Showing papers on "Monte Carlo molecular modeling published in 2020"

Monte Carlo Methods for Particle Transport

Abstract: Acknowledgments About the Author Introduction History of Monte Carlo Simulation Status of Monte Carlo Codes Motivation for Writing This Book Overview of the Book Recommendations to Instructors Author's Expectation References Random Variables and Sampling Introduction Random Variables Discrete Random Variable Continuous Random Variable Notes on pdf and cdf Characteristics Random Numbers Derivation of the Fundamental Formulation of Monte Carlo (FFMC) Sampling One-Dimensional Density Functions Analytical Inversion Numerical Inversion Probability Mixing Method Rejection Technique Numerical Evaluation Table Lookup Sampling Multidimensional Density Functions Example Procedures for Sampling a Few Commonly Used Distributions Normal Distribution Watt Spectrum Cosine and Sine Function Sampling Remarks References Problems Random Number Generation (RNG) Introduction Random Number Generation Approaches Pseudorandom Number Generators (PRNGs) Congruential Generators Multiple Recursive Generator Testing Randomness x2-Test Frequency Test Serial Test Gap Test Poker Test Moment Test Serial Correlation Test Serial Test via Plotting Examples for PRNG Tests Evaluation of PRNG Based on Period and Average Serial Test via Plotting Remarks References Problems Fundamentals of Probability and Statistics Introduction Expectation Value One-Dimensional Density Function Multidimensional Density Function Useful Theorems Associated with the "True Variance" Definition of Sample Expectation Values Used in Statistics Sample Mean Expected Value of the Sample Variance Precision and Accuracy of a Statistical Process Uniform Distribution Bernoulli and Binomial Distributions Geometric Distribution Poisson Distribution Normal ("Gaussian") Distribution Limit Theorems and Their Applications Corollary to the de Moivre-Laplace Limit Theorem Central Limit Theorem Formulations of Uncertainty and Relative Error for a Random Process General Random Process Special Case of Bernoulli Process Confidence Interval for Finite Sampling Introduction to Student's t-Distribution Determination of Confidence Interval and Application of the t-Distribution Test of Normality of Distribution Test of Skewness Coefficient Shapiro-Wilk Test for Normality References Problems Integrals and Associated Variance Reduction Techniques Introduction Estimation of Integrals Variance Reduction Techniques Associated with Integrals Importance Sampling Correlation Sampling Technique Stratified Sampling Technique Combined Sampling Remarks References Problems Fixed-Source Monte Carlo Particle Transport Introduction Introduction to the Linear Boltzmann Equation Introduction the Monte Carlo Method Determination of Free Flight, i.e., Path-Length Selection of Interaction Type Selection of Scattering Angle A Monte Carlo Algorithm for Estimation of Transmitted Particles Perturbation Calculations via Correlated Sampling Analysis of Monte Carlo Results Remarks References Problems Variance Reduction Techniques in Particle Transport Introduction Effectiveness of Variance Reduction Algorithms Biasing of Density Functions Implicit Capture (or Survival Biasing) Russian Roulette Biasing the Path-Length to the Next Collision Exponential Transformation Forced Collision Splitting Techniques Geometric Splitting with Russian Roulette Energy Splitting with Russian Roulette Angular Splitting with Russian Roulette Weight-Window Technique Application of Combination of Importance Sampling, pdf biasing, and Splitting Technique in Particle Transport Importance (Adjoint) Function Methodology in Deterministic Transport Theory Determination of Detector Response Use of Deterministic Importance (Adjoint) Function for Importance Sampling Remarks References Problems Tallying Introduction Major Quantities in a Particle Transport Simulation Tallying in a Steady-State System Collision Estimator Path-Length Estimator Surface-Crossing Estimator Analytical Estimator Tallying in a Time-Dependent System Tallies in Nonanalog Simulations Estimation of Relative Error Associated Physical Quantities Propagation of Error Remarks References Problems Geometry and Particle Tracking Introduction Discussion on a Combinatorial Geometry Approach Definition of Surfaces Definition of Cells Examples Description of Boundary Conditions Particle Tracking Remarks References Problems Eigenvalue or Criticality Monte Carlo Particle Transport Introduction Theory of Power-Iteration for Eigenvalue Problems Monte Carlo Eigenvalue Calculation Random Variables Associated with a Fission Process Direction of Fission Neutrons Monte Carlo Simulation of a Criticality Problem Estimators for Sampling Fission Neutrons Issues Associated with the Standard Eigenvalue Calculation Procedure Diagnostic Methods for Source Convergence Fission Matrix (FM) Methodology Issues Associated with the FM Method Remarks References Problems Vector and Parallel Processing of Monte Carlo Methods Introduction Vector Processing Vector Performance Parallel Processing Parallel Performance Vectorization of Monte Carlo Methods Parallelization of the Monte Carlo Methods Other Possible Parallel Monte Carlo Algorithms Development of a Parallel Algorithm Using MPI Remarks References Problems Appendices One to Six

Quantifying the Uncertainty in Model Parameters Using Gaussian Process-Based Markov Chain Monte Carlo: An Application to Cardiac Electrophysiological Models

Abstract: Estimation of patient-specific model parameters is important for personalized modeling, although sparse and noisy clinical data can introduce significant uncertainty in the estimated parameter values This importance source of uncertainty, if left unquantified, will lead to unknown variability in model outputs that hinder their reliable adoptions Probabilistic estimation model parameters, however, remains an unresolved challenge because standard Markov Chain Monte Carlo sampling requires repeated model simulations that are computationally infeasible A common solution is to replace the simulation model with a computationally-efficient surrogate for a faster sampling However, by sampling from an approximation of the exact posterior probability density function (pdf) of the parameters, the efficiency is gained at the expense of sampling accuracy In this paper, we address this issue by integrating surrogate modeling into Metropolis Hasting (MH) sampling of the exact posterior pdfs to improve its acceptance rate It is done by first quickly constructing a Gaussian process (GP) surrogate of the exact posterior pdfs using deterministic optimization This efficient surrogate is then used to modify commonly-used proposal distributions in MH sampling such that only proposals accepted by the surrogate will be tested by the exact posterior pdf for acceptance/rejection, reducing unnecessary model simulations at unlikely candidates Synthetic and real-data experiments using the presented method show a significant gain in computational efficiency without compromising the accuracy In addition, insights into the non-identifiability and heterogeneity of tissue properties can be gained from the obtained posterior distributions

High-efficiency monte carlo molecular simulation method for calculating water/benzene liquid phase interfacial tension by means of improved ewald sum

Abstract: A high-efficiency Monte Carlo molecular simulation method for calculating a benzene and water liquid phase interfacial tension by means of an improved Ewald sum, said method comprising the following steps: step A: initializing conformation: preparing two simulation boxes, the size of both being (30×30×45)-(35×35×55), placing 1200-2000 water molecules on grid points of a first box, and placing 230-380 benzene molecules on grid points of a second box; step B: simulation force field selection: using a TraPPE force field for the benzene molecules, and using a TIP4P/2005 force field for the water molecules; step C: respectively performing a Monte Carlo simulation on the two boxes under a canonical ensemble; step D: putting the water box and the benzene box together along the z direction to form a single (30×30×90A)-(35×35×110A) large box, and performing 50000-80000 Monte Carlo cycles, so that the system is re-balanced; step E: after the system is balanced, entering a data collection stage. The method provides a common process for molecular simulation, and improves the calculation means of an Ewald sum portion, such that after using the Ewald sum calculation means, the overall simulation efficiency may be increased by 20%.