We here use quantum retrodiction to produce a rigorous refinement of the theory put forward in Phys. Rev. E {\bf 83}, 056118 (2011). We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte-Carlo simulation with single-molecule quantum trajectories supports the self-consistency of our approach.

Yttria-stabilized zirconia (YSZ) is of interest to the aerospace community, notably for its application as a thermal barrier coating for turbine engine components. In such an application, diffusion of both oxygen ions and cations is of concern. Oxygen diffusion can lead to deterioration of a coated part, and often necessitates an environmental barrier coating. Cation diffusion in YSZ is much slower than oxygen diffusion. However, such diffusion is a mechanism by which creep takes place, potentially affecting the mechanical integrity and phase stability of the coating. In other applications, the high oxygen diffusivity of YSZ is useful, and makes the material of interest for use as a solid-state electrolyte in fuel cells. The kinetic Monte Carlo (kMC) method offers a number of advantages compared with the more widely known molecular dynamics simulation method. In particular, kMC is much more efficient for the study of processes, such as diffusion, that involve infrequent events. We describe the results of kinetic Monte Carlo computer simulations of oxygen and cation diffusion in YSZ. Using diffusive energy barriers from ab initio calculations and from the literature, we present results on the temperature dependence of oxygen and cation diffusivity, and on the dependence of the diffusivities on yttria concentration and oxygen sublattice vacancy concentration. We also present results of the effect on diffusivity of oxygen vacancies in the vicinity of the barrier cations that determine the oxygen diffusion energy barriers.

A novel Stochastic Event-Driven Molecular Dynamics (SEDMD) algorithm is developed for the simulation of polymer chains suspended in a solvent. The polymers are represented as chains of hard spheres tethered by square wells and interact with the solvent particles with hard core potentials. The algorithm uses Event-Driven Molecular Dynamics (EDMD) for the simulation of the polymer chain and the interactions between the chain beads and the surrounding solvent particles. The interactions between the solvent particles themselves are not treated deterministically as in event-driven algorithms, rather, the momentum and energy exchange in the solvent is determined stochastically using the Direct Simulation Monte Carlo (DSMC) method. The coupling between the solvent and the solute is consistently represented at the particle level, however, unlike full MD simulations of both the solvent and the solute, the spatial structure of the solvent is ignored. The algorithm is described in detail and applied to the study of the dynamics of a polymer chain tethered to a hard wall subjected to uniform shear. The algorithm closely reproduces full MD simulations with two orders of magnitude greater efficiency. Results do not confirm the existence of periodic (cycling) motion of the polymer chain.

It is experimentally observed and theoretically proved that the distance between topmost layers of a metal surface has a contraction. However, well-known potentials such as Lennard-Jones and Morse potentials lead to an expansion of the surface inter-layer distance. Such simple potentials therefore cannot be used to study metal surface relaxation. In this paper, extensive Monte Carlo simulations are used to study the silver (111) surface with both the Gupta potential (GP) and the Embedded Atom Method (EAM) potential. Our results of the lattice relaxation at the (111) surface of silver show indeed a contraction for both potentials at low temperatures in agreement with experiments and early theories. However at higher temperatures, the EAM potential yields a surface melting at $\simeq 700$ K very low with respect to the experimental bulk melting at $\simeq 1235$ K while the GP yields a surface melting at $\simeq 1000$ K closer to the bulk one. In addition, we observe with the EAM potential an anomalous thermal expansion, i. e. the surface contraction becomes a surface dilatation with respect to the bulk, at $\simeq 900$ K. The Gupta potential does not show this behavior.We compare our results with different experimental and numerical results.

The meaningful investigation of many problems in statistics can be solved through Monte Carlo methods. Monte Carlo studies can help solve problems that are mathematically intractable through the analysis of random samples from populations whose characteristics are known to the researcher. Using Monte Carlo simulation, the values of a statistic are observed in many samples drawn from that known population. The statistic's sampling distribution is then estimated by the relative frequency distribution actually observed in the study. The many samples are usually generated artificially through the use of computer algorithms. This paper discusses how one chooses a pseudo-random number generator, and then discusses how to use these generators to simulate data from normal and multivariate normal distributions. Several examples are provided of how one might sample from a pseudo population and the statistics that are commonly calculated during a Monte Carlo investigation. The many trials that might be used when investigating Type I and Type II errors are outlined. The paper ends with a discussion of the processes that might be used to verify that a researcher's simulation process is doing what it was intended to do. Four appendixes contain Statistical Analysis System programming code examples and a FORTRAN code example for generating data. (Contains 1 table and 38 references.) (SLD)

The meaningful investigation of many problems in statistics can be solved through Monte Carlo methods. Monte Carlo studies can help solve problems that are mathematically intractable through the analysis of random samples from populations whose characteristics are known to the researcher. Using Monte Carlo simulation, the values of a statistic are observed in many samples drawn from that known population. The statistic's sampling distribution is then estimated by the relative frequency distribution actually observed in the study. The many samples are usually generated artificially through the use of computer algorithms. This paper discusses how one chooses a pseudo-random number generator, and then discusses how to use these generators to simulate data from normal and multivariate normal distributions. Several examples are provided of how one might sample from a pseudo population and the statistics that are commonly calculated during a Monte Carlo investigation. The many trials that might be used when investigating Type I and Type II errors are outlined. The paper ends with a discussion of the processes that might be used to verify that a researcher's simulation process is doing what it was intended to do. Four appendixes contain Statistical Analysis System programming code examples and a FORTRAN code example for generating data. (Contains 1 table and 38 references.) (SLD)

In the past few years, Army aviation accidents have been on the rise, due largely to increases in mission frequency and complexity, and diminishing resources. The magnitude of the resulting losses (casualties, dollars, equipment) has prompted the Commanding General of the Army Safety Center to demand a complete examination of the way safety hazards and subsequent safety controls are evaluated and selected. This project integrates value focused thinking, Monte Carlo simulation, and integer programming in response to this demand by developing and using a methodology that effectively identifies and evaluates portfolios of controls. An integer program generates portfolios of controls that maximize the reduction of hazards that contribute to Army aviation accidents. Monte Carlo simulation using the bootstrap method is used to simulate the number and types of losses resulting from accidents that occur in 100,000 UH-60 flying hours. A value model has been developed to quantify the severity of these losses. The expected performance of the portfolios of controls is calculated as the anticipated decrease in severity of losses resulting from implementation of those controls.

The radiation field over a broken stratocumulus cloud deck is simulated by the Monte Carlo method. We conducted four experiments to investigate the main factor for the observed shortwave reflectively over the FIRE flight 2 leg 5, in which reflectivity decreases almost linearly from the cloud center to cloud edge while the cloud top height and the brightness temperature remain almost constant through out the clouds. From our results, the geometry effect, however, did not contribute significantly to what has been observed. We found that the variation of the volume extinction coefficient as a function of its relative position in the cloud affects the reflectivity efficiently. Additional check of the brightness temperature of each experiment also confirms this conclusion. The cloud microphysical data showed some interesting features. We found that the cloud droplet spectrum is nearly log-normal distributed when the clouds were solid. However, whether the shift of cloud droplet spectrum toward the larger end is not certain. The decrease of number density from cloud center to cloud edges seems to have more significant effects on the optical properties.

Estimating the failure time of a product with a high degree of confidence is a difficult endeavor. Clearly, if the product is inexpensive and fails quickly, extensive tests can be run to make prediction more accurate. When the item under scrutiny is expensive, not prone to failure, or both, calculating accurate estimates and confidence bounds (CBs) becomes more difficult. Furthermore, many methods currently in use are prone to error, sometimes making a critical part appear more reliable than it actually is. Much of our military uses end-items that fall into this category. The lives of our soldiers, sailors, airmen, and Marines often depend on accurate reliability estimates for the equipment and weapons they work on every day. This thesis first introduces reliability and the common techniques for measuring it. Secondly, it shows that these estimates are often biased. Next, this bias is quantified using Monte Carlo simulation and corrected through simple tables and equations. The tables and equations can be used to map nominal confidence bounds to actual confidence bounds. Lastly, these results are applied to a Marine Corps program and a test run at a major automotive brake system manufacturer. These examples will illustrate the impact of uncorrected bias and what can be done to correct it.

We derive the exact dual to the Bosonic Hubbard model. The dual variables take the form of conserved current loops (local and global). Previously this has been done only for the very soft core model at very high density. No such approximations are made here. In particular, the dual of the hard core model is shown to have a very simple form which is then used to construct an efficient Monte Carlo algorithm which is quite similar to the World Line algorithm but with some important differences. For example, with this algorithm we can measure easily the correlation function of the order parameter (Green function), a quantity which is extremely difficult to measure with the standard World Line algorithm. We demonstrate the algorithm for the one and two dimensional hardcore Bosonic Hubbard models. We present new results especially for the Green function and zero mode filling fraction in the two dimensional hardcore model.

Localization dynamics of excitons was studied for ZnO/MgZnO and CdZnO/MgZnO quantum wells (QW). The experimental photoluminescence (PL) and absorption data were compared with the results of Monte Carlo simulation in which the excitonic hopping was modeled. The temperature-dependent PL linewidth and Stokes shift were found to be in a qualitatively reasonable agreement with the hopping model, with accounting for an additional inhomogeneous broadening for the case of linewidth. The density of localized states used in the simulation for the CdZnO QW was consistent with the absorption spectrum taken at 5 K.

To synthesize diffusion MR measurements from Monte-Carlo simulation using tissue models with sizes comparable to those of scan voxels. Larger regions enable restricting structures to be modeled in greater detail and improve accuracy and precision in synthesized diffusion-weighted measurements. We employ a localized intersection checking algorithm during substrate construction and dynamical simulation. Although common during dynamics simulation, a dynamically constructed intersection map is also applied here during substrate construction, facilitating construction of much larger substrates than would be possible with a naive "brute-force" approach. We investigate the approach's performance using a packed cylinder model of white matter, investigating optimal execution time for simulations, convergence of synthesized signals and variance in diffusion-weighted measurements over a wide range of acquisition parameters. The scheme is demonstrated with cylinder-based substrates but is also readily applicable to other geometric primitives, such as spheres or triangles. The algorithm enables models with far larger substrates to be run with no additional computational cost. The improved sampling reduces bias and variance in synthetic measurements. The new method improves accuracy, precision, and reproducibility of synthetic measurements in Monte-Carlo simulation-based data synthesis. The larger substrates it makes possible are better able to capture the complexity of the tissue we are modeling, leading to reduced bias and variance in synthesised data, compared to existing implementation of MC simulations.

The rules that specify how the information contained in DNA codes amino acids, is called "the genetic code". Using a simplified version of the Penna nodel, we are using computer simulations to investigate the importance of the genetic code and the number of amino acids in Nature on population dynamics. We find that the genetic code is not a random pairing of codons to amino acids and the number of amino acids in Nature is an optimum under mutations.

Preliminary results of Monte-Carlo simulation on Extensive Air Showers (EAS) (Ne=100,000) core is reported. For the first collision at the top of the atmosphere, high multiplicity (high rapidity, density) and a large Pt (1.5GeV average) model is assumed. Most of the simulated cores show a complicated structure.

We study the efficiency of the incomplete enumeration algorithm for linear and branched polymers. There is a qualitative difference in the efficiency in these two cases. The average time to generate an independent sample of $n$ sites for large $n$ varies as $n^2$ for linear polymers, but as $exp(c n^{\alpha})$ for branched (undirected and directed) polymers, where $0

The experimental data of extensive air showers (EAS) accompanied by gamma-families, with total energy greater than 10 TeV, were compared with a Monte Carlo simulation with a rising cross section proportional to E sup 0.04 for the p-air inelastic cross section. It is found that the absolute intensity of size spectrum of such EAS is strongly affected by the primary protons intensity at 10 to the 15th power approx. 10 to the 16th power eV region and the experimental size spectrum agrees with the simulated spectra for the p-poor primary composition better than the p-rich one.