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Monte Carlo simulation

Arghya Chakravorty, Zhe Jia, Lin Li, Shan Zhao, Emil Alexov
Typically, the ensemble average polar component of solvation energy (∆G_polar^solv) of a macromolecule is computed using molecular dynamics (MD) or Monte Carlo (MC) simulations to generate conformational ensemble and then single/rigid conformation solvation energy calculation is performed on each of snapshots. The primary objective of this work is to demonstrate that Poisson-Boltzmann (PB) based approach using a Gaussian-based smooth dielectric function for macromolecular modeling previously developed by us (Li et al...
January 19, 2018: Journal of Chemical Theory and Computation
Hukum Chandra, Sushil Kumar, Kaustav Aditya
Binary data are often of interest in many small areas of applications. The use of standard small area estimation methods based on linear mixed models becomes problematic for such data. An empirical plug-in predictor (EPP) under a unit-level generalized linear mixed model with logit link function is often used for the estimation of a small area proportion. However, this EPP requires the availability of unit-level population information for auxiliary data that may not be always accessible. As a consequence, in many practical situations, this EPP approach cannot be applied...
January 19, 2018: Biometrical Journal. Biometrische Zeitschrift
Oleg Buller, Hong Wang, Wenchong Wang, Lifeng Chi, Andreas Heuer
The pre-patterning of a substrate to create energetically more attractive or repulsive regions allows one to generate a variety of structures in physical vapor deposition experiments. A particularly interesting structure is generated if the energetically attractive region forms a rectangular grid. For specific combinations of the particle flux, the substrate temperature and the lattice size it is possible to generate exactly one cluster per cell, giving rise to nucleation control. Here, we show that the experimental observations of nucleation control can be very well understood from a theoretical perspective...
January 19, 2018: Physical Chemistry Chemical Physics: PCCP
Elham Hosseinzadeh, Nooshin Banaee, Hassan Ali Nedaie
Aim: The aim of this study is to calculate neutron contamination at the presence of circular cones irradiating by 18 MV photons using Monte Carlo code. Background: Small photon fields are one of the most useful methods in radiotherapy. One of the techniques for shaping small photon beams is applying circular cones made of lead. Using this method in high energy photon due to neutron contamination is a crucial issue. Materials and methods: Initially, Varian linac producing 18 MV photons was simulated and after validating the code, various circular cones were also simulated...
January 2018: Reports of Practical Oncology and Radiotherapy
Fernando Racimo, Jeremy J Berg, Joseph K Pickrell
An open question in human evolution is the importance of polygenic adaptation: adaptive changes in the mean of a multifactorial trait due to shifts in allele frequencies across many loci. In recent years, several methods have been developed to detect polygenic adaptation using loci identified in genome-wide association studies (GWAS). Though powerful, these methods suffer from limited interpretability: they can detect which sets of populations have evidence for polygenic adaptation, but are unable to reveal where in the history of multiple populations these processes occurred...
January 18, 2018: Genetics
Shun Okushima, Toshihiro Kawakatsu
We perform a series of Monte Carlo simulations on an interface between a liquid crystal (LC) material in isotropic phase in its bulk and a surfactant membrane. These two objects are simulated using coarse-grained molecular models. We estimate physical properties of the membrane such as the interfacial tension and the bending rigidity, focusing on the anchoring effects of the membrane on the LC. According to our simulation results, when the strength of the homeotropic anchoring denoted by the anchoring parameter ξ is increased, the interfacial tension decreases and the bending rigidity first increases in ξ<ξ_{m}, and it then decreases in ξ_{m}<ξ...
November 2017: Physical Review. E
Markus Wallerberger, Emanuel Gull
The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and programming bugs. However, the testing paradigms developed for deterministic algorithms have proven to be ill suited for stochastic algorithms. In this paper we demonstrate explicitly how the technique of statistical hypothesis testing, which is in wide use in other fields of science, can be used to devise automatic and reliable tests for Monte Carlo methods, and we show that these tests are able to detect some of the common problems encountered in stochastic scientific simulations...
November 2017: Physical Review. E
Francisco Vega Reyes, Antonio Lasanta, Andrés Santos, Vicente Garzó
The dynamical properties of a tracer or impurity particle immersed in a host gas of inelastic and rough hard spheres in the homogeneous cooling state is studied. Specifically, the breakdown of energy equipartition as characterized by the tracer/host ratios of translational and rotational temperatures is analyzed by exploring a wide spectrum of values of the control parameters of the system (masses, moments of inertia, sizes, and coefficients of restitution). Three complementary approaches are considered. On the theoretical side, the Boltzmann and Boltzmann-Lorentz equations (both assuming the molecular chaos ansatz) are solved by means of a multitemperature Maxwellian approximation for the velocity distribution functions...
November 2017: Physical Review. E
Anna Yu Solovyova, Ekaterina A Elfimova, Alexey O Ivanov, Philip J Camp
The effects of particle-size polydispersity on the magnetostatic properties of concentrated ferrofluids are studied using theory and computer simulation. The second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)1063-651X10.1103/PhysRevE.64.041405] has been extended by calculating additional terms of higher order in the dipolar coupling constant in the expansions of the initial magnetic susceptibility and the magnetization curve. The theoretical predictions have been tested rigorously against results from Monte Carlo simulations of model monodisperse, bidisperse, and highly polydisperse ferrofluids...
November 2017: Physical Review. E
David Santillán, Juan-Carlos Mosquera, Luis Cueto-Felgueroso
Hydraulic fracture trajectories in rocks and other materials are highly affected by spatial heterogeneity in their mechanical properties. Understanding the complexity and structure of fluid-driven fractures and their deviation from the predictions of homogenized theories is a practical problem in engineering and geoscience. We conduct a Monte Carlo simulation study to characterize the influence of heterogeneous mechanical properties on the trajectories of hydraulic fractures propagating in elastic media. We generate a large number of random fields of mechanical properties and simulate pressure-driven fracture propagation using a phase-field model...
November 2017: Physical Review. E
Akhilesh Pandey, Avanish Kumar, Sanjay Puri
Dyson demonstrated an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. We introduce finite-range Coulomb gas (FRCG) models via a Brownian matrix process, and study them analytically and by Monte Carlo simulations. These models yield new universality classes, and provide a theoretical framework for the study of banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has the effective range d=b^{2}/N=α^{2}/N, for large N matrix dimensionality...
November 2017: Physical Review. E
Nathan Rebello, Vaidyanathan Sethuraman, Gregory Blachut, Christopher J Ellison, C Grant Willson, Venkat Ganesan
Single chain in mean-field Monte Carlo simulations were employed to study the self-assembly of block copolymers (BCP) in thin films that use trapezoidal guidelines to direct the orientation and alignment of lamellar patterns. The present study explored the influence of sidewall interactions and geometry of the trapezoidal guidelines on the self-assembly of perpendicularly oriented lamellar morphologies. When both the sidewall and the top surface exhibit preferential interactions to the same block of the BCP, trapezoidal guidelines with intermediate taper angles were found to result in less defective perpendicularly orientated morphologies...
November 2017: Physical Review. E
Lei Wang
Boltzmann machines are physics informed generative models with broad applications in machine learning. They model the probability distribution of an input data set with latent variables and generate new samples accordingly. Applying the Boltzmann machines back to physics, they are ideal recommender systems to accelerate the Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann machines can even give different cluster Monte Carlo algorithms...
November 2017: Physical Review. E
Stephan Mertens, Iwan Jensen, Robert M Ziff
The number of clusters per site n(p) in percolation at the critical point p=p_{c} is not itself a universal quantity; it depends upon the lattice and percolation type (site or bond). However, many of its properties, including finite-size corrections, scaling behavior with p, and amplitude ratios, show various degrees of universal behavior. Some of these are universal in the sense that the behavior depends upon the shape of the system, but not lattice type. Here, we elucidate the various levels of universality for elements of n(p) both theoretically and by carrying out extensive studies on several two- and three-dimensional systems, by high-order series analysis, Monte Carlo simulation, and exact enumeration...
November 2017: Physical Review. E
Zoltán Néda, Ferenc Járai-Szabó, Szilárd Boda
The Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a one-dimensional (1D) lattice. Cells can grow with constant speed and continuously nucleate on the empty sites. We offer an alternative mean-field-like approach for describing theoretically the dynamics and derive an analytical cell-size distribution function. Our method reproduces the same scaling laws as the KJMA theory and has the advantage that it leads to a simple closed form for the cell-size distribution function. It is shown that a Weibull distribution is appropriate for describing the final cell-size distribution...
October 2017: Physical Review. E
Zhenjiu Wang, Fakher F Assaad, Francesco Parisen Toldin
We introduce a quantum Monte Carlo method at finite temperature for interacting fermionic models in the canonical ensemble, where the conservation of the particle number is enforced. Although general thermodynamic arguments ensure the equivalence of the canonical and the grand-canonical ensembles in the thermodynamic limit, their approach to the infinite-volume limit is distinctively different. Observables computed in the canonical ensemble generically display a finite-size correction proportional to the inverse volume, whereas in the grand-canonical ensemble the approach is exponential in the ratio of the linear size over the correlation length...
October 2017: Physical Review. E
Cody A Melton, Lubos Mitas
We study several aspects of the recently introduced fixed-phase spinor diffusion Monte Carlo method, in particular, its relation to the fixed-node method and its potential use as a general approach for electronic structure calculations. We illustrate constructions of spinor-based wave functions with the full space-spin symmetry without assigning up or down spin labels to particular electrons, effectively "complexifying" even ordinary real-valued wave functions for Hamiltonians without spin terms. Interestingly, with proper choice of the simulation parameters and spin variables, such fixed-phase calculations enable one to reach also the fixed-node limit...
October 2017: Physical Review. E
T Cary, R R P Singh, R T Scalettar
We explore the phase diagram of Ising spins on one-dimensional chains that criss-cross in two perpendicular directions and that are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian that has been proposed as a model of magnetic behavior in Nb_{12}O_{29} and also, conceptually, as a geometry that is intermediate between one and two dimensions. Using mean-field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases...
October 2017: Physical Review. E
D B Abraham, A Maciołek, A Squarcini, O Vasilyev
We examine in detail the theoretical foundations of striking long-range couplings emerging in arrays of fluid cells connected by narrow channels by using a lattice gas (Ising model) description of a system. We present a reexamination of the well known exact determination of the two-point correlation function along the edge of a channel using the transfer matrix technique and a different interpretation is provided. The explicit form of the correlation length is found to grow exponentially with the cross section of the channels at the bulk two-phase coexistence...
October 2017: Physical Review. E
M Kumar, S Chatterjee, R Paul, S Puri
We present a comprehensive Monte Carlo study of domain growth in the random-bond XY model with nonconserved kinetics. The presence of quenched disorder slows down domain growth in d=2,3. In d=2, we observe power-law growth with a disorder-dependent exponent on the time scales of our simulation. In d=3, we see the signature of an asymptotically logarithmic growth regime. The scaling functions for the real-space correlation function are seen to be independent of the disorder. However, the same does not apply for the two-time autocorrelation function, demonstrating the breakdown of superuniversality...
October 2017: Physical Review. E
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