Markov Chain Monte Carlo from Lagrangian Dynamics
Lan, Shiwei; Stathopoulos, Vasileios; Shahbaba, Babak; Girolami, Mark
2014-01-01
Hamiltonian Monte Carlo (HMC) improves the computational e ciency of the Metropolis-Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC's benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to Lagrangian dynamics. Experimental results suggests that our method improves RHMC's overall computational e ciency in the cases considered. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/Codes.html) in order to allow replication of the results reported in this paper. PMID:26240515
Accelerated Monte Carlo by Embedded Cluster Dynamics
NASA Astrophysics Data System (ADS)
Brower, R. C.; Gross, N. A.; Moriarty, K. J. M.
1991-07-01
We present an overview of the new methods for embedding Ising spins in continuous fields to achieve accelerated cluster Monte Carlo algorithms. The methods of Brower and Tamayo and Wolff are summarized and variations are suggested for the O( N) models based on multiple embedded Z2 spin components and/or correlated projections. Topological features are discussed for the XY model and numerical simulations presented for d=2, d=3 and mean field theory lattices.
Pattern Recognition for a Flight Dynamics Monte Carlo Simulation
NASA Technical Reports Server (NTRS)
Restrepo, Carolina; Hurtado, John E.
2011-01-01
The design, analysis, and verification and validation of a spacecraft relies heavily on Monte Carlo simulations. Modern computational techniques are able to generate large amounts of Monte Carlo data but flight dynamics engineers lack the time and resources to analyze it all. The growing amounts of data combined with the diminished available time of engineers motivates the need to automate the analysis process. Pattern recognition algorithms are an innovative way of analyzing flight dynamics data efficiently. They can search large data sets for specific patterns and highlight critical variables so analysts can focus their analysis efforts. This work combines a few tractable pattern recognition algorithms with basic flight dynamics concepts to build a practical analysis tool for Monte Carlo simulations. Current results show that this tool can quickly and automatically identify individual design parameters, and most importantly, specific combinations of parameters that should be avoided in order to prevent specific system failures. The current version uses a kernel density estimation algorithm and a sequential feature selection algorithm combined with a k-nearest neighbor classifier to find and rank important design parameters. This provides an increased level of confidence in the analysis and saves a significant amount of time.
Bias in Dynamic Monte Carlo Alpha Calculations
Sweezy, Jeremy Ed; Nolen, Steven Douglas; Adams, Terry R.; Trahan, Travis John
2015-02-06
A 1/N bias in the estimate of the neutron time-constant (commonly denoted as α) has been seen in dynamic neutronic calculations performed with MCATK. In this paper we show that the bias is most likely caused by taking the logarithm of a stochastic quantity. We also investigate the known bias due to the particle population control method used in MCATK. We conclude that this bias due to the particle population control method is negligible compared to other sources of bias.
Relaxation dynamics in small clusters: A modified Monte Carlo approach
Pal, Barnana
2008-02-01
Relaxation dynamics in two-dimensional atomic clusters consisting of mono-atomic particles interacting through Lennard-Jones (L-J) potential has been investigated using Monte Carlo simulation. A modification of the conventional Metropolis algorithm is proposed to introduce realistic thermal motion of the particles moving in the interacting L-J potential field. The proposed algorithm leads to a quick equilibration from the nonequilibrium cluster configuration in a certain temperature regime, where the relaxation time ({tau}), measured in terms of Monte Carlo Steps (MCS) per particle, vary inversely with the square root of system temperature ({radical}T) and pressure (P); {tau} {proportional_to} (P{radical}T){sup -1}. From this a realistic correlation between MCS and time has been predicted.
Monte Carlo Study of Real Time Dynamics on the Lattice
NASA Astrophysics Data System (ADS)
Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F.; Vartak, Sohan; Warrington, Neill C.
2016-08-01
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from a highly oscillatory phase of the path integral. In this Letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and, in principle, applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.
Dynamic Load Balancing of Parallel Monte Carlo Transport Calculations
O'Brien, M; Taylor, J; Procassini, R
2004-12-22
The performance of parallel Monte Carlo transport calculations which use both spatial and particle parallelism is increased by dynamically assigning processors to the most worked domains. Since the particle work load varies over the course of the simulation, this algorithm determines each cycle if dynamic load balancing would speed up the calculation. If load balancing is required, a small number of particle communications are initiated in order to achieve load balance. This method has decreased the parallel run time by more than a factor of three for certain criticality calculations.
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.
Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo
White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; ...
2015-07-07
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficientmore » as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.« less
2010-10-20
The "Monte Carlo Benchmark" (MCB) is intended to model the computatiional performance of Monte Carlo algorithms on parallel architectures. It models the solution of a simple heuristic transport equation using a Monte Carlo technique. The MCB employs typical features of Monte Carlo algorithms such as particle creation, particle tracking, tallying particle information, and particle destruction. Particles are also traded among processors using MPI calls.
Thermally activated repolarization of antiferromagnetic particles: Monte Carlo dynamics
NASA Astrophysics Data System (ADS)
Soloviev, S. V.; Popkov, A. F.; Knizhnik, A. A.; Iskandarova, I. M.
2017-02-01
Based on the equation of motion of an antiferromagnetic moment, taking into account a random field of thermal fluctuations, we propose a Monte Carlo (MC) scheme for the numerical simulation of the evolutionary dynamics of an antiferromagnetic particle, corresponding to the Langevin dynamics in the Kramers theory for the two-well potential. Conditions for the selection of the sphere of fluctuations of random deviations of the antiferromagnetic vector at an MC time step are found. A good agreement with the theory of Kramers thermal relaxation is demonstrated for varying temperatures and heights of energy barrier over a wide range of integration time steps in an overdamped regime. Based on the developed scheme, we performed illustrative calculations of the temperature drift of the exchange bias under the fast annealing of a ferromagnet-antiferromagnet structure, taking into account the random variation of anisotropy directions in antiferromagnetic grains and their sizes. The proposed approach offers promise for modeling magnetic sensors and spintronic memory devices containing heterostructures with antiferromagnetic layers.
Surface reconstruction in reactive dynamics: A kinetic Monte Carlo approach
NASA Astrophysics Data System (ADS)
Noussiou, V. K.; Provata, A.
2007-07-01
The oscillatory CO oxidation reaction on the restructuring surface of Pt(1 0 0) is studied through a mesoscopic kinetic Monte Carlo (KMC) approach. The present model is an extension of the standard ZGB model with specific attention to the emergence of oscillations in surface reactions. A square and a purely hexagonal lattice are used as substrates on which the CO oxidation reaction steps take place. The dynamics of the reaction on the two substrates exhibit the ZGB kinetic phase transitions, at different kinetic parameter values for each substrate. Surface reconstruction is modelled through switching between the two lattice types. Oscillations are produced in those parametric areas where the steady state concentrations on the two substrates are considerably different. The parametric area where notable oscillations are observed is narrow, but is greatly enhanced when different sticking coefficients of oxygen are taken into account. CO diffusion introduced microscopically to the model on the hexagonal lattice shifts the kinetic transition points and increases considerably the time needed to reach the steady state.
Efficiency in nonequilibrium molecular dynamics Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Radak, Brian K.; Roux, Benoît
2016-10-01
Hybrid algorithms combining nonequilibrium molecular dynamics and Monte Carlo (neMD/MC) offer a powerful avenue for improving the sampling efficiency of computer simulations of complex systems. These neMD/MC algorithms are also increasingly finding use in applications where conventional approaches are impractical, such as constant-pH simulations with explicit solvent. However, selecting an optimal nonequilibrium protocol for maximum efficiency often represents a non-trivial challenge. This work evaluates the efficiency of a broad class of neMD/MC algorithms and protocols within the theoretical framework of linear response theory. The approximations are validated against constant pH-MD simulations and shown to provide accurate predictions of neMD/MC performance. An assessment of a large set of protocols confirms (both theoretically and empirically) that a linear work protocol gives the best neMD/MC performance. Finally, a well-defined criterion for optimizing the time parameters of the protocol is proposed and demonstrated with an adaptive algorithm that improves the performance on-the-fly with minimal cost.
Monte Carlo-based simulation of dynamic jaws tomotherapy
Sterpin, E.; Chen, Y.; Chen, Q.; Lu, W.; Mackie, T. R.; Vynckier, S.
2011-09-15
Purpose: Original TomoTherapy systems may involve a trade-off between conformity and treatment speed, the user being limited to three slice widths (1.0, 2.5, and 5.0 cm). This could be overcome by allowing the jaws to define arbitrary fields, including very small slice widths (<1 cm), which are challenging for a beam model. The aim of this work was to incorporate the dynamic jaws feature into a Monte Carlo (MC) model called TomoPen, based on the MC code PENELOPE, previously validated for the original TomoTherapy system. Methods: To keep the general structure of TomoPen and its efficiency, the simulation strategy introduces several techniques: (1) weight modifiers to account for any jaw settings using only the 5 cm phase-space file; (2) a simplified MC based model called FastStatic to compute the modifiers faster than pure MC; (3) actual simulation of dynamic jaws. Weight modifiers computed with both FastStatic and pure MC were compared. Dynamic jaws simulations were compared with the convolution/superposition (C/S) of TomoTherapy in the ''cheese'' phantom for a plan with two targets longitudinally separated by a gap of 3 cm. Optimization was performed in two modes: asymmetric jaws-constant couch speed (''running start stop,'' RSS) and symmetric jaws-variable couch speed (''symmetric running start stop,'' SRSS). Measurements with EDR2 films were also performed for RSS for the formal validation of TomoPen with dynamic jaws. Results: Weight modifiers computed with FastStatic were equivalent to pure MC within statistical uncertainties (0.5% for three standard deviations). Excellent agreement was achieved between TomoPen and C/S for both asymmetric jaw opening/constant couch speed and symmetric jaw opening/variable couch speed, with deviations well within 2%/2 mm. For RSS procedure, agreement between C/S and measurements was within 2%/2 mm for 95% of the points and 3%/3 mm for 98% of the points, where dose is greater than 30% of the prescription dose (gamma analysis
Kalos, M.
2006-05-09
The Monte Carlo example programs VARHATOM and DMCATOM are two small, simple FORTRAN programs that illustrate the use of the Monte Carlo Mathematical technique for calculating the ground state energy of the hydrogen atom.
Inchworm Monte Carlo for exact non-adiabatic dynamics. I. Theory and algorithms
NASA Astrophysics Data System (ADS)
Chen, Hsing-Ta; Cohen, Guy; Reichman, David R.
2017-02-01
In this paper, we provide a detailed description of the inchworm Monte Carlo formalism for the exact study of real-time non-adiabatic dynamics. This method optimally recycles Monte Carlo information from earlier times to greatly suppress the dynamical sign problem. Using the example of the spin-boson model, we formulate the inchworm expansion in two distinct ways: The first with respect to an expansion in the system-bath coupling and the second as an expansion in the diabatic coupling. The latter approach motivates the development of a cumulant version of the inchworm Monte Carlo method, which has the benefit of improved scaling. This paper deals completely with methodology, while Paper II provides a comprehensive comparison of the performance of the inchworm Monte Carlo algorithms to other exact methodologies as well as a discussion of the relative advantages and disadvantages of each.
NASA Astrophysics Data System (ADS)
Chen, Hsing-Ta; Cohen, Guy; Reichman, David R.
2017-02-01
In this second paper of a two part series, we present extensive benchmark results for two different inchworm Monte Carlo expansions for the spin-boson model. Our results are compared to previously developed numerically exact approaches for this problem. A detailed discussion of convergence and error propagation is presented. Our results and analysis allow for an understanding of the benefits and drawbacks of inchworm Monte Carlo compared to other approaches for exact real-time non-adiabatic quantum dynamics.
Brown, F.B.; Sutton, T.M.
1996-02-01
This report is composed of the lecture notes from the first half of a 32-hour graduate-level course on Monte Carlo methods offered at KAPL. These notes, prepared by two of the principle developers of KAPL`s RACER Monte Carlo code, cover the fundamental theory, concepts, and practices for Monte Carlo analysis. In particular, a thorough grounding in the basic fundamentals of Monte Carlo methods is presented, including random number generation, random sampling, the Monte Carlo approach to solving transport problems, computational geometry, collision physics, tallies, and eigenvalue calculations. Furthermore, modern computational algorithms for vector and parallel approaches to Monte Carlo calculations are covered in detail, including fundamental parallel and vector concepts, the event-based algorithm, master/slave schemes, parallel scaling laws, and portability issues.
NASA Astrophysics Data System (ADS)
Guan, Fada
Monte Carlo method has been successfully applied in simulating the particles transport problems. Most of the Monte Carlo simulation tools are static and they can only be used to perform the static simulations for the problems with fixed physics and geometry settings. Proton therapy is a dynamic treatment technique in the clinical application. In this research, we developed a method to perform the dynamic Monte Carlo simulation of proton therapy using Geant4 simulation toolkit. A passive-scattering treatment nozzle equipped with a rotating range modulation wheel was modeled in this research. One important application of the Monte Carlo simulation is to predict the spatial dose distribution in the target geometry. For simplification, a mathematical model of a human body is usually used as the target, but only the average dose over the whole organ or tissue can be obtained rather than the accurate spatial dose distribution. In this research, we developed a method using MATLAB to convert the medical images of a patient from CT scanning into the patient voxel geometry. Hence, if the patient voxel geometry is used as the target in the Monte Carlo simulation, the accurate spatial dose distribution in the target can be obtained. A data analysis tool---root was used to score the simulation results during a Geant4 simulation and to analyze the data and plot results after simulation. Finally, we successfully obtained the accurate spatial dose distribution in part of a human body after treating a patient with prostate cancer using proton therapy.
Molecular Dynamics, Monte Carlo Simulations, and Langevin Dynamics: A Computational Review
Paquet, Eric; Viktor, Herna L.
2015-01-01
Macromolecular structures, such as neuraminidases, hemagglutinins, and monoclonal antibodies, are not rigid entities. Rather, they are characterised by their flexibility, which is the result of the interaction and collective motion of their constituent atoms. This conformational diversity has a significant impact on their physicochemical and biological properties. Among these are their structural stability, the transport of ions through the M2 channel, drug resistance, macromolecular docking, binding energy, and rational epitope design. To assess these properties and to calculate the associated thermodynamical observables, the conformational space must be efficiently sampled and the dynamic of the constituent atoms must be simulated. This paper presents algorithms and techniques that address the abovementioned issues. To this end, a computational review of molecular dynamics, Monte Carlo simulations, Langevin dynamics, and free energy calculation is presented. The exposition is made from first principles to promote a better understanding of the potentialities, limitations, applications, and interrelations of these computational methods. PMID:25785262
NASA Astrophysics Data System (ADS)
Tringe, J. W.; Ileri, N.; Levie, H. W.; Stroeve, P.; Ustach, V.; Faller, R.; Renaud, P.
2015-08-01
We use Molecular Dynamics and Monte Carlo simulations to examine molecular transport phenomena in nanochannels, explaining four orders of magnitude difference in wheat germ agglutinin (WGA) protein diffusion rates observed by fluorescence correlation spectroscopy (FCS) and by direct imaging of fluorescently-labeled proteins. We first use the ESPResSo Molecular Dynamics code to estimate the surface transport distance for neutral and charged proteins. We then employ a Monte Carlo model to calculate the paths of protein molecules on surfaces and in the bulk liquid transport medium. Our results show that the transport characteristics depend strongly on the degree of molecular surface coverage. Atomic force microscope characterization of surfaces exposed to WGA proteins for 1000 s show large protein aggregates consistent with the predicted coverage. These calculations and experiments provide useful insight into the details of molecular motion in confined geometries.
Hybrid Monte Carlo/Molecular Dynamics Simulation of a Refractory Metal High Entropy Alloy
NASA Astrophysics Data System (ADS)
Widom, Michael; Huhn, W. P.; Maiti, S.; Steurer, W.
2014-01-01
The high entropy alloy containing refractory metals Mo-Nb-Ta-W has a body-centered cubic structure, which is not surprising given the complete mutual solubility in BCC solid solutions of all pairs of the constituent elements. However, first principles total energy calculations for the binaries reveal a set of distinct energy minimizing structures implying the likelihood of chemically ordered low-temperature phases. We apply a hybrid Monte Carlo and molecular dynamics method to evaluate the temperature-dependent chemical order. Monte Carlo species swaps allow for equilibration of the structure that cannot be achieved by conventional molecular dynamics. At 300 K (27 °C), a cesium-chloride ordering emerges between mixed (Nb,Ta) sites and mixed (Mo,W) sites. This order is lost at elevated temperatures.
Cluster Monte Carlo dynamics for the antiferromagnetic Ising model on a triangular lattice
NASA Astrophysics Data System (ADS)
Zhang, G. M.; Yang, C. Z.
1994-11-01
Within the general cluster framework of Kandel, Ben-Av, and Domany, we develop a cluster algorithm for Monte Carlo simulations of the antiferromagnetic Ising model on a triangular lattice. The algorithm does not suffer from problems of metastability and is extremely efficient even at T=0, which allows us to extract the static exponent η=0.5 as well as the effective dynamical critical exponent of the algorithm z=0.64+/-0.02.
Monte Carlo Study of Real Time Dynamics on the Lattice.
Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F; Vartak, Sohan; Warrington, Neill C
2016-08-19
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from a highly oscillatory phase of the path integral. In this Letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and, in principle, applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.
Monte Carlo Reliability Analysis.
1987-10-01
to Stochastic Processes , Prentice-Hall, Englewood Cliffs, NJ, 1975. (5) R. E. Barlow and F. Proscham, Statistical TheorX of Reliability and Life...Lewis and Z. Tu, "Monte Carlo Reliability Modeling by Inhomogeneous ,Markov Processes, Reliab. Engr. 16, 277-296 (1986). (4) E. Cinlar, Introduction
Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models
NASA Astrophysics Data System (ADS)
Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido
2016-06-01
We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.
A Grand Canonical Monte Carlo-Brownian dynamics algorithm for simulating ion channels.
Im, W; Seefeld, S; Roux, B
2000-01-01
A computational algorithm based on Grand Canonical Monte Carlo (GCMC) and Brownian Dynamics (BD) is described to simulate the movement of ions in membrane channels. The proposed algorithm, GCMC/BD, allows the simulation of ion channels with a realistic implementation of boundary conditions of concentration and transmembrane potential. The method is consistent with a statistical mechanical formulation of the equilibrium properties of ion channels (; Biophys. J. 77:139-153). The GCMC/BD algorithm is illustrated with simulations of simple test systems and of the OmpF porin of Escherichia coli. The approach provides a framework for simulating ion permeation in the context of detailed microscopic models. PMID:10920012
Development of a dynamic simulation mode in Serpent 2 Monte Carlo code
Leppaenen, J.
2013-07-01
This paper presents a dynamic neutron transport mode, currently being implemented in the Serpent 2 Monte Carlo code for the purpose of simulating short reactivity transients with temperature feedback. The transport routine is introduced and validated by comparison to MCNP5 calculations. The method is also tested in combination with an internal temperature feedback module, which forms the inner part of a multi-physics coupling scheme in Serpent 2. The demo case for the coupled calculation is a reactivity-initiated accident (RIA) in PWR fuel. (authors)
Wollaber, Allan Benton
2016-06-16
This is a powerpoint presentation which serves as lecture material for the Parallel Computing summer school. It goes over the fundamentals of the Monte Carlo calculation method. The material is presented according to the following outline: Introduction (background, a simple example: estimating π), Why does this even work? (The Law of Large Numbers, The Central Limit Theorem), How to sample (inverse transform sampling, rejection), and An example from particle transport.
Monte Carlo eikonal scattering
NASA Astrophysics Data System (ADS)
Gibbs, W. R.; Dedonder, J. P.
2012-08-01
Background: The eikonal approximation is commonly used to calculate heavy-ion elastic scattering. However, the full evaluation has only been done (without the use of Monte Carlo techniques or additional approximations) for α-α scattering.Purpose: Develop, improve, and test the Monte Carlo eikonal method for elastic scattering over a wide range of nuclei, energies, and angles.Method: Monte Carlo evaluation is used to calculate heavy-ion elastic scattering for heavy nuclei including the center-of-mass correction introduced in this paper and the Coulomb interaction in terms of a partial-wave expansion. A technique for the efficient expansion of the Glauber amplitude in partial waves is developed.Results: Angular distributions are presented for a number of nuclear pairs over a wide energy range using nucleon-nucleon scattering parameters taken from phase-shift analyses and densities from independent sources. We present the first calculations of the Glauber amplitude, without further approximation, and with realistic densities for nuclei heavier than helium. These densities respect the center-of-mass constraints. The Coulomb interaction is included in these calculations.Conclusion: The center-of-mass and Coulomb corrections are essential. Angular distributions can be predicted only up to certain critical angles which vary with the nuclear pairs and the energy, but we point out that all critical angles correspond to a momentum transfer near 1 fm-1.
A new Monte Carlo method for dynamical evolution of non-spherical stellar systems
NASA Astrophysics Data System (ADS)
Vasiliev, Eugene
2015-01-01
We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after each timestep using local velocity diffusion coefficients from the standard two-body relaxation theory. The potential and diffusion coefficients are updated after an interval of time that is a small fraction of the relaxation time, but may be longer than the dynamical time. Thus, our approach is a bridge between the Spitzer's formulation of the Monte Carlo method and the temporally smoothed self-consistent field method. The primary advantages are the ability to follow the secular evolution of shape of the stellar system, and the possibility of scaling the amount of two-body relaxation to the necessary value, unrelated to the actual number of particles in the simulation. Possible future applications of this approach in galaxy dynamics include the problem of consumption of stars by a massive black hole in a non-spherical galactic nucleus, evolution of binary supermassive black holes, and the influence of chaos on the shape of galaxies, while for globular clusters it may be used for studying the influence of rotation.
Dynamic measurements and uncertainty estimation of clinical thermometers using Monte Carlo method
NASA Astrophysics Data System (ADS)
Ogorevc, Jaka; Bojkovski, Jovan; Pušnik, Igor; Drnovšek, Janko
2016-09-01
Clinical thermometers in intensive care units are used for the continuous measurement of body temperature. This study describes a procedure for dynamic measurement uncertainty evaluation in order to examine the requirements for clinical thermometer dynamic properties in standards and recommendations. In this study thermistors were used as temperature sensors, transient temperature measurements were performed in water and air and the measurement data were processed for the investigation of thermometer dynamic properties. The thermometers were mathematically modelled. A Monte Carlo method was implemented for dynamic measurement uncertainty evaluation. The measurement uncertainty was analysed for static and dynamic conditions. Results showed that dynamic uncertainty is much larger than steady-state uncertainty. The results of dynamic uncertainty analysis were applied on an example of clinical measurements and were compared to current requirements in ISO standard for clinical thermometers. It can be concluded that there was no need for dynamic evaluation of clinical thermometers for continuous measurement, while dynamic measurement uncertainty was within the demands of target uncertainty. Whereas in the case of intermittent predictive thermometers, the thermometer dynamic properties had a significant impact on the measurement result. Estimation of dynamic uncertainty is crucial for the assurance of traceable and comparable measurements.
Johannesson, G; Chow, F K; Glascoe, L; Glaser, R E; Hanley, W G; Kosovic, B; Krnjajic, M; Larsen, S C; Lundquist, J K; Mirin, A A; Nitao, J J; Sugiyama, G A
2005-11-16
Atmospheric releases of hazardous materials are highly effective means to impact large populations. We propose an atmospheric event reconstruction framework that couples observed data and predictive computer-intensive dispersion models via Bayesian methodology. Due to the complexity of the model framework, a sampling-based approach is taken for posterior inference that combines Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) strategies.
Monte Carlo fluorescence microtomography
NASA Astrophysics Data System (ADS)
Cong, Alexander X.; Hofmann, Matthias C.; Cong, Wenxiang; Xu, Yong; Wang, Ge
2011-07-01
Fluorescence microscopy allows real-time monitoring of optical molecular probes for disease characterization, drug development, and tissue regeneration. However, when a biological sample is thicker than 1 mm, intense scattering of light would significantly degrade the spatial resolution of fluorescence microscopy. In this paper, we develop a fluorescence microtomography technique that utilizes the Monte Carlo method to image fluorescence reporters in thick biological samples. This approach is based on an l0-regularized tomography model and provides an excellent solution. Our studies on biomimetic tissue scaffolds have demonstrated that the proposed approach is capable of localizing and quantifying the distribution of optical molecular probe accurately and reliably.
Dynamic load balancing for petascale quantum Monte Carlo applications: The Alias method
NASA Astrophysics Data System (ADS)
Sudheer, C. D.; Krishnan, S.; Srinivasan, A.; Kent, P. R. C.
2013-02-01
Diffusion Monte Carlo is a highly accurate Quantum Monte Carlo method for electronic structure calculations of materials, but it requires frequent load balancing or population redistribution steps to maintain efficiency on parallel machines. This step can be a significant factor affecting performance, and will become more important as the number of processing elements increases. We propose a new dynamic load balancing algorithm, the Alias Method, and evaluate it theoretically and empirically. An important feature of the new algorithm is that the load can be perfectly balanced with each process receiving at most one message. It is also optimal in the maximum size of messages received by any process. We also optimize its implementation to reduce network contention, a process facilitated by the low messaging requirement of the algorithm: a simple renumbering of the MPI ranks based on proximity and a space filling curve significantly improves the MPI Allgather performance. Empirical results on the petaflop Cray XT Jaguar supercomputer at ORNL show up to 30% improvement in performance on 120,000 cores. The load balancing algorithm may be straightforwardly implemented in existing codes. The algorithm may also be employed by any method with many near identical computational tasks that require load balancing.
Dynamic load balancing for petascale quantum Monte Carlo applications: The Alias method
Sudheer, C. D.; Krishnan, S.; Srinivasan, A.; Kent, P. R. C.
2013-02-01
Diffusion Monte Carlo is the most accurate widely used Quantum Monte Carlo method for the electronic structure of materials, but it requires frequent load balancing or population redistribution steps to maintain efficiency and avoid accumulation of systematic errors on parallel machines. The load balancing step can be a significant factor affecting performance, and will become more important as the number of processing elements increases. We propose a new dynamic load balancing algorithm, the Alias Method, and evaluate it theoretically and empirically. An important feature of the new algorithm is that the load can be perfectly balanced with each process receiving at most one message. It is also optimal in the maximum size of messages received by any process. We also optimize its implementation to reduce network contention, a process facilitated by the low messaging requirement of the algorithm. Empirical results on the petaflop Cray XT Jaguar supercomputer at ORNL showing up to 30% improvement in performance on 120,000 cores. The load balancing algorithm may be straightforwardly implemented in existing codes. The algorithm may also be employed by any method with many near identical computational tasks that requires load balancing.
Dynamic Monte Carlo rate constants for magnetic Hamiltonians coupled to a phonon bath
NASA Astrophysics Data System (ADS)
Solomon, Lazarus; Novotny, Mark
2007-03-01
For quantitative comparisons between experimental time- dependent measurements and dynamic Monte Carlo simulations, a relation between the time constant in the simulation and real time is necessary. We calculate the transition rate for spin S system using the lattice frame method for a rigid spin cluster in an elastic medium [1]. We compare this with the transition rate for an Ising spin 12 system using the quantum- mechanical density-matrix method [2] with the results of ref [1,3]. These transition probabilities are different from those of either the Glauber or the Metropolis dynamics, and reflect the properties of the bosonic bath. Comparison with recent experiments [4] will be discussed. [1] E. M. Chudnovsky, D. A. Garanin, and R. Schilling (PRB 72, 2006) [2] K. Park, M. A. Novotny, and P. A. Rikvold (PRE 66, 2002) [3] K Saito, S. Takesue, and S. Miyashita, (PRE 61, 2002) [4] T. Meunier et al (Condensed Matter, 2006)
A Variable Coefficient Method for Accurate Monte Carlo Simulation of Dynamic Asset Price
NASA Astrophysics Data System (ADS)
Li, Yiming; Hung, Chih-Young; Yu, Shao-Ming; Chiang, Su-Yun; Chiang, Yi-Hui; Cheng, Hui-Wen
2007-07-01
In this work, we propose an adaptive Monte Carlo (MC) simulation technique to compute the sample paths for the dynamical asset price. In contrast to conventional MC simulation with constant drift and volatility (μ,σ), our MC simulation is performed with variable coefficient methods for (μ,σ) in the solution scheme, where the explored dynamic asset pricing model starts from the formulation of geometric Brownian motion. With the method of simultaneously updated (μ,σ), more than 5,000 runs of MC simulation are performed to fulfills basic accuracy of the large-scale computation and suppresses statistical variance. Daily changes of stock market index in Taiwan and Japan are investigated and analyzed.
Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study
Christov, Ivan P.
2016-08-15
In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the real time propagation can be a challenge.
NASA Astrophysics Data System (ADS)
Inoue, Jun-Ichi
2011-03-01
We analytically derive deterministic equations of order parameters such as spontaneous magnetization in infinite-range quantum spin systems obeying quantum Monte Carlo dynamics. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. We discuss several possible applications of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we argue the ground state searching for infinite-range random spin systems via quantum adiabatic evolution. We were financially supported by Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science, No. 22500195.
Semiclassical Monte-Carlo approach for modelling non-adiabatic dynamics in extended molecules
Gorshkov, Vyacheslav N.; Tretiak, Sergei; Mozyrsky, Dmitry
2013-01-01
Modelling of non-adiabatic dynamics in extended molecular systems and solids is a next frontier of atomistic electronic structure theory. The underlying numerical algorithms should operate only with a few quantities (that can be efficiently obtained from quantum chemistry), provide a controlled approximation (which can be systematically improved) and capture important phenomena such as branching (multiple products), detailed balance and evolution of electronic coherences. Here we propose a new algorithm based on Monte-Carlo sampling of classical trajectories, which satisfies the above requirements and provides a general framework for existing surface hopping methods for non-adiabatic dynamics simulations. In particular, our algorithm can be viewed as a post-processing technique for analysing numerical results obtained from the conventional surface hopping approaches. Presented numerical tests for several model problems demonstrate efficiency and accuracy of the new method. PMID:23864100
Replica exchange Monte Carlo simulations of the ising spin glass: Static and dynamic properties
NASA Astrophysics Data System (ADS)
Yucesoy, Burcu
Spin glasses have been the subject of intense study and considerable controversy for decades, and the low-temperature phase of short-range spin glasses is still poorly understood. Our main goal is to improve our understanding in this area and find an answer to the following question: Are there only a single pair or a countable infinity of pure states in the low temperature phase of the EA spin glass? To that aim we first start by introducing spin glasses and provide a brief history of their research, then proceed to describe our method of simulation, the parallel tempering Monte Carlo algorithm. Next, we present the results of a large-scale numerical study of the equilibrium three-dimensional Edwards-Anderson Ising spin glass with Gaussian disorder. In order to understand how the parallel tempering algorithm works, we measure various static, as well as dynamical quantities, such as the autocorrelation times and round-trip times for the parallel tempering Monte Carlo method. We examine the correlation between static and dynamic observables for ˜ 5000 disorder realizations and up to 1000 spins down to temperatures at 20% of the critical temperature, and our results show that autocorrelation times are directly correlated with the roughness of the free-energy landscape. In the following chapters, the three- and four-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied again via large scale Monte Carlo simulations at low temperatures, deep within the spin glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. We arrive to the following conclusion: The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a
COOL: A code for dynamic Monte Carlo simulation of molecular dynamics
NASA Astrophysics Data System (ADS)
Barletta, Paolo
2011-02-01
COOL is a program to simulate evaporative and sympathetic cooling for a mixture of two gases co-trapped in a harmonic potential. The collisions involved are assumed to be exclusively elastic, and losses are due to evaporation from the trap. Each particle is followed individually in its trajectory, consequently properties such as spatial densities or energy distributions can be readily evaluated. The code can be used sequentially, by employing one output as input for another run. The code can be easily generalised to describe more complicated processes, such as the inclusion of inelastic collisions, or the possible presence of more than two species in the trap. Program summaryProgram title: COOL Catalogue identifier: AEHJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1 111 674 No. of bytes in distributed program, including test data, etc.: 18 618 045 Distribution format: tar.gz Programming language: C++ Computer: Desktop Operating system: Linux RAM: 500 Mbytes Classification: 16.7, 23 Nature of problem: Simulation of the sympathetic process occurring for two molecular gases co-trapped in a deep optical trap. Solution method: The Direct Simulation Monte Carlo method exploits the decoupling, over a short time period, of the inter-particle interaction from the trapping potential. The particle dynamics is thus exclusively driven by the external optical field. The rare interparticle collisions are considered with an acceptance/rejection mechanism, that is by comparing a random number to the collisional probability defined in terms of the inter-particle cross section and centre-of-mass energy. All particles in the trap are individually simulated so that at each time step a number of useful quantities, such as
Schierz, Philipp; Zierenberg, Johannes; Janke, Wolfhard
2015-10-07
Molecular Dynamics (MD) and Monte Carlo (MC) simulations are the most popular simulation techniques for many-particle systems. Although they are often applied to similar systems, it is unclear to which extent one has to expect quantitative agreement of the two simulation techniques. In this work, we present a quantitative comparison of MD and MC simulations in the microcanonical ensemble. For three test examples, we study first- and second-order phase transitions with a focus on liquid-gas like transitions. We present MD analysis techniques to compensate for conservation law effects due to linear and angular momentum conservation. Additionally, we apply the weighted histogram analysis method to microcanonical histograms reweighted from MD simulations. By this means, we are able to estimate the density of states from many microcanonical simulations at various total energies. This further allows us to compute estimates of canonical expectation values.
NASA Astrophysics Data System (ADS)
Dhiman, Isha; Gupta, Arvind Kumar
2016-03-01
This work is devoted to the development of a novel theoretical approach, named hybrid approach, to handle a localized bottleneck in a symmetrically coupled two-channel totally asymmetric simple exclusion process with Langmuir kinetics. The hybrid approach is combined with singular perturbation technique to get steady-state phase diagrams and density profiles. We have thoroughly examined the role played by the strength of bottleneck, binding constant and lane-changing rate in the system dynamics. The appearances of bottleneck-induced shock, a bottleneck phase and Meissner phase are explained. Further, the critical values of bottleneck rate are identified, which signify the changes in the topology of phase diagram. It is also found that an increase in lane-changing rate as well as unequal attachment, detachment rates weaken the bottleneck effect. Our theoretical arguments are in good agreement with extensively performed Monte Carlo simulations.
Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo
Zen, Andrea; Luo, Ye Mazzola, Guglielmo Sorella, Sandro; Guidoni, Leonardo
2015-04-14
Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article, we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous density functional theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab initio simulations of complex chemical systems.
Dynamical evolution of the Oort cloud. I. A Monte Carlo simulation. II. A theoretical approach
Remy, F.; Mignard, F.
1985-07-01
A Monte Carlo model is used to trace the dynamical evolution of the Oort cloud of comets to its ultimate end. After a review of previous simulations, the necessity of considering perturbations of the aphelion distance because of passing stars, the density of passing stars, and the three-body problem of sun-star-comet is discussed. For convenience, the solar gravitation is assumed to be zero as a star passes. It is also assumed that the initial cometary distribution had a perihelion near the orbits of Uranus-Neptune. Six orbital elements are calculated to obtain orbital distributions for the population in the Oort cloud. The cloud is estimated to contain 10 trillion comets, which would satisfy the present apparition rate of new comets. 34 references.
Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo.
Zen, Andrea; Luo, Ye; Mazzola, Guglielmo; Guidoni, Leonardo; Sorella, Sandro
2015-04-14
Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article, we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous density functional theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab initio simulations of complex chemical systems.
Path Integral Monte Carlo and Density Functional Molecular Dynamics Simulations of Warm Dense Matter
NASA Astrophysics Data System (ADS)
Militzer, Burkhard; Driver, Kevin
2011-10-01
We analyze the applicability of two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), to study the regime of warm dense matter. We discuss the advantages as well as the limitations of each method and propose directions for future development. Results for dense, liquid helium, where both methods have been applied, demonstrate the range of each method's applicability. Comparison of the equations of state from simulations with analytical theories and free energy models show that DFT is useful for temperatures below 100000 K and then PIMC provides accurate results for all higher temperatures. We characterize the structure of the liquid in terms of pair correlation functions and study the closure of the band gap with increasing density and temperature. Finally, we discuss simulations of heavier elements and demonstrate the reliability are both methods in such cases with preliminary results.
Semiclassical Monte Carlo: a first principles approach to non-adiabatic molecular dynamics.
White, Alexander J; Gorshkov, Vyacheslav N; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-11-14
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.
Marcus, Ryan C.
2012-07-25
MCMini is a proof of concept that demonstrates the possibility for Monte Carlo neutron transport using OpenCL with a focus on performance. This implementation, written in C, shows that tracing particles and calculating reactions on a 3D mesh can be done in a highly scalable fashion. These results demonstrate a potential path forward for MCNP or other Monte Carlo codes.
Solution of deterministic-stochastic epidemic models by dynamical Monte Carlo method
NASA Astrophysics Data System (ADS)
Aièllo, O. E.; Haas, V. J.; daSilva, M. A. A.; Caliri, A.
2000-07-01
This work is concerned with dynamical Monte Carlo (MC) method and its application to models originally formulated in a continuous-deterministic approach. Specifically, a susceptible-infected-removed-susceptible (SIRS) model is used in order to analyze aspects of the dynamical MC algorithm and achieve its applications in epidemic contexts. We first examine two known approaches to the dynamical interpretation of the MC method and follow with the application of one of them in the SIRS model. The working method chosen is based on the Poisson process where hierarchy of events, properly calculated waiting time between events, and independence of the events simulated, are the basic requirements. To verify the consistence of the method, some preliminary MC results are compared against exact steady-state solutions and other general numerical results (provided by Runge-Kutta method): good agreement is found. Finally, a space-dependent extension of the SIRS model is introduced and treated by MC. The results are interpreted under and in accordance with aspects of the herd-immunity concept.
Quantum Gibbs ensemble Monte Carlo
Fantoni, Riccardo; Moroni, Saverio
2014-09-21
We present a path integral Monte Carlo method which is the full quantum analogue of the Gibbs ensemble Monte Carlo method of Panagiotopoulos to study the gas-liquid coexistence line of a classical fluid. Unlike previous extensions of Gibbs ensemble Monte Carlo to include quantum effects, our scheme is viable even for systems with strong quantum delocalization in the degenerate regime of temperature. This is demonstrated by an illustrative application to the gas-superfluid transition of {sup 4}He in two dimensions.
NASA Astrophysics Data System (ADS)
Vogel, Thomas; Perez, Danny; Junghans, Christoph
2014-03-01
We show direct formal relationships between the Wang-Landau iteration [PRL 86, 2050 (2001)], metadynamics [PNAS 99, 12562 (2002)] and statistical temperature molecular dynamics [PRL 97, 050601 (2006)], the major Monte Carlo and molecular dynamics work horses for sampling from a generalized, multicanonical ensemble. We aim at helping to consolidate the developments in the different areas by indicating how methodological advancements can be transferred in a straightforward way, avoiding the parallel, largely independent, developments tracks observed in the past.
Meli, Massimiliano; Morra, Giulia; Colombo, Giorgio
2008-01-01
The early stages of peptide aggregation are currently not accessible by experimental techniques at atomic resolution. In this article, we address this problem through the application of a mixed simulation scheme in which a preliminary coarse-grained Monte Carlo analysis of the free-energy landscape is used to identify representative conformations of the aggregates and subsequent all-atom molecular dynamics simulations are used to analyze in detail possible pathways for the stabilization of oligomers. This protocol was applied to systems consisting of multiple copies of the model peptide GNNQQNY, whose detailed structures in the aggregated state have been recently solved in another study. The analysis of the various trajectories provides dynamical and structural insight into the details of aggregation. In particular, the simulations suggest a hierarchical mechanism characterized by the initial formation of stable parallel β-sheet dimers and identify the formation of the polar zipper motif as a fundamental feature for the stabilization of initial oligomers. Simulation results are consistent with experimentally derived observations and provide an atomically detailed view of the putative initial stages of fibril formation. PMID:18263661
Weare, Jonathan; Dinner, Aaron R.; Roux, Benoît
2016-01-01
A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method. PMID:26918826
An Event-Driven Hybrid Molecular Dynamics and Direct Simulation Monte Carlo Algorithm
Donev, A; Garcia, A L; Alder, B J
2007-07-30
A novel 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 (MD) 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.
Infectious Disease Dynamics Inferred from Genetic Data via Sequential Monte Carlo.
Smith, R A; Ionides, E L; King, A A
2017-04-08
Genetic sequences from pathogens can provide information about infectious disease dynamics that may supplement or replace information from other epidemiological observations. Most currently available methods first estimate phylogenetic trees from sequence data, then estimate a transmission model conditional on these phylogenies. Outside limited classes of models, existing methods are unable to enforce logical consistency between the model of transmission and that underlying the phylogenetic reconstruction. Such conicts in assumptions can lead to bias in the resulting inferences. Here, we develop a general, statistically efficient, plug-and-play method to jointly estimate both disease transmission and phylogeny using genetic data and, if desired, other epidemiological observations. This method explicitly connects the model of transmission and the model of phylogeny so as to avoid the aforementioned inconsistency.We demonstrate the feasibility of our approach through simulation and apply it to estimate stage-specific infectiousness in a subepidemic of HIV in Detroit, Michigan. In a supplement, we prove that our approach is a valid sequential Monte Carlo algorithm. While we focus on how these methods may be applied to population-level models of infectious disease, their scope is more general. These methods may be applied in other biological systems where one seeks to infer population dynamics from genetic sequences, and they may also find application for evolutionary models with phenotypic rather than genotypic data.
NASA Astrophysics Data System (ADS)
Mühlbacher, Lothar; Ankerhold, Joachim
2005-05-01
Electron transfer (ET) across molecular chains including an impurity is studied based on a recently improved real-time path-integral Monte Carlo (PIMC) approach [L. Mühlbacher, J. Ankerhold, and C. Escher, J. Chem. Phys. 121 12696 (2004)]. The reduced electronic dynamics is studied for various bridge lengths and defect site energies. By determining intersite hopping rates from PIMC simulations up to moderate times, the relaxation process in the extreme long-time limit is captured within a sequential transfer model. The total transfer rate is extracted and shown to be enhanced for certain defect site energies. Superexchange turns out to be relevant for extreme gap energies only and then gives rise to different dynamical signatures for high- and low-lying defects. Further, it is revealed that the entire bridge compound approaches a steady state on a much shorter time scale than that related to the total transfer. This allows for a simplified description of ET along donor-bridge-acceptor systems in the long-time range.
Wormhole Hamiltonian Monte Carlo
Lan, Shiwei; Streets, Jeffrey; Shahbaba, Babak
2015-01-01
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to another. To address this issue, we propose a novel Bayesian inference approach based on Markov Chain Monte Carlo. Our method can effectively sample from multimodal distributions, especially when the dimension is high and the modes are isolated. To this end, it exploits and modifies the Riemannian geometric properties of the target distribution to create wormholes connecting modes in order to facilitate moving between them. Further, our proposed method uses the regeneration technique in order to adapt the algorithm by identifying new modes and updating the network of wormholes without affecting the stationary distribution. To find new modes, as opposed to redis-covering those previously identified, we employ a novel mode searching algorithm that explores a residual energy function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function. PMID:25861551
Wormhole Hamiltonian Monte Carlo.
Lan, Shiwei; Streets, Jeffrey; Shahbaba, Babak
2014-07-31
In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to another. To address this issue, we propose a novel Bayesian inference approach based on Markov Chain Monte Carlo. Our method can effectively sample from multimodal distributions, especially when the dimension is high and the modes are isolated. To this end, it exploits and modifies the Riemannian geometric properties of the target distribution to create wormholes connecting modes in order to facilitate moving between them. Further, our proposed method uses the regeneration technique in order to adapt the algorithm by identifying new modes and updating the network of wormholes without affecting the stationary distribution. To find new modes, as opposed to redis-covering those previously identified, we employ a novel mode searching algorithm that explores a residual energy function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function.
COOL: A code for Dynamic Monte Carlo Simulation of molecular dynamics
NASA Astrophysics Data System (ADS)
Barletta, Paolo
2012-02-01
Cool is a program to simulate evaporative and sympathetic cooling for a mixture of two gases co-trapped in an harmonic potential. The collisions involved are assumed to be exclusively elastic, and losses are due to evaporation from the trap. Each particle is followed individually in its trajectory, consequently properties such as spatial densities or energy distributions can be readily evaluated. The code can be used sequentially, by employing one output as input for another run. The code can be easily generalised to describe more complicated processes, such as the inclusion of inelastic collisions, or the possible presence of more than two species in the trap. New version program summaryProgram title: COOL Catalogue identifier: AEHJ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHJ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1 097 733 No. of bytes in distributed program, including test data, etc.: 18 425 722 Distribution format: tar.gz Programming language: C++ Computer: Desktop Operating system: Linux RAM: 500 Mbytes Classification: 16.7, 23 Catalogue identifier of previous version: AEHJ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 182 (2011) 388 Does the new version supersede the previous version?: Yes Nature of problem: Simulation of the sympathetic process occurring for two molecular gases co-trapped in a deep optical trap. Solution method: The Direct Simulation Monte Carlo method exploits the decoupling, over a short time period, of the inter-particle interaction from the trapping potential. The particle dynamics is thus exclusively driven by the external optical field. The rare inter-particle collisions are considered with an acceptance/rejection mechanism, that is, by comparing a random number to the collisional probability
Isotropic Monte Carlo Grain Growth
Mason, J.
2013-04-25
IMCGG performs Monte Carlo simulations of normal grain growth in metals on a hexagonal grid in two dimensions with periodic boundary conditions. This may be performed with either an isotropic or a misorientation - and incliantion-dependent grain boundary energy.
A dynamic Monte Carlo study of anomalous current voltage behaviour in organic solar cells
Feron, K. Fell, C. J.; Zhou, X.; Belcher, W. J.; Dastoor, P. C.
2014-12-07
We present a dynamic Monte Carlo (DMC) study of s-shaped current-voltage (I-V) behaviour in organic solar cells. This anomalous behaviour causes a substantial decrease in fill factor and thus power conversion efficiency. We show that this s-shaped behaviour is induced by charge traps that are located at the electrode interface rather than in the bulk of the active layer, and that the anomaly becomes more pronounced with increasing trap depth or density. Furthermore, the s-shape anomaly is correlated with interface recombination, but not bulk recombination, thus highlighting the importance of controlling the electrode interface. While thermal annealing is known to remove the s-shape anomaly, the reason has been not clear, since these treatments induce multiple simultaneous changes to the organic solar cell structure. The DMC modelling indicates that it is the removal of aluminium clusters at the electrode, which act as charge traps, that removes the anomalous I-V behaviour. Finally, this work shows that the s-shape becomes less pronounced with increasing electron-hole recombination rate; suggesting that efficient organic photovoltaic material systems are more susceptible to these electrode interface effects.
Bousige, Colin; Boţan, Alexandru; Coasne, Benoît; Ulm, Franz-Josef; Pellenq, Roland J.-M.
2015-03-21
We report an efficient atom-scale reconstruction method that consists of combining the Hybrid Reverse Monte Carlo algorithm (HRMC) with Molecular Dynamics (MD) in the framework of a simulated annealing technique. In the spirit of the experimentally constrained molecular relaxation technique [Biswas et al., Phys. Rev. B 69, 195207 (2004)], this modified procedure offers a refined strategy in the field of reconstruction techniques, with special interest for heterogeneous and disordered solids such as amorphous porous materials. While the HRMC method generates physical structures, thanks to the use of energy penalties, the combination with MD makes the method at least one order of magnitude faster than HRMC simulations to obtain structures of similar quality. Furthermore, in order to ensure the transferability of this technique, we provide rational arguments to select the various input parameters such as the relative weight ω of the energy penalty with respect to the structure optimization. By applying the method to disordered porous carbons, we show that adsorption properties provide data to test the global texture of the reconstructed sample but are only weakly sensitive to the presence of defects. In contrast, the vibrational properties such as the phonon density of states are found to be very sensitive to the local structure of the sample.
A Kushner-Stratonovich Monte Carlo filter applied to nonlinear dynamical system identification
NASA Astrophysics Data System (ADS)
Sarkar, S.; Chowdhury, S. R.; Venugopal, M.; Vasu, R. M.; Roy, D.
2014-03-01
A Monte Carlo filter, based on the idea of averaging over characteristics and fashioned after a particle-based time-discretized approximation to the Kushner-Stratonovich (KS) nonlinear filtering equation, is proposed. A key aspect of the new filter is the gain-like additive update, designed to approximate the innovation integral in the KS equation and implemented through an annealing-type iterative procedure, which is aimed at rendering the innovation (observation-prediction mismatch) for a given time-step to a zero-mean Brownian increment corresponding to the measurement noise. This may be contrasted with the weight-based multiplicative updates in most particle filters that are known to precipitate the numerical problem of weight collapse within a finite-ensemble setting. A study to estimate the a-priori error bounds in the proposed scheme is undertaken. The numerical evidence, presently gathered from the assessed performance of the proposed and a few other competing filters on a class of nonlinear dynamic system identification and target tracking problems, is suggestive of the remarkably improved convergence and accuracy of the new filter.
Monte Carlo studies of folding, dynamics, and stability in alpha-helices.
Shental-Bechor, Dalit; Kirca, Safak; Ben-Tal, Nir; Haliloglu, Turkan
2005-04-01
Folding simulations of polyalanine peptides were carried out using an off-lattice Monte Carlo simulation technique. The peptide was represented as a chain of residues, each of which contains two interaction sites: one corresponding to the C(alpha) atom and the other to the side chain. A statistical potential was used to describe the interaction between these sites. The preferred conformations of the peptide chain on the energy surface, starting from several initial conditions, were searched by perturbations on its generalized coordinates with the Metropolis criterion. We observed that, at low temperatures, the effective energy was low and the helix content high. The calculated helix propagation (s) and nucleation (sigma) parameters of the Zimm-Bragg model were in reasonable agreement with the empirical data. Exploration of the energy surface of the alanine-based peptides (AAQAA)(3) and AAAAA(AAARA)(3)A demonstrated that their behavior is similar to that of polyalanine, in regard to their effective energy, helix content, and the temperature-dependence of their helicity. In contrast, stable secondary structures were not observed for (Gly)(20) at similar temperatures, which is consistent with the nonfolder nature of this peptide. The fluctuations in the slowest dynamics mode, which describe the elastic behavior of the chain, showed that as the temperature decreases, the polyalanine peptides become stiffer and retain conformations with higher helix content. Clustering of conformations during the folding phase implied that polyalanine folds into a helix through fewer numbers of intermediate conformations as the temperature decreases.
NASA Astrophysics Data System (ADS)
Li, Yuan; Ma, Yu; Li, Juan; Jiang, Xiaoming; Hu, Wenbing
2012-03-01
We report dynamic Monte Carlo simulations of microphase separated diblock copolymers, to investigate how crystallization of one species could accelerate the subsequent crystallization of another species. Although the lattice copolymer model brings a boundary constraint to the long periods of microdomains, the single-molecular-level force balance between two blocks and its change can be revealed in this simple approach. We found two contrastable acceleration mechanisms: (1) the metastable lamellar crystals of one species become thicker at higher crystallization temperatures, sacrificing its microphase interfacial area to make a larger coil-stretching of another amorphous species and hence to accelerate subsequent crystallization of the latter with a more favorable conformation. (2) While in the case allowing chain-sliding in the crystal, the equilibrated lamellar crystals of one species become thinner at higher temperatures, sacrificing its thermal stability to gain a higher conformational entropy of another amorphous species and hence to accelerate subsequent crystallization of the latter with a stronger tension at the block junction. Parallel situations of experiments have been discussed.
Molecular dynamics and Monte Carlo simulations for protein–ligand binding and inhibitor design☆
Cole, Daniel J.; Tirado-Rives, Julian; Jorgensen, William L.
2014-01-01
Background Non-nucleoside inhibitors of HIV reverse transcriptase are an important component of treatment against HIV infection. Novel inhibitors are sought that increase potency against variants that contain the Tyr181Cys mutation. Methods Molecular dynamics based free energy perturbation simulations have been run to study factors that contribute to protein–ligand binding, and the results are compared with those from previous Monte Carlo based simulations and activity data. Results Predictions of protein–ligand binding modes are very consistent for the two simulation methods, which are attributed to the use of an enhanced sampling protocol. The Tyr181Cys binding pocket supports large, hydrophobic substituents, which is in good agreement with experiment. Conclusions Although some discrepancies exist between the results of the two simulation methods and experiment, free energy perturbation simulations can be used to rapidly test small molecules for gains in binding affinity. General significance Free energy perturbation methods show promise in providing fast, reliable and accurate data that can be used to complement experiment in lead optimization projects. This article is part of a Special Issue entitled “Recent developments of molecular dynamics”. PMID:25196360
Path integral Monte Carlo and density functional molecular dynamics simulations of hot, dense helium
NASA Astrophysics Data System (ADS)
Militzer, B.
2009-04-01
Two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), are applied to study hot, dense helium in the density-temperature range of 0.387-5.35gcm-3 and 500K-1.28×108K . One coherent equation of state is derived by combining DFT-MD data at lower temperatures with PIMC results at higher temperatures. Good agreement between both techniques is found in an intermediate-temperature range. For the highest temperatures, the PIMC results converge to the Debye-Hückel limiting law. In order to derive the entropy, a thermodynamically consistent free-energy fit is used that reproduces the internal energies and pressure derived from the first-principles simulations. The equation of state is presented in the form of a table as well as a fit and is compared with different free-energy models. Pair-correlation functions and the electronic density of states are discussed. Shock Hugoniot curves are compared with recent laser shock-wave experiments.
Davis, Mitchell A.; Dunn, Andrew K.
2015-01-01
Few methods exist that can accurately handle dynamic light scattering in the regime between single and highly multiple scattering. We demonstrate dynamic light scattering Monte Carlo (DLS-MC), a numerical method by which the electric field autocorrelation function may be calculated for arbitrary geometries if the optical properties and particle motion are known or assumed. DLS-MC requires no assumptions regarding the number of scattering events, the final form of the autocorrelation function, or the degree of correlation between scattering events. Furthermore, the method is capable of rapidly determining the effect of particle motion changes on the autocorrelation function in heterogeneous samples. We experimentally validated the method and demonstrated that the simulations match both the expected form and the experimental results. We also demonstrate the perturbation capabilities of the method by calculating the autocorrelation function of flow in a representation of mouse microvasculature and determining the sensitivity to flow changes as a function of depth. PMID:26191723
Monte Carlo calculation of dynamical properties of the two-dimensional Hubbard model
NASA Technical Reports Server (NTRS)
White, S. R.; Scalapino, D. J.; Sugar, R. L.; Bickers, N. E.
1989-01-01
A new method is introduced for analytically continuing imaginary-time data from quantum Monte Carlo calculations to the real-frequency axis. The method is based on a least-squares-fitting procedure with constraints of positivity and smoothness on the real-frequency quantities. Results are shown for the single-particle spectral-weight function and density of states for the half-filled, two-dimensional Hubbard model.
NASA Astrophysics Data System (ADS)
Gereben, Orsolya; Pusztai, László
2013-10-01
The liquid structure of tetrachloroethene has been investigated on the basis of measured neutron and X-ray scattering structure factors, applying molecular dynamics simulations and reverse Monte Carlo (RMC) modeling with flexible molecules and interatomic potentials. As no complete all-atom force field parameter set could be found for this planar molecule, the closest matching all-atom Optimized Potentials for Liquid Simulations (OPLS-AA) intra-molecular parameter set was improved by equilibrium bond length and angle parameters coming from electron diffraction experiments [I. L. Karle and J. Karle, J. Chem. Phys. 20, 63 (1952)]. In addition, four different intra-molecular charge distribution sets were tried, so in total, eight different molecular dynamics simulations were performed. The best parameter set was selected by calculating the mean square difference between the calculated total structure factors and the corresponding experimental data. The best parameter set proved to be the one that uses the electron diffraction based intra-molecular parameters and the charges qC = 0.1 and qCl = -0.05. The structure was further successfully refined by applying RMC computer modeling with flexible molecules that were kept together by interatomic potentials. Correlation functions concerning the orientation of molecular axes and planes were also determined. They reveal that the molecules closest to each other exclusively prefer the parallel orientation of both the molecular axes and planes. Molecules forming the first maximum of the center-center distribution have a preference for <30° and >60° axis orientation and >60° molecular plane arrangement. A second coordination sphere at ˜11 Å and a very small third one at ˜16 Å can be found as well, without preference for any axis or plane orientation.
Chen, Yunjie; Roux, Benoît
2014-09-21
Hybrid schemes combining the strength of molecular dynamics (MD) and Metropolis Monte Carlo (MC) offer a promising avenue to improve the sampling efficiency of computer simulations of complex systems. A number of recently proposed hybrid methods consider new configurations generated by driving the system via a non-equilibrium MD (neMD) trajectory, which are subsequently treated as putative candidates for Metropolis MC acceptance or rejection. To obey microscopic detailed balance, it is necessary to alter the momentum of the system at the beginning and/or the end of the neMD trajectory. This strict rule then guarantees that the random walk in configurational space generated by such hybrid neMD-MC algorithm will yield the proper equilibrium Boltzmann distribution. While a number of different constructs are possible, the most commonly used prescription has been to simply reverse the momenta of all the particles at the end of the neMD trajectory ("one-end momentum reversal"). Surprisingly, it is shown here that the choice of momentum reversal prescription can have a considerable effect on the rate of convergence of the hybrid neMD-MC algorithm, with the simple one-end momentum reversal encountering particularly acute problems. In these neMD-MC simulations, different regions of configurational space end up being essentially isolated from one another due to a very small transition rate between regions. In the worst-case scenario, it is almost as if the configurational space does not constitute a single communicating class that can be sampled efficiently by the algorithm, and extremely long neMD-MC simulations are needed to obtain proper equilibrium probability distributions. To address this issue, a novel momentum reversal prescription, symmetrized with respect to both the beginning and the end of the neMD trajectory ("symmetric two-ends momentum reversal"), is introduced. Illustrative simulations demonstrate that the hybrid neMD-MC algorithm robustly yields a correct
Dynamical Models for NGC 6503 Using a Markov Chain Monte Carlo Technique
NASA Astrophysics Data System (ADS)
Puglielli, David; Widrow, Lawrence M.; Courteau, Stéphane
2010-06-01
We use Bayesian statistics and Markov chain Monte Carlo (MCMC) techniques to construct dynamical models for the spiral galaxy NGC 6503. The constraints include surface brightness (SB) profiles which display a Freeman Type II structure; H I and ionized gas rotation curves; the stellar rotation, which is nearly coincident with the ionized gas curve; and the line of sight stellar dispersion, which displays a σ-drop at the center. The galaxy models consist of a Sérsic bulge, an exponential disk with an optional inner truncation and a cosmologically motivated dark halo. The Bayesian/MCMC technique yields the joint posterior probability distribution function for the input parameters, allowing constraints on model parameters such as the halo cusp strength, structural parameters for the disk and bulge, and mass-to-light ratios. We examine several interpretations of the data: the Type II SB profile may be due to dust extinction, to an inner truncated disk, or to a ring of bright stars, and we test separate fits to the gas and stellar rotation curves to determine if the gas traces the gravitational potential. We test each of these scenarios for bar stability, ruling out dust extinction. We also find that the gas likely does not trace the gravitational potential, since the predicted stellar rotation curve, which includes asymmetric drift, is then inconsistent with the observed stellar rotation curve. The disk is well fit by an inner-truncated profile, but the possibility of ring formation by a bar to reproduce the Type II profile is also a realistic model. We further find that the halo must have a cuspy profile with γ >~ 1; the bulge has a lower M/L than the disk, suggesting a star-forming component in the center of the galaxy; and the bulge, as expected for this late-type galaxy, has a low Sérsic index with nb ~ 1-2, suggesting a formation history dominated by secular evolution.
Constant-pH Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulation Method.
Chen, Yunjie; Roux, Benoît
2015-08-11
A computational method is developed to carry out explicit solvent simulations of complex molecular systems under conditions of constant pH. In constant-pH simulations, preidentified ionizable sites are allowed to spontaneously protonate and deprotonate as a function of time in response to the environment and the imposed pH. The method, based on a hybrid scheme originally proposed by H. A. Stern (J. Chem. Phys. 2007, 126, 164112), consists of carrying out short nonequilibrium molecular dynamics (neMD) switching trajectories to generate physically plausible configurations with changed protonation states that are subsequently accepted or rejected according to a Metropolis Monte Carlo (MC) criterion. To ensure microscopic detailed balance arising from such nonequilibrium switches, the atomic momenta are altered according to the symmetric two-ends momentum reversal prescription. To achieve higher efficiency, the original neMD-MC scheme is separated into two steps, reducing the need for generating a large number of unproductive and costly nonequilibrium trajectories. In the first step, the protonation state of a site is randomly attributed via a Metropolis MC process on the basis of an intrinsic pKa; an attempted nonequilibrium switch is generated only if this change in protonation state is accepted. This hybrid two-step inherent pKa neMD-MC simulation method is tested with single amino acids in solution (Asp, Glu, and His) and then applied to turkey ovomucoid third domain and hen egg-white lysozyme. Because of the simple linear increase in the computational cost relative to the number of titratable sites, the present method is naturally able to treat extremely large systems.
SU-E-T-238: Monte Carlo Estimation of Cerenkov Dose for Photo-Dynamic Radiotherapy
Chibani, O; Price, R; Ma, C; Eldib, A; Mora, G
2014-06-01
Purpose: Estimation of Cerenkov dose from high-energy megavoltage photon and electron beams in tissue and its impact on the radiosensitization using Protoporphyrine IX (PpIX) for tumor targeting enhancement in radiotherapy. Methods: The GEPTS Monte Carlo code is used to generate dose distributions from 18MV Varian photon beam and generic high-energy (45-MV) photon and (45-MeV) electron beams in a voxel-based tissueequivalent phantom. In addition to calculating the ionization dose, the code scores Cerenkov energy released in the wavelength range 375–425 nm corresponding to the pick of the PpIX absorption spectrum (Fig. 1) using the Frank-Tamm formula. Results: The simulations shows that the produced Cerenkov dose suitable for activating PpIX is 4000 to 5500 times lower than the overall radiation dose for all considered beams (18MV, 45 MV and 45 MeV). These results were contradictory to the recent experimental studies by Axelsson et al. (Med. Phys. 38 (2011) p 4127), where Cerenkov dose was reported to be only two orders of magnitude lower than the radiation dose. Note that our simulation results can be corroborated by a simple model where the Frank and Tamm formula is applied for electrons with 2 MeV/cm stopping power generating Cerenkov photons in the 375–425 nm range and assuming these photons have less than 1mm penetration in tissue. Conclusion: The Cerenkov dose generated by high-energy photon and electron beams may produce minimal clinical effect in comparison with the photon fluence (or dose) commonly used for photo-dynamic therapy. At the present time, it is unclear whether Cerenkov radiation is a significant contributor to the recently observed tumor regression for patients receiving radiotherapy and PpIX versus patients receiving radiotherapy only. The ongoing study will include animal experimentation and investigation of dose rate effects on PpIX response.
NASA Astrophysics Data System (ADS)
Andricioaei, Ioan; Straub, John E.
1997-12-01
Generalized Monte Carlo and molecular dynamics algorithms which provide enhanced sampling of the phase space in the calculation of equilibrium thermodynamic properties is presented. The algorithm samples trial moves from a generalized statistical distribution derived from a modification of the Gibbs-Shannon entropy proposed by Tsallis. Results for a one-dimensional model potential demonstrate that the algorithm leads to a greatly enhanced rate of barrier crossing and convergence in the calculation of equilibrium averages. Comparison is made with standard Metropolis Monte Carlo and the J-walking algorithm of Franz, Freeman and Doll. Application to a 13-atom Lennard-Jones cluster demonstrates the ease with which the algorithm may be applied to complex molecular systems.
NASA Astrophysics Data System (ADS)
Syuhada, Ibnu; Rosikhin, Ahmad; Marimpul, Rinaldo; Noor, Fatimah A.; Winata, Toto
2017-02-01
This study concerns hybrid Monte Carlo and molecular dynamics (MD/MC) methods involving a recipe for creating nickel carbide that can be applied to the graphene growth process. The time-stamped force-bias Monte Carlo (tfMC) method was used for taking care of the bond switching (BS) rate due to the concentration of carbon atoms in the nickel catalyst. It was found that the hybrid MD/MC method promotes the nickel carbide system to vibrational bond switching. This study also revealed that carbon atoms in metal catalyst are not spread randomly but rather prefer to gather in groups. This phenomenon is not caused by the BS rate only, but also by cohesive–adhesive competition between carbon and nickel atoms.
Monte-Carlo particle dynamics in a variable specific impulse magnetoplasma rocket
Ilin, A.V.; Diaz, F.R.C.; Squire, J.P.
1999-01-01
The self-consistent mathematical model in a Variable Specific Impulse Magnetoplasma Rocket (VASIMR) is examined. Of particular importance is the effect of a magnetic nozzle in enhancing the axial momentum of the exhaust. Also, different geometries and rocket symmetries are considered. The magnetic configuration is modeled with an adaptable mesh, which increases accuracy without compromising the speed of the simulation. The single particle trajectories are integrated with an adaptive time-scheme, which can quickly solve extensive Monte-Carlo simulations for systems of hundred thousands of particles in a reasonable time (1--2 hours) and without the need for a powerful supercomputer.
Challenges of Monte Carlo Transport
Long, Alex Roberts
2016-06-10
These are slides from a presentation for Parallel Summer School at Los Alamos National Laboratory. Solving discretized partial differential equations (PDEs) of interest can require a large number of computations. We can identify concurrency to allow parallel solution of discrete PDEs. Simulated particles histories can be used to solve the Boltzmann transport equation. Particle histories are independent in neutral particle transport, making them amenable to parallel computation. Physical parameters and method type determine the data dependencies of particle histories. Data requirements shape parallel algorithms for Monte Carlo. Then, Parallel Computational Physics and Parallel Monte Carlo are discussed and, finally, the results are given. The mesh passing method greatly simplifies the IMC implementation and allows simple load-balancing. Using MPI windows and passive, one-sided RMA further simplifies the implementation by removing target synchronization. The author is very interested in implementations of PGAS that may allow further optimization for one-sided, read-only memory access (e.g. Open SHMEM). The MPICH_RMA_OVER_DMAPP option and library is required to make one-sided messaging scale on Trinitite - Moonlight scales poorly. Interconnect specific libraries or functions are likely necessary to ensure performance. BRANSON has been used to directly compare the current standard method to a proposed method on idealized problems. The mesh passing algorithm performs well on problems that are designed to show the scalability of the particle passing method. BRANSON can now run load-imbalanced, dynamic problems. Potential avenues of improvement in the mesh passing algorithm will be implemented and explored. A suite of test problems that stress DD methods will elucidate a possible path forward for production codes.
Proton Upset Monte Carlo Simulation
NASA Technical Reports Server (NTRS)
O'Neill, Patrick M.; Kouba, Coy K.; Foster, Charles C.
2009-01-01
The Proton Upset Monte Carlo Simulation (PROPSET) program calculates the frequency of on-orbit upsets in computer chips (for given orbits such as Low Earth Orbit, Lunar Orbit, and the like) from proton bombardment based on the results of heavy ion testing alone. The software simulates the bombardment of modern microelectronic components (computer chips) with high-energy (.200 MeV) protons. The nuclear interaction of the proton with the silicon of the chip is modeled and nuclear fragments from this interaction are tracked using Monte Carlo techniques to produce statistically accurate predictions.
The Rational Hybrid Monte Carlo algorithm
NASA Astrophysics Data System (ADS)
Clark, Michael
2006-12-01
The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is performed using a rational approximation in place the usual inverse quark matrix kernel is one of these developments. This algorithm has been found to be extremely beneficial in many areas of lattice QCD (chiral fermions, finite temperature, Wilson fermions etc.). We review the algorithm and some of these benefits, and we compare against other recent algorithm developements. We conclude with an update of the Berlin wall plot comparing costs of all popular fermion formulations.
Mayawala, Kapil; Vlachos, Dionisios G; Edwards, Jeremy S
2006-06-01
Bimolecular reactions in the plasma membrane, such as receptor dimerization, are a key signaling step for many signaling systems. For receptors to dimerize, they must first diffuse until a collision happens, upon which a dimerization reaction may occur. Therefore, study of the dynamics of cell signaling on the membrane may require the use of a spatial modeling framework. Despite the availability of spatial simulation methods, e.g., stochastic spatial Monte Carlo (MC) simulation and partial differential equation (PDE) based approaches, many biological models invoke well-mixed assumptions without completely evaluating the importance of spatial organization. Whether one is to utilize a spatial or non-spatial simulation framework is therefore an important decision. In order to evaluate the importance of spatial effects a priori, i.e., without performing simulations, we have assessed the applicability of a dimensionless number, known as second Damköhler number (Da), defined here as the ratio of time scales of collision and reaction, for 2-dimensional bimolecular reactions. Our study shows that dimerization reactions in the plasma membrane with Da approximately >0.1 (tested in the receptor density range of 10(2)-10(5)/microm(2)) require spatial modeling. We also evaluated the effective reaction rate constants of MC and simple deterministic PDEs. Our simulations show that the effective reaction rate constant decreases with time due to time dependent changes in the spatial distribution of receptors. As a result, the effective reaction rate constant of simple PDEs can differ from that of MC by up to two orders of magnitude. Furthermore, we show that the fluctuations in the number of copies of signaling proteins (noise) may also depend on the diffusion properties of the system. Finally, we used the spatial MC model to explore the effect of plasma membrane heterogeneities, such as receptor localization and reduced diffusivity, on the dimerization rate. Interestingly, our
Multilevel sequential Monte Carlo samplers
Beskos, Alexandros; Jasra, Ajay; Law, Kody; Tempone, Raul; Zhou, Yan
2016-08-24
Here, we study the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with the step-size level h_{L}. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levels ${\\infty}$ >h_{0}>h_{1 }...>h_{L}. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. In conclusion, it is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context.
Multilevel sequential Monte Carlo samplers
Beskos, Alexandros; Jasra, Ajay; Law, Kody; ...
2016-08-24
Here, we study the approximation of expectations w.r.t. probability distributions associated to the solution of partial differential equations (PDEs); this scenario appears routinely in Bayesian inverse problems. In practice, one often has to solve the associated PDE numerically, using, for instance finite element methods and leading to a discretisation bias, with the step-size level hL. In addition, the expectation cannot be computed analytically and one often resorts to Monte Carlo methods. In the context of this problem, it is known that the introduction of the multilevel Monte Carlo (MLMC) method can reduce the amount of computational effort to estimate expectations, for a given level of error. This is achieved via a telescoping identity associated to a Monte Carlo approximation of a sequence of probability distributions with discretisation levelsmore » $${\\infty}$$ >h0>h1 ...>hL. In many practical problems of interest, one cannot achieve an i.i.d. sampling of the associated sequence of probability distributions. A sequential Monte Carlo (SMC) version of the MLMC method is introduced to deal with this problem. In conclusion, it is shown that under appropriate assumptions, the attractive property of a reduction of the amount of computational effort to estimate expectations, for a given level of error, can be maintained within the SMC context.« less
Suitable Candidates for Monte Carlo Solutions.
ERIC Educational Resources Information Center
Lewis, Jerome L.
1998-01-01
Discusses Monte Carlo methods, powerful and useful techniques that rely on random numbers to solve deterministic problems whose solutions may be too difficult to obtain using conventional mathematics. Reviews two excellent candidates for the application of Monte Carlo methods. (ASK)
A Classroom Note on Monte Carlo Integration.
ERIC Educational Resources Information Center
Kolpas, Sid
1998-01-01
The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing random sampling simulations with a computer. Presents a program written in Quick BASIC simulating the steps of the Monte Carlo method. (ASK)
Applications of Monte Carlo Methods in Calculus.
ERIC Educational Resources Information Center
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Discusses the application of probabilistic ideas, especially Monte Carlo simulation, to calculus. Describes some applications using the Monte Carlo method: Riemann sums; maximizing and minimizing a function; mean value theorems; and testing conjectures. (YP)
NASA Astrophysics Data System (ADS)
Monceau, Pascal; Hsiao, Pai-Yi
2002-09-01
We study the Wolff cluster size distributions obtained from Monte Carlo simulations of the Ising phase transition on Sierpinski fractals with Hausdorff dimensions Df between 2 and 3. These distributions are shown to be invariant when going from an iteration step of the fractal to the next under a scaling of the cluster sizes involving the exponent (β/ν)+(γ/ν). Moreover, the decay of the autocorrelation functions at the critical points enables us to calculate the Wolff dynamical critical exponents z for three different values of Df. The Wolff algorithm is more efficient in reducing the critical slowing down when Df is lowered.
NASA Technical Reports Server (NTRS)
Haviland, J. K.
1974-01-01
The results are reported of two unrelated studies. The first was an investigation of the formulation of the equations for non-uniform unsteady flows, by perturbation of an irrotational flow to obtain the linear Green's equation. The resulting integral equation was found to contain a kernel which could be expressed as the solution of the adjoint flow equation, a linear equation for small perturbations, but with non-constant coefficients determined by the steady flow conditions. It is believed that the non-uniform flow effects may prove important in transonic flutter, and that in such cases, the use of doublet type solutions of the wave equation would then prove to be erroneous. The second task covered an initial investigation into the use of the Monte Carlo method for solution of acoustical field problems. Computed results are given for a rectangular room problem, and for a problem involving a circular duct with a source located at the closed end.
GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA
NASA Astrophysics Data System (ADS)
Spiechowicz, J.; Kostur, M.; Machura, L.
2015-06-01
This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases.
Monte Carlo Simulation of Plumes Spectral Emission
2005-06-07
Henyey − Greenstein scattering indicatrix SUBROUTINE Calculation of spectral (group) phase function of Monte - Carlo Simulation of Plumes...calculations; b) Computing code SRT-RTMC-NSM intended for narrow band Spectral Radiation Transfer Ray Tracing Simulation by the Monte - Carlo method with...project) Computing codes for random ( Monte - Carlo ) simulation of molecular lines with reference to a problem of radiation transfer
Monte Carlo Simulation for Perusal and Practice.
ERIC Educational Resources Information Center
Brooks, Gordon P.; Barcikowski, Robert S.; Robey, Randall R.
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…
Luo, Ye Sorella, Sandro; Zen, Andrea
2014-11-21
We present a systematic study of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo. In this approach, a damped Langevin molecular dynamics is employed by using a statistical evaluation of the forces acting on each atom by means of quantum Monte Carlo. This allows the use of an highly correlated wave function parametrized by several variational parameters and describing quite accurately the Born-Oppenheimer energy surface, as long as these parameters are determined at the minimum energy condition. However, in a statistical method both the minimization method and the evaluation of the atomic forces are affected by the statistical noise. In this work, we study systematically the accuracy and reliability of this scheme by targeting the vibrational frequencies of simple molecules such as the water monomer, hydrogen sulfide, sulfur dioxide, ammonia, and phosphine. We show that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort. This work provides convincing evidence that this molecular dynamics scheme can be safely applied also to realistic systems containing several atoms.
NASA Astrophysics Data System (ADS)
González, W.; Lallena, A. M.; Alfonso, R.
2011-06-01
Micro-multileaf collimators are devices that are added to LINAC heads for stereotactic radiosurgery. In this work, the performance of an Elekta Precise LINAC with a dynamic micro-multileaf collimator manufactured by 3D-line has been studied. Monte Carlo simulations based on PENELOPE code and measurements with three different detectors (PTW Semiflex 31010 chamber, PTW PinPoint 31016 chamber and PTW Diode 60008) have been carried out. Simulations were tuned by reproducing the experimental TPR20, 10 quality index, providing a nice description of both the PDD curve and the transverse profiles at the two depths measured. The geometry of the micro-multileaf collimator was tested by calculating the transmission through it, and it was needed to significantly reduce the leaf separation indicated by the manufacturer to reproduce the experimental results. An approximate simulation in which the transport of the particles traversing the dynamic micro-multileaf collimator was described in a simplified way was analyzed, providing good agreement with the full simulations. With the MC model fixed, output factors for various field sizes were calculated and compared to the experimental ones, obtaining good agreement. Percentage depth doses (PDDs) and transverse profiles at two depths measured with the diode for small fields were well reproduced by the simulation, while the measurements performed with the PinPoint chamber showed differences in the PDDs, at large depths, and transverse profiles, at the penumbra. Monte Carlo simulations and Semiflex and diode measurements, performed for a 7.0 cm × 7.0 cm field, were in nice agreement, while those obtained with the PinPoint chamber showed differences that increased with the depth in water. At the phantom entrance, all measurements showed non-negligible differences that made Monte Carlo a good option to estimate the absorbed dose in this region.
González, W; Lallena, A M; Alfonso, R
2011-06-07
Micro-multileaf collimators are devices that are added to LINAC heads for stereotactic radiosurgery. In this work, the performance of an Elekta Precise LINAC with a dynamic micro-multileaf collimator manufactured by 3D-line has been studied. Monte Carlo simulations based on PENELOPE code and measurements with three different detectors (PTW Semiflex 31010 chamber, PTW PinPoint 31016 chamber and PTW Diode 60008) have been carried out. Simulations were tuned by reproducing the experimental TPR(20, 10) quality index, providing a nice description of both the PDD curve and the transverse profiles at the two depths measured. The geometry of the micro-multileaf collimator was tested by calculating the transmission through it, and it was needed to significantly reduce the leaf separation indicated by the manufacturer to reproduce the experimental results. An approximate simulation in which the transport of the particles traversing the dynamic micro-multileaf collimator was described in a simplified way was analyzed, providing good agreement with the full simulations. With the MC model fixed, output factors for various field sizes were calculated and compared to the experimental ones, obtaining good agreement. Percentage depth doses (PDDs) and transverse profiles at two depths measured with the diode for small fields were well reproduced by the simulation, while the measurements performed with the PinPoint chamber showed differences in the PDDs, at large depths, and transverse profiles, at the penumbra. Monte Carlo simulations and Semiflex and diode measurements, performed for a 7.0 cm × 7.0 cm field, were in nice agreement, while those obtained with the PinPoint chamber showed differences that increased with the depth in water. At the phantom entrance, all measurements showed non-negligible differences that made Monte Carlo a good option to estimate the absorbed dose in this region.
Gartner, Thomas E; Epps, Thomas H; Jayaraman, Arthi
2016-11-08
We describe an extension of the Gibbs ensemble molecular dynamics (GEMD) method for studying phase equilibria. Our modifications to GEMD allow for direct control over particle transfer between phases and improve the method's numerical stability. Additionally, we found that the modified GEMD approach had advantages in computational efficiency in comparison to a hybrid Monte Carlo (MC)/MD Gibbs ensemble scheme in the context of the single component Lennard-Jones fluid. We note that this increase in computational efficiency does not compromise the close agreement of phase equilibrium results between the two methods. However, numerical instabilities in the GEMD scheme hamper GEMD's use near the critical point. We propose that the computationally efficient GEMD simulations can be used to map out the majority of the phase window, with hybrid MC/MD used as a follow up for conditions under which GEMD may be unstable (e.g., near-critical behavior). In this manner, we can capitalize on the contrasting strengths of these two methods to enable the efficient study of phase equilibria for systems that present challenges for a purely stochastic GEMC method, such as dense or low temperature systems, and/or those with complex molecular topologies.
Zimmerman, G.B.
1997-06-24
Monte Carlo methods appropriate to simulate the transport of x-rays, neutrons, ion and electrons in Inertial Confinement Fusion targets are described and analyzed. The Implicit Monte Carlo method of x-ray transport handles symmetry within indirect drive ICF hohlraums well, but can be improved 50X in efficiency by angular biasing the x-rays towards the fuel capsule. Accurate simulation of thermonuclear burns nd burn diagnostics involves detailed particle source spectra, charged particle ranges, inflight reaction kinematics, corrections for bulk and thermal Doppler effects and variance reduction to obtain adequate statistics for rare events. It is found that the effects of angular Coulomb scattering must be included in models of charged particle transport through heterogeneous materials.
Womersley, J. . Dept. of Physics)
1992-10-01
The D0 detector at the Fermilab Tevatron began its first data taking run in May 1992. For analysis of the expected 25 pb[sup [minus]1] data sample, roughly half a million simulated events will be needed. The GEANT-based Monte Carlo program used to generate these events is described, together with comparisons to test beam data. Some novel techniques used to speed up execution and simplify geometrical input are described.
Rota, R; Casulleras, J; Mazzanti, F; Boronat, J
2015-03-21
We present a method based on the path integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose phase δ acts as an adjustable parameter. By using high-order approximations for the quantum propagator, it is possible to obtain Monte Carlo data all the way from purely imaginary time to δ values near the limit of real time. As a consequence, it is possible to infer accurately the spectral functions using simple inversion algorithms. We test this approach in the calculation of the dynamic structure function S(q, ω) of two one-dimensional model systems, harmonic and quartic oscillators, for which S(q, ω) can be exactly calculated. We notice a clear improvement in the calculation of the dynamic response with respect to the common approach based on the inverse Laplace transform of the imaginary-time correlation function.
NASA Astrophysics Data System (ADS)
Rota, R.; Casulleras, J.; Mazzanti, F.; Boronat, J.
2015-03-01
We present a method based on the path integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose phase δ acts as an adjustable parameter. By using high-order approximations for the quantum propagator, it is possible to obtain Monte Carlo data all the way from purely imaginary time to δ values near the limit of real time. As a consequence, it is possible to infer accurately the spectral functions using simple inversion algorithms. We test this approach in the calculation of the dynamic structure function S(q, ω) of two one-dimensional model systems, harmonic and quartic oscillators, for which S(q, ω) can be exactly calculated. We notice a clear improvement in the calculation of the dynamic response with respect to the common approach based on the inverse Laplace transform of the imaginary-time correlation function.
NASA Astrophysics Data System (ADS)
Pandey, Ras; Ruskin, Heather; Mannion, Rachel
2001-03-01
Using a direct Monte Carlo method we study the population dynamics of cells, i.e., macrophages (N_M), helper T-cells (N_H), cytotoxic cells (N_C), and antigens (N_V), with an HIV immune response model. Cells interact with eact other with a set of rules based on known HIV response. Cells can be mobile with a probability P_mob with a local motility-bias and viruses can mutate with a probability P_mut. Computer simulations are performed on cubic lattices with a number of independent runs. Population of cellular elements with the Monte Carlo time steps are monitored at a function of mutation at two extreme values of mobility, P_mob = 0, 1. We find that, in absence of mobility (P_mob = 0), the helper T-cells grow nonmonotonically before reaching saturation while the viral population grows monotonically to a constant value. On the other hand, cellular mobility (P_mob=1) enhances the viral growth and reduces the stimulative T-cell growth. The relative magnitude of the steady-state density of helper cell and viral infected cells determine the level of infection. Viral population dominates over the helper T-Cells above a critical mutation threshold (p_c) while helper T-Cells dominates below p_c. Nature of transition depends on mobility.
NASA Astrophysics Data System (ADS)
Chern, Shyh-Shi; Cárdenas, Alfredo E.; Coalson, Rob D.
2001-10-01
Three-dimensional dynamic Monte Carlo simulations of polymer translocation through a cylindrical hole in a planar slab under the influence of an external driving force are performed. The driving force is intended to emulate the effect of a static electric field applied in an electrolytic solution containing charged monomer particles, as is relevant to the translocation of certain biopolymers through protein channel pores embedded in cell membranes. The time evolution of the probability distribution of the translocation coordinate (the number of monomers that have passed through the pore) is extracted from three-dimensional (3-D) simulations over a range of polymer chain lengths. These distributions are compared to the predictions of a 1-D Smoluchowski equation model of the translocation coordinate dynamics. Good agreement is found, with the effective diffusion constant for the 1-D Smoluchowski model being nearly independent of chain length.
NASA Astrophysics Data System (ADS)
Kamibayashi, Yuki; Miura, Shinichi
2016-08-01
In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction.
Applications of Maxent to quantum Monte Carlo
Silver, R.N.; Sivia, D.S.; Gubernatis, J.E. ); Jarrell, M. . Dept. of Physics)
1990-01-01
We consider the application of maximum entropy methods to the analysis of data produced by computer simulations. The focus is the calculation of the dynamical properties of quantum many-body systems by Monte Carlo methods, which is termed the Analytical Continuation Problem.'' For the Anderson model of dilute magnetic impurities in metals, we obtain spectral functions and transport coefficients which obey Kondo Universality.'' 24 refs., 7 figs.
Commissioning of 6 MV medical linac for dynamic MLC-based IMRT on Monte Carlo code GEANT4.
Okamoto, Hiroyuki; Fujita, Yukio; Sakama, Kyoko; Saitoh, Hidetoshi; Kanai, Tatsuaki; Itami, Jun; Kohno, Toshiyuki
2014-07-01
Monte Carlo simulation is the most accurate tool for calculating dose distributions. In particular, the Electron Gamma shower computer code has been widely used for multi-purpose research in radiotherapy, but Monte Carlo GEANT4 (GEometry ANd Tracking) is rare for radiotherapy with photon beams and needs to be verified further under various irradiation conditions, particularly multi-leaf collimator-based intensity-modulated radiation therapy (MLC-based IMRT). In this study, GEANT4 was used for modeling of a 6 MV linac for dynamic MLC-based IMRT. To verify the modeling of our linac, we compared the calculated data with the measured depth-dose for a 10 × 10 cm(2) field and the measured dose profile for a 35 × 35 cm(2) field. Moreover, 120 MLCs were modeled on the GEANT4. Five tests of MLC modeling were performed: (I) MLC transmission, (II) MLC transmission profile including intra- and inter-leaf leakage, (III) tongue-and-groove leakage, (IV) a simple field with different field sizes by use of MLC and (V) a dynamic MLC-based IMRT field. For all tests, the calculations were compared with measurements of an ionization chamber and radiographic film. The calculations agreed with the measurements: MLC transmissions by calculations and measurements were 1.76 ± 0.01 and 1.87 ± 0.01 %, respectively. In gamma evaluation method (3 %/3 mm), the pass rates of the (IV) and (V) tests were 98.5 and 97.0 %, respectively. Furthermore, tongue-and-groove leakage could be calculated by GEANT4, and it agreed with the film measurements. The procedure of commissioning of dynamic MLC-based IMRT for GEANT4 is proposed in this study.
A Monte Carlo Approach to Population Dynamics of Cell in an HIV Immune Response Model
NASA Astrophysics Data System (ADS)
Mannion, Rachel; Ruskin, Heather; Pandey, Ras
2000-03-01
A direct Monte Carlo method is used to study the growth and decay of celluar elements, macrophages (N_H), helper T-cells (N_H), cytotoxic cells (N_C), and antigens (N_V), with an HIV immune response model. A set of rule-based logical interactions among the cells are considered. Cells divide and decay on a discrete lattice as a result of immune mechanism implemented via the inter- and intra-cellular interactions. Viral mutation is considered probabilistically (P_mut). Cells are mobile with their local motility-bias and the overall mobility is controlled by cellular mobility (P_mob). Computer simulations are performed on different lattice sizes with a number of independent runs for each parameter for averaging. Cellular mobility (P_mob=1) enhances the viral growth and reduces the stimulative T-cell growth. As a function of viral mutation rate, the interplay between the steady- state density of helper T-cells (ρ_H) and the viruses (ρ_V), leads to interesting predictions regarding the degree of infection including AIDS. For example, below a mutation threshold, (P_mut <= P_c), while the relative T-cell count (- Δ0 = ρ_H-ρV > 0) is not as alarming, above the threshold, viral population increasingly dominates as a function of the mutation rate with the onset of a continuous transition Δ ρ0 ∝ (P_mut - P_c)^β β ~= 0.574 ± 0.016 as P_mut → Pc in absence cellular mobility.
Semistochastic Projector Monte Carlo Method
NASA Astrophysics Data System (ADS)
Petruzielo, F. R.; Holmes, A. A.; Changlani, Hitesh J.; Nightingale, M. P.; Umrigar, C. J.
2012-12-01
We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.
Edison, John R; Monson, Peter A
2013-06-21
This article addresses the accuracy of a dynamic mean field theory (DMFT) for fluids in porous materials [P. A. Monson, J. Chem. Phys. 128, 084701 (2008)]. The theory is used to study the relaxation processes of fluids in pores driven by step changes made to a bulk reservoir in contact with the pore. We compare the results of the DMFT to those obtained by averaging over large numbers of dynamic Monte Carlo (DMC) simulation trajectories. The problem chosen for comparison is capillary condensation in slit pores, driven by step changes in the chemical potential in the bulk reservoir and involving a nucleation process via the formation of a liquid bridge. The principal difference between the DMFT results and DMC is the replacement of a distribution of nucleation times and location along the pore for the formation of liquid bridges by a single time and location. DMFT is seen to yield an otherwise qualitatively accurate description of the dynamic behavior.
NASA Astrophysics Data System (ADS)
Pasini, José Miguel; Cordero, Patricio
2001-04-01
We study a one-dimensional granular gas of pointlike particles not subject to gravity between two walls at temperatures Tleft and Tright. The system exhibits two distinct regimes, depending on the normalized temperature difference Δ=(Tright- Tleft)/(Tright+Tleft): one completely fluidized and one in which a cluster coexists with the fluidized gas. When Δ is above a certain threshold, cluster formation is fully inhibited, obtaining a completely fluidized state. The mechanism that produces these two phases is explained. In the fluidized state the velocity distribution function exhibits peculiar non-Gaussian features. For this state, comparison between integration of the Boltzmann equation using the direct-simulation Monte Carlo method and results stemming from microscopic Newtonian molecular dynamics gives good coincidence, establishing that the non-Gaussian features observed do not arise from the onset of correlations.
NASA Astrophysics Data System (ADS)
Kai, Takeshi; Yokoya, Akinari; Ukai, Masatoshi; Fujii, Kentaro; Watanabe, Ritsuko
2015-10-01
The thermalization length and spatial distribution of electrons in liquid water were simulated for initial electron energies ranging from 0.1 eV to 100 keV using a dynamic Monte Carlo code. The results showed that electrons were decelerated for thermalization over a longer time period than was previously predicted. This long thermalization time significantly contributed to the series of processes from initial ionization to hydration. We further studied the particular deceleration process of electrons at an incident energy of 1 eV, focusing on the temporal evolution of total track length, mean traveling distance, and energy distributions of decelerating electrons. The initial prehydration time and thermalization periods were estimated to be approximately 50 and 220 fs, respectively, indicating that the initial prehydration began before or contemporaneously with the thermal equilibrium. Based on these results, the prehydrated electrons were suggested to play an important role during multiple DNA damage induction.
Pasini, J M; Cordero, P
2001-04-01
We study a one-dimensional granular gas of pointlike particles not subject to gravity between two walls at temperatures T(left) and T(right). The system exhibits two distinct regimes, depending on the normalized temperature difference Delta=(T(right)-T(left))/(T(right)+T(left)): one completely fluidized and one in which a cluster coexists with the fluidized gas. When Delta is above a certain threshold, cluster formation is fully inhibited, obtaining a completely fluidized state. The mechanism that produces these two phases is explained. In the fluidized state the velocity distribution function exhibits peculiar non-Gaussian features. For this state, comparison between integration of the Boltzmann equation using the direct-simulation Monte Carlo method and results stemming from microscopic Newtonian molecular dynamics gives good coincidence, establishing that the non-Gaussian features observed do not arise from the onset of correlations.
Lee, Kyoung O; Holmes, Thomas W; Calderon, Adan F; Gardner, Robin P
2012-05-01
Using a Monte Carlo (MC) simulation, random walks were used for pebble tracking in a two-dimensional geometry in the presence of a biased gravity field. We investigated the effect of viscosity damping in the presence of random Gaussian fluctuations. The particle tracks were generated by Molecular Dynamics (MD) simulation for a Pebble Bed Reactor. The MD simulations were conducted in the interaction of noncohesive Hertz-Mindlin theory where the random walk MC simulation has a correlation with the MD simulation. This treatment can easily be extended to include the generation of transient gamma-ray spectra from a single pebble that contains a radioactive tracer. Then the inverse analysis thereof could be made to determine the uncertainty of the realistic measurement of transient positions of that pebble by any given radiation detection system designed for that purpose.
Multidimensional stochastic approximation Monte Carlo
NASA Astrophysics Data System (ADS)
Zablotskiy, Sergey V.; Ivanov, Victor A.; Paul, Wolfgang
2016-06-01
Stochastic Approximation Monte Carlo (SAMC) has been established as a mathematically founded powerful flat-histogram Monte Carlo method, used to determine the density of states, g (E ) , of a model system. We show here how it can be generalized for the determination of multidimensional probability distributions (or equivalently densities of states) of macroscopic or mesoscopic variables defined on the space of microstates of a statistical mechanical system. This establishes this method as a systematic way for coarse graining a model system, or, in other words, for performing a renormalization group step on a model. We discuss the formulation of the Kadanoff block spin transformation and the coarse-graining procedure for polymer models in this language. We also apply it to a standard case in the literature of two-dimensional densities of states, where two competing energetic effects are present g (E1,E2) . We show when and why care has to be exercised when obtaining the microcanonical density of states g (E1+E2) from g (E1,E2) .
Single scatter electron Monte Carlo
Svatos, M.M.
1997-03-01
A single scatter electron Monte Carlo code (SSMC), CREEP, has been written which bridges the gap between existing transport methods and modeling real physical processes. CREEP simulates ionization, elastic and bremsstrahlung events individually. Excitation events are treated with an excitation-only stopping power. The detailed nature of these simulations allows for calculation of backscatter and transmission coefficients, backscattered energy spectra, stopping powers, energy deposits, depth dose, and a variety of other associated quantities. Although computationally intense, the code relies on relatively few mathematical assumptions, unlike other charged particle Monte Carlo methods such as the commonly-used condensed history method. CREEP relies on sampling the Lawrence Livermore Evaluated Electron Data Library (EEDL) which has data for all elements with an atomic number between 1 and 100, over an energy range from approximately several eV (or the binding energy of the material) to 100 GeV. Compounds and mixtures may also be used by combining the appropriate element data via Bragg additivity.
NASA Astrophysics Data System (ADS)
Alcaraz, Olga; Trullàs, Joaquim; Tahara, Shuta; Kawakita, Yukinobu; Takeda, Shin'ichi
2016-09-01
The results of the structural properties of molten copper chloride are reported from high-energy X-ray diffraction measurements, reverse Monte Carlo modeling method, and molecular dynamics simulations using a polarizable ion model. The simulated X-ray structure factor reproduces all trends observed experimentally, in particular the shoulder at around 1 Å-1 related to intermediate range ordering, as well as the partial copper-copper correlations from the reverse Monte Carlo modeling, which cannot be reproduced by using a simple rigid ion model. It is shown that the shoulder comes from intermediate range copper-copper correlations caused by the polarized chlorides.
NASA Astrophysics Data System (ADS)
Cepeda, Jose; Luna, Byron Quan; Nadim, Farrokh
2013-04-01
An essential component of a quantitative landslide hazard assessment is establishing the extent of the endangered area. This task requires accurate prediction of the run-out behaviour of a landslide, which includes the estimation of the run-out distance, run-out width, velocities, pressures, and depth of the moving mass and the final configuration of the deposits. One approach to run-out modelling is to reproduce accurately the dynamics of the propagation processes. A number of dynamic numerical models are able to compute the movement of the flow over irregular topographic terrains (3-D) controlled by a complex interaction between mechanical properties that may vary in space and time. Given the number of unknown parameters and the fact that most of the rheological parameters cannot be measured in the laboratory or field, the parametrization of run-out models is very difficult in practice. For this reason, the application of run-out models is mostly used for back-analysis of past events and very few studies have attempted to achieve forward predictions. Consequently all models are based on simplified descriptions that attempt to reproduce the general features of the failed mass motion through the use of parameters (mostly controlling shear stresses at the base of the moving mass) which account for aspects not explicitly described or oversimplified. The uncertainties involved in the run-out process have to be approached in a stochastic manner. It is of significant importance to develop methods for quantifying and properly handling the uncertainties in dynamic run-out models, in order to allow a more comprehensive approach to quantitative risk assessment. A method was developed to compute the variation in run-out intensities by using a dynamic run-out model (MassMov2D) and a probabilistic framework based on a Monte Carlo simulation in order to analyze the effect of the uncertainty of input parameters. The probability density functions of the rheological parameters
Wu, D; He, X T; Yu, W; Fritzsche, S
2017-02-01
A physical model based on a Monte Carlo approach is proposed to calculate the ionization dynamics of hot-solid-density plasmas within particle-in-cell (PIC) simulations, and where the impact (collision) ionization (CI), electron-ion recombination (RE), and ionization potential depression (IPD) by surrounding plasmas are taken into consideration self-consistently. When compared with other models, which are applied in the literature for plasmas near thermal equilibrium, the temporal relaxation of ionization dynamics can also be simulated by the proposed model. Besides, this model is general and can be applied for both single elements and alloys with quite different compositions. The proposed model is implemented into a PIC code, with (final) ionization equilibriums sustained by competitions between CI and its inverse process (i.e., RE). Comparisons between the full model and model without IPD or RE are performed. Our results indicate that for bulk aluminium at temperature of 1 to 1000 eV, (i) the averaged ionization degree increases by including IPD; while (ii) the averaged ionization degree is significantly over estimated when the RE is neglected. A direct comparison from the PIC code is made with the existing models for the dependence of averaged ionization degree on thermal equilibrium temperatures and shows good agreements with that generated from Saha-Boltzmann model and/or FLYCHK code.
NASA Astrophysics Data System (ADS)
Wu, D.; He, X. T.; Yu, W.; Fritzsche, S.
2017-02-01
A physical model based on a Monte Carlo approach is proposed to calculate the ionization dynamics of hot-solid-density plasmas within particle-in-cell (PIC) simulations, and where the impact (collision) ionization (CI), electron-ion recombination (RE), and ionization potential depression (IPD) by surrounding plasmas are taken into consideration self-consistently. When compared with other models, which are applied in the literature for plasmas near thermal equilibrium, the temporal relaxation of ionization dynamics can also be simulated by the proposed model. Besides, this model is general and can be applied for both single elements and alloys with quite different compositions. The proposed model is implemented into a PIC code, with (final) ionization equilibriums sustained by competitions between CI and its inverse process (i.e., RE). Comparisons between the full model and model without IPD or RE are performed. Our results indicate that for bulk aluminium at temperature of 1 to 1000 eV, (i) the averaged ionization degree increases by including IPD; while (ii) the averaged ionization degree is significantly over estimated when the RE is neglected. A direct comparison from the PIC code is made with the existing models for the dependence of averaged ionization degree on thermal equilibrium temperatures and shows good agreements with that generated from Saha-Boltzmann model and/or FLYCHK code.
A Monte Carlo approach to water management
NASA Astrophysics Data System (ADS)
Koutsoyiannis, D.
2012-04-01
Common methods for making optimal decisions in water management problems are insufficient. Linear programming methods are inappropriate because hydrosystems are nonlinear with respect to their dynamics, operation constraints and objectives. Dynamic programming methods are inappropriate because water management problems cannot be divided into sequential stages. Also, these deterministic methods cannot properly deal with the uncertainty of future conditions (inflows, demands, etc.). Even stochastic extensions of these methods (e.g. linear-quadratic-Gaussian control) necessitate such drastic oversimplifications of hydrosystems that may make the obtained results irrelevant to the real world problems. However, a Monte Carlo approach is feasible and can form a general methodology applicable to any type of hydrosystem. This methodology uses stochastic simulation to generate system inputs, either unconditional or conditioned on a prediction, if available, and represents the operation of the entire system through a simulation model as faithful as possible, without demanding a specific mathematical form that would imply oversimplifications. Such representation fully respects the physical constraints, while at the same time it evaluates the system operation constraints and objectives in probabilistic terms, and derives their distribution functions and statistics through Monte Carlo simulation. As the performance criteria of a hydrosystem operation will generally be highly nonlinear and highly nonconvex functions of the control variables, a second Monte Carlo procedure, implementing stochastic optimization, is necessary to optimize system performance and evaluate the control variables of the system. The latter is facilitated if the entire representation is parsimonious, i.e. if the number of control variables is kept at a minimum by involving a suitable system parameterization. The approach is illustrated through three examples for (a) a hypothetical system of two reservoirs
Monte Carlo Shower Counter Studies
NASA Technical Reports Server (NTRS)
Snyder, H. David
1991-01-01
Activities and accomplishments related to the Monte Carlo shower counter studies are summarized. A tape of the VMS version of the GEANT software was obtained and installed on the central computer at Gallaudet University. Due to difficulties encountered in updating this VMS version, a decision was made to switch to the UNIX version of the package. This version was installed and used to generate the set of data files currently accessed by various analysis programs. The GEANT software was used to write files of data for positron and proton showers. Showers were simulated for a detector consisting of 50 alternating layers of lead and scintillator. Each file consisted of 1000 events at each of the following energies: 0.1, 0.5, 2.0, 10, 44, and 200 GeV. Data analysis activities related to clustering, chi square, and likelihood analyses are summarized. Source code for the GEANT user subprograms and data analysis programs are provided along with example data plots.
Goujon, Florent; Malfreyt, Patrice; Simon, Jean-Marc; Boutin, Anne; Rousseau, Bernard; Fuchs, Alain H
2004-12-22
The Monte Carlo (MC) and molecular dynamics (MD) methodologies are now well established for computing equilibrium properties in homogeneous fluids. This is not yet the case for the direct simulation of two-phase systems, which exhibit nonuniformity of the density distribution across the interface. We have performed direct MC and MD simulations of the liquid-gas interface of n-pentane using a standard force-field model. We obtained density and pressure components profiles along the direction normal to the interface that can be very different, depending on the truncation and long range correction strategies. We discuss the influence on predicted properties of different potential truncation schemes implemented in both MC and MD simulations. We show that the MD and MC profiles can be made in agreement by using a Lennard-Jones potential truncated via a polynomial function that makes the first and second derivatives of the potential continuous at the cutoff distance. In this case however, the predicted thermodynamic properties (phase envelope, surface tension) deviate from experiments, because of the changes made in the potential. A further readjustment of the potential parameters is needed if one wants to use this method. We conclude that a straightforward use of bulk phase force fields in MD simulations may lead to some physical inconsistencies when computing interfacial properties.
Prasad, Manish; Conforti, Patrick F; Garrison, Barbara J
2007-08-28
The coarse grained chemical reaction model is enhanced to build a molecular dynamics (MD) simulation framework with an embedded Monte Carlo (MC) based reaction scheme. The MC scheme utilizes predetermined reaction chemistry, energetics, and rate kinetics of materials to incorporate chemical reactions occurring in a substrate into the MD simulation. The kinetics information is utilized to set the probabilities for the types of reactions to perform based on radical survival times and reaction rates. Implementing a reaction involves changing the reactants species types which alters their interaction potentials and thus produces the required energy change. We discuss the application of this method to study the initiation of ultraviolet laser ablation in poly(methyl methacrylate). The use of this scheme enables the modeling of all possible photoexcitation pathways in the polymer. It also permits a direct study of the role of thermal, mechanical, and chemical processes that can set off ablation. We demonstrate that the role of laser induced heating, thermomechanical stresses, pressure wave formation and relaxation, and thermochemical decomposition of the polymer substrate can be investigated directly by suitably choosing the potential energy and chemical reaction energy landscape. The results highlight the usefulness of such a modeling approach by showing that various processes in polymer ablation are intricately linked leading to the transformation of the substrate and its ejection. The method, in principle, can be utilized to study systems where chemical reactions are expected to play a dominant role or interact strongly with other physical processes.
NASA Astrophysics Data System (ADS)
Khelashvili, George A.; Scott, H. L.
2004-05-01
We have carried out atomic level molecular dynamics and Monte Carlo simulations of hydrated 18:0 sphingomyelin (SM)-cholesterol (CHOL) bilayers at temperatures of 20 and 50 °C. The simulated systems each contained 266 SM, 122 CHOL, and 11861 water molecules. Each simulation was run for 10 ns under semi-isotropic pressure boundary conditions. The particle-mesh Ewald method was used for long-range electrostatic interactions. Properties of the systems were calculated over the final 3 ns. We compare the properties of 20 and 50 °C bilayer systems with each other, with experimental data, and with experimental and simulated properties of pure SM bilayers and dipalmitoyl phospatidyl choline (DPPC)-CHOL bilayers. The simulations reveal an overall similarity of both systems, despite the 30 °C temperature difference which brackets the pure SM main phase transition. The area per molecule, lipid chain order parameter profiles, atom distributions, and electron density profiles are all very similar for the two simulated systems. Consistent with simulations from our lab and others, we find strong intramolecular hydrogen bonding in SM molecules between the phosphate ester oxygen and the hydroxyl hydrogen atoms. We also find that cholesterol hydroxyl groups tend to form hydrogen bonds primarily with SM carbonyl, methyl, and amide moieties and to a lesser extent methyl and hydroxyl oxygens.
NASA Astrophysics Data System (ADS)
Wang, Lecheng; Xie, Daiqian
2012-08-01
We report finite temperature quantum mechanical simulations of structural and dynamical properties of ArN-CO2 clusters using a path integral Monte Carlo algorithm. The simulations are based on a newly developed analytical Ar-CO2 interaction potential obtained by fitting ab initio results to an anisotropic two-dimensional Morse/Long-range function. The calculated distributions of argon atoms around the CO2 molecule in ArN-CO2 clusters with different sizes are consistent to the previous studies of the configurations of the clusters. A first-order perturbation theory is used to quantitatively predict the CO2 vibrational frequency shift in different clusters. The first-solvation shell is completed at N = 17. Interestingly, our simulations for larger ArN-CO2 clusters showed several different structures of the argon shell around the doped CO2 molecule. The observed two distinct peaks (2338.8 and 2344.5 cm-1) in the υ3 band of CO2 may be due to the different arrangements of argon atoms around the dopant molecule.
NASA Astrophysics Data System (ADS)
Mühlbacher, Lothar; Ankerhold, Joachim; Escher, Charlotte
2004-12-01
An improved real-time quantum Monte Carlo procedure is presented and applied to describe the electronic transfer dynamics along molecular chains. The model consists of discrete electronic sites coupled to a thermal environment which is integrated out exactly within the path integral formulation. The approach is numerically exact and its results reduce to known analytical findings (Marcus theory, golden rule) in proper limits. Special attention is paid to the role of superexchange and sequential hopping at lower temperatures in symmetric donor-bridge-acceptor systems. In contrast to previous approximate studies, superexchange turns out to play a significant role only for extremely high-lying bridges where the transfer is basically frozen or for extremely low temperatures where for weaker dissipation a description in terms of rate constants is no longer feasible. For bridges with increasing length an algebraic decrease of the yield is found for short as well as for long bridges. The approach can be extended to electronic systems with more complicated topologies including impurities and in presence of external time-dependent forces.
NASA Astrophysics Data System (ADS)
Edison, John R.; Monson, Peter A.
2013-06-01
This article addresses the accuracy of a dynamic mean field theory (DMFT) for fluids in porous materials [P. A. Monson, J. Chem. Phys. 128, 084701 (2008)], 10.1063/1.2837287. The theory is used to study the relaxation processes of fluids in pores driven by step changes made to a bulk reservoir in contact with the pore. We compare the results of the DMFT to those obtained by averaging over large numbers of dynamic Monte Carlo (DMC) simulation trajectories. The problem chosen for comparison is capillary condensation in slit pores, driven by step changes in the chemical potential in the bulk reservoir and involving a nucleation process via the formation of a liquid bridge. The principal difference between the DMFT results and DMC is the replacement of a distribution of nucleation times and location along the pore for the formation of liquid bridges by a single time and location. DMFT is seen to yield an otherwise qualitatively accurate description of the dynamic behavior.
Watanabe, Hiroshi; Yukawa, Satoshi; Novotny, M A; Ito, Nobuyasu
2006-08-01
We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to exp(constbeta) in the Ising, sqrt[beta] in the classical XY, and beta in the classical Heisenberg spin systems with inverse temperature beta, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to (rho(cp)-rho)(-d) with the closest packing density rho(cp), density rho, and dimension d of the systems. We construct and implement a rejection-free Monte Carlo method for the hard-disk system. The RFMC has a greater computational efficiency at high densities, and the density dependence of the efficiency is as predicted by our arguments.
Improved Monte Carlo Renormalization Group Method
DOE R&D Accomplishments Database
Gupta, R.; Wilson, K. G.; Umrigar, C.
1985-01-01
An extensive program to analyze critical systems using an Improved Monte Carlo Renormalization Group Method (IMCRG) being undertaken at LANL and Cornell is described. Here we first briefly review the method and then list some of the topics being investigated.
Extra Chance Generalized Hybrid Monte Carlo
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; Sanz-Serna, J. M.
2015-01-01
We study a method, Extra Chance Generalized Hybrid Monte Carlo, to avoid rejections in the Hybrid Monte Carlo method and related algorithms. In the spirit of delayed rejection, whenever a rejection would occur, extra work is done to find a fresh proposal that, hopefully, may be accepted. We present experiments that clearly indicate that the additional work per sample carried out in the extra chance approach clearly pays in terms of the quality of the samples generated.
Error in Monte Carlo, quasi-error in Quasi-Monte Carlo
NASA Astrophysics Data System (ADS)
Kleiss, Ronald; Lazopoulos, Achilleas
2006-07-01
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the absence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account for the error improvement advertised by the Quasi-Monte Carlo method. We advocate the construction of an estimator of stochastic nature, based on the ensemble of pointsets with a particular discrepancy value. We investigate the consequences of this choice and give some first empirical results on the suggested estimators.
Monte Carlo docking with ubiquitin.
Cummings, M. D.; Hart, T. N.; Read, R. J.
1995-01-01
The development of general strategies for the performance of docking simulations is prerequisite to the exploitation of this powerful computational method. Comprehensive strategies can only be derived from docking experiences with a diverse array of biological systems, and we have chosen the ubiquitin/diubiquitin system as a learning tool for this process. Using our multiple-start Monte Carlo docking method, we have reconstructed the known structure of diubiquitin from its two halves as well as from two copies of the uncomplexed monomer. For both of these cases, our relatively simple potential function ranked the correct solution among the lowest energy configurations. In the experiments involving the ubiquitin monomer, various structural modifications were made to compensate for the lack of flexibility and for the lack of a covalent bond in the modeled interaction. Potentially flexible regions could be identified using available biochemical and structural information. A systematic conformational search ruled out the possibility that the required covalent bond could be formed in one family of low-energy configurations, which was distant from the observed dimer configuration. A variety of analyses was performed on the low-energy dockings obtained in the experiment involving structurally modified ubiquitin. Characterization of the size and chemical nature of the interface surfaces was a powerful adjunct to our potential function, enabling us to distinguish more accurately between correct and incorrect dockings. Calculations with the structure of tetraubiquitin indicated that the dimer configuration in this molecule is much less favorable than that observed in the diubiquitin structure, for a simple monomer-monomer pair. Based on the analysis of our results, we draw conclusions regarding some of the approximations involved in our simulations, the use of diverse chemical and biochemical information in experimental design and the analysis of docking results, as well as
Solano, Carlos J F; Pothula, Karunakar R; Prajapati, Jigneshkumar D; De Biase, Pablo M; Noskov, Sergei Yu; Kleinekathöfer, Ulrich
2016-05-10
All-atom molecular dynamics simulations have a long history of applications studying ion and substrate permeation across biological and artificial pores. While offering unprecedented insights into the underpinning transport processes, MD simulations are limited in time-scales and ability to simulate physiological membrane potentials or asymmetric salt solutions and require substantial computational power. While several approaches to circumvent all of these limitations were developed, Brownian dynamics simulations remain an attractive option to the field. The main limitation, however, is an apparent lack of protein flexibility important for the accurate description of permeation events. In the present contribution, we report an extension of the Brownian dynamics scheme which includes conformational dynamics. To achieve this goal, the dynamics of amino-acid residues was incorporated into the many-body potential of mean force and into the Langevin equations of motion. The developed software solution, called BROMOCEA, was applied to ion transport through OmpC as a test case. Compared to fully atomistic simulations, the results show a clear improvement in the ratio of permeating anions and cations. The present tests strongly indicate that pore flexibility can enhance permeation properties which will become even more important in future applications to substrate translocation.
Quantum Monte Carlo methods for nuclear physics
Carlson, Joseph A.; Gandolfi, Stefano; Pederiva, Francesco; Pieper, Steven C.; Schiavilla, Rocco; Schmidt, K. E,; Wiringa, Robert B.
2014-10-19
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
Quantum Monte Carlo methods for nuclear physics
Carlson, Joseph A.; Gandolfi, Stefano; Pederiva, Francesco; ...
2014-10-19
Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-bodymore » interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.« less
Quantum Monte Carlo methods for nuclear physics
Carlson, J.; Gandolfi, S.; Pederiva, F.; ...
2015-09-09
Quantum Monte Carlo methods have proved valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments, and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. The nuclear interactions and currents are reviewed along with a description of the continuum quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit,more » and three-body interactions. A variety of results are presented, including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. Low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars are also described. Furthermore, a coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.« less
Quantum Monte Carlo methods for nuclear physics
Carlson, J.; Gandolfi, S.; Pederiva, F.; Pieper, Steven C.; Schiavilla, R.; Schmidt, K. E.; Wiringa, R. B.
2015-09-09
Quantum Monte Carlo methods have proved valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments, and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. The nuclear interactions and currents are reviewed along with a description of the continuum quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. A variety of results are presented, including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. Low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars are also described. Furthermore, a coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
Quantum Monte Carlo methods for nuclear physics
NASA Astrophysics Data System (ADS)
Carlson, J.; Gandolfi, S.; Pederiva, F.; Pieper, Steven C.; Schiavilla, R.; Schmidt, K. E.; Wiringa, R. B.
2015-07-01
Quantum Monte Carlo methods have proved valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab initio calculations reproduce many low-lying states, moments, and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. The nuclear interactions and currents are reviewed along with a description of the continuum quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. A variety of results are presented, including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. Low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars are also described. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.
THE MCNPX MONTE CARLO RADIATION TRANSPORT CODE
WATERS, LAURIE S.; MCKINNEY, GREGG W.; DURKEE, JOE W.; FENSIN, MICHAEL L.; JAMES, MICHAEL R.; JOHNS, RUSSELL C.; PELOWITZ, DENISE B.
2007-01-10
MCNPX (Monte Carlo N-Particle eXtended) is a general-purpose Monte Carlo radiation transport code with three-dimensional geometry and continuous-energy transport of 34 particles and light ions. It contains flexible source and tally options, interactive graphics, and support for both sequential and multi-processing computer platforms. MCNPX is based on MCNP4B, and has been upgraded to most MCNP5 capabilities. MCNP is a highly stable code tracking neutrons, photons and electrons, and using evaluated nuclear data libraries for low-energy interaction probabilities. MCNPX has extended this base to a comprehensive set of particles and light ions, with heavy ion transport in development. Models have been included to calculate interaction probabilities when libraries are not available. Recent additions focus on the time evolution of residual nuclei decay, allowing calculation of transmutation and delayed particle emission. MCNPX is now a code of great dynamic range, and the excellent neutronics capabilities allow new opportunities to simulate devices of interest to experimental particle physics; particularly calorimetry. This paper describes the capabilities of the current MCNPX version 2.6.C, and also discusses ongoing code development.
Monte Carlo analysis: error of extrapolated thermal conductivity from molecular dynamics simulations
Liu, Xiang-Yang; Andersson, Anders David
2016-11-07
In this short report, we give an analysis of the extrapolated thermal conductivity of UO2 from earlier molecular dynamics (MD) simulations [1]. Because almost all material properties are functions of temperature, e.g. fission gas release, the fuel thermal conductivity is the most important parameter from a model sensitivity perspective [2]. Thus, it is useful to perform such analysis.
Monte Carlos studies of critical and dynamic phenomena in mixed bond Ising model
NASA Astrophysics Data System (ADS)
Santos-Filho, J. B.; Moreno, N. O.; de Albuquerque, Douglas F.
2010-11-01
The phase transition of a random mixed-bond Ising ferromagnet on a cubic lattice model is studied both numerically and analytically. In this work, we use the Metropolis and Wolff algorithm with histogram technique and finite size scaling theory to simulate the dynamics of the system. We obtained the thermodynamic quantities such as magnetization, susceptibility, and specific heat. Our results were compared with those obtained using a new technique in effective field theory that employs similar probability distribution within the framework of two-site clusters.
Monte Carlo simulations of the short time dynamics of a first-order irreversible phase transition
NASA Astrophysics Data System (ADS)
Albano, Ezequiel V.
2001-09-01
The ZGB model (Ziff-Gulari-Barshad, Phys. Rev. Lett. 56 (1986) 2553) for the catalytic oxidation of carbon monoxide has a single parameter given by the normalized partial pressure of CO molecules ( PCO). For PCO⩾ PCOCoex≃0.52583 the surface of the catalyst becomes irreversibly covered by CO molecules and the system cannot escape from this state. However, for PCO slightly below PCOCoex the system reaches an active stationary state. So, just at PCOCoex a sharp first-order irreversible phase transition is observed. It is shown that a study of the short time dynamics of the ZGB model allows to obtain a fairly accurate evaluation of the upper spinodal point given by PCOUsp≃0.52675(5). This figure is in excellent agreement with extensive simulations performed using the constant coverage ensemble.
Electronic structure quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Bajdich, Michal; Mitas, Lubos
2009-04-01
Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. The QMC approaches combine analytical insights with stochastic computational techniques for efficient solution of several classes of important many-body problems such as the stationary Schrödinger equation. QMC methods of various flavors have been applied to a great variety of systems spanning continuous and lattice quantum models, molecular and condensed systems, BEC-BCS ultracold condensates, nuclei, etc. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion Hamiltonians. Some of the key QMC achievements include direct treatment of electron correlation, accuracy in predicting energy differences and favorable scaling in the system size. Calculations of atoms, molecules, clusters and solids have demonstrated QMC applicability to real systems with hundreds of electrons while providing 90-95% of the correlation energy and energy differences typically within a few percent of experiments. Advances in accuracy beyond these limits are hampered by the so-called fixed-node approximation which is used to circumvent the notorious fermion sign problem. Many-body nodes of fermion states and their properties have therefore become one of the important topics for further progress in predictive power and efficiency of QMC calculations. Some of our recent results on the wave function nodes and related nodal domain topologies will be briefly reviewed. This includes analysis of few-electron systems and descriptions of exact and approximate nodes using transformations and projections of the highly-dimensional nodal hypersurfaces into the 3D space. Studies of fermion nodes offer new insights into topological properties of eigenstates such as explicit demonstrations that generic fermionic ground states exhibit the minimal number of two nodal domains. Recently proposed trial wave functions based on Pfaffians with
Parallel tempering Monte Carlo in LAMMPS.
Rintoul, Mark Daniel; Plimpton, Steven James; Sears, Mark P.
2003-11-01
We present here the details of the implementation of the parallel tempering Monte Carlo technique into a LAMMPS, a heavily used massively parallel molecular dynamics code at Sandia. This technique allows for many replicas of a system to be run at different simulation temperatures. At various points in the simulation, configurations can be swapped between different temperature environments and then continued. This allows for large regions of energy space to be sampled very quickly, and allows for minimum energy configurations to emerge in very complex systems, such as large biomolecular systems. By including this algorithm into an existing code, we immediately gain all of the previous work that had been put into LAMMPS, and allow this technique to quickly be available to the entire Sandia and international LAMMPS community. Finally, we present an example of this code applied to folding a small protein.
Monte Carlo simulation of a dynamical fermion problem: The light q sup 2 q sup 2 system
Grondin, G. . Dept. of Physics Oak Ridge National Lab., TN )
1991-01-01
We present results from a Guided Random Walk Monte Carlo simulation of the light q{sup 2}{bar q}{sup 2} system in a Coulomb-plus-linear quark potential model using an Intel iPSC/860 hypercube. A solvable model problem is first considered, after which we study the full q{sup 2}{bar q}{sup 2} system in (J,I) = (2,2) and (2,0) sectors. We find evidence for no bound states below the vector-vector threshold in these systems. 17 refs., 6 figs.
NASA Astrophysics Data System (ADS)
Kalinko, Aleksandr; Bauer, Matthias; Timoshenko, Janis; Kuzmin, Alexei
2016-11-01
Classical molecular dynamics (MD) and reverse Monte Carlo methods coupled with ab initio multiple-scattering extended x-ray absorption fine structure (EXAFS) calculations were used for modeling of scheelite-type AWO4 (A = Ca, Sr, Ba) W L 3-edge EXAFS spectra. The two theoretical approaches are complementary and allowed us to perform analysis of full EXAFS spectra. Both methods reproduce well the structure and dynamics of tungstates in the outer coordination shells, however the classical MD simulations underestimate the W-O bond MSRD due to a neglect of quantum zero-point-motion. The thermal vibration amplitudes, correlation effects and anisotropy of the tungstate structure were also estimated.
NASA Astrophysics Data System (ADS)
Gauthier, Michel G.
with a very wide range of polymer lengths. We thus propose a new Monte Carlo method based on a one-dimensional random-walk representation of the translocation problem that can easily be used to study chain lengths as large as 10' monomers. This model works in conjunction with an exact calculation technique to compute the key results of the translocation events such as the probability to occur and the average time duration. It is used to validate previous and make new theoretical predictions about translocation dynamics as the polymer and channel lengths are varied. It is also applied to the study of chain heterogeneity effects.
NASA Astrophysics Data System (ADS)
Lísal, Martin; Brennan, John K.; Smith, William R.
2009-03-01
We present an alternative formulation of the reaction ensemble dissipative particle dynamics (RxDPD) method [M. Lísal, J. K. Brennan, and W. R. Smith, J. Chem. Phys. 125, 16490 (2006)], a mesoscale simulation technique for studying polymer systems in reaction equilibrium. The RxDPD method combines elements of dissipative particle dynamics (DPD) and reaction ensemble Monte Carlo (RxMC), and is primarily targeted for the prediction of the system composition, thermodynamic properties, and phase behavior of reaction equilibrium polymer systems. The alternative formulation of the RxDPD method is demonstrated by considering a supramolecular diblock copolymer (SDC) melt in which two homopolymers, An and Bm, can reversibly bond at terminal binding sites to form a diblock copolymer, AnBm. We consider the effect of the terminal binding sites and the chemical incompatibility between A- and B-segments on the phase behavior. Both effects are found to strongly influence the resulting phase behavior. Due to the reversible nature of the binding, the SDC melt can be treated as the reaction equilibrium system An+Bm⇌AnBm. To simulate the An+Bm⇌AnBm melt, the system contains, in addition to full An, Bm, and AnBm polymers, two fractional polymers: one fractional polymer either fAn or fBm, and one fractional polymer fAnBm, which have fractional particles at the ends of the polymer chains. These fractional particles are coupled to the system via a coupling parameter. The time evolution of the system is governed by the DPD equations of motion, accompanied by random changes in the coupling parameter. Random changes in the coupling parameter mimic forward and reverse reaction steps as in the RxMC approach, and they are accepted with a probability derived from the expanded ensemble grand canonical partition function. Unlike the original RxDPD method that considers coupling of entire fractional polymers to the system, the expanded ensemble framework allows a stepwise coupling, thus
Quantum speedup of Monte Carlo methods.
Montanaro, Ashley
2015-09-08
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.
Self-learning Monte Carlo method
NASA Astrophysics Data System (ADS)
Liu, Junwei; Qi, Yang; Meng, Zi Yang; Fu, Liang
2017-01-01
Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup.
Adiabatic optimization versus diffusion Monte Carlo methods
NASA Astrophysics Data System (ADS)
Jarret, Michael; Jordan, Stephen P.; Lackey, Brad
2016-10-01
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k -SAT at k =2 ,3 ,4 .
Quantum speedup of Monte Carlo methods
Montanaro, Ashley
2015-01-01
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently. PMID:26528079
Monte Carlo inversion of seismic data
NASA Technical Reports Server (NTRS)
Wiggins, R. A.
1972-01-01
The analytic solution to the linear inverse problem provides estimates of the uncertainty of the solution in terms of standard deviations of corrections to a particular solution, resolution of parameter adjustments, and information distribution among the observations. It is shown that Monte Carlo inversion, when properly executed, can provide all the same kinds of information for nonlinear problems. Proper execution requires a relatively uniform sampling of all possible models. The expense of performing Monte Carlo inversion generally requires strategies to improve the probability of finding passing models. Such strategies can lead to a very strong bias in the distribution of models examined unless great care is taken in their application.
Parallel Markov chain Monte Carlo simulations.
Ren, Ruichao; Orkoulas, G
2007-06-07
With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.
Interaction picture density matrix quantum Monte Carlo
Malone, Fionn D. Lee, D. K. K.; Foulkes, W. M. C.; Blunt, N. S.; Shepherd, James J.; Spencer, J. S.
2015-07-28
The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.
Geodesic Monte Carlo on Embedded Manifolds
Byrne, Simon; Girolami, Mark
2013-01-01
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024
Parallel Markov chain Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Ren, Ruichao; Orkoulas, G.
2007-06-01
With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.
Monte Carlo simulation of neutron scattering instruments
Seeger, P.A.
1995-12-31
A library of Monte Carlo subroutines has been developed for the purpose of design of neutron scattering instruments. Using small-angle scattering as an example, the philosophy and structure of the library are described and the programs are used to compare instruments at continuous wave (CW) and long-pulse spallation source (LPSS) neutron facilities. The Monte Carlo results give a count-rate gain of a factor between 2 and 4 using time-of-flight analysis. This is comparable to scaling arguments based on the ratio of wavelength bandwidth to resolution width.
Gliksman, N R; Skibbens, R V; Salmon, E D
1993-01-01
Microtubules (MTs) in newt mitotic spindles grow faster than MTs in the interphase cytoplasmic microtubule complex (CMTC), yet spindle MTs do not have the long lengths or lifetimes of the CMTC microtubules. Because MTs undergo dynamic instability, it is likely that changes in the durations of growth or shortening are responsible for this anomaly. We have used a Monte Carlo computer simulation to examine how changes in the number of MTs and changes in the catastrophe and rescue frequencies of dynamic instability may be responsible for the cell cycle dependent changes in MT characteristics. We used the computer simulations to model interphase-like or mitotic-like MT populations on the basis of the dynamic instability parameters available from newt lung epithelial cells in vivo. We started with parameters that produced MT populations similar to the interphase newt lung cell CMTC. In the simulation, increasing the number of MTs and either increasing the frequency of catastrophe or decreasing the frequency of rescue reproduced the changes in MT dynamics measured in vivo between interphase and mitosis. Images PMID:8298190
Zen, Andrea; Coccia, Emanuele; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo
2014-03-11
Diradical molecules are essential species involved in many organic and inorganic chemical reactions. The computational study of their electronic structure is often challenging, because a reliable description of the correlation, and in particular of the static one, requires multireference techniques. The Jastrow correlated antisymmetrized geminal power (JAGP) is a compact and efficient wave function ansatz, based on the valence-bond representation, which can be used within quantum Monte Carlo (QMC) approaches. The AGP part can be rewritten in terms of molecular orbitals, obtaining a multideterminant expansion with zero-seniority number. In the present work we demonstrate the capability of the JAGP ansatz to correctly describe the electronic structure of two diradical prototypes: the orthogonally twisted ethylene, C2H4, and the methylene, CH2, representing respectively a homosymmetric and heterosymmetric system. In the orthogonally twisted ethylene, we find a degeneracy of π and π* molecular orbitals, as correctly predicted by multireference procedures, and our best estimates of the twisting barrier, using respectively the variational Monte Carlo (VMC) and the lattice regularized diffusion Monte Carlo (LRDMC) methods, are 71.9(1) and 70.2(2) kcal/mol, in very good agreement with the high-level MR-CISD+Q value, 69.2 kcal/mol. In the methylene we estimate an adiabatic triplet-singlet (X̃(3)B1-ã(1)A1) energy gap of 8.32(7) and 8.64(6) kcal/mol, using respectively VMC and LRDMC, consistently with the experimental-derived finding for Te, 9.363 kcal/mol. On the other hand, we show that the simple ansatz of a Jastrow correlated single determinant (JSD) wave function is unable to provide an accurate description of the electronic structure in these diradical molecules, both at variational level (VMC torsional barrier of C2H4 of 99.3(2) kcal/mol, triplet-singlet energy gap of CH2 of 13.45(10) kcal/mol) and, more remarkably, in the fixed-nodes projection schemes (LRDMC
Maier, Thomas A; Alvarez, Gonzalo; Summers, Michael Stuart; Schulthess, Thomas C
2010-01-01
Using dynamic cluster quantum Monte Carlo simulations, we study the superconducting behavior of a 1=8 doped two-dimensional Hubbard model with imposed unidirectional stripelike charge-density-wave modulation. We find a significant increase of the pairing correlations and critical temperature relative to the homogeneous system when the modulation length scale is sufficiently large. With a separable form of the irreducible particle-particle vertex, we show that optimized superconductivity is obtained for a moderate modulation strength due to a delicate balance between the modulation enhanced pairing interaction, and a concomitant suppression of the bare particle-particle excitations by a modulation reduction of the quasiparticle weight.
NASA Technical Reports Server (NTRS)
Gann, R. C.; Chakravarty, S.; Chester, G. V.
1978-01-01
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.
Structure and dynamics of Ebola virus matrix protein VP40 by a coarse-grained Monte Carlo simulation
NASA Astrophysics Data System (ADS)
Pandey, Ras; Farmer, Barry
Ebola virus matrix protein VP40 (consisting of 326 residues) plays a critical role in viral assembly and its functions such as regulation of viral transcription, packaging, and budding of mature virions into the plasma membrane of infected cells. How does the protein VP40 go through structural evolution during the viral life cycle remains an open question? Using a coarse-grained Monte Carlo simulation we investigate the structural evolution of VP40 as a function of temperature with the input of a knowledge-based residue-residue interaction. A number local and global physical quantities (e.g. mobility profile, contact map, radius of gyration, structure factor) are analyzed with our large-scale simulations. Our preliminary data show that the structure of the protein evolves through different state with well-defined morphologies which can be identified and quantified via a detailed analysis of structure factor.
Scalable Domain Decomposed Monte Carlo Particle Transport
O'Brien, Matthew Joseph
2013-12-05
In this dissertation, we present the parallel algorithms necessary to run domain decomposed Monte Carlo particle transport on large numbers of processors (millions of processors). Previous algorithms were not scalable, and the parallel overhead became more computationally costly than the numerical simulation.
Monte Carlo Simulation of Counting Experiments.
ERIC Educational Resources Information Center
Ogden, Philip M.
A computer program to perform a Monte Carlo simulation of counting experiments was written. The program was based on a mathematical derivation which started with counts in a time interval. The time interval was subdivided to form a binomial distribution with no two counts in the same subinterval. Then the number of subintervals was extended to…
A comparison of Monte Carlo generators
Golan, Tomasz
2015-05-15
A comparison of GENIE, NEUT, NUANCE, and NuWro Monte Carlo neutrino event generators is presented using a set of four observables: protons multiplicity, total visible energy, most energetic proton momentum, and π{sup +} two-dimensional energy vs cosine distribution.
Monte Carlo studies of uranium calorimetry
Brau, J.; Hargis, H.J.; Gabriel, T.A.; Bishop, B.L.
1985-01-01
Detailed Monte Carlo calculations of uranium calorimetry are presented which reveal a significant difference in the responses of liquid argon and plastic scintillator in uranium calorimeters. Due to saturation effects, neutrons from the uranium are found to contribute only weakly to the liquid argon signal. Electromagnetic sampling inefficiencies are significant and contribute substantially to compensation in both systems. 17 references.
Structural Reliability and Monte Carlo Simulation.
ERIC Educational Resources Information Center
Laumakis, P. J.; Harlow, G.
2002-01-01
Analyzes a simple boom structure and assesses its reliability using elementary engineering mechanics. Demonstrates the power and utility of Monte-Carlo simulation by showing that such a simulation can be implemented more readily with results that compare favorably to the theoretical calculations. (Author/MM)
Search and Rescue Monte Carlo Simulation.
1985-03-01
confidence interval ) of the number of lives saved. A single page output and computer graphic present the information to the user in an easily understood...format. The confidence interval can be reduced by making additional runs of this Monte Carlo model. (Author)
Monte Carlo methods in genetic analysis
Lin, Shili
1996-12-31
Many genetic analyses require computation of probabilities and likelihoods of pedigree data. With more and more genetic marker data deriving from new DNA technologies becoming available to researchers, exact computations are often formidable with standard statistical methods and computational algorithms. The desire to utilize as much available data as possible, coupled with complexities of realistic genetic models, push traditional approaches to their limits. These methods encounter severe methodological and computational challenges, even with the aid of advanced computing technology. Monte Carlo methods are therefore increasingly being explored as practical techniques for estimating these probabilities and likelihoods. This paper reviews the basic elements of the Markov chain Monte Carlo method and the method of sequential imputation, with an emphasis upon their applicability to genetic analysis. Three areas of applications are presented to demonstrate the versatility of Markov chain Monte Carlo for different types of genetic problems. A multilocus linkage analysis example is also presented to illustrate the sequential imputation method. Finally, important statistical issues of Markov chain Monte Carlo and sequential imputation, some of which are unique to genetic data, are discussed, and current solutions are outlined. 72 refs.
Monte Carlo studies of ARA detector optimization
NASA Astrophysics Data System (ADS)
Stockham, Jessica
2013-04-01
The Askaryan Radio Array (ARA) is a neutrino detector deployed in the Antarctic ice sheet near the South Pole. The array is designed to detect ultra high energy neutrinos in the range of 0.1-10 EeV. Detector optimization is studied using Monte Carlo simulations.
Harnessing graphical structure in Markov chain Monte Carlo learning
Stolorz, P.E.; Chew P.C.
1996-12-31
The Monte Carlo method is recognized as a useful tool in learning and probabilistic inference methods common to many datamining problems. Generalized Hidden Markov Models and Bayes nets are especially popular applications. However, the presence of multiple modes in many relevant integrands and summands often renders the method slow and cumbersome. Recent mean field alternatives designed to speed things up have been inspired by experience gleaned from physics. The current work adopts an approach very similar to this in spirit, but focusses instead upon dynamic programming notions as a basis for producing systematic Monte Carlo improvements. The idea is to approximate a given model by a dynamic programming-style decomposition, which then forms a scaffold upon which to build successively more accurate Monte Carlo approximations. Dynamic programming ideas alone fail to account for non-local structure, while standard Monte Carlo methods essentially ignore all structure. However, suitably-crafted hybrids can successfully exploit the strengths of each method, resulting in algorithms that combine speed with accuracy. The approach relies on the presence of significant {open_quotes}local{close_quotes} information in the problem at hand. This turns out to be a plausible assumption for many important applications. Example calculations are presented, and the overall strengths and weaknesses of the approach are discussed.
Markov Chain Monte Carlo and Irreversibility
NASA Astrophysics Data System (ADS)
Ottobre, Michela
2016-06-01
Markov Chain Monte Carlo (MCMC) methods are statistical methods designed to sample from a given measure π by constructing a Markov chain that has π as invariant measure and that converges to π. Most MCMC algorithms make use of chains that satisfy the detailed balance condition with respect to π; such chains are therefore reversible. On the other hand, recent work [18, 21, 28, 29] has stressed several advantages of using irreversible processes for sampling. Roughly speaking, irreversible diffusions converge to equilibrium faster (and lead to smaller asymptotic variance as well). In this paper we discuss some of the recent progress in the study of nonreversible MCMC methods. In particular: i) we explain some of the difficulties that arise in the analysis of nonreversible processes and we discuss some analytical methods to approach the study of continuous-time irreversible diffusions; ii) most of the rigorous results on irreversible diffusions are available for continuous-time processes; however, for computational purposes one needs to discretize such dynamics. It is well known that the resulting discretized chain will not, in general, retain all the good properties of the process that it is obtained from. In particular, if we want to preserve the invariance of the target measure, the chain might no longer be reversible. Therefore iii) we conclude by presenting an MCMC algorithm, the SOL-HMC algorithm [23], which results from a nonreversible discretization of a nonreversible dynamics.
MontePython: Implementing Quantum Monte Carlo using Python
NASA Astrophysics Data System (ADS)
Nilsen, Jon Kristian
2007-11-01
We present a cross-language C++/Python program for simulations of quantum mechanical systems with the use of Quantum Monte Carlo (QMC) methods. We describe a system for which to apply QMC, the algorithms of variational Monte Carlo and diffusion Monte Carlo and we describe how to implement theses methods in pure C++ and C++/Python. Furthermore we check the efficiency of the implementations in serial and parallel cases to show that the overhead using Python can be negligible. Program summaryProgram title: MontePython Catalogue identifier: ADZP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 49 519 No. of bytes in distributed program, including test data, etc.: 114 484 Distribution format: tar.gz Programming language: C++, Python Computer: PC, IBM RS6000/320, HP, ALPHA Operating system: LINUX Has the code been vectorised or parallelized?: Yes, parallelized with MPI Number of processors used: 1-96 RAM: Depends on physical system to be simulated Classification: 7.6; 16.1 Nature of problem: Investigating ab initio quantum mechanical systems, specifically Bose-Einstein condensation in dilute gases of 87Rb Solution method: Quantum Monte Carlo Running time: 225 min with 20 particles (with 4800 walkers moved in 1750 time steps) on 1 AMD Opteron TM Processor 2218 processor; Production run for, e.g., 200 particles takes around 24 hours on 32 such processors.
Multiple-time-stepping generalized hybrid Monte Carlo methods
Escribano, Bruno; Akhmatskaya, Elena; Reich, Sebastian; Azpiroz, Jon M.
2015-01-01
Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2–4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.
Modeling focusing Gaussian beams in a turbid medium with Monte Carlo simulations.
Hokr, Brett H; Bixler, Joel N; Elpers, Gabriel; Zollars, Byron; Thomas, Robert J; Yakovlev, Vladislav V; Scully, Marlan O
2015-04-06
Monte Carlo techniques are the gold standard for studying light propagation in turbid media. Traditional Monte Carlo techniques are unable to include wave effects, such as diffraction; thus, these methods are unsuitable for exploring focusing geometries where a significant ballistic component remains at the focal plane. Here, a method is presented for accurately simulating photon propagation at the focal plane, in the context of a traditional Monte Carlo simulation. This is accomplished by propagating ballistic photons along trajectories predicted by Gaussian optics until they undergo an initial scattering event, after which, they are propagated through the medium by a traditional Monte Carlo technique. Solving a known problem by building upon an existing Monte Carlo implementation allows this method to be easily implemented in a wide variety of existing Monte Carlo simulations, greatly improving the accuracy of those models for studying dynamics in a focusing geometry.
Atomistic Monte Carlo Simulation of Lipid Membranes
Wüstner, Daniel; Sklenar, Heinz
2014-01-01
Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol. PMID:24469314
Classical Trajectory and Monte Carlo Techniques
NASA Astrophysics Data System (ADS)
Olson, Ronald
The classical trajectory Monte Carlo (CTMC) method originated with Hirschfelder, who studied the H + D2 exchange reaction using a mechanical calculator [58.1]. With the availability of computers, the CTMC method was actively applied to a large number of chemical systems to determine reaction rates, and final state vibrational and rotational populations (see, e.g., Karplus et al. [58.2]). For atomic physics problems, a major step was introduced by Abrines and Percival [58.3] who employed Kepler's equations and the Bohr-Sommerfield model for atomic hydrogen to investigate electron capture and ionization for intermediate velocity collisions of H+ + H. An excellent description is given by Percival and Richards [58.4]. The CTMC method has a wide range of applicability to strongly-coupled systems, such as collisions by multiply-charged ions [58.5]. In such systems, perturbation methods fail, and basis set limitations of coupled-channel molecular- and atomic-orbital techniques have difficulty in representing the multitude of activeexcitation, electron capture, and ionization channels. Vector- and parallel-processors now allow increasingly detailed study of the dynamics of the heavy projectile and target, along with the active electrons.
Monte Carlo Particle Transport: Algorithm and Performance Overview
Gentile, N; Procassini, R; Scott, H
2005-06-02
Monte Carlo methods are frequently used for neutron and radiation transport. These methods have several advantages, such as relative ease of programming and dealing with complex meshes. Disadvantages include long run times and statistical noise. Monte Carlo photon transport calculations also often suffer from inaccuracies in matter temperature due to the lack of implicitness. In this paper we discuss the Monte Carlo algorithm as it is applied to neutron and photon transport, detail the differences between neutron and photon Monte Carlo, and give an overview of the ways the numerical method has been modified to deal with issues that arise in photon Monte Carlo simulations.
An enhanced Monte Carlo outlier detection method.
Zhang, Liangxiao; Li, Peiwu; Mao, Jin; Ma, Fei; Ding, Xiaoxia; Zhang, Qi
2015-09-30
Outlier detection is crucial in building a highly predictive model. In this study, we proposed an enhanced Monte Carlo outlier detection method by establishing cross-prediction models based on determinate normal samples and analyzing the distribution of prediction errors individually for dubious samples. One simulated and three real datasets were used to illustrate and validate the performance of our method, and the results indicated that this method outperformed Monte Carlo outlier detection in outlier diagnosis. After these outliers were removed, the value of validation by Kovats retention indices and the root mean square error of prediction decreased from 3.195 to 1.655, and the average cross-validation prediction error decreased from 2.0341 to 1.2780. This method helps establish a good model by eliminating outliers. © 2015 Wiley Periodicals, Inc.
Status of Monte Carlo at Los Alamos
Thompson, W.L.; Cashwell, E.D.
1980-01-01
At Los Alamos the early work of Fermi, von Neumann, and Ulam has been developed and supplemented by many followers, notably Cashwell and Everett, and the main product today is the continuous-energy, general-purpose, generalized-geometry, time-dependent, coupled neutron-photon transport code called MCNP. The Los Alamos Monte Carlo research and development effort is concentrated in Group X-6. MCNP treats an arbitrary three-dimensional configuration of arbitrary materials in geometric cells bounded by first- and second-degree surfaces and some fourth-degree surfaces (elliptical tori). Monte Carlo has evolved into perhaps the main method for radiation transport calculations at Los Alamos. MCNP is used in every technical division at the Laboratory by over 130 users about 600 times a month accounting for nearly 200 hours of CDC-7600 time.
Monte Carlo simulations on SIMD computer architectures
Burmester, C.P.; Gronsky, R.; Wille, L.T.
1992-03-01
Algorithmic considerations regarding the implementation of various materials science applications of the Monte Carlo technique to single instruction multiple data (SMM) computer architectures are presented. In particular, implementation of the Ising model with nearest, next nearest, and long range screened Coulomb interactions on the SIMD architecture MasPar MP-1 (DEC mpp-12000) series of massively parallel computers is demonstrated. Methods of code development which optimize processor array use and minimize inter-processor communication are presented including lattice partitioning and the use of processor array spanning tree structures for data reduction. Both geometric and algorithmic parallel approaches are utilized. Benchmarks in terms of Monte Carlo updates per second for the MasPar architecture are presented and compared to values reported in the literature from comparable studies on other architectures.
Status of Monte Carlo at Los Alamos
Thompson, W.L.; Cashwell, E.D.; Godfrey, T.N.K.; Schrandt, R.G.; Deutsch, O.L.; Booth, T.E.
1980-05-01
Four papers were presented by Group X-6 on April 22, 1980, at the Oak Ridge Radiation Shielding Information Center (RSIC) Seminar-Workshop on Theory and Applications of Monte Carlo Methods. These papers are combined into one report for convenience and because they are related to each other. The first paper (by Thompson and Cashwell) is a general survey about X-6 and MCNP and is an introduction to the other three papers. It can also serve as a resume of X-6. The second paper (by Godfrey) explains some of the details of geometry specification in MCNP. The third paper (by Cashwell and Schrandt) illustrates calculating flux at a point with MCNP; in particular, the once-more-collided flux estimator is demonstrated. Finally, the fourth paper (by Thompson, Deutsch, and Booth) is a tutorial on some variance-reduction techniques. It should be required for a fledging Monte Carlo practitioner.
Fission Matrix Capability for MCNP Monte Carlo
NASA Astrophysics Data System (ADS)
Brown, Forrest; Carney, Sean; Kiedrowski, Brian; Martin, William
2014-06-01
We describe recent experience and results from implementing a fission matrix capability into the MCNP Monte Carlo code. The fission matrix can be used to provide estimates of the fundamental mode fission distribution, the dominance ratio, the eigenvalue spectrum, and higher mode forward and adjoint eigenfunctions of the fission neutron source distribution. It can also be used to accelerate the convergence of the power method iterations and to provide basis functions for higher-order perturbation theory. The higher-mode fission sources can be used in MCNP to determine higher-mode forward fluxes and tallies, and work is underway to provide higher-mode adjoint-weighted fluxes and tallies. Past difficulties and limitations of the fission matrix approach are overcome with a new sparse representation of the matrix, permitting much larger and more accurate fission matrix representations. The new fission matrix capabilities provide a significant advance in the state-of-the-art for Monte Carlo criticality calculations.
Quantum Monte Carlo applied to solids
Shulenburger, Luke; Mattsson, Thomas R.
2013-12-01
We apply diffusion quantum Monte Carlo to a broad set of solids, benchmarking the method by comparing bulk structural properties (equilibrium volume and bulk modulus) to experiment and density functional theory (DFT) based theories. The test set includes materials with many different types of binding including ionic, metallic, covalent, and van der Waals. We show that, on average, the accuracy is comparable to or better than that of DFT when using the new generation of functionals, including one hybrid functional and two dispersion corrected functionals. The excellent performance of quantum Monte Carlo on solids is promising for its application to heterogeneous systems and high-pressure/high-density conditions. Important to the results here is the application of a consistent procedure with regards to the several approximations that are made, such as finite-size corrections and pseudopotential approximations. This test set allows for any improvements in these methods to be judged in a systematic way.
Inhomogeneous Monte Carlo simulations of dermoscopic spectroscopy
NASA Astrophysics Data System (ADS)
Gareau, Daniel S.; Li, Ting; Jacques, Steven; Krueger, James
2012-03-01
Clinical skin-lesion diagnosis uses dermoscopy: 10X epiluminescence microscopy. Skin appearance ranges from black to white with shades of blue, red, gray and orange. Color is an important diagnostic criteria for diseases including melanoma. Melanin and blood content and distribution impact the diffuse spectral remittance (300-1000nm). Skin layers: immersion medium, stratum corneum, spinous epidermis, basal epidermis and dermis as well as laterally asymmetric features (eg. melanocytic invasion) were modeled in an inhomogeneous Monte Carlo model.
Recovering intrinsic fluorescence by Monte Carlo modeling.
Müller, Manfred; Hendriks, Benno H W
2013-02-01
We present a novel way to recover intrinsic fluorescence in turbid media based on Monte Carlo generated look-up tables and making use of a diffuse reflectance measurement taken at the same location. The method has been validated on various phantoms with known intrinsic fluorescence and is benchmarked against photon-migration methods. This new method combines more flexibility in the probe design with fast reconstruction and showed similar reconstruction accuracy as found in other reconstruction methods.
Monte Carlo approach to Estrada index
NASA Astrophysics Data System (ADS)
Gutman, Ivan; Radenković, Slavko; Graovac, Ante; Plavšić, Dejan
2007-09-01
Let G be a graph on n vertices, and let λ1, λ2, …, λn be its eigenvalues. The Estrada index of G is a recently introduced molecular structure descriptor, defined as EE=∑i=1ne. Using a Monte Carlo approach, and treating the graph eigenvalues as random variables, we deduce approximate expressions for EE, in terms of the number of vertices and number of edges, of very high accuracy.
Nonequilibrium Candidate Monte Carlo Simulations with Configurational Freezing Schemes.
Giovannelli, Edoardo; Gellini, Cristina; Pietraperzia, Giangaetano; Cardini, Gianni; Chelli, Riccardo
2014-10-14
Nonequilibrium Candidate Monte Carlo simulation [Nilmeier et al., Proc. Natl. Acad. Sci. U.S.A. 2011, 108, E1009-E1018] is a tool devised to design Monte Carlo moves with high acceptance probabilities that connect uncorrelated configurations. Such moves are generated through nonequilibrium driven dynamics, producing candidate configurations accepted with a Monte Carlo-like criterion that preserves the equilibrium distribution. The probability of accepting a candidate configuration as the next sample in the Markov chain basically depends on the work performed on the system during the nonequilibrium trajectory and increases with decreasing such a work. It is thus strategically relevant to find ways of producing nonequilibrium moves with low work, namely moves where dissipation is as low as possible. This is the goal of our methodology, in which we combine Nonequilibrium Candidate Monte Carlo with Configurational Freezing schemes developed by Nicolini et al. (J. Chem. Theory Comput. 2011, 7, 582-593). The idea is to limit the configurational sampling to particles of a well-established region of the simulation sample, namely the region where dissipation occurs, while leaving fixed the other particles. This allows to make the system relaxation faster around the region perturbed by the finite-time switching move and hence to reduce the dissipated work, eventually enhancing the probability of accepting the generated move. Our combined approach enhances significantly configurational sampling, as shown by the case of a bistable dimer immersed in a dense fluid.
Path Integral Monte Carlo Methods for Fermions
NASA Astrophysics Data System (ADS)
Ethan, Ethan; Dubois, Jonathan; Ceperley, David
2014-03-01
In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte Carlo procedure from sampling paths that cause the many-body density matrix to change sign. Unfortunately, this high-dimensional nodal surface is not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperatue path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems. Support from DOE DE-FG52-09NA29456, DE-AC52-07NA27344, LLNL LDRD 10- ERD-058, and the Lawrence Scholar program.
Teaching Ionic Solvation Structure with a Monte Carlo Liquid Simulation Program
ERIC Educational Resources Information Center
Serrano, Agostinho; Santos, Flavia M. T.; Greca, Ileana M.
2004-01-01
The use of molecular dynamics and Monte Carlo methods has provided efficient means to stimulate the behavior of molecular liquids and solutions. A Monte Carlo simulation program is used to compute the structure of liquid water and of water as a solvent to Na(super +), Cl(super -), and Ar on a personal computer to show that it is easily feasible to…
An Overview of the Monte Carlo Application ToolKit (MCATK)
Trahan, Travis John
2016-01-07
MCATK is a C++ component-based Monte Carlo neutron-gamma transport software library designed to build specialized applications and designed to provide new functionality in existing general-purpose Monte Carlo codes like MCNP; it was developed with Agile software engineering methodologies under the motivation to reduce costs. The characteristics of MCATK can be summarized as follows: MCATK physics – continuous energy neutron-gamma transport with multi-temperature treatment, static eigenvalue (k and α) algorithms, time-dependent algorithm, fission chain algorithms; MCATK geometry – mesh geometries, solid body geometries. MCATK provides verified, unit-tested Monte Carlo components, flexibility in Monte Carlo applications development, and numerous tools such as geometry and cross section plotters. Recent work has involved deterministic and Monte Carlo analysis of stochastic systems. Static and dynamic analysis is discussed, and the results of a dynamic test problem are given.
Monte Carlo Volcano Seismic Moment Tensors
NASA Astrophysics Data System (ADS)
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
Four decades of implicit Monte Carlo
Wollaber, Allan B.
2016-02-23
In 1971, Fleck and Cummings derived a system of equations to enable robust Monte Carlo simulations of time-dependent, thermal radiative transfer problems. Denoted the “Implicit Monte Carlo” (IMC) equations, their solution remains the de facto standard of high-fidelity radiative transfer simulations. Over the course of 44 years, their numerical properties have become better understood, and accuracy enhancements, novel acceleration methods, and variance reduction techniques have been suggested. In this review, we rederive the IMC equations—explicitly highlighting assumptions as they are made—and outfit the equations with a Monte Carlo interpretation. We put the IMC equations in context with other approximate forms of the radiative transfer equations and present a new demonstration of their equivalence to another well-used linearization solved with deterministic transport methods for frequency-independent problems. We discuss physical and numerical limitations of the IMC equations for asymptotically small time steps, stability characteristics and the potential of maximum principle violations for large time steps, and solution behaviors in an asymptotically thick diffusive limit. We provide a new stability analysis for opacities with general monomial dependence on temperature. Here, we consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.
Four decades of implicit Monte Carlo
Wollaber, Allan B.
2016-02-23
In 1971, Fleck and Cummings derived a system of equations to enable robust Monte Carlo simulations of time-dependent, thermal radiative transfer problems. Denoted the “Implicit Monte Carlo” (IMC) equations, their solution remains the de facto standard of high-fidelity radiative transfer simulations. Over the course of 44 years, their numerical properties have become better understood, and accuracy enhancements, novel acceleration methods, and variance reduction techniques have been suggested. In this review, we rederive the IMC equations—explicitly highlighting assumptions as they are made—and outfit the equations with a Monte Carlo interpretation. We put the IMC equations in context with other approximate formsmore » of the radiative transfer equations and present a new demonstration of their equivalence to another well-used linearization solved with deterministic transport methods for frequency-independent problems. We discuss physical and numerical limitations of the IMC equations for asymptotically small time steps, stability characteristics and the potential of maximum principle violations for large time steps, and solution behaviors in an asymptotically thick diffusive limit. We provide a new stability analysis for opacities with general monomial dependence on temperature. Here, we consider spatial accuracy limitations of the IMC equations and discussion acceleration and variance reduction techniques.« less
NASA Astrophysics Data System (ADS)
Zheng, Bo-Xiao; Kretchmer, Joshua S.; Shi, Hao; Zhang, Shiwei; Chan, Garnet Kin-Lic
2017-01-01
We investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one- and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA-DMET exhibits faster asymptotic convergence towards the thermodynamic limit. We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U /t =2 ,4 ,6 . These results compare favorably with the best data available in the literature, and help resolve earlier uncertainties in the moment for U /t =2 .
Monte Carlo simulation of intercalated carbon nanotubes.
Mykhailenko, Oleksiy; Matsui, Denis; Prylutskyy, Yuriy; Le Normand, Francois; Eklund, Peter; Scharff, Peter
2007-01-01
Monte Carlo simulations of the single- and double-walled carbon nanotubes (CNT) intercalated with different metals have been carried out. The interrelation between the length of a CNT, the number and type of metal atoms has also been established. This research is aimed at studying intercalated systems based on CNTs and d-metals such as Fe and Co. Factors influencing the stability of these composites have been determined theoretically by the Monte Carlo method with the Tersoff potential. The modeling of CNTs intercalated with metals by the Monte Carlo method has proved that there is a correlation between the length of a CNT and the number of endo-atoms of specific type. Thus, in the case of a metallic CNT (9,0) with length 17 bands (3.60 nm), in contrast to Co atoms, Fe atoms are extruded out of the CNT if the number of atoms in the CNT is not less than eight. Thus, this paper shows that a CNT of a certain size can be intercalated with no more than eight Fe atoms. The systems investigated are stabilized by coordination of 3d-atoms close to the CNT wall with a radius-vector of (0.18-0.20) nm. Another characteristic feature is that, within the temperature range of (400-700) K, small systems exhibit ground-state stabilization which is not characteristic of the higher ones. The behavior of Fe and Co endo-atoms between the walls of a double-walled carbon nanotube (DW CNT) is explained by a dominating van der Waals interaction between the Co atoms themselves, which is not true for the Fe atoms.
Quantum Monte Carlo for vibrating molecules
Brown, W.R. |
1996-08-01
Quantum Monte Carlo (QMC) has successfully computed the total electronic energies of atoms and molecules. The main goal of this work is to use correlation function quantum Monte Carlo (CFQMC) to compute the vibrational state energies of molecules given a potential energy surface (PES). In CFQMC, an ensemble of random walkers simulate the diffusion and branching processes of the imaginary-time time dependent Schroedinger equation in order to evaluate the matrix elements. The program QMCVIB was written to perform multi-state VMC and CFQMC calculations and employed for several calculations of the H{sub 2}O and C{sub 3} vibrational states, using 7 PES`s, 3 trial wavefunction forms, two methods of non-linear basis function parameter optimization, and on both serial and parallel computers. In order to construct accurate trial wavefunctions different wavefunctions forms were required for H{sub 2}O and C{sub 3}. In order to construct accurate trial wavefunctions for C{sub 3}, the non-linear parameters were optimized with respect to the sum of the energies of several low-lying vibrational states. In order to stabilize the statistical error estimates for C{sub 3} the Monte Carlo data was collected into blocks. Accurate vibrational state energies were computed using both serial and parallel QMCVIB programs. Comparison of vibrational state energies computed from the three C{sub 3} PES`s suggested that a non-linear equilibrium geometry PES is the most accurate and that discrete potential representations may be used to conveniently determine vibrational state energies.
Status of Monte-Carlo Event Generators
Hoeche, Stefan; /SLAC
2011-08-11
Recent progress on general-purpose Monte-Carlo event generators is reviewed with emphasis on the simulation of hard QCD processes and subsequent parton cascades. Describing full final states of high-energy particle collisions in contemporary experiments is an intricate task. Hundreds of particles are typically produced, and the reactions involve both large and small momentum transfer. The high-dimensional phase space makes an exact solution of the problem impossible. Instead, one typically resorts to regarding events as factorized into different steps, ordered descending in the mass scales or invariant momentum transfers which are involved. In this picture, a hard interaction, described through fixed-order perturbation theory, is followed by multiple Bremsstrahlung emissions off initial- and final-state and, finally, by the hadronization process, which binds QCD partons into color-neutral hadrons. Each of these steps can be treated independently, which is the basic concept inherent to general-purpose event generators. Their development is nowadays often focused on an improved description of radiative corrections to hard processes through perturbative QCD. In this context, the concept of jets is introduced, which allows to relate sprays of hadronic particles in detectors to the partons in perturbation theory. In this talk, we briefly review recent progress on perturbative QCD in event generation. The main focus lies on the general-purpose Monte-Carlo programs HERWIG, PYTHIA and SHERPA, which will be the workhorses for LHC phenomenology. A detailed description of the physics models included in these generators can be found in [8]. We also discuss matrix-element generators, which provide the parton-level input for general-purpose Monte Carlo.
Monte Carlo algorithm for free energy calculation.
Bi, Sheng; Tong, Ning-Hua
2015-07-01
We propose a Monte Carlo algorithm for the free energy calculation based on configuration space sampling. An upward or downward temperature scan can be used to produce F(T). We implement this algorithm for the Ising model on a square lattice and triangular lattice. Comparison with the exact free energy shows an excellent agreement. We analyze the properties of this algorithm and compare it with the Wang-Landau algorithm, which samples in energy space. This method is applicable to general classical statistical models. The possibility of extending it to quantum systems is discussed.
MBR Monte Carlo Simulation in PYTHIA8
NASA Astrophysics Data System (ADS)
Ciesielski, R.
We present the MBR (Minimum Bias Rockefeller) Monte Carlo simulation of (anti)proton-proton interactions and its implementation in the PYTHIA8 event generator. We discuss the total, elastic, and total-inelastic cross sections, and three contributions from diffraction dissociation processes that contribute to the latter: single diffraction, double diffraction, and central diffraction or double-Pomeron exchange. The event generation follows a renormalized-Regge-theory model, successfully tested using CDF data. Based on the MBR-enhanced PYTHIA8 simulation, we present cross-section predictions for the LHC and beyond, up to collision energies of 50 TeV.
Monte Carlo procedure for protein design
NASA Astrophysics Data System (ADS)
Irbäck, Anders; Peterson, Carsten; Potthast, Frank; Sandelin, Erik
1998-11-01
A method for sequence optimization in protein models is presented. The approach, which has inherited its basic philosophy from recent work by Deutsch and Kurosky [Phys. Rev. Lett. 76, 323 (1996)] by maximizing conditional probabilities rather than minimizing energy functions, is based upon a different and very efficient multisequence Monte Carlo scheme. By construction, the method ensures that the designed sequences represent good folders thermodynamically. A bootstrap procedure for the sequence space search is devised making very large chains feasible. The algorithm is successfully explored on the two-dimensional HP model [K. F. Lau and K. A. Dill, Macromolecules 32, 3986 (1989)] with chain lengths N=16, 18, and 32.
Monte Carlo methods to calculate impact probabilities
NASA Astrophysics Data System (ADS)
Rickman, H.; Wiśniowski, T.; Wajer, P.; Gabryszewski, R.; Valsecchi, G. B.
2014-09-01
Context. Unraveling the events that took place in the solar system during the period known as the late heavy bombardment requires the interpretation of the cratered surfaces of the Moon and terrestrial planets. This, in turn, requires good estimates of the statistical impact probabilities for different source populations of projectiles, a subject that has received relatively little attention, since the works of Öpik (1951, Proc. R. Irish Acad. Sect. A, 54, 165) and Wetherill (1967, J. Geophys. Res., 72, 2429). Aims: We aim to work around the limitations of the Öpik and Wetherill formulae, which are caused by singularities due to zero denominators under special circumstances. Using modern computers, it is possible to make good estimates of impact probabilities by means of Monte Carlo simulations, and in this work, we explore the available options. Methods: We describe three basic methods to derive the average impact probability for a projectile with a given semi-major axis, eccentricity, and inclination with respect to a target planet on an elliptic orbit. One is a numerical averaging of the Wetherill formula; the next is a Monte Carlo super-sizing method using the target's Hill sphere. The third uses extensive minimum orbit intersection distance (MOID) calculations for a Monte Carlo sampling of potentially impacting orbits, along with calculations of the relevant interval for the timing of the encounter allowing collision. Numerical experiments are carried out for an intercomparison of the methods and to scrutinize their behavior near the singularities (zero relative inclination and equal perihelion distances). Results: We find an excellent agreement between all methods in the general case, while there appear large differences in the immediate vicinity of the singularities. With respect to the MOID method, which is the only one that does not involve simplifying assumptions and approximations, the Wetherill averaging impact probability departs by diverging toward
Markov chain Monte Carlo without likelihoods.
Marjoram, Paul; Molitor, John; Plagnol, Vincent; Tavare, Simon
2003-12-23
Many stochastic simulation approaches for generating observations from a posterior distribution depend on knowing a likelihood function. However, for many complex probability models, such likelihoods are either impossible or computationally prohibitive to obtain. Here we present a Markov chain Monte Carlo method for generating observations from a posterior distribution without the use of likelihoods. It can also be used in frequentist applications, in particular for maximum-likelihood estimation. The approach is illustrated by an example of ancestral inference in population genetics. A number of open problems are highlighted in the discussion.
Discovering correlated fermions using quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Wagner, Lucas K.; Ceperley, David M.
2016-09-01
It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.
Marcus, Ryan C.
2012-07-24
Overview of this presentation is (1) Exascale computing - different technologies, getting there; (2) high-performance proof-of-concept MCMini - features and results; and (3) OpenCL toolkit - Oatmeal (OpenCL Automatic Memory Allocation Library) - purpose and features. Despite driver issues, OpenCL seems like a good, hardware agnostic tool. MCMini demonstrates the possibility for GPGPU-based Monte Carlo methods - it shows great scaling for HPC application and algorithmic equivalence. Oatmeal provides a flexible framework to aid in the development of scientific OpenCL codes.
Quantum Monte Carlo calculations for light nuclei
Wiringa, R.B.
1998-08-01
Quantum Monte Carlo calculations of ground and low-lying excited states for nuclei with A {le} 8 are made using a realistic Hamiltonian that fits NN scattering data. Results for more than 30 different (j{sup {prime}}, T) states, plus isobaric analogs, are obtained and the known excitation spectra are reproduced reasonably well. Various density and momentum distributions and electromagnetic form factors and moments have also been computed. These are the first microscopic calculations that directly produce nuclear shell structure from realistic NN interactions.
Introduction to Cluster Monte Carlo Algorithms
NASA Astrophysics Data System (ADS)
Luijten, E.
This chapter provides an introduction to cluster Monte Carlo algorithms for classical statistical-mechanical systems. A brief review of the conventional Metropolis algorithm is given, followed by a detailed discussion of the lattice cluster algorithm developed by Swendsen and Wang and the single-cluster variant introduced by Wolff. For continuum systems, the geometric cluster algorithm of Dress and Krauth is described. It is shown how their geometric approach can be generalized to incorporate particle interactions beyond hardcore repulsions, thus forging a connection between the lattice and continuum approaches. Several illustrative examples are discussed.
Cluster hybrid Monte Carlo simulation algorithms.
Plascak, J A; Ferrenberg, Alan M; Landau, D P
2002-06-01
We show that addition of Metropolis single spin flips to the Wolff cluster-flipping Monte Carlo procedure leads to a dramatic increase in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the Metropolis or heat bath algorithms in systems where just cluster flipping is not immediately obvious (such as the spin-3/2 Ising model) can substantially reduce the statistical errors of the simulations. A further advantage of these methods is that systematic errors introduced by the use of imperfect random-number generation may be largely healed by hybridizing single spin flips with cluster flipping.
Cluster hybrid Monte Carlo simulation algorithms
NASA Astrophysics Data System (ADS)
Plascak, J. A.; Ferrenberg, Alan M.; Landau, D. P.
2002-06-01
We show that addition of Metropolis single spin flips to the Wolff cluster-flipping Monte Carlo procedure leads to a dramatic increase in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the Metropolis or heat bath algorithms in systems where just cluster flipping is not immediately obvious (such as the spin-3/2 Ising model) can substantially reduce the statistical errors of the simulations. A further advantage of these methods is that systematic errors introduced by the use of imperfect random-number generation may be largely healed by hybridizing single spin flips with cluster flipping.
Monte Carlo simulation for the transport beamline
NASA Astrophysics Data System (ADS)
Romano, F.; Attili, A.; Cirrone, G. A. P.; Carpinelli, M.; Cuttone, G.; Jia, S. B.; Marchetto, F.; Russo, G.; Schillaci, F.; Scuderi, V.; Tramontana, A.; Varisano, A.
2013-07-01
In the framework of the ELIMED project, Monte Carlo (MC) simulations are widely used to study the physical transport of charged particles generated by laser-target interactions and to preliminarily evaluate fluence and dose distributions. An energy selection system and the experimental setup for the TARANIS laser facility in Belfast (UK) have been already simulated with the GEANT4 (GEometry ANd Tracking) MC toolkit. Preliminary results are reported here. Future developments are planned to implement a MC based 3D treatment planning in order to optimize shots number and dose delivery.
State-of-the-art Monte Carlo 1988
Soran, P.D.
1988-06-28
Particle transport calculations in highly dimensional and physically complex geometries, such as detector calibration, radiation shielding, space reactors, and oil-well logging, generally require Monte Carlo transport techniques. Monte Carlo particle transport can be performed on a variety of computers ranging from APOLLOs to VAXs. Some of the hardware and software developments, which now permit Monte Carlo methods to be routinely used, are reviewed in this paper. The development of inexpensive, large, fast computer memory, coupled with fast central processing units, permits Monte Carlo calculations to be performed on workstations, minicomputers, and supercomputers. The Monte Carlo renaissance is further aided by innovations in computer architecture and software development. Advances in vectorization and parallelization architecture have resulted in the development of new algorithms which have greatly reduced processing times. Finally, the renewed interest in Monte Carlo has spawned new variance reduction techniques which are being implemented in large computer codes. 45 refs.
Monte Carlo Methods for Bridging the Timescale Gap
NASA Astrophysics Data System (ADS)
Wilding, Nigel; Landau, David P.
We identify the origin, and elucidate the character of the extended time-scales that plague computer simulation studies of first and second order phase transitions. A brief survey is provided of a number of new and existing techniques that attempt to circumvent these problems. Attention is then focused on two novel methods with which we have particular experience: “Wang-Landau sampling” and Phase Switch Monte Carlo. Detailed case studies are made of the application of the Wang-Landau approach to calculate the density of states of the 2D Ising model and the Edwards-Anderson spin glass. The principles and operation of Phase Switch Monte Carlo are described and its utility in tackling ‘difficult’ first order phase transitions is illustrated via a case study of hard-sphere freezing. We conclude with a brief overview of promising new methods for the improvement of deterministic, spin dynamics simulations.
Minimising biases in full configuration interaction quantum Monte Carlo.
Vigor, W A; Spencer, J S; Bearpark, M J; Thom, A J W
2015-03-14
We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov chain in its present form. We construct the Markov matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining the Markov chain. Despite the simplicity of a system with only two determinants, it still reveals a population control bias inherent to the FCIQMC algorithm. We investigate the effect of simulation parameters on the population control bias for the neon atom and suggest simulation setups to, in general, minimise the bias. We show a reweight ing scheme to remove the bias caused by population control commonly used in diffusion Monte Carlo [Umrigar et al., J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step.
Cluster Monte Carlo methods for the FePt Hamiltonian
NASA Astrophysics Data System (ADS)
Lyberatos, A.; Parker, G. J.
2016-02-01
Cluster Monte Carlo methods for the classical spin Hamiltonian of FePt with long range exchange interactions are presented. We use a combination of the Swendsen-Wang (or Wolff) and Metropolis algorithms that satisfies the detailed balance condition and ergodicity. The algorithms are tested by calculating the temperature dependence of the magnetization, susceptibility and heat capacity of L10-FePt nanoparticles in a range including the critical region. The cluster models yield numerical results in good agreement within statistical error with the standard single-spin flipping Monte Carlo method. The variation of the spin autocorrelation time with grain size is used to deduce the dynamic exponent of the algorithms. Our cluster models do not provide a more accurate estimate of the magnetic properties at equilibrium.
Monte Carlo Methodology Serves Up a Software Success
NASA Technical Reports Server (NTRS)
2003-01-01
Widely used for the modeling of gas flows through the computation of the motion and collisions of representative molecules, the Direct Simulation Monte Carlo method has become the gold standard for producing research and engineering predictions in the field of rarefied gas dynamics. Direct Simulation Monte Carlo was first introduced in the early 1960s by Dr. Graeme Bird, a professor at the University of Sydney, Australia. It has since proved to be a valuable tool to the aerospace and defense industries in providing design and operational support data, as well as flight data analysis. In 2002, NASA brought to the forefront a software product that maintains the same basic physics formulation of Dr. Bird's method, but provides effective modeling of complex, three-dimensional, real vehicle simulations and parallel processing capabilities to handle additional computational requirements, especially in areas where computational fluid dynamics (CFD) is not applicable. NASA's Direct Simulation Monte Carlo Analysis Code (DAC) software package is now considered the Agency s premier high-fidelity simulation tool for predicting vehicle aerodynamics and aerothermodynamic environments in rarified, or low-density, gas flows.
Discrete diffusion Monte Carlo for frequency-dependent radiative transfer
Densmore, Jeffrey D; Kelly, Thompson G; Urbatish, Todd J
2010-11-17
Discrete Diffusion Monte Carlo (DDMC) is a technique for increasing the efficiency of Implicit Monte Carlo radiative-transfer simulations. In this paper, we develop an extension of DDMC for frequency-dependent radiative transfer. We base our new DDMC method on a frequency-integrated diffusion equation for frequencies below a specified threshold. Above this threshold we employ standard Monte Carlo. With a frequency-dependent test problem, we confirm the increased efficiency of our new DDMC technique.
Mile, Viktória; Gereben, Orsolya; Kohara, Shinji; Pusztai, László
2012-08-16
A detailed study of the microscopic structure of two electrolyte solutions, cesium fluoride (CsF) and cesium iodide (CsI) in water, is presented. For revealing the influence of salt concentration on the structure, CsF solutions at concentrations of 15.1 and 32.3 mol % and CsI solutions at concentrations of 1.0 and 3.9 mol % are investigated. For each concentration, we combine total scattering structure factors from neutron and X-ray diffraction and 10 partial radial distribution functions from molecular dynamics simulations in one single structural model, generated by reverse Monte Carlo modeling. For the present solutions we show that the level of consistency between simulations that use simple pair potentials and experimental structure factors is at least semiquantitative for even the extremely highly concentrated CsF solutions. Remaining inconsistencies seem to be caused primarily by water-water distribution functions, whereas slightly problematic parts appear on the ion-oxygen partials, too. As a final result, we obtained particle configurations from reverse Monte Carlo modeling that were in quantitative agreement with both sets of diffraction data and most of the MD simulated partial radial distribution functions. From the particle coordinates, distributions of the number of first neighbors as well as angular correlation functions were calculated. The average number of water molecules around cations in both materials decreases from about 8.0 to about 5.1 as concentration increases, whereas the same quantity for the anions (X) changes from about 5.3 to about 3.7 in the case of CsF and from about 6.2 to about 4.0 in the case of CsI. The average angle of X···H-O particle arrangements, characteristic of anion-water hydrogen bonds, is closer to 180° than that found for O···H-O arrangements (water-water hydrogen bonds) at higher concentrations.
Monte Carlo modeling of spatial coherence: free-space diffraction
Fischer, David G.; Prahl, Scott A.; Duncan, Donald D.
2008-01-01
We present a Monte Carlo method for propagating partially coherent fields through complex deterministic optical systems. A Gaussian copula is used to synthesize a random source with an arbitrary spatial coherence function. Physical optics and Monte Carlo predictions of the first- and second-order statistics of the field are shown for coherent and partially coherent sources for free-space propagation, imaging using a binary Fresnel zone plate, and propagation through a limiting aperture. Excellent agreement between the physical optics and Monte Carlo predictions is demonstrated in all cases. Convergence criteria are presented for judging the quality of the Monte Carlo predictions. PMID:18830335
Monte Carlo simulations within avalanche rescue
NASA Astrophysics Data System (ADS)
Reiweger, Ingrid; Genswein, Manuel; Schweizer, Jürg
2016-04-01
Refining concepts for avalanche rescue involves calculating suitable settings for rescue strategies such as an adequate probing depth for probe line searches or an optimal time for performing resuscitation for a recovered avalanche victim in case of additional burials. In the latter case, treatment decisions have to be made in the context of triage. However, given the low number of incidents it is rarely possible to derive quantitative criteria based on historical statistics in the context of evidence-based medicine. For these rare, but complex rescue scenarios, most of the associated concepts, theories, and processes involve a number of unknown "random" parameters which have to be estimated in order to calculate anything quantitatively. An obvious approach for incorporating a number of random variables and their distributions into a calculation is to perform a Monte Carlo (MC) simulation. We here present Monte Carlo simulations for calculating the most suitable probing depth for probe line searches depending on search area and an optimal resuscitation time in case of multiple avalanche burials. The MC approach reveals, e.g., new optimized values for the duration of resuscitation that differ from previous, mainly case-based assumptions.
Calculating Pi Using the Monte Carlo Method
NASA Astrophysics Data System (ADS)
Williamson, Timothy
2013-11-01
During the summer of 2012, I had the opportunity to participate in a research experience for teachers at the center for sustainable energy at Notre Dame University (RET @ cSEND) working with Professor John LoSecco on the problem of using antineutrino detection to accurately determine the fuel makeup and operating power of nuclear reactors. During full power operation, a reactor may produce 1021 antineutrinos per second with approximately 100 per day being detected. While becoming familiar with the design and operation of the detectors, and how total antineutrino flux could be obtained from such a small sample, I read about a simulation program called Monte Carlo. Further investigation led me to the Monte Carlo method page of Wikipedia2 where I saw an example of approximating pi using this simulation. Other examples where this method was applied were typically done with computer simulations2 or purely mathematical.3 It is my belief that this method may be easily related to the students by performing the simple activity of sprinkling rice on an arc drawn in a square. The activity that follows was inspired by those simulations and was used by my AP Physics class last year with very good results.
Multilevel Monte Carlo simulation of Coulomb collisions
Rosin, M.S.; Ricketson, L.F.; Dimits, A.M.; Caflisch, R.E.; Cohen, B.I.
2014-10-01
We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau–Fokker–Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ε, the computational cost of the method is O(ε{sup −2}) or O(ε{sup −2}(lnε){sup 2}), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε{sup −3}) for direct simulation Monte Carlo or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10{sup −5}. We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.
Geometrical Monte Carlo simulation of atmospheric turbulence
NASA Astrophysics Data System (ADS)
Yuksel, Demet; Yuksel, Heba
2013-09-01
Atmospheric turbulence has a significant impact on the quality of a laser beam propagating through the atmosphere over long distances. Turbulence causes intensity scintillation and beam wander from propagation through turbulent eddies of varying sizes and refractive index. This can severely impair the operation of target designation and Free-Space Optical (FSO) communications systems. In addition, experimenting on an FSO communication system is rather tedious and difficult. The interferences of plentiful elements affect the result and cause the experimental outcomes to have bigger error variance margins than they are supposed to have. Especially when we go into the stronger turbulence regimes the simulation and analysis of the turbulence induced beams require delicate attention. We propose a new geometrical model to assess the phase shift of a laser beam propagating through turbulence. The atmosphere along the laser beam propagation path will be modeled as a spatial distribution of spherical bubbles with refractive index discontinuity calculated from a Gaussian distribution with the mean value being the index of air. For each statistical representation of the atmosphere, the path of rays will be analyzed using geometrical optics. These Monte Carlo techniques will assess the phase shift as a summation of the phases that arrive at the same point at the receiver. Accordingly, there would be dark and bright spots at the receiver that give an idea regarding the intensity pattern without having to solve the wave equation. The Monte Carlo analysis will be compared with the predictions of wave theory.
Scalable Domain Decomposed Monte Carlo Particle Transport
NASA Astrophysics Data System (ADS)
O'Brien, Matthew Joseph
In this dissertation, we present the parallel algorithms necessary to run domain decomposed Monte Carlo particle transport on large numbers of processors (millions of processors). Previous algorithms were not scalable, and the parallel overhead became more computationally costly than the numerical simulation. The main algorithms we consider are: • Domain decomposition of constructive solid geometry: enables extremely large calculations in which the background geometry is too large to fit in the memory of a single computational node. • Load Balancing: keeps the workload per processor as even as possible so the calculation runs efficiently. • Global Particle Find: if particles are on the wrong processor, globally resolve their locations to the correct processor based on particle coordinate and background domain. • Visualizing constructive solid geometry, sourcing particles, deciding that particle streaming communication is completed and spatial redecomposition. These algorithms are some of the most important parallel algorithms required for domain decomposed Monte Carlo particle transport. We demonstrate that our previous algorithms were not scalable, prove that our new algorithms are scalable, and run some of the algorithms up to 2 million MPI processes on the Sequoia supercomputer.
Discrete range clustering using Monte Carlo methods
NASA Technical Reports Server (NTRS)
Chatterji, G. B.; Sridhar, B.
1993-01-01
For automatic obstacle avoidance guidance during rotorcraft low altitude flight, a reliable model of the nearby environment is needed. Such a model may be constructed by applying surface fitting techniques to the dense range map obtained by active sensing using radars. However, for covertness, passive sensing techniques using electro-optic sensors are desirable. As opposed to the dense range map obtained via active sensing, passive sensing algorithms produce reliable range at sparse locations, and therefore, surface fitting techniques to fill the gaps in the range measurement are not directly applicable. Both for automatic guidance and as a display for aiding the pilot, these discrete ranges need to be grouped into sets which correspond to objects in the nearby environment. The focus of this paper is on using Monte Carlo methods for clustering range points into meaningful groups. One of the aims of the paper is to explore whether simulated annealing methods offer significant advantage over the basic Monte Carlo method for this class of problems. We compare three different approaches and present application results of these algorithms to a laboratory image sequence and a helicopter flight sequence.
CosmoMC: Cosmological MonteCarlo
NASA Astrophysics Data System (ADS)
Lewis, Antony; Bridle, Sarah
2011-06-01
We present a fast Markov Chain Monte-Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent CMB experiments and provide parameter constraints, including sigma_8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass (m_nu < 0.3eV), equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendices we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters.
Quantum Monte Carlo for atoms and molecules
Barnett, R.N.
1989-11-01
The diffusion quantum Monte Carlo with fixed nodes (QMC) approach has been employed in studying energy-eigenstates for 1--4 electron systems. Previous work employing the diffusion QMC technique yielded energies of high quality for H{sub 2}, LiH, Li{sub 2}, and H{sub 2}O. Here, the range of calculations with this new approach has been extended to include additional first-row atoms and molecules. In addition, improvements in the previously computed fixed-node energies of LiH, Li{sub 2}, and H{sub 2}O have been obtained using more accurate trial functions. All computations were performed within, but are not limited to, the Born-Oppenheimer approximation. In our computations, the effects of variation of Monte Carlo parameters on the QMC solution of the Schroedinger equation were studied extensively. These parameters include the time step, renormalization time and nodal structure. These studies have been very useful in determining which choices of such parameters will yield accurate QMC energies most efficiently. Generally, very accurate energies (90--100% of the correlation energy is obtained) have been computed with single-determinant trail functions multiplied by simple correlation functions. Improvements in accuracy should be readily obtained using more complex trial functions.
Chemical application of diffusion quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Reynolds, P. J.; Lester, W. A., Jr.
1983-10-01
The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. As an example the singlet-triplet splitting of the energy of the methylene molecule CH2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on our VAX 11/780, and second by explicitly writing vector code for all loops longer than a crossover length C. The speed of the codes relative to one another as a function of C, and relative to the VAX is discussed. Since CH2 has only eight electrons, most of the loops in this application are fairly short. The longest inner loops run over the set of atomic basis functions. The CPU time dependence obtained versus the number of basis functions is discussed and compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures. Finally, preliminary work on restructuring the algorithm to compute the separate Monte Carlo realizations in parallel is discussed.
Multilevel Monte Carlo simulation of Coulomb collisions
Rosin, M. S.; Ricketson, L. F.; Dimits, A. M.; ...
2014-05-29
We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau–Fokker–Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ε , the computational cost of the method is O(ε–2) or (ε–2(lnε)2), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε–3) for direct simulation Monte Carlo or binary collision methods.more » We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10–5. Lastly, we discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.« less
Multilevel Monte Carlo simulation of Coulomb collisions
Rosin, M. S.; Ricketson, L. F.; Dimits, A. M.; Caflisch, R. E.; Cohen, B. I.
2014-05-29
We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau–Fokker–Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ε , the computational cost of the method is O(ε^{–2}) or (ε^{–2}(lnε)^{2}), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε^{–3}) for direct simulation Monte Carlo or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10^{–5}. Lastly, we discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.
Quantum Monte Carlo Endstation for Petascale Computing
Lubos Mitas
2011-01-26
NCSU research group has been focused on accomplising the key goals of this initiative: establishing new generation of quantum Monte Carlo (QMC) computational tools as a part of Endstation petaflop initiative for use at the DOE ORNL computational facilities and for use by computational electronic structure community at large; carrying out high accuracy quantum Monte Carlo demonstration projects in application of these tools to the forefront electronic structure problems in molecular and solid systems; expanding the impact of QMC methods and approaches; explaining and enhancing the impact of these advanced computational approaches. In particular, we have developed quantum Monte Carlo code (QWalk, www.qwalk.org) which was significantly expanded and optimized using funds from this support and at present became an actively used tool in the petascale regime by ORNL researchers and beyond. These developments have been built upon efforts undertaken by the PI's group and collaborators over the period of the last decade. The code was optimized and tested extensively on a number of parallel architectures including petaflop ORNL Jaguar machine. We have developed and redesigned a number of code modules such as evaluation of wave functions and orbitals, calculations of pfaffians and introduction of backflow coordinates together with overall organization of the code and random walker distribution over multicore architectures. We have addressed several bottlenecks such as load balancing and verified efficiency and accuracy of the calculations with the other groups of the Endstation team. The QWalk package contains about 50,000 lines of high quality object-oriented C++ and includes also interfaces to data files from other conventional electronic structure codes such as Gamess, Gaussian, Crystal and others. This grant supported PI for one month during summers, a full-time postdoc and partially three graduate students over the period of the grant duration, it has resulted in 13
Finding organic vapors - a Monte Carlo approach
NASA Astrophysics Data System (ADS)
Vuollekoski, Henri; Boy, Michael; Kerminen, Veli-Matti; Kulmala, Markku
2010-05-01
drawbacks in accuracy, the inability to find diurnal variation and the lack of size resolution. Here, we aim to shed some light onto the problem by applying an ad hoc Monte Carlo algorithm to a well established aerosol dynamical model, the University of Helsinki Multicomponent Aerosol model (UHMA). By performing a side-by-side comparison with measurement data within the algorithm, this approach has the significant advantage of decreasing the amount of manual labor. But more importantly, by basing the comparison on particle number size distribution data - a quantity that can be quite reliably measured - the accuracy of the results is good.
Graphics Processing Unit Accelerated Hirsch-Fye Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Moore, Conrad; Abu Asal, Sameer; Rajagoplan, Kaushik; Poliakoff, David; Caprino, Joseph; Tomko, Karen; Thakur, Bhupender; Yang, Shuxiang; Moreno, Juana; Jarrell, Mark
2012-02-01
In Dynamical Mean Field Theory and its cluster extensions, such as the Dynamic Cluster Algorithm, the bottleneck of the algorithm is solving the self-consistency equations with an impurity solver. Hirsch-Fye Quantum Monte Carlo is one of the most commonly used impurity and cluster solvers. This work implements optimizations of the algorithm, such as enabling large data re-use, suitable for the Graphics Processing Unit (GPU) architecture. The GPU's sheer number of concurrent parallel computations and large bandwidth to many shared memories takes advantage of the inherent parallelism in the Green function update and measurement routines, and can substantially improve the efficiency of the Hirsch-Fye impurity solver.
Chemical accuracy from quantum Monte Carlo for the benzene dimer
Azadi, Sam; Cohen, R. E.
2015-09-14
We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of −2.3(4) and −2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is −2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.
Monte Carlo simulations of electron transport in strongly attaching gases
NASA Astrophysics Data System (ADS)
Petrovic, Zoran; Miric, Jasmina; Simonovic, Ilija; Bosnjakovic, Danko; Dujko, Sasa
2016-09-01
Extensive loss of electrons in strongly attaching gases imposes significant difficulties in Monte Carlo simulations at low electric field strengths. In order to compensate for such losses, some kind of rescaling procedures must be used. In this work, we discuss two rescaling procedures for Monte Carlo simulations of electron transport in strongly attaching gases: (1) discrete rescaling, and (2) continuous rescaling. The discrete rescaling procedure is based on duplication of electrons randomly chosen from the remaining swarm at certain discrete time steps. The continuous rescaling procedure employs a dynamically defined fictitious ionization process with the constant collision frequency chosen to be equal to the attachment collision frequency. These procedures should not in any way modify the distribution function. Monte Carlo calculations of transport coefficients for electrons in SF6 and CF3I are performed in a wide range of electric field strengths. However, special emphasis is placed upon the analysis of transport phenomena in the limit of lower electric fields where the transport properties are strongly affected by electron attachment. Two important phenomena arise: (1) the reduction of the mean energy with increasing E/N for electrons in SF6, and (2) the occurrence of negative differential conductivity in the bulk drift velocity of electrons in both SF6 and CF3I.
Chemical accuracy from quantum Monte Carlo for the benzene dimer.
Azadi, Sam; Cohen, R E
2015-09-14
We report an accurate study of interactions between benzene molecules using variational quantum Monte Carlo (VMC) and diffusion quantum Monte Carlo (DMC) methods. We compare these results with density functional theory using different van der Waals functionals. In our quantum Monte Carlo (QMC) calculations, we use accurate correlated trial wave functions including three-body Jastrow factors and backflow transformations. We consider two benzene molecules in the parallel displaced geometry, and find that by highly optimizing the wave function and introducing more dynamical correlation into the wave function, we compute the weak chemical binding energy between aromatic rings accurately. We find optimal VMC and DMC binding energies of -2.3(4) and -2.7(3) kcal/mol, respectively. The best estimate of the coupled-cluster theory through perturbative triplets/complete basis set limit is -2.65(2) kcal/mol [Miliordos et al., J. Phys. Chem. A 118, 7568 (2014)]. Our results indicate that QMC methods give chemical accuracy for weakly bound van der Waals molecular interactions, comparable to results from the best quantum chemistry methods.
Monte Carlo Studies of the Fcc Ising Model.
NASA Astrophysics Data System (ADS)
Polgreen, Thomas Lee
Monte Carlo simulations are performed on the antiferromagnetic fcc Ising model which is relevant to the binary alloy CuAu. The model exhibits a first-order ordering transition as a function of temperature. The lattice free energy of the model is determined for all temperatures. By matching free energies of the ordered and disordered phases, the transition temperature is determined to be T(,t) = 1.736 J where J is the coupling constant of the model. The free energy as determined by series expansion and the Kikuchi cluster variation method is compared with the Monte Carlo results. These methods work well for the ordered phase, but not for the disordered phase. A determination of the pair correlation in the disordered phase along the {100} direction indicates a correlation length of (DBLTURN) 2.5a at the phase transition. The correlation length exhibits mean-field-like temperature dependence. The Cowley-Warren short range order parameters are determined as a function of temperature for the first twelve nearest-neighbor shells of this model. The Monte Carlo results are used to determine the free parameter in a mean-field-like class of theories described by Clapp and Moss. The ability of these theories to predict ratios between pair potentials is tested with these results. In addition, evidence of a region of heterophase fluctuations is presented in agreement with x-ray diffuse scattering measurements on Cu(,3)Au. The growth of order following a rapid quench from disorder is studied by means of a dynamic Monte Carlo simulation. The results compare favorably with the Landau theory proposed by Chan for temperatures near the first-order phase transition. For lower temperatures, the results are in agreement with the theories of Lifshitz and Allen and Chan. In the intermediate temperature range, our extension of Chan's theory is able to explain our simulation results and recent experimental results.
Monte Carlo-Minimization and Monte Carlo Recursion Approaches to Structure and Free Energy.
NASA Astrophysics Data System (ADS)
Li, Zhenqin
1990-08-01
Biological systems are intrinsically "complex", involving many degrees of freedom, heterogeneity, and strong interactions among components. For the simplest of biological substances, e.g., biomolecules, which obey the laws of thermodynamics, we may attempt a statistical mechanical investigational approach. Even for these simplest many -body systems, assuming microscopic interactions are completely known, current computational methods in characterizing the overall structure and free energy face the fundamental challenge of an exponential amount of computation, with the rise in the number of degrees of freedom. As an attempt to surmount such problems, two computational procedures, the Monte Carlo-minimization and Monte Carlo recursion methods, have been developed as general approaches to the determination of structure and free energy of a complex thermodynamic system. We describe, in Chapter 2, the Monte Carlo-minimization method, which attempts to simulate natural protein folding processes and to overcome the multiple-minima problem. The Monte Carlo-minimization procedure has been applied to a pentapeptide, Met-enkephalin, leading consistently to the lowest energy structure, which is most likely to be the global minimum structure for Met-enkephalin in the absence of water, given the ECEPP energy parameters. In Chapter 3 of this thesis, we develop a Monte Carlo recursion method to compute the free energy of a given physical system with known interactions, which has been applied to a 32-particle Lennard-Jones fluid. In Chapter 4, we describe an efficient implementation of the recursion procedure, for the computation of the free energy of liquid water, with both MCY and TIP4P potential parameters for water. As a further demonstration of the power of the recursion method for calculating free energy, a general formalism of cluster formation from monatomic vapor is developed in Chapter 5. The Gibbs free energy of constrained clusters can be computed efficiently using the
Monte Carlo simulation of classical spin models with chaotic billiards.
Suzuki, Hideyuki
2013-11-01
It has recently been shown that the computing abilities of Boltzmann machines, or Ising spin-glass models, can be implemented by chaotic billiard dynamics without any use of random numbers. In this paper, we further numerically investigate the capabilities of the chaotic billiard dynamics as a deterministic alternative to random Monte Carlo methods by applying it to classical spin models in statistical physics. First, we verify that the billiard dynamics can yield samples that converge to the true distribution of the Ising model on a small lattice, and we show that it appears to have the same convergence rate as random Monte Carlo sampling. Second, we apply the billiard dynamics to finite-size scaling analysis of the critical behavior of the Ising model and show that the phase-transition point and the critical exponents are correctly obtained. Third, we extend the billiard dynamics to spins that take more than two states and show that it can be applied successfully to the Potts model. We also discuss the possibility of extensions to continuous-valued models such as the XY model.
Monte Carlo simulation of classical spin models with chaotic billiards
NASA Astrophysics Data System (ADS)
Suzuki, Hideyuki
2013-11-01
It has recently been shown that the computing abilities of Boltzmann machines, or Ising spin-glass models, can be implemented by chaotic billiard dynamics without any use of random numbers. In this paper, we further numerically investigate the capabilities of the chaotic billiard dynamics as a deterministic alternative to random Monte Carlo methods by applying it to classical spin models in statistical physics. First, we verify that the billiard dynamics can yield samples that converge to the true distribution of the Ising model on a small lattice, and we show that it appears to have the same convergence rate as random Monte Carlo sampling. Second, we apply the billiard dynamics to finite-size scaling analysis of the critical behavior of the Ising model and show that the phase-transition point and the critical exponents are correctly obtained. Third, we extend the billiard dynamics to spins that take more than two states and show that it can be applied successfully to the Potts model. We also discuss the possibility of extensions to continuous-valued models such as the XY model.
Monte Carlo Simulation of Endlinking Oligomers
NASA Technical Reports Server (NTRS)
Hinkley, Jeffrey A.; Young, Jennifer A.
1998-01-01
This report describes initial efforts to model the endlinking reaction of phenylethynyl-terminated oligomers. Several different molecular weights were simulated using the Bond Fluctuation Monte Carlo technique on a 20 x 20 x 20 unit lattice with periodic boundary conditions. After a monodisperse "melt" was equilibrated, chain ends were linked whenever they came within the allowed bond distance. Ends remained reactive throughout, so that multiple links were permitted. Even under these very liberal crosslinking assumptions, geometrical factors limited the degree of crosslinking. Average crosslink functionalities were 2.3 to 2.6; surprisingly, they did not depend strongly on the chain length. These results agreed well with the degrees of crosslinking inferred from experiment in a cured phenylethynyl-terminated polyimide oligomer.
Exploring theory space with Monte Carlo reweighting
Gainer, James S.; Lykken, Joseph; Matchev, Konstantin T.; ...
2014-10-13
Theories of new physics often involve a large number of unknown parameters which need to be scanned. Additionally, a putative signal in a particular channel may be due to a variety of distinct models of new physics. This makes experimental attempts to constrain the parameter space of motivated new physics models with a high degree of generality quite challenging. We describe how the reweighting of events may allow this challenge to be met, as fully simulated Monte Carlo samples generated for arbitrary benchmark models can be effectively re-used. Specifically, we suggest procedures that allow more efficient collaboration between theorists andmore » experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.« less
Chemical application of diffusion quantum Monte Carlo
NASA Technical Reports Server (NTRS)
Reynolds, P. J.; Lester, W. A., Jr.
1984-01-01
The diffusion quantum Monte Carlo (QMC) method gives a stochastic solution to the Schroedinger equation. This approach is receiving increasing attention in chemical applications as a result of its high accuracy. However, reducing statistical uncertainty remains a priority because chemical effects are often obtained as small differences of large numbers. As an example, the single-triplet splitting of the energy of the methylene molecule CH sub 2 is given. The QMC algorithm was implemented on the CYBER 205, first as a direct transcription of the algorithm running on the VAX 11/780, and second by explicitly writing vector code for all loops longer than a crossover length C. The speed of the codes relative to one another as a function of C, and relative to the VAX, are discussed. The computational time dependence obtained versus the number of basis functions is discussed and this is compared with that obtained from traditional quantum chemistry codes and that obtained from traditional computer architectures.
Monte Carlo calculation for microplanar beam radiography.
Company, F Z; Allen, B J; Mino, C
2000-09-01
In radiography the scattered radiation from the off-target region decreases the contrast of the target image. We propose that a bundle of collimated, closely spaced, microplanar beams can reduce the scattered radiation and eliminate the effect of secondary electron dose, thus increasing the image dose contrast in the detector. The lateral and depth dose distributions of 20-200 keV microplanar beams are investigated using the EGS4 Monte Carlo code to calculate the depth doses and dose profiles in a 6 cm x 6 cm x 6 cm tissue phantom. The maximum dose on the primary beam axis (peak) and the minimum inter-beam scattered dose (valley) are compared at different photon energies and the optimum energy range for microbeam radiography is found. Results show that a bundle of closely spaced microplanar beams can give superior contrast imaging to a single macrobeam of the same overall area.
Lunar Regolith Albedos Using Monte Carlos
NASA Technical Reports Server (NTRS)
Wilson, T. L.; Andersen, V.; Pinsky, L. S.
2003-01-01
The analysis of planetary regoliths for their backscatter albedos produced by cosmic rays (CRs) is important for space exploration and its potential contributions to science investigations in fundamental physics and astrophysics. Albedos affect all such experiments and the personnel that operate them. Groups have analyzed the production rates of various particles and elemental species by planetary surfaces when bombarded with Galactic CR fluxes, both theoretically and by means of various transport codes, some of which have emphasized neutrons. Here we report on the preliminary results of our current Monte Carlo investigation into the production of charged particles, neutrons, and neutrinos by the lunar surface using FLUKA. In contrast to previous work, the effects of charm are now included.
Accuracy control in Monte Carlo radiative calculations
NASA Technical Reports Server (NTRS)
Almazan, P. Planas
1993-01-01
The general accuracy law that rules the Monte Carlo, ray-tracing algorithms used commonly for the calculation of the radiative entities in the thermal analysis of spacecraft are presented. These entities involve transfer of radiative energy either from a single source to a target (e.g., the configuration factors). or from several sources to a target (e.g., the absorbed heat fluxes). In fact, the former is just a particular case of the latter. The accuracy model is later applied to the calculation of some specific radiative entities. Furthermore, some issues related to the implementation of such a model in a software tool are discussed. Although only the relative error is considered through the discussion, similar results can be derived for the absolute error.
Noncovalent Interactions by Quantum Monte Carlo.
Dubecký, Matúš; Mitas, Lubos; Jurečka, Petr
2016-05-11
Quantum Monte Carlo (QMC) is a family of stochastic methods for solving quantum many-body problems such as the stationary Schrödinger equation. The review introduces basic notions of electronic structure QMC based on random walks in real space as well as its advances and adaptations to systems with noncovalent interactions. Specific issues such as fixed-node error cancellation, construction of trial wave functions, and efficiency considerations that allow for benchmark quality QMC energy differences are described in detail. Comprehensive overview of articles covers QMC applications to systems with noncovalent interactions over the last three decades. The current status of QMC with regard to efficiency, applicability, and usability by nonexperts together with further considerations about QMC developments, limitations, and unsolved challenges are discussed as well.
Hybrid algorithms in quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Kim, Jeongnim; Esler, Kenneth P.; McMinis, Jeremy; Morales, Miguel A.; Clark, Bryan K.; Shulenburger, Luke; Ceperley, David M.
2012-12-01
With advances in algorithms and growing computing powers, quantum Monte Carlo (QMC) methods have become a leading contender for high accuracy calculations for the electronic structure of realistic systems. The performance gain on recent HPC systems is largely driven by increasing parallelism: the number of compute cores of a SMP and the number of SMPs have been going up, as the Top500 list attests. However, the available memory as well as the communication and memory bandwidth per element has not kept pace with the increasing parallelism. This severely limits the applicability of QMC and the problem size it can handle. OpenMP/MPI hybrid programming provides applications with simple but effective solutions to overcome efficiency and scalability bottlenecks on large-scale clusters based on multi/many-core SMPs. We discuss the design and implementation of hybrid methods in QMCPACK and analyze its performance on current HPC platforms characterized by various memory and communication hierarchies.
Monte Carlo applications to acoustical field solutions
NASA Technical Reports Server (NTRS)
Haviland, J. K.; Thanedar, B. D.
1973-01-01
The Monte Carlo technique is proposed for the determination of the acoustical pressure-time history at chosen points in a partial enclosure, the central idea of this technique being the tracing of acoustical rays. A statistical model is formulated and an algorithm for pressure is developed, the conformity of which is examined by two approaches and is shown to give the known results. The concepts that are developed are applied to the determination of the transient field due to a sound source in a homogeneous medium in a rectangular enclosure with perfect reflecting walls, and the results are compared with those presented by Mintzer based on the Laplace transform approach, as well as with a normal mode solution.
Monte Carlo modeling and meteor showers
NASA Technical Reports Server (NTRS)
Kulikova, N. V.
1987-01-01
Prediction of short lived increases in the cosmic dust influx, the concentration in lower thermosphere of atoms and ions of meteor origin and the determination of the frequency of micrometeor impacts on spacecraft are all of scientific and practical interest and all require adequate models of meteor showers at an early stage of their existence. A Monte Carlo model of meteor matter ejection from a parent body at any point of space was worked out by other researchers. This scheme is described. According to the scheme, the formation of ten well known meteor streams was simulated and the possibility of genetic affinity of each of them with the most probable parent comet was analyzed. Some of the results are presented.
Green's function Monte Carlo in nuclear physics
Carlson, J.
1990-01-01
We review the status of Green's Function Monte Carlo (GFMC) methods as applied to problems in nuclear physics. New methods have been developed to handle the spin and isospin degrees of freedom that are a vital part of any realistic nuclear physics problem, whether at the level of quarks or nucleons. We discuss these methods and then summarize results obtained recently for light nuclei, including ground state energies, three-body forces, charge form factors and the coulomb sum. As an illustration of the applicability of GFMC to quark models, we also consider the possible existence of bound exotic multi-quark states within the framework of flux-tube quark models. 44 refs., 8 figs., 1 tab.
Resist develop prediction by Monte Carlo simulation
NASA Astrophysics Data System (ADS)
Sohn, Dong-Soo; Jeon, Kyoung-Ah; Sohn, Young-Soo; Oh, Hye-Keun
2002-07-01
Various resist develop models have been suggested to express the phenomena from the pioneering work of Dill's model in 1975 to the recent Shipley's enhanced notch model. The statistical Monte Carlo method can be applied to the process such as development and post exposure bake. The motions of developer during development process were traced by using this method. We have considered that the surface edge roughness of the resist depends on the weight percentage of protected and de-protected polymer in the resist. The results are well agreed with other papers. This study can be helpful for the developing of new photoresist and developer that can be used to pattern the device features smaller than 100 nm.
Geometric Monte Carlo and black Janus geometries
NASA Astrophysics Data System (ADS)
Bak, Dongsu; Kim, Chanju; Kim, Kyung Kiu; Min, Hyunsoo; Song, Jeong-Pil
2017-04-01
We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.
Monte Carlo simulations of medical imaging modalities
Estes, G.P.
1998-09-01
Because continuous-energy Monte Carlo radiation transport calculations can be nearly exact simulations of physical reality (within data limitations, geometric approximations, transport algorithms, etc.), it follows that one should be able to closely approximate the results of many experiments from first-principles computations. This line of reasoning has led to various MCNP studies that involve simulations of medical imaging modalities and other visualization methods such as radiography, Anger camera, computerized tomography (CT) scans, and SABRINA particle track visualization. It is the intent of this paper to summarize some of these imaging simulations in the hope of stimulating further work, especially as computer power increases. Improved interpretation and prediction of medical images should ultimately lead to enhanced medical treatments. It is also reasonable to assume that such computations could be used to design new or more effective imaging instruments.
Exploring theory space with Monte Carlo reweighting
Gainer, James S.; Lykken, Joseph; Matchev, Konstantin T.; Mrenna, Stephen; Park, Myeonghun
2014-10-13
Theories of new physics often involve a large number of unknown parameters which need to be scanned. Additionally, a putative signal in a particular channel may be due to a variety of distinct models of new physics. This makes experimental attempts to constrain the parameter space of motivated new physics models with a high degree of generality quite challenging. We describe how the reweighting of events may allow this challenge to be met, as fully simulated Monte Carlo samples generated for arbitrary benchmark models can be effectively re-used. Specifically, we suggest procedures that allow more efficient collaboration between theorists and experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.
The Monte Carlo Method. Popular Lectures in Mathematics.
ERIC Educational Resources Information Center
Sobol', I. M.
The Monte Carlo Method is a method of approximately solving mathematical and physical problems by the simulation of random quantities. The principal goal of this booklet is to suggest to specialists in all areas that they will encounter problems which can be solved by the Monte Carlo Method. Part I of the booklet discusses the simulation of random…
Economic Risk Analysis: Using Analytical and Monte Carlo Techniques.
ERIC Educational Resources Information Center
O'Donnell, Brendan R.; Hickner, Michael A.; Barna, Bruce A.
2002-01-01
Describes the development and instructional use of a Microsoft Excel spreadsheet template that facilitates analytical and Monte Carlo risk analysis of investment decisions. Discusses a variety of risk assessment methods followed by applications of the analytical and Monte Carlo methods. Uses a case study to illustrate use of the spreadsheet tool…
A Primer in Monte Carlo Integration Using Mathcad
ERIC Educational Resources Information Center
Hoyer, Chad E.; Kegerreis, Jeb S.
2013-01-01
The essentials of Monte Carlo integration are presented for use in an upper-level physical chemistry setting. A Mathcad document that aids in the dissemination and utilization of this information is described and is available in the Supporting Information. A brief outline of Monte Carlo integration is given, along with ideas and pedagogy for…
NASA Astrophysics Data System (ADS)
Brolin, Gustav; Sjögreen Gleisner, Katarina; Ljungberg, Michael
2013-05-01
In dynamic renal scintigraphy, the main interest is the radiopharmaceutical redistribution as a function of time. Quality control (QC) of renal procedures often relies on phantom experiments to compare image-based results with the measurement setup. A phantom with a realistic anatomy and time-varying activity distribution is therefore desirable. This work describes a pharmacokinetic (PK) compartment model for 99mTc-MAG3, used for defining a dynamic whole-body activity distribution within a digital phantom (XCAT) for accurate Monte Carlo (MC)-based images for QC. Each phantom structure is assigned a time-activity curve provided by the PK model, employing parameter values consistent with MAG3 pharmacokinetics. This approach ensures that the total amount of tracer in the phantom is preserved between time points, and it allows for modifications of the pharmacokinetics in a controlled fashion. By adjusting parameter values in the PK model, different clinically realistic scenarios can be mimicked, regarding, e.g., the relative renal uptake and renal transit time. Using the MC code SIMIND, a complete set of renography images including effects of photon attenuation, scattering, limited spatial resolution and noise, are simulated. The obtained image data can be used to evaluate quantitative techniques and computer software in clinical renography.
Brolin, Gustav; Gleisner, Katarina Sjögreen; Ljungberg, Michael
2013-05-21
In dynamic renal scintigraphy, the main interest is the radiopharmaceutical redistribution as a function of time. Quality control (QC) of renal procedures often relies on phantom experiments to compare image-based results with the measurement setup. A phantom with a realistic anatomy and time-varying activity distribution is therefore desirable. This work describes a pharmacokinetic (PK) compartment model for (99m)Tc-MAG3, used for defining a dynamic whole-body activity distribution within a digital phantom (XCAT) for accurate Monte Carlo (MC)-based images for QC. Each phantom structure is assigned a time-activity curve provided by the PK model, employing parameter values consistent with MAG3 pharmacokinetics. This approach ensures that the total amount of tracer in the phantom is preserved between time points, and it allows for modifications of the pharmacokinetics in a controlled fashion. By adjusting parameter values in the PK model, different clinically realistic scenarios can be mimicked, regarding, e.g., the relative renal uptake and renal transit time. Using the MC code SIMIND, a complete set of renography images including effects of photon attenuation, scattering, limited spatial resolution and noise, are simulated. The obtained image data can be used to evaluate quantitative techniques and computer software in clinical renography.
NASA Astrophysics Data System (ADS)
Chen, Ji; Ren, Xinguo; Li, Xin-Zheng; Alfè, Dario; Wang, Enge
2014-07-01
The finite-temperature phase diagram of hydrogen in the region of phase IV and its neighborhood was studied using the ab initio molecular dynamics (MD) and the ab initio path-integral molecular dynamics (PIMD). The electronic structures were analyzed using the density-functional theory (DFT), the random-phase approximation, and the diffusion Monte Carlo (DMC) methods. Taking the state-of-the-art DMC results as benchmark, comparisons of the energy differences between structures generated from the MD and PIMD simulations, with molecular and dissociated hydrogens, respectively, in the weak molecular layers of phase IV, indicate that standard functionals in DFT tend to underestimate the dissociation barrier of the weak molecular layers in this mixed phase. Because of this underestimation, inclusion of the quantum nuclear effects (QNEs) in PIMD using electronic structures generated with these functionals leads to artificially dissociated hydrogen layers in phase IV and an error compensation between the neglect of QNEs and the deficiencies of these functionals in standard ab initio MD simulations exists. This analysis partly rationalizes why earlier ab initio MD simulations complement so well the experimental observations. The temperature and pressure dependencies for the stability of phase IV were also studied in the end and compared with earlier results.
Accelerated GPU based SPECT Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Garcia, Marie-Paule; Bert, Julien; Benoit, Didier; Bardiès, Manuel; Visvikis, Dimitris
2016-06-01
Monte Carlo (MC) modelling is widely used in the field of single photon emission computed tomography (SPECT) as it is a reliable technique to simulate very high quality scans. This technique provides very accurate modelling of the radiation transport and particle interactions in a heterogeneous medium. Various MC codes exist for nuclear medicine imaging simulations. Recently, new strategies exploiting the computing capabilities of graphical processing units (GPU) have been proposed. This work aims at evaluating the accuracy of such GPU implementation strategies in comparison to standard MC codes in the context of SPECT imaging. GATE was considered the reference MC toolkit and used to evaluate the performance of newly developed GPU Geant4-based Monte Carlo simulation (GGEMS) modules for SPECT imaging. Radioisotopes with different photon energies were used with these various CPU and GPU Geant4-based MC codes in order to assess the best strategy for each configuration. Three different isotopes were considered: 99m Tc, 111In and 131I, using a low energy high resolution (LEHR) collimator, a medium energy general purpose (MEGP) collimator and a high energy general purpose (HEGP) collimator respectively. Point source, uniform source, cylindrical phantom and anthropomorphic phantom acquisitions were simulated using a model of the GE infinia II 3/8" gamma camera. Both simulation platforms yielded a similar system sensitivity and image statistical quality for the various combinations. The overall acceleration factor between GATE and GGEMS platform derived from the same cylindrical phantom acquisition was between 18 and 27 for the different radioisotopes. Besides, a full MC simulation using an anthropomorphic phantom showed the full potential of the GGEMS platform, with a resulting acceleration factor up to 71. The good agreement with reference codes and the acceleration factors obtained support the use of GPU implementation strategies for improving computational efficiency
Monte Carlo scatter correction for SPECT
NASA Astrophysics Data System (ADS)
Liu, Zemei
The goal of this dissertation is to present a quantitatively accurate and computationally fast scatter correction method that is robust and easily accessible for routine applications in SPECT imaging. A Monte Carlo based scatter estimation method is investigated and developed further. The Monte Carlo simulation program SIMIND (Simulating Medical Imaging Nuclear Detectors), was specifically developed to simulate clinical SPECT systems. The SIMIND scatter estimation (SSE) method was developed further using a multithreading technique to distribute the scatter estimation task across multiple threads running concurrently on multi-core CPU's to accelerate the scatter estimation process. An analytical collimator that ensures less noise was used during SSE. The research includes the addition to SIMIND of charge transport modeling in cadmium zinc telluride (CZT) detectors. Phenomena associated with radiation-induced charge transport including charge trapping, charge diffusion, charge sharing between neighboring detector pixels, as well as uncertainties in the detection process are addressed. Experimental measurements and simulation studies were designed for scintillation crystal based SPECT and CZT based SPECT systems to verify and evaluate the expanded SSE method. Jaszczak Deluxe and Anthropomorphic Torso Phantoms (Data Spectrum Corporation, Hillsborough, NC, USA) were used for experimental measurements and digital versions of the same phantoms employed during simulations to mimic experimental acquisitions. This study design enabled easy comparison of experimental and simulated data. The results have consistently shown that the SSE method performed similarly or better than the triple energy window (TEW) and effective scatter source estimation (ESSE) methods for experiments on all the clinical SPECT systems. The SSE method is proven to be a viable method for scatter estimation for routine clinical use.
Accelerated GPU based SPECT Monte Carlo simulations.
Garcia, Marie-Paule; Bert, Julien; Benoit, Didier; Bardiès, Manuel; Visvikis, Dimitris
2016-06-07
Monte Carlo (MC) modelling is widely used in the field of single photon emission computed tomography (SPECT) as it is a reliable technique to simulate very high quality scans. This technique provides very accurate modelling of the radiation transport and particle interactions in a heterogeneous medium. Various MC codes exist for nuclear medicine imaging simulations. Recently, new strategies exploiting the computing capabilities of graphical processing units (GPU) have been proposed. This work aims at evaluating the accuracy of such GPU implementation strategies in comparison to standard MC codes in the context of SPECT imaging. GATE was considered the reference MC toolkit and used to evaluate the performance of newly developed GPU Geant4-based Monte Carlo simulation (GGEMS) modules for SPECT imaging. Radioisotopes with different photon energies were used with these various CPU and GPU Geant4-based MC codes in order to assess the best strategy for each configuration. Three different isotopes were considered: (99m) Tc, (111)In and (131)I, using a low energy high resolution (LEHR) collimator, a medium energy general purpose (MEGP) collimator and a high energy general purpose (HEGP) collimator respectively. Point source, uniform source, cylindrical phantom and anthropomorphic phantom acquisitions were simulated using a model of the GE infinia II 3/8" gamma camera. Both simulation platforms yielded a similar system sensitivity and image statistical quality for the various combinations. The overall acceleration factor between GATE and GGEMS platform derived from the same cylindrical phantom acquisition was between 18 and 27 for the different radioisotopes. Besides, a full MC simulation using an anthropomorphic phantom showed the full potential of the GGEMS platform, with a resulting acceleration factor up to 71. The good agreement with reference codes and the acceleration factors obtained support the use of GPU implementation strategies for improving computational
Parton shower Monte Carlo event generators
NASA Astrophysics Data System (ADS)
Webber, Bryan
2011-12-01
A parton shower Monte Carlo event generator is a computer program designed to simulate the final states of high-energy collisions in full detail down to the level of individual stable particles. The aim is to generate a large number of simulated collision events, each consisting of a list of final-state particles and their momenta, such that the probability to produce an event with a given list is proportional (approximately) to the probability that the corresponding actual event is produced in the real world. The Monte Carlo method makes use of pseudorandom numbers to simulate the event-to-event fluctuations intrinsic to quantum processes. The simulation normally begins with a hard subprocess, shown as a black blob in Figure 1, in which constituents of the colliding particles interact at a high momentum scale to produce a few outgoing fundamental objects: Standard Model quarks, leptons and/or gauge or Higgs bosons, or hypothetical particles of some new theory. The partons (quarks and gluons) involved, as well as any new particles with colour, radiate virtual gluons, which can themselves emit further gluons or produce quark-antiquark pairs, leading to the formation of parton showers (brown). During parton showering the interaction scale falls and the strong interaction coupling rises, eventually triggering the process of hadronization (yellow), in which the partons are bound into colourless hadrons. On the same scale, the initial-state partons in hadronic collisions are confined in the incoming hadrons. In hadron-hadron collisions, the other constituent partons of the incoming hadrons undergo multiple interactions which produce the underlying event (green). Many of the produced hadrons are unstable, so the final stage of event generation is the simulation of the hadron decays.
Fission Matrix Capability for MCNP Monte Carlo
Carney, Sean E.; Brown, Forrest B.; Kiedrowski, Brian C.; Martin, William R.
2012-09-05
In a Monte Carlo criticality calculation, before the tallying of quantities can begin, a converged fission source (the fundamental eigenvector of the fission kernel) is required. Tallies of interest may include powers, absorption rates, leakage rates, or the multiplication factor (the fundamental eigenvalue of the fission kernel, k{sub eff}). Just as in the power iteration method of linear algebra, if the dominance ratio (the ratio of the first and zeroth eigenvalues) is high, many iterations of neutron history simulations are required to isolate the fundamental mode of the problem. Optically large systems have large dominance ratios, and systems containing poor neutron communication between regions are also slow to converge. The fission matrix method, implemented into MCNP[1], addresses these problems. When Monte Carlo random walk from a source is executed, the fission kernel is stochastically applied to the source. Random numbers are used for: distances to collision, reaction types, scattering physics, fission reactions, etc. This method is used because the fission kernel is a complex, 7-dimensional operator that is not explicitly known. Deterministic methods use approximations/discretization in energy, space, and direction to the kernel. Consequently, they are faster. Monte Carlo directly simulates the physics, which necessitates the use of random sampling. Because of this statistical noise, common convergence acceleration methods used in deterministic methods do not work. In the fission matrix method, we are using the random walk information not only to build the next-iteration fission source, but also a spatially-averaged fission kernel. Just like in deterministic methods, this involves approximation and discretization. The approximation is the tallying of the spatially-discretized fission kernel with an incorrect fission source. We address this by making the spatial mesh fine enough that this error is negligible. As a consequence of discretization we get a
Vectorized Monte Carlo methods for reactor lattice analysis
NASA Technical Reports Server (NTRS)
Brown, F. B.
1984-01-01
Some of the new computational methods and equivalent mathematical representations of physics models used in the MCV code, a vectorized continuous-enery Monte Carlo code for use on the CYBER-205 computer are discussed. While the principal application of MCV is the neutronics analysis of repeating reactor lattices, the new methods used in MCV should be generally useful for vectorizing Monte Carlo for other applications. For background, a brief overview of the vector processing features of the CYBER-205 is included, followed by a discussion of the fundamentals of Monte Carlo vectorization. The physics models used in the MCV vectorized Monte Carlo code are then summarized. The new methods used in scattering analysis are presented along with details of several key, highly specialized computational routines. Finally, speedups relative to CDC-7600 scalar Monte Carlo are discussed.
Reconstruction of Monte Carlo replicas from Hessian parton distributions
NASA Astrophysics Data System (ADS)
Hou, Tie-Jiun; Gao, Jun; Huston, Joey; Nadolsky, Pavel; Schmidt, Carl; Stump, Daniel; Wang, Bo-Ting; Xie, Ke Ping; Dulat, Sayipjamal; Pumplin, Jon; Yuan, C. P.
2017-03-01
We explore connections between two common methods for quantifying the uncertainty in parton distribution functions (PDFs), based on the Hessian error matrix and Monte-Carlo sampling. CT14 parton distributions in the Hessian representation are converted into Monte-Carlo replicas by a numerical method that reproduces important properties of CT14 Hessian PDFs: the asymmetry of CT14 uncertainties and positivity of individual parton distributions. The ensembles of CT14 Monte-Carlo replicas constructed this way at NNLO and NLO are suitable for various collider applications, such as cross section reweighting. Master formulas for computation of asymmetric standard deviations in the Monte-Carlo representation are derived. A correction is proposed to address a bias in asymmetric uncertainties introduced by the Taylor series approximation. A numerical program is made available for conversion of Hessian PDFs into Monte-Carlo replicas according to normal, log-normal, and Watt-Thorne sampling procedures.
Analysis of real-time networks with monte carlo methods
NASA Astrophysics Data System (ADS)
Mauclair, C.; Durrieu, G.
2013-12-01
Communication networks in embedded systems are ever more large and complex. A better understanding of the dynamics of these networks is necessary to use them at best and lower costs. Todays tools are able to compute upper bounds of end-to-end delays that a packet being sent through the network could suffer. However, in the case of asynchronous networks, those worst end-to-end delay (WEED) cases are rarely observed in practice or through simulations due to the scarce situations that lead to worst case scenarios. A novel approach based on Monte Carlo methods is suggested to study the effects of the asynchrony on the performances.
Monte Carlo studies of model Langmuir monolayers.
Opps, S B; Yang, B; Gray, C G; Sullivan, D E
2001-04-01
This paper examines some of the basic properties of a model Langmuir monolayer, consisting of surfactant molecules deposited onto a water subphase. The surfactants are modeled as rigid rods composed of a head and tail segment of diameters sigma(hh) and sigma(tt), respectively. The tails consist of n(t) approximately 4-7 effective monomers representing methylene groups. These rigid rods interact via site-site Lennard-Jones potentials with different interaction parameters for the tail-tail, head-tail, and head-head interactions. In a previous paper, we studied the ground-state properties of this system using a Landau approach. In the present paper, Monte Carlo simulations were performed in the canonical ensemble to elucidate the finite-temperature behavior of this system. Simulation techniques, incorporating a system of dynamic filters, allow us to decrease CPU time with negligible statistical error. This paper focuses on several of the key parameters, such as density, head-tail diameter mismatch, and chain length, responsible for driving transitions from uniformly tilted to untilted phases and between different tilt-ordered phases. Upon varying the density of the system, with sigma(hh)=sigma(tt), we observe a transition from a tilted (NNN)-condensed phase to an untilted-liquid phase and, upon comparison with recent experiments with fatty acid-alcohol and fatty acid-ester mixtures [M. C. Shih, M. K. Durbin, A. Malik, P. Zschack, and P. Dutta, J. Chem. Phys. 101, 9132 (1994); E. Teer, C. M. Knobler, C. Lautz, S. Wurlitzer, J. Kildae, and T. M. Fischer, J. Chem. Phys. 106, 1913 (1997)], we identify this as the L'(2)/Ov-L1 phase boundary. By varying the head-tail diameter ratio, we observe a decrease in T(c) with increasing mismatch. However, as the chain length was increased we observed that the transition temperatures increased and differences in T(c) due to head-tail diameter mismatch were diminished. In most of the present research, the water was treated as a hard
Monte Carlo studies of model Langmuir monolayers
NASA Astrophysics Data System (ADS)
Opps, S. B.; Yang, B.; Gray, C. G.; Sullivan, D. E.
2001-04-01
This paper examines some of the basic properties of a model Langmuir monolayer, consisting of surfactant molecules deposited onto a water subphase. The surfactants are modeled as rigid rods composed of a head and tail segment of diameters σhh and σtt, respectively. The tails consist of nt~4-7 effective monomers representing methylene groups. These rigid rods interact via site-site Lennard-Jones potentials with different interaction parameters for the tail-tail, head-tail, and head-head interactions. In a previous paper, we studied the ground-state properties of this system using a Landau approach. In the present paper, Monte Carlo simulations were performed in the canonical ensemble to elucidate the finite-temperature behavior of this system. Simulation techniques, incorporating a system of dynamic filters, allow us to decrease CPU time with negligible statistical error. This paper focuses on several of the key parameters, such as density, head-tail diameter mismatch, and chain length, responsible for driving transitions from uniformly tilted to untilted phases and between different tilt-ordered phases. Upon varying the density of the system, with σhh=σtt, we observe a transition from a tilted (NNN)-condensed phase to an untilted-liquid phase and, upon comparison with recent experiments with fatty acid-alcohol and fatty acid-ester mixtures [M. C. Shih, M. K. Durbin, A. Malik, P. Zschack, and P. Dutta, J. Chem. Phys. 101, 9132 (1994); E. Teer, C. M. Knobler, C. Lautz, S. Wurlitzer, J. Kildae, and T. M. Fischer, J. Chem. Phys. 106, 1913 (1997)], we identify this as the L'2/Ov-L1 phase boundary. By varying the head-tail diameter ratio, we observe a decrease in Tc with increasing mismatch. However, as the chain length was increased we observed that the transition temperatures increased and differences in Tc due to head-tail diameter mismatch were diminished. In most of the present research, the water was treated as a hard surface, whereby the surfactants are only
NASA Astrophysics Data System (ADS)
Stiff-Roberts, Adrienne; Atewologun, Ayomide
A semi-empirical method for investigating the performance of OPVs in resonant infrared, matrix-assisted pulsed laser evaporation (RIR-MAPLE) films is explored. Emulsion-based RIR-MAPLE offers a unique experimental backdrop for investigating trends through simulation and gaining a better understanding of how different thin film characteristics impact OPV device performance. A novel multi-scale formulation of the Dynamic Monte Carlo (DMC) model is developed based on observable morphology features. Specifically, using confocal microscopy, we observe the presence of micro-scale regimes of pure materials and nano-scale regions of the composite blend. This enables us to assign weighted percentages to DMC implementations on two different scales: the microscale and nanoscale regions. In addition to this, we use input simulation parameters acquired by characterization of as-deposited films. The semi-empirical multi-scale model presented serves as a unique simulation opportunity for exploring different properties of RIR-MAPLE deposited OPVs, their effects on OPV performance and potential design routes for improving device efficiencies. This work was supported, in part, by the Office of Naval Research under Grant N00014-10-1-0481 and the NSF Triangle MRSEC on Soft Matter.
NASA Astrophysics Data System (ADS)
Nedea, S. V.; Frijns, A. J. H.; van Steenhoven, A. A.; Markvoort, A. J.; Hilbers, P. A. J.
2005-05-01
We present a hybrid method to study the properties of hard-sphere gas molecules confined between two hard walls of a microchannel. The coupling between Molecular Dynamics(MD) and Monte Carlo(MC) simulations is introduced in order to combine the advantages of the MD and MC simulations, by performing MD near the boundaries for the accuracy of the interactions with the wall, and MC in the bulk because of the low computational cost. The effect of different gas densities, starting from a rarefied gas (reduced density η=πna3/6=0.001, where n=number density, a=molecular diameter) to a dense hard-sphere gas (η=0.25), is investigated. We characterize the influence of different η's and size of molecules on the equilibrium properties of the gas in a microchannel. The effect of the particle size on the simulation results, which is very small in case of a dilute gas, is increasing with η. Comparisons between MD, MC and hybrid MD-MC simulation results are done, and comparisons between MD, MC, and hybrid MD-MC computational costs are outlined.
On the time scale associated with Monte Carlo simulations
Bal, Kristof M. Neyts, Erik C.
2014-11-28
Uniform-acceptance force-bias Monte Carlo (fbMC) methods have been shown to be a powerful technique to access longer timescales in atomistic simulations allowing, for example, phase transitions and growth. Recently, a new fbMC method, the time-stamped force-bias Monte Carlo (tfMC) method, was derived with inclusion of an estimated effective timescale; this timescale, however, does not seem able to explain some of the successes the method. In this contribution, we therefore explicitly quantify the effective timescale tfMC is able to access for a variety of systems, namely a simple single-particle, one-dimensional model system, the Lennard-Jones liquid, an adatom on the Cu(100) surface, a silicon crystal with point defects and a highly defected graphene sheet, in order to gain new insights into the mechanisms by which tfMC operates. It is found that considerable boosts, up to three orders of magnitude compared to molecular dynamics, can be achieved for solid state systems by lowering of the apparent activation barrier of occurring processes, while not requiring any system-specific input or modifications of the method. We furthermore address the pitfalls of using the method as a replacement or complement of molecular dynamics simulations, its ability to explicitly describe correct dynamics and reaction mechanisms, and the association of timescales to MC simulations in general.
On the time scale associated with Monte Carlo simulations.
Bal, Kristof M; Neyts, Erik C
2014-11-28
Uniform-acceptance force-bias Monte Carlo (fbMC) methods have been shown to be a powerful technique to access longer timescales in atomistic simulations allowing, for example, phase transitions and growth. Recently, a new fbMC method, the time-stamped force-bias Monte Carlo (tfMC) method, was derived with inclusion of an estimated effective timescale; this timescale, however, does not seem able to explain some of the successes the method. In this contribution, we therefore explicitly quantify the effective timescale tfMC is able to access for a variety of systems, namely a simple single-particle, one-dimensional model system, the Lennard-Jones liquid, an adatom on the Cu(100) surface, a silicon crystal with point defects and a highly defected graphene sheet, in order to gain new insights into the mechanisms by which tfMC operates. It is found that considerable boosts, up to three orders of magnitude compared to molecular dynamics, can be achieved for solid state systems by lowering of the apparent activation barrier of occurring processes, while not requiring any system-specific input or modifications of the method. We furthermore address the pitfalls of using the method as a replacement or complement of molecular dynamics simulations, its ability to explicitly describe correct dynamics and reaction mechanisms, and the association of timescales to MC simulations in general.
Subtle Monte Carlo Updates in Dense Molecular Systems.
Bottaro, Sandro; Boomsma, Wouter; E Johansson, Kristoffer; Andreetta, Christian; Hamelryck, Thomas; Ferkinghoff-Borg, Jesper
2012-02-14
Although Markov chain Monte Carlo (MC) simulation is a potentially powerful approach for exploring conformational space, it has been unable to compete with molecular dynamics (MD) in the analysis of high density structural states, such as the native state of globular proteins. Here, we introduce a kinetic algorithm, CRISP, that greatly enhances the sampling efficiency in all-atom MC simulations of dense systems. The algorithm is based on an exact analytical solution to the classic chain-closure problem, making it possible to express the interdependencies among degrees of freedom in the molecule as correlations in a multivariate Gaussian distribution. We demonstrate that our method reproduces structural variation in proteins with greater efficiency than current state-of-the-art Monte Carlo methods and has real-time simulation performance on par with molecular dynamics simulations. The presented results suggest our method as a valuable tool in the study of molecules in atomic detail, offering a potential alternative to molecular dynamics for probing long time-scale conformational transitions.
Wang, Huiyuan; Mo, H. J.; Yang, Xiaohu; Lin, W. P.; Jing, Y. P.
2014-10-10
Simulating the evolution of the local universe is important for studying galaxies and the intergalactic medium in a way free of cosmic variance. Here we present a method to reconstruct the initial linear density field from an input nonlinear density field, employing the Hamiltonian Markov Chain Monte Carlo (HMC) algorithm combined with Particle-mesh (PM) dynamics. The HMC+PM method is applied to cosmological simulations, and the reconstructed linear density fields are then evolved to the present day with N-body simulations. These constrained simulations accurately reproduce both the amplitudes and phases of the input simulations at various z. Using a PM model with a grid cell size of 0.75 h {sup –1} Mpc and 40 time steps in the HMC can recover more than half of the phase information down to a scale k ∼ 0.85 h Mpc{sup –1} at high z and to k ∼ 3.4 h Mpc{sup –1} at z = 0, which represents a significant improvement over similar reconstruction models in the literature, and indicates that our model can reconstruct the formation histories of cosmic structures over a large dynamical range. Adopting PM models with higher spatial and temporal resolutions yields even better reconstructions, suggesting that our method is limited more by the availability of computer resource than by principle. Dynamic models of structure evolution adopted in many earlier investigations can induce non-Gaussianity in the reconstructed linear density field, which in turn can cause large systematic deviations in the predicted halo mass function. Such deviations are greatly reduced or absent in our reconstruction.
Properties of reactive oxygen species by quantum Monte Carlo.
Zen, Andrea; Trout, Bernhardt L; Guidoni, Leonardo
2014-07-07
The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of chemistry, biology, and atmospheric science. Nevertheless, the electronic structure of such species is a challenge for ab initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution, and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been recently shown to effectively describe the statical and dynamical correlation of different molecular systems. In particular, we have studied the oxygen molecule, the superoxide anion, the nitric oxide radical and anion, the hydroxyl and hydroperoxyl radicals and their corresponding anions, and the hydrotrioxyl radical. Overall, the methodology was able to correctly describe the geometrical and electronic properties of these systems, through compact but fully-optimised basis sets and with a computational cost which scales as N(3) - N(4), where N is the number of electrons. This work is therefore opening the way to the accurate study of the energetics and of the reactivity of large and complex oxygen species by first principles.
Properties of reactive oxygen species by quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Zen, Andrea; Trout, Bernhardt L.; Guidoni, Leonardo
2014-07-01
The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of chemistry, biology, and atmospheric science. Nevertheless, the electronic structure of such species is a challenge for ab initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution, and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been recently shown to effectively describe the statical and dynamical correlation of different molecular systems. In particular, we have studied the oxygen molecule, the superoxide anion, the nitric oxide radical and anion, the hydroxyl and hydroperoxyl radicals and their corresponding anions, and the hydrotrioxyl radical. Overall, the methodology was able to correctly describe the geometrical and electronic properties of these systems, through compact but fully-optimised basis sets and with a computational cost which scales as N3 - N4, where N is the number of electrons. This work is therefore opening the way to the accurate study of the energetics and of the reactivity of large and complex oxygen species by first principles.
Properties of reactive oxygen species by quantum Monte Carlo
Zen, Andrea; Trout, Bernhardt L.; Guidoni, Leonardo
2014-07-07
The electronic properties of the oxygen molecule, in its singlet and triplet states, and of many small oxygen-containing radicals and anions have important roles in different fields of chemistry, biology, and atmospheric science. Nevertheless, the electronic structure of such species is a challenge for ab initio computational approaches because of the difficulties to correctly describe the statical and dynamical correlation effects in presence of one or more unpaired electrons. Only the highest-level quantum chemical approaches can yield reliable characterizations of their molecular properties, such as binding energies, equilibrium structures, molecular vibrations, charge distribution, and polarizabilities. In this work we use the variational Monte Carlo (VMC) and the lattice regularized Monte Carlo (LRDMC) methods to investigate the equilibrium geometries and molecular properties of oxygen and oxygen reactive species. Quantum Monte Carlo methods are used in combination with the Jastrow Antisymmetrized Geminal Power (JAGP) wave function ansatz, which has been recently shown to effectively describe the statical and dynamical correlation of different molecular systems. In particular, we have studied the oxygen molecule, the superoxide anion, the nitric oxide radical and anion, the hydroxyl and hydroperoxyl radicals and their corresponding anions, and the hydrotrioxyl radical. Overall, the methodology was able to correctly describe the geometrical and electronic properties of these systems, through compact but fully-optimised basis sets and with a computational cost which scales as N{sup 3} − N{sup 4}, where N is the number of electrons. This work is therefore opening the way to the accurate study of the energetics and of the reactivity of large and complex oxygen species by first principles.
Iterative acceleration methods for Monte Carlo and deterministic criticality calculations
Urbatsch, T.J.
1995-11-01
If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.
Monte Carlo simulation of chromatin stretching
NASA Astrophysics Data System (ADS)
Aumann, Frank; Lankas, Filip; Caudron, Maïwen; Langowski, Jörg
2006-04-01
We present Monte Carlo (MC) simulations of the stretching of a single 30nm chromatin fiber. The model approximates the DNA by a flexible polymer chain with Debye-Hückel electrostatics and uses a two-angle zigzag model for the geometry of the linker DNA connecting the nucleosomes. The latter are represented by flat disks interacting via an attractive Gay-Berne potential. Our results show that the stiffness of the chromatin fiber strongly depends on the linker DNA length. Furthermore, changing the twisting angle between nucleosomes from 90° to 130° increases the stiffness significantly. An increase in the opening angle from 22° to 34° leads to softer fibers for small linker lengths. We observe that fibers containing a linker histone at each nucleosome are stiffer compared to those without the linker histone. The simulated persistence lengths and elastic moduli agree with experimental data. Finally, we show that the chromatin fiber does not behave as an isotropic elastic rod, but its rigidity depends on the direction of deformation: Chromatin is much more resistant to stretching than to bending.
Monte Carlo simulations of Protein Adsorption
NASA Astrophysics Data System (ADS)
Sharma, Sumit; Kumar, Sanat K.; Belfort, Georges
2008-03-01
Amyloidogenic diseases, such as, Alzheimer's are caused by adsorption and aggregation of partially unfolded proteins. Adsorption of proteins is a concern in design of biomedical devices, such as dialysis membranes. Protein adsorption is often accompanied by conformational rearrangements in protein molecules. Such conformational rearrangements are thought to affect many properties of adsorbed protein molecules such as their adhesion strength to the surface, biological activity, and aggregation tendency. It has been experimentally shown that many naturally occurring proteins, upon adsorption to hydrophobic surfaces, undergo a helix to sheet or random coil secondary structural rearrangement. However, to better understand the equilibrium structural complexities of this phenomenon, we have performed Monte Carlo (MC) simulations of adsorption of a four helix bundle, modeled as a lattice protein, and studied the adsorption behavior and equilibrium protein conformations at different temperatures and degrees of surface hydrophobicity. To study the free energy and entropic effects on adsorption, Canonical ensemble MC simulations have been combined with Weighted Histogram Analysis Method(WHAM). Conformational transitions of proteins on surfaces will be discussed as a function of surface hydrophobicity and compared to analogous bulk transitions.
Finding Planet Nine: a Monte Carlo approach
NASA Astrophysics Data System (ADS)
de la Fuente Marcos, C.; de la Fuente Marcos, R.
2016-06-01
Planet Nine is a hypothetical planet located well beyond Pluto that has been proposed in an attempt to explain the observed clustering in physical space of the perihelia of six extreme trans-Neptunian objects or ETNOs. The predicted approximate values of its orbital elements include a semimajor axis of 700 au, an eccentricity of 0.6, an inclination of 30°, and an argument of perihelion of 150°. Searching for this putative planet is already under way. Here, we use a Monte Carlo approach to create a synthetic population of Planet Nine orbits and study its visibility statistically in terms of various parameters and focusing on the aphelion configuration. Our analysis shows that, if Planet Nine exists and is at aphelion, it might be found projected against one out of the four specific areas in the sky. Each area is linked to a particular value of the longitude of the ascending node and two of them are compatible with an apsidal anti-alignment scenario. In addition and after studying the current statistics of ETNOs, a cautionary note on the robustness of the perihelia clustering is presented.
Monte Carlo Simulation of Surface Reactions
NASA Astrophysics Data System (ADS)
Brosilow, Benjamin J.
A Monte-Carlo study of the catalytic reaction of CO and O_2 over transition metal surfaces is presented, using generalizations of a model proposed by Ziff, Gulari and Barshad (ZGB). A new "constant -coverage" algorithm is described and applied to the model in order to elucidate the behavior near the model's first -order transition, and to draw an analogy between this transition and first-order phase transitions in equilibrium systems. The behavior of the model is then compared to the behavior of CO oxidation systems over Pt single-crystal catalysts. This comparison leads to the introduction of a new variation of the model in which one of the reacting species requires a large ensemble of vacant surface sites in order to adsorb. Further, it is shown that precursor adsorption and an effective Eley-Rideal mechanism must also be included in the model in order to obtain detailed agreement with experiment. Finally, variations of the model on finite and two component lattices are studied as models for low temperature CO oxidation over Noble Metal/Reducible Oxide and alloy catalysts.
Commensurabilities between ETNOs: a Monte Carlo survey
NASA Astrophysics Data System (ADS)
de la Fuente Marcos, C.; de la Fuente Marcos, R.
2016-07-01
Many asteroids in the main and trans-Neptunian belts are trapped in mean motion resonances with Jupiter and Neptune, respectively. As a side effect, they experience accidental commensurabilities among themselves. These commensurabilities define characteristic patterns that can be used to trace the source of the observed resonant behaviour. Here, we explore systematically the existence of commensurabilities between the known ETNOs using their heliocentric and barycentric semimajor axes, their uncertainties, and Monte Carlo techniques. We find that the commensurability patterns present in the known ETNO population resemble those found in the main and trans-Neptunian belts. Although based on small number statistics, such patterns can only be properly explained if most, if not all, of the known ETNOs are subjected to the resonant gravitational perturbations of yet undetected trans-Plutonian planets. We show explicitly that some of the statistically significant commensurabilities are compatible with the Planet Nine hypothesis; in particular, a number of objects may be trapped in the 5:3 and 3:1 mean motion resonances with a putative Planet Nine with semimajor axis ˜700 au.
Silver, R.N.; Gubernatis, J.E.; Sivia, D.S. ); Jarrell, M. . Dept. of Physics)
1990-01-01
In this article we describe the results of a new method for calculating the dynamical properties of the Anderson model. QMC generates data about the Matsubara Green's functions in imaginary time. To obtain dynamical properties, one must analytically continue these data to real time. This is an extremely ill-posed inverse problem similar to the inversion of a Laplace transform from incomplete and noisy data. Our method is a general one, applicable to the calculation of dynamical properties from a wide variety of quantum simulations. We use Bayesian methods of statistical inference to determine the dynamical properties based on both the QMC data and any prior information we may have such as sum rules, symmetry, high frequency limits, etc. This provides a natural means of combining perturbation theory and numerical simulations in order to understand dynamical many-body problems. Specifically we use the well-established maximum entropy (ME) method for image reconstruction. We obtain the spectral density and transport coefficients over the entire range of model parameters accessible by QMC, with data having much larger statistical error than required by other proposed analytic continuation methods.
Quantum Monte Carlo: Faster, More Reliable, And More Accurate
NASA Astrophysics Data System (ADS)
Anderson, Amos Gerald
2010-06-01
The Schrodinger Equation has been available for about 83 years, but today, we still strain to apply it accurately to molecules of interest. The difficulty is not theoretical in nature, but practical, since we're held back by lack of sufficient computing power. Consequently, effort is applied to find acceptable approximations to facilitate real time solutions. In the meantime, computer technology has begun rapidly advancing and changing the way we think about efficient algorithms. For those who can reorganize their formulas to take advantage of these changes and thereby lift some approximations, incredible new opportunities await. Over the last decade, we've seen the emergence of a new kind of computer processor, the graphics card. Designed to accelerate computer games by optimizing quantity instead of quality in processor, they have become of sufficient quality to be useful to some scientists. In this thesis, we explore the first known use of a graphics card to computational chemistry by rewriting our Quantum Monte Carlo software into the requisite "data parallel" formalism. We find that notwithstanding precision considerations, we are able to speed up our software by about a factor of 6. The success of a Quantum Monte Carlo calculation depends on more than just processing power. It also requires the scientist to carefully design the trial wavefunction used to guide simulated electrons. We have studied the use of Generalized Valence Bond wavefunctions to simply, and yet effectively, captured the essential static correlation in atoms and molecules. Furthermore, we have developed significantly improved two particle correlation functions, designed with both flexibility and simplicity considerations, representing an effective and reliable way to add the necessary dynamic correlation. Lastly, we present our method for stabilizing the statistical nature of the calculation, by manipulating configuration weights, thus facilitating efficient and robust calculations. Our
Combinatorial geometry domain decomposition strategies for Monte Carlo simulations
Li, G.; Zhang, B.; Deng, L.; Mo, Z.; Liu, Z.; Shangguan, D.; Ma, Y.; Li, S.; Hu, Z.
2013-07-01
Analysis and modeling of nuclear reactors can lead to memory overload for a single core processor when it comes to refined modeling. A method to solve this problem is called 'domain decomposition'. In the current work, domain decomposition algorithms for a combinatorial geometry Monte Carlo transport code are developed on the JCOGIN (J Combinatorial Geometry Monte Carlo transport INfrastructure). Tree-based decomposition and asynchronous communication of particle information between domains are described in the paper. Combination of domain decomposition and domain replication (particle parallelism) is demonstrated and compared with that of MERCURY code. A full-core reactor model is simulated to verify the domain decomposition algorithms using the Monte Carlo particle transport code JMCT (J Monte Carlo Transport Code), which has being developed on the JCOGIN infrastructure. Besides, influences of the domain decomposition algorithms to tally variances are discussed. (authors)
Bayesian phylogeny analysis via stochastic approximation Monte Carlo.
Cheon, Sooyoung; Liang, Faming
2009-11-01
Monte Carlo methods have received much attention in the recent literature of phylogeny analysis. However, the conventional Markov chain Monte Carlo algorithms, such as the Metropolis-Hastings algorithm, tend to get trapped in a local mode in simulating from the posterior distribution of phylogenetic trees, rendering the inference ineffective. In this paper, we apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm, to Bayesian phylogeny analysis. Our method is compared with two popular Bayesian phylogeny software, BAMBE and MrBayes, on simulated and real datasets. The numerical results indicate that our method outperforms BAMBE and MrBayes. Among the three methods, SAMC produces the consensus trees which have the highest similarity to the true trees, and the model parameter estimates which have the smallest mean square errors, but costs the least CPU time.
Monte Carlo variance reduction approaches for non-Boltzmann tallies
Booth, T.E.
1992-12-01
Quantities that depend on the collective effects of groups of particles cannot be obtained from the standard Boltzmann transport equation. Monte Carlo estimates of these quantities are called non-Boltzmann tallies and have become increasingly important recently. Standard Monte Carlo variance reduction techniques were designed for tallies based on individual particles rather than groups of particles. Experience with non-Boltzmann tallies and analog Monte Carlo has demonstrated the severe limitations of analog Monte Carlo for many non-Boltzmann tallies. In fact, many calculations absolutely require variance reduction methods to achieve practical computation times. Three different approaches to variance reduction for non-Boltzmann tallies are described and shown to be unbiased. The advantages and disadvantages of each of the approaches are discussed.
OBJECT KINETIC MONTE CARLO SIMULATIONS OF CASCADE ANNEALING IN TUNGSTEN
Nandipati, Giridhar; Setyawan, Wahyu; Heinisch, Howard L.; Roche, Kenneth J.; Kurtz, Richard J.; Wirth, Brian D.
2014-03-31
The objective of this work is to study the annealing of primary cascade damage created by primary knock-on atoms (PKAs) of various energies, at various temperatures in bulk tungsten using the object kinetic Monte Carlo (OKMC) method.
Monte Carlo simulations: Hidden errors from ``good'' random number generators
NASA Astrophysics Data System (ADS)
Ferrenberg, Alan M.; Landau, D. P.; Wong, Y. Joanna
1992-12-01
The Wolff algorithm is now accepted as the best cluster-flipping Monte Carlo algorithm for beating ``critical slowing down.'' We show how this method can yield incorrect answers due to subtle correlations in ``high quality'' random number generators.
The dynamical activation-relaxation technique (DART): an on-the-fly kinetic Monte-Carlo algorithm
NASA Astrophysics Data System (ADS)
El-Mellouhi, Fadwa; Cote, Michel; Lewis, Laurent J.; Mousseau, Normand
2008-03-01
We present DART, the dynamical activation-relaxation technique, that combines the activation-relaxation technique (ART nouveau) with a non-lattice KMC method that allows the on-the-fly identification of barriers and the full treatment of lattice deformations. Most KMC schemes rely on the use of a fixed list of events and barriers, which are drawn with the proper weight during the simulation. While this works well for a number of problems (such as metal-on-metal growth), it cannot be used for processes where the events may change with time. DART overcomes this limitation. ART nouveau has been used extensively for the study of activated mechanisms in different materials within both an empirical and an ab-initio description of the systems. In the DART implementation, KMC moves are based on a catalog of events constructed on-the-fly using ART. After each KMC move, this catalog is updated so as to take into account new environments that may appear. A topological description of the structure of the system at each moment allows the method to identify rapidly these new environments and to move forward efficiently. In this talk, we will describe the method and present the case of interstitial diffusion in Si. Our results are compared with previous molecular-dynamics and on-lattice KMC simulations.
Monte Carlo next-event estimates from thermal collisions
Hendricks, J.S.; Prael, R.E.
1990-01-01
A new approximate method has been developed by Richard E. Prael to allow S({alpha},{beta}) thermal collision contributions to next-event estimators in Monte Carlo calculations. The new technique is generally applicable to next-event estimator contributions from any discrete probability distribution. The method has been incorporated into Version 4 of the production Monte Carlo neutron and photon radiation transport code MCNP. 9 refs.
Multiscale Monte Carlo equilibration: Pure Yang-Mills theory
NASA Astrophysics Data System (ADS)
Endres, Michael G.; Brower, Richard C.; Detmold, William; Orginos, Kostas; Pochinsky, Andrew V.
2015-12-01
We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.
Development of Monte Carlo Capability for Orion Parachute Simulations
NASA Technical Reports Server (NTRS)
Moore, James W.
2011-01-01
Parachute test programs employ Monte Carlo simulation techniques to plan testing and make critical decisions related to parachute loads, rate-of-descent, or other parameters. This paper describes the development and use of a MATLAB-based Monte Carlo tool for three parachute drop test simulations currently used by NASA. The Decelerator System Simulation (DSS) is a legacy 6 Degree-of-Freedom (DOF) simulation used to predict parachute loads and descent trajectories. The Decelerator System Simulation Application (DSSA) is a 6-DOF simulation that is well suited for modeling aircraft extraction and descent of pallet-like test vehicles. The Drop Test Vehicle Simulation (DTVSim) is a 2-DOF trajectory simulation that is convenient for quick turn-around analysis tasks. These three tools have significantly different software architectures and do not share common input files or output data structures. Separate Monte Carlo tools were initially developed for each simulation. A recently-developed simulation output structure enables the use of the more sophisticated DSSA Monte Carlo tool with any of the core-simulations. The task of configuring the inputs for the nominal simulation is left to the existing tools. Once the nominal simulation is configured, the Monte Carlo tool perturbs the input set according to dispersion rules created by the analyst. These rules define the statistical distribution and parameters to be applied to each simulation input. Individual dispersed parameters are combined to create a dispersed set of simulation inputs. The Monte Carlo tool repeatedly executes the core-simulation with the dispersed inputs and stores the results for analysis. The analyst may define conditions on one or more output parameters at which to collect data slices. The tool provides a versatile interface for reviewing output of large Monte Carlo data sets while preserving the capability for detailed examination of individual dispersed trajectories. The Monte Carlo tool described in
Improved Collision Modeling for Direct Simulation Monte Carlo Methods
2011-03-01
number is a measure of the rarefaction of a gas , and will be explained more thoroughly in the following chap- ter. Continuum solvers that use Navier...Limits on Mathematical Models [4] Kn=0.1, and the flow can be considered rarefied above that value. Direct Simulation Monte Carlo (DSMC) is a stochastic...method which utilizes the Monte Carlo statistical model to simulate gas behavior, which is very useful for these rarefied atmosphere hypersonic
Study of the Transition Flow Regime using Monte Carlo Methods
NASA Technical Reports Server (NTRS)
Hassan, H. A.
1999-01-01
This NASA Cooperative Agreement presents a study of the Transition Flow Regime Using Monte Carlo Methods. The topics included in this final report are: 1) New Direct Simulation Monte Carlo (DSMC) procedures; 2) The DS3W and DS2A Programs; 3) Papers presented; 4) Miscellaneous Applications and Program Modifications; 5) Solution of Transitional Wake Flows at Mach 10; and 6) Turbulence Modeling of Shock-Dominated Fows with a k-Enstrophy Formulation.
Confidence and efficiency scaling in variational quantum Monte Carlo calculations
NASA Astrophysics Data System (ADS)
Delyon, F.; Bernu, B.; Holzmann, Markus
2017-02-01
Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time-discretized diffusion process. We present a robust and practical method to determine the effective variance of general observables and show how to verify the equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling laws of the efficiency illustrated by variational Monte Carlo calculations on the two-dimensional electron gas.
CosmoPMC: Cosmology sampling with Population Monte Carlo
NASA Astrophysics Data System (ADS)
Kilbinger, Martin; Benabed, Karim; Cappé, Olivier; Coupon, Jean; Cardoso, Jean-François; Fort, Gersende; McCracken, Henry Joy; Prunet, Simon; Robert, Christian P.; Wraith, Darren
2012-12-01
CosmoPMC is a Monte-Carlo sampling method to explore the likelihood of various cosmological probes. The sampling engine is implemented with the package pmclib. It is called Population MonteCarlo (PMC), which is a novel technique to sample from the posterior. PMC is an adaptive importance sampling method which iteratively improves the proposal to approximate the posterior. This code has been introduced, tested and applied to various cosmology data sets.
Green's function Monte Carlo calculations of /sup 4/He
Carlson, J.A.
1988-01-01
Green's Function Monte Carlo methods have been developed to study the ground state properties of light nuclei. These methods are shown to reproduce results of Faddeev calculations for A = 3, and are then used to calculate ground state energies, one- and two-body distribution functions, and the D-state probability for the alpha particle. Results are compared to variational Monte Carlo calculations for several nuclear interaction models. 31 refs.
Successful combination of the stochastic linearization and Monte Carlo methods
NASA Technical Reports Server (NTRS)
Elishakoff, I.; Colombi, P.
1993-01-01
A combination of a stochastic linearization and Monte Carlo techniques is presented for the first time in literature. A system with separable nonlinear damping and nonlinear restoring force is considered. The proposed combination of the energy-wise linearization with the Monte Carlo method yields an error under 5 percent, which corresponds to the error reduction associated with the conventional stochastic linearization by a factor of 4.6.
de Finetti Priors using Markov chain Monte Carlo computations.
Bacallado, Sergio; Diaconis, Persi; Holmes, Susan
2015-07-01
Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or three way models for discrete exponential families using polynomial priors and Gröbner bases.
de Finetti Priors using Markov chain Monte Carlo computations
Bacallado, Sergio; Diaconis, Persi; Holmes, Susan
2015-01-01
Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or three way models for discrete exponential families using polynomial priors and Gröbner bases. PMID:26412947
Monte Carlo methods and applications in nuclear physics
Carlson, J.
1990-01-01
Monte Carlo methods for studying few- and many-body quantum systems are introduced, with special emphasis given to their applications in nuclear physics. Variational and Green's function Monte Carlo methods are presented in some detail. The status of calculations of light nuclei is reviewed, including discussions of the three-nucleon-interaction, charge and magnetic form factors, the coulomb sum rule, and studies of low-energy radiative transitions. 58 refs., 12 figs.
Event-chain Monte Carlo for classical continuous spin models
NASA Astrophysics Data System (ADS)
Michel, Manon; Mayer, Johannes; Krauth, Werner
2015-10-01
We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of magnitude, although it remains slower than the Wolff cluster algorithm. In the three-dimensional XY spin glass model at low temperature, the event-chain algorithm is far superior to the other algorithms.
NASA Astrophysics Data System (ADS)
Benhenni, Malika; Stachoň, Martin; Gadéa, Florent Xavier; Yousfi, Mohammed; Kalus, René
2016-09-01
A hybrid dynamical method based on the classical treatment of nuclei and the quantum treatment of electrons was used to calculate momentum transfer and dissociation cross-sections for collisions of neon dimer cations with neon atoms. For the inclusion of nuclear quantum effects, a semi-empirical factor was introduced to correct the hybrid momentum transfer cross-sections at low collision energies. Both uncorrected and quantum corrected hybrid cross-sections were used to calculate the {{Ne}}2+ mobility, and longitudinal and transverse characteristic diffusion energies over a wide range of the reduced electric field. Furthermore, the {{Ne}}2+ dissociation rate constant was calculated and compared to measured data. In addition, an approximate inverse method based on an effective isotropic interaction potential was also used to calculate the momentum transfer cross-sections and related transport data.
NASA Astrophysics Data System (ADS)
Monceau, P.; Hsiao, P.-Y.
2003-02-01
We study the cluster size distributions generated by the Wolff algorithm in the framework of the Ising model on Sierpinski fractals with Hausdorff dimension Df between 1 and 2. We show that these distributions exhibit a scaling property involving the magnetic exponent yh associated with one of the eigen-direction of the renormalization flows. We suggest that a single cluster tends to invade the whole lattice as Df tends towards the lower critical dimension of the Ising model, namely 1. The autocorrelation times associated with the Wolff and Swendsen-Wang algorithms enable us to calculate dynamical exponents; the cluster algorithms are shown to be more efficient in reducing the critical slowing down when Df is lowered.
Lakkaraju, Sirish Kaushik; Raman, E Prabhu; Yu, Wenbo; MacKerell, Alexander D
2014-06-10
Solute sampling of explicit bulk-phase aqueous environments in grand canonical (GC) ensemble simulations suffer from poor convergence due to low insertion probabilities of the solutes. To address this, we developed an iterative procedure involving Grand Canonical-like Monte Carlo (GCMC) and molecular dynamics (MD) simulations. Each iteration involves GCMC of both the solutes and water followed by MD, with the excess chemical potential (μex) of both the solute and the water oscillated to attain their target concentrations in the simulation system. By periodically varying the μex of the water and solutes over the GCMC-MD iterations, solute exchange probabilities and the spatial distributions of the solutes improved. The utility of the oscillating-μex GCMC-MD method is indicated by its ability to approximate the hydration free energy (HFE) of the individual solutes in aqueous solution as well as in dilute aqueous mixtures of multiple solutes. For seven organic solutes: benzene, propane, acetaldehyde, methanol, formamide, acetate, and methylammonium, the average μex of the solutes and the water converged close to their respective HFEs in both 1 M standard state and dilute aqueous mixture systems. The oscillating-μex GCMC methodology is also able to drive solute sampling in proteins in aqueous environments as shown using the occluded binding pocket of the T4 lysozyme L99A mutant as a model system. The approach was shown to satisfactorily reproduce the free energy of binding of benzene as well as sample the functional group requirements of the occluded pocket consistent with the crystal structures of known ligands bound to the L99A mutant as well as their relative binding affinities.
DPEMC: A Monte Carlo for double diffraction
NASA Astrophysics Data System (ADS)
Boonekamp, M.; Kúcs, T.
2005-05-01
We extend the POMWIG Monte Carlo generator developed by B. Cox and J. Forshaw, to include new models of central production through inclusive and exclusive double Pomeron exchange in proton-proton collisions. Double photon exchange processes are described as well, both in proton-proton and heavy-ion collisions. In all contexts, various models have been implemented, allowing for comparisons and uncertainty evaluation and enabling detailed experimental simulations. Program summaryTitle of the program:DPEMC, version 2.4 Catalogue identifier: ADVF Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVF Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer: any computer with the FORTRAN 77 compiler under the UNIX or Linux operating systems Operating system: UNIX; Linux Programming language used: FORTRAN 77 High speed storage required:<25 MB No. of lines in distributed program, including test data, etc.: 71 399 No. of bytes in distributed program, including test data, etc.: 639 950 Distribution format: tar.gz Nature of the physical problem: Proton diffraction at hadron colliders can manifest itself in many forms, and a variety of models exist that attempt to describe it [A. Bialas, P.V. Landshoff, Phys. Lett. B 256 (1991) 540; A. Bialas, W. Szeremeta, Phys. Lett. B 296 (1992) 191; A. Bialas, R.A. Janik, Z. Phys. C 62 (1994) 487; M. Boonekamp, R. Peschanski, C. Royon, Phys. Rev. Lett. 87 (2001) 251806; Nucl. Phys. B 669 (2003) 277; R. Enberg, G. Ingelman, A. Kissavos, N. Timneanu, Phys. Rev. Lett. 89 (2002) 081801; R. Enberg, G. Ingelman, L. Motyka, Phys. Lett. B 524 (2002) 273; R. Enberg, G. Ingelman, N. Timneanu, Phys. Rev. D 67 (2003) 011301; B. Cox, J. Forshaw, Comput. Phys. Comm. 144 (2002) 104; B. Cox, J. Forshaw, B. Heinemann, Phys. Lett. B 540 (2002) 26; V. Khoze, A. Martin, M. Ryskin, Phys. Lett. B 401 (1997) 330; Eur. Phys. J. C 14 (2000) 525; Eur. Phys. J. C 19 (2001) 477; Erratum, Eur. Phys. J. C 20 (2001) 599; Eur
kmos: A lattice kinetic Monte Carlo framework
NASA Astrophysics Data System (ADS)
Hoffmann, Max J.; Matera, Sebastian; Reuter, Karsten
2014-07-01
Kinetic Monte Carlo (kMC) simulations have emerged as a key tool for microkinetic modeling in heterogeneous catalysis and other materials applications. Systems, where site-specificity of all elementary reactions allows a mapping onto a lattice of discrete active sites, can be addressed within the particularly efficient lattice kMC approach. To this end we describe the versatile kmos software package, which offers a most user-friendly implementation, execution, and evaluation of lattice kMC models of arbitrary complexity in one- to three-dimensional lattice systems, involving multiple active sites in periodic or aperiodic arrangements, as well as site-resolved pairwise and higher-order lateral interactions. Conceptually, kmos achieves a maximum runtime performance which is essentially independent of lattice size by generating code for the efficiency-determining local update of available events that is optimized for a defined kMC model. For this model definition and the control of all runtime and evaluation aspects kmos offers a high-level application programming interface. Usage proceeds interactively, via scripts, or a graphical user interface, which visualizes the model geometry, the lattice occupations and rates of selected elementary reactions, while allowing on-the-fly changes of simulation parameters. We demonstrate the performance and scaling of kmos with the application to kMC models for surface catalytic processes, where for given operation conditions (temperature and partial pressures of all reactants) central simulation outcomes are catalytic activity and selectivities, surface composition, and mechanistic insight into the occurrence of individual elementary processes in the reaction network.
Lattice Monte Carlo simulations of polymer melts
NASA Astrophysics Data System (ADS)
Hsu, Hsiao-Ping
2014-12-01
We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction 0.5. In order to reduce the local density fluctuations, we test a pre-packing process for the preparation of the initial configurations of the polymer melts, before the excluded volume interaction is switched on completely. This process leads to a significantly faster decrease of the number of overlapping monomers on the lattice. This is useful for simulating very large systems, where the statistical properties of the model with a marginally incomplete elimination of excluded volume violations are the same as those of the model with strictly excluded volume. We find that the internal mean square end-to-end distance for moderately stiff chains in a melt can be very well described by a freely rotating chain model with a precise estimate of the bond-bond orientational correlation between two successive bond vectors in equilibrium. The plot of the probability distributions of the reduced end-to-end distance of chains of different stiffness also shows that the data collapse is excellent and described very well by the Gaussian distribution for ideal chains. However, while our results confirm the systematic deviations between Gaussian statistics for the chain structure factor Sc(q) [minimum in the Kratky-plot] found by Wittmer et al. [EPL 77, 56003 (2007)] for fully flexible chains in a melt, we show that for the available chain length these deviations are no longer visible, when the chain stiffness is included. The mean square bond length and the compressibility estimated from collective structure factors depend slightly on the stiffness of the chains.
Monte-Carlo simulation of Callisto's exosphere
NASA Astrophysics Data System (ADS)
Vorburger, A.; Wurz, P.; Lammer, H.; Barabash, S.; Mousis, O.
2015-12-01
We model Callisto's exosphere based on its ice as well as non-ice surface via the use of a Monte-Carlo exosphere model. For the ice component we implement two putative compositions that have been computed from two possible extreme formation scenarios of the satellite. One composition represents the oxidizing state and is based on the assumption that the building blocks of Callisto were formed in the protosolar nebula and the other represents the reducing state of the gas, based on the assumption that the satellite accreted from solids condensed in the jovian sub-nebula. For the non-ice component we implemented the compositions of typical CI as well as L type chondrites. Both chondrite types have been suggested to represent Callisto's non-ice composition best. As release processes we consider surface sublimation, ion sputtering and photon-stimulated desorption. Particles are followed on their individual trajectories until they either escape Callisto's gravitational attraction, return to the surface, are ionized, or are fragmented. Our density profiles show that whereas the sublimated species dominate close to the surface on the sun-lit side, their density profiles (with the exception of H and H2) decrease much more rapidly than the sputtered particles. The Neutral gas and Ion Mass (NIM) spectrometer, which is part of the Particle Environment Package (PEP), will investigate Callisto's exosphere during the JUICE mission. Our simulations show that NIM will be able to detect sublimated and sputtered particles from both the ice and non-ice surface. NIM's measured chemical composition will allow us to distinguish between different formation scenarios.
Monte Carlo implementation of polarized hadronization
NASA Astrophysics Data System (ADS)
Matevosyan, Hrayr H.; Kotzinian, Aram; Thomas, Anthony W.
2017-01-01
We study the polarized quark hadronization in a Monte Carlo (MC) framework based on the recent extension of the quark-jet framework, where a self-consistent treatment of the quark polarization transfer in a sequential hadronization picture has been presented. Here, we first adopt this approach for MC simulations of the hadronization process with a finite number of produced hadrons, expressing the relevant probabilities in terms of the eight leading twist quark-to-quark transverse-momentum-dependent (TMD) splitting functions (SFs) for elementary q →q'+h transition. We present explicit expressions for the unpolarized and Collins fragmentation functions (FFs) of unpolarized hadrons emitted at rank 2. Further, we demonstrate that all the current spectator-type model calculations of the leading twist quark-to-quark TMD SFs violate the positivity constraints, and we propose a quark model based ansatz for these input functions that circumvents the problem. We validate our MC framework by explicitly proving the absence of unphysical azimuthal modulations of the computed polarized FFs, and by precisely reproducing the earlier derived explicit results for rank-2 pions. Finally, we present the full results for pion unpolarized and Collins FFs, as well as the corresponding analyzing powers from high statistics MC simulations with a large number of produced hadrons for two different model input elementary SFs. The results for both sets of input functions exhibit the same general features of an opposite signed Collins function for favored and unfavored channels at large z and, at the same time, demonstrate the flexibility of the quark-jet framework by producing significantly different dependences of the results at mid to low z for the two model inputs.
Quantum Monte Carlo with directed loops.
Syljuåsen, Olav F; Sandvik, Anders W
2002-10-01
We introduce the concept of directed loops in stochastic series expansion and path-integral quantum Monte Carlo methods. Using the detailed balance rules for directed loops, we show that it is possible to smoothly connect generally applicable simulation schemes (in which it is necessary to include backtracking processes in the loop construction) to more restricted loop algorithms that can be constructed only for a limited range of Hamiltonians (where backtracking can be avoided). The "algorithmic discontinuities" between general and special points (or regions) in parameter space can hence be eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg antiferromagnet in an external magnetic field. We show that directed-loop simulations are very efficient for the full range of magnetic fields (zero to the saturation point) and anisotropies. In particular, for weak fields and anisotropies, the autocorrelations are significantly reduced relative to those of previous approaches. The back-tracking probability vanishes continuously as the isotropic Heisenberg point is approached. For the XY model, we show that back tracking can be avoided for all fields extending up to the saturation field. The method is hence particularly efficient in this case. We use directed-loop simulations to study the magnetization process in the two-dimensional Heisenberg model at very low temperatures. For LxL lattices with L up to 64, we utilize the step structure in the magnetization curve to extract gaps between different spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the transverse susceptibility in the thermodynamic limit: chi( perpendicular )=0.0659+/-0.0002.
Perturbation Monte Carlo methods for tissue structure alterations.
Nguyen, Jennifer; Hayakawa, Carole K; Mourant, Judith R; Spanier, Jerome
2013-01-01
This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15-25% of the scattering parameters.
Implications of Monte Carlo Statistical Errors in Criticality Safety Assessments
Pevey, Ronald E.
2005-09-15
Most criticality safety calculations are performed using Monte Carlo techniques because of Monte Carlo's ability to handle complex three-dimensional geometries. For Monte Carlo calculations, the more histories sampled, the lower the standard deviation of the resulting estimates. The common intuition is, therefore, that the more histories, the better; as a result, analysts tend to run Monte Carlo analyses as long as possible (or at least to a minimum acceptable uncertainty). For Monte Carlo criticality safety analyses, however, the optimization situation is complicated by the fact that procedures usually require that an extra margin of safety be added because of the statistical uncertainty of the Monte Carlo calculations. This additional safety margin affects the impact of the choice of the calculational standard deviation, both on production and on safety. This paper shows that, under the assumptions of normally distributed benchmarking calculational errors and exact compliance with the upper subcritical limit (USL), the standard deviation that optimizes production is zero, but there is a non-zero value of the calculational standard deviation that minimizes the risk of inadvertently labeling a supercritical configuration as subcritical. Furthermore, this value is shown to be a simple function of the typical benchmarking step outcomes--the bias, the standard deviation of the bias, the upper subcritical limit, and the number of standard deviations added to calculated k-effectives before comparison to the USL.
NASA Astrophysics Data System (ADS)
Ottosson, R. O.; Karlsson, A.; Behrens, C. F.
2010-08-01
The pencil beam dose calculation method is frequently used in modern radiation therapy treatment planning regardless of the fact that it is documented inaccurately for cases involving large density variations. The inaccuracies are larger for higher beam energies. As a result, low energy beams are conventionally used for lung treatments. The aim of this study was to analyze the advantages and disadvantages of dynamic IMRT treatment planning for high and low photon energy in order to assess if deviating from the conventional low energy approach could be favorable in some cases. Furthermore, the influence of motion on the dose distribution was investigated. Four non-small cell lung cancer cases were selected for this study. Inverse planning was conducted using Varian Eclipse. A total number of 31 dynamic IMRT plans, distributed amongst the four cases, were created ranging from PTV conformity weighted to normal tissue sparing weighted. All optimized treatment plans were calculated using three different calculation algorithms (PBC, AAA and MC). In order to study the influence of motion, two virtual lung phantoms were created. The idea was to mimic two different situations: one where the GTV is located centrally in the PTV and another where the GTV was close to the edge of the PTV. PBC is in poor agreement with MC and AAA for all cases and treatment plans. AAA overestimates the dose, compared to MC. This effect is more pronounced for 15 than 6 MV. AAA and MC both predict similar perturbations in dose distributions when moving the GTV to the edge of the PTV. PBC, however, predicts results contradicting those of AAA and MC. This study shows that PB-based dose calculation algorithms are clinically insufficient for patient geometries involving large density inhomogeneities. AAA is in much better agreement with MC, but even a small overestimation of the dose level by the algorithm might lead to a large part of the PTV being underdosed. It is advisable to use low energy as a
Quantum Monte Carlo Endstation for Petascale Computing
David Ceperley
2011-03-02
CUDA GPU platform. We restructured the CPU algorithms to express additional parallelism, minimize GPU-CPU communication, and efficiently utilize the GPU memory hierarchy. Using mixed precision on GT200 GPUs and MPI for intercommunication and load balancing, we observe typical full-application speedups of approximately 10x to 15x relative to quad-core Xeon CPUs alone, while reproducing the double-precision CPU results within statistical error. We developed an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and used it to construct a primary ultra-high-pressure calibration based on the equation of state of cubic boron nitride. We computed the static contribution to the free energy with the QMC method and obtained the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. We computed the anharmonic Raman frequency shift with QMC simulations as a function of pressure and temperature, allowing optical pressure calibration. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron method is applicable to first-row solids, providing a new reference for ab initio calculations of solids and benchmarks for pseudopotential accuracy. We compared experimental and theoretical results on the momentum distribution and the quasiparticle renormalization factor in sodium. From an x-ray Compton-profile measurement of the valence-electron momentum density, we derived its discontinuity at the Fermi wavevector finding an accurate measure of the renormalization factor that we compared with quantum-Monte-Carlo and G0W0 calculations performed both on crystalline sodium and on the homogeneous electron gas. Our calculated results are in good agreement with the experiment. We have been studying the heat of formation for various Kubas complexes of molecular
Monte Carlo simulation of quantum Zeno effect in the brain
NASA Astrophysics Data System (ADS)
Georgiev, Danko
2015-12-01
Environmental decoherence appears to be the biggest obstacle for successful construction of quantum mind theories. Nevertheless, the quantum physicist Henry Stapp promoted the view that the mind could utilize quantum Zeno effect to influence brain dynamics and that the efficacy of such mental efforts would not be undermined by environmental decoherence of the brain. To address the physical plausibility of Stapp's claim, we modeled the brain using quantum tunneling of an electron in a multiple-well structure such as the voltage sensor in neuronal ion channels and performed Monte Carlo simulations of quantum Zeno effect exerted by the mind upon the brain in the presence or absence of environmental decoherence. The simulations unambiguously showed that the quantum Zeno effect breaks down for timescales greater than the brain decoherence time. To generalize the Monte Carlo simulation results for any n-level quantum system, we further analyzed the change of brain entropy due to the mind probing actions and proved a theorem according to which local projections cannot decrease the von Neumann entropy of the unconditional brain density matrix. The latter theorem establishes that Stapp's model is physically implausible but leaves a door open for future development of quantum mind theories provided the brain has a decoherence-free subspace.
Stochastic Kinetic Monte Carlo algorithms for long-range Hamiltonians
Mason, D R; Rudd, R E; Sutton, A P
2003-10-13
We present a higher order kinetic Monte Carlo methodology suitable to model the evolution of systems in which the transition rates are non- trivial to calculate or in which Monte Carlo moves are likely to be non- productive flicker events. The second order residence time algorithm first introduced by Athenes et al.[1] is rederived from the n-fold way algorithm of Bortz et al.[2] as a fully stochastic algorithm. The second order algorithm can be dynamically called when necessary to eliminate unproductive flickering between a metastable state and its neighbors. An algorithm combining elements of the first order and second order methods is shown to be more efficient, in terms of the number of rate calculations, than the first order or second order methods alone while remaining statistically identical. This efficiency is of prime importance when dealing with computationally expensive rate functions such as those arising from long- range Hamiltonians. Our algorithm has been developed for use when considering simulations of vacancy diffusion under the influence of elastic stress fields. We demonstrate the improved efficiency of the method over that of the n-fold way in simulations of vacancy diffusion in alloys. Our algorithm is seen to be an order of magnitude more efficient than the n-fold way in these simulations. We show that when magnesium is added to an Al-2at.%Cu alloy, this has the effect of trapping vacancies. When trapping occurs, we see that our algorithm performs thousands of events for each rate calculation performed.
Monte Carlo dose verification for intensity-modulated arc therapy
NASA Astrophysics Data System (ADS)
Li, X. Allen; Ma, Lijun; Naqvi, Shahid; Shih, Rompin; Yu, Cedric
2001-09-01
Intensity-modulated arc therapy (IMAT), a technique which combines beam rotation and dynamic multileaf collimation, has been implemented in our clinic. Dosimetric errors can be created by the inability of the planning system to accurately account for the effects of tissue inhomogeneities and physical characteristics of the multileaf collimator (MLC). The objective of this study is to explore the use of Monte Carlo (MC) simulation for IMAT dose verification. The BEAM/DOSXYZ Monte Carlo system was implemented to perform dose verification for the IMAT treatment. The implementation includes the simulation of the linac head/MLC (Elekta SL20), the conversion of patient CT images and beam arrangement for 3D dose calculation, the calculation of gantry rotation and leaf motion by a series of static beams and the development of software to automate the entire MC process. The MC calculations were verified by measurements for conventional beam settings. The agreement was within 2%. The IMAT dose distributions generated by a commercial forward planning system (RenderPlan, Elekta) were compared with those calculated by the MC package. For the cases studied, discrepancies of over 10% were found between the MC and the RenderPlan dose calculations. These discrepancies were due in part to the inaccurate dose calculation of the RenderPlan system. The computation time for the IMAT MC calculation was in the range of 20-80 min on 15 Pentium-III computers. The MC method was also useful in verifying the beam apertures used in the IMAT treatments.
Bayesian Monte Carlo and Maximum Likelihood Approach for ...
Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficien
Parallel implementation of a Monte Carlo molecular stimulation program
Carvalho; Gomes; Cordeiro
2000-05-01
Molecular simulation methods such as molecular dynamics and Monte Carlo are fundamental for the theoretical calculation of macroscopic and microscopic properties of chemical and biochemical systems. These methods often rely on heavy computations, and one sometimes feels the need to run them in powerful massively parallel machines. For moderate problem sizes, however, a not so powerful and less expensive solution based on a network of workstations may be quite satisfactory. In the present work, the strategy adopted in the development of a parallel version is outlined, using the message passing model, of a molecular simulation code to be used in a network of workstations. This parallel code is the adaptation of an older sequential code using the Metropolis Monte Carlo method. In this case, the message passing interface was used as the interprocess communications library, although the code could be easily adapted for other message passing systems such as the parallel virtual machine. For simple systems it is shown that speedups of 2 can be achieved for four processes with this cheap solution. For bigger and more complex simulated systems, even better speedups might be obtained, which indicates that the presented approach is appropriate for the efficient use of a network of workstations in parallel processing.
Energy-Driven Kinetic Monte Carlo Method and Its Application in Fullerene Coalescence.
Ding, Feng; Yakobson, Boris I
2014-09-04
Mimicking the conventional barrier-based kinetic Monte Carlo simulation, an energy-driven kinetic Monte Carlo (EDKMC) method was developed to study the structural transformation of carbon nanomaterials. The new method is many orders magnitude faster than standard molecular dynamics or Monte Marlo (MC) simulations and thus allows us to explore rare events within a reasonable computational time. As an example, the temperature dependence of fullerene coalescence was studied. The simulation, for the first time, revealed that short capped single-walled carbon nanotubes (SWNTs) appear as low-energy metastable structures during the structural evolution.
Chen, Yunjie; Roux, Benoît
2015-08-11
Molecular dynamics (MD) trajectories based on a classical equation of motion provide a straightforward, albeit somewhat inefficient approach, to explore and sample the configurational space of a complex molecular system. While a broad range of techniques can be used to accelerate and enhance the sampling efficiency of classical simulations, only algorithms that are consistent with the Boltzmann equilibrium distribution yield a proper statistical mechanical computational framework. Here, a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained (FG) and coarse-grained (CG) representations of a system is designed to improve sampling efficiency by combining the strength of nonequilibrium molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration of an atomic system is dynamically propagated for some period of time using equilibrium MD; (2) the resulting FG configuration is mapped onto a simplified CG model; (3) the CG model is propagated for a brief time interval to yield a new CG configuration; (4) the resulting CG configuration is used as a target to guide the evolution of the FG system; (5) the FG configuration (from step 1) is driven via a nonequilibrium MD (neMD) simulation toward the CG target; (6) the resulting FG configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-ends momentum reversal prescription is used for the neMD trajectories of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The enhanced sampling achieved with the method is illustrated with a model system with hindered diffusion and explicit-solvent peptide simulations. Illustrative tests indicate that the method can yield a speedup of about 80 times for the model system and up
Monte Carlo Techniques for Nuclear Systems - Theory Lectures
Brown, Forrest B.
2016-11-29
These are lecture notes for a Monte Carlo class given at the University of New Mexico. The following topics are covered: course information; nuclear eng. review & MC; random numbers and sampling; computational geometry; collision physics; tallies and statistics; eigenvalue calculations I; eigenvalue calculations II; eigenvalue calculations III; variance reduction; parallel Monte Carlo; parameter studies; fission matrix and higher eigenmodes; doppler broadening; Monte Carlo depletion; HTGR modeling; coupled MC and T/H calculations; fission energy deposition. Solving particle transport problems with the Monte Carlo method is simple - just simulate the particle behavior. The devil is in the details, however. These lectures provide a balanced approach to the theory and practice of Monte Carlo simulation codes. The first lectures provide an overview of Monte Carlo simulation methods, covering the transport equation, random sampling, computational geometry, collision physics, and statistics. The next lectures focus on the state-of-the-art in Monte Carlo criticality simulations, covering the theory of eigenvalue calculations, convergence analysis, dominance ratio calculations, bias in Keff and tallies, bias in uncertainties, a case study of a realistic calculation, and Wielandt acceleration techniques. The remaining lectures cover advanced topics, including HTGR modeling and stochastic geometry, temperature dependence, fission energy deposition, depletion calculations, parallel calculations, and parameter studies. This portion of the class focuses on using MCNP to perform criticality calculations for reactor physics and criticality safety applications. It is an intermediate level class, intended for those with at least some familiarity with MCNP. Class examples provide hands-on experience at running the code, plotting both geometry and results, and understanding the code output. The class includes lectures & hands-on computer use for a variety of Monte Carlo calculations
Meaningful timescales from Monte Carlo simulations of particle systems with hard-core interactions
NASA Astrophysics Data System (ADS)
Costa, Liborio I.
2016-12-01
A new Markov Chain Monte Carlo method for simulating the dynamics of particle systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is associated with minima in the energy landscape, in the proposed method, the state of the system is associated with the set of paths traveled by the atoms and the transition probabilities for an atom to be displaced are proportional to the corresponding velocities. In this way, the number of possible state-to-state transitions is reduced to a discrete set, and a direct link between the Monte Carlo time step and true physical time is naturally established. The resulting rejection-free algorithm is validated against event-driven molecular dynamics: the equilibrium and non-equilibrium dynamics of hard disks converge to the exact results with decreasing displacement size.
Coherent Scattering Imaging Monte Carlo Simulation
NASA Astrophysics Data System (ADS)
Hassan, Laila Abdulgalil Rafik
Conventional mammography has poor contrast between healthy and cancerous tissues due to the small difference in attenuation properties. Coherent scatter potentially provides more information because interference of coherently scattered radiation depends on the average intermolecular spacing, and can be used to characterize tissue types. However, typical coherent scatter analysis techniques are not compatible with rapid low dose screening techniques. Coherent scatter slot scan imaging is a novel imaging technique which provides new information with higher contrast. In this work a simulation of coherent scatter was performed for slot scan imaging to assess its performance and provide system optimization. In coherent scatter imaging, the coherent scatter is exploited using a conventional slot scan mammography system with anti-scatter grids tilted at the characteristic angle of cancerous tissues. A Monte Carlo simulation was used to simulate the coherent scatter imaging. System optimization was performed across several parameters, including source voltage, tilt angle, grid distances, grid ratio, and shielding geometry. The contrast increased as the grid tilt angle increased beyond the characteristic angle for the modeled carcinoma. A grid tilt angle of 16 degrees yielded the highest contrast and signal to noise ratio (SNR). Also, contrast increased as the source voltage increased. Increasing grid ratio improved contrast at the expense of decreasing SNR. A grid ratio of 10:1 was sufficient to give a good contrast without reducing the intensity to a noise level. The optimal source to sample distance was determined to be such that the source should be located at the focal distance of the grid. A carcinoma lump of 0.5x0.5x0.5 cm3 in size was detectable which is reasonable considering the high noise due to the usage of relatively small number of incident photons for computational reasons. A further study is needed to study the effect of breast density and breast thickness
Uncertainty Analyses for Localized Tallies in Monte Carlo Eigenvalue Calculations
Mervin, Brenden T.; Maldonado, G Ivan; Mosher, Scott W; Wagner, John C
2011-01-01
It is well known that statistical estimates obtained from Monte Carlo criticality simulations can be adversely affected by cycle-to-cycle correlations in the fission source. In addition there are several other more fundamental issues that may lead to errors in Monte Carlo results. These factors can have a significant impact on the calculated eigenvalue, localized tally means and their associated standard deviations. In fact, modern Monte Carlo computational tools may generate standard deviation estimates that are a factor of five or more lower than the true standard deviation for a particular tally due to the inter-cycle correlations in the fission source. The magnitude of this under-prediction can climb as high as one hundred when combined with an ill-converged fission source or poor sampling techniques. Since Monte Carlo methods are widely used in reactor analysis (as a benchmarking tool) and criticality safety applications, an in-depth understanding of the effects of these issues must be developed in order to support the practical use of Monte Carlo software packages. A rigorous statistical analysis of localized tally results in eigenvalue calculations is presented using the SCALE/KENO-VI and MCNP Monte Carlo codes. The purpose of this analysis is to investigate the under-prediction in the uncertainty and its sensitivity to problem characteristics and calculational parameters, and to provide a comparative study between the two codes with respect to this under-prediction. It is shown herein that adequate source convergence along with proper specification of Monte Carlo parameters can reduce the magnitude of under-prediction in the uncertainty to reasonable levels; below a factor of 2 when inter-cycle correlations in the fission source are not a significant factor. In addition, through the use of a modified sampling procedure, the effects of inter-cycle correlations on both the mean value and standard deviation estimates can be isolated.
The Monte Carlo code MCPTV--Monte Carlo dose calculation in radiation therapy with carbon ions.
Karg, Juergen; Speer, Stefan; Schmidt, Manfred; Mueller, Reinhold
2010-07-07
The Monte Carlo code MCPTV is presented. MCPTV is designed for dose calculation in treatment planning in radiation therapy with particles and especially carbon ions. MCPTV has a voxel-based concept and can perform a fast calculation of the dose distribution on patient CT data. Material and density information from CT are taken into account. Electromagnetic and nuclear interactions are implemented. Furthermore the algorithm gives information about the particle spectra and the energy deposition in each voxel. This can be used to calculate the relative biological effectiveness (RBE) for each voxel. Depth dose distributions are compared to experimental data giving good agreement. A clinical example is shown to demonstrate the capabilities of the MCPTV dose calculation.
bhlight: GENERAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS WITH MONTE CARLO TRANSPORT
Ryan, B. R.; Gammie, C. F.; Dolence, J. C.
2015-07-01
We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and to a slowly accreting Kerr black hole in axisymmetry.
A study of Monte Carlo radiative transfer through fractal clouds
Gautier, C.; Lavallec, D.; O`Hirok, W.; Ricchiazzi, P.
1996-04-01
An understanding of radiation transport (RT) through clouds is fundamental to studies of the earth`s radiation budget and climate dynamics. The transmission through horizontally homogeneous clouds has been studied thoroughly using accurate, discreet ordinates radiative transfer models. However, the applicability of these results to general problems of global radiation budget is limited by the plane parallel assumption and the fact that real clouds fields show variability, both vertically and horizontally, on all size scales. To understand how radiation interacts with realistic clouds, we have used a Monte Carlo radiative transfer model to compute the details of the photon-cloud interaction on synthetic cloud fields. Synthetic cloud fields, generated by a cascade model, reproduce the scaling behavior, as well as the cloud variability observed and estimated from cloud satellite data.
Synchronous parallel kinetic Monte Carlo Diffusion in Heterogeneous Systems
Martinez Saez, Enrique; Hetherly, Jeffery; Caro, Jose A
2010-12-06
A new hybrid Molecular Dynamics-kinetic Monte Carlo algorithm has been developed in order to study the basic mechanisms taking place in diffusion in concentrated alloys under the action of chemical and stress fields. Parallel implementation of the k-MC part based on a recently developed synchronous algorithm [1. Compo Phys. 227 (2008) 3804-3823] resorting on the introduction of a set of null events aiming at synchronizing the time for the different subdomains, added to the parallel efficiency of MD, provides the computer power required to evaluate jump rates 'on the flight', incorporating in this way the actual driving force emerging from chemical potential gradients, and the actual environment-dependent jump rates. The time gain has been analyzed and the parallel performance reported. The algorithm is tested on simple diffusion problems to verify its accuracy.
Direct simulation Monte Carlo investigation of hydrodynamic instabilities in gases
NASA Astrophysics Data System (ADS)
Gallis, M. A.; Koehler, T. P.; Torczynski, J. R.; Plimpton, S. J.
2016-11-01
The Rayleigh-Taylor instability (RTI) is investigated using the Direct Simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, two-dimensional and three-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode-perturbed interfaces between two atmospheric-pressure monatomic gases. The DSMC simulations reproduce all qualitative features of the RTI and are in reasonable quantitative agreement with existing theoretical and empirical models in the linear, nonlinear, and self-similar regimes. At late times, the instability is seen to exhibit a self-similar behavior, in agreement with experimental observations. For the conditions simulated, diffusion can influence the initial instability growth significantly.
Reactive Monte Carlo sampling with an ab initio potential
Leiding, Jeff; Coe, Joshua D.
2016-05-04
Here, we present the first application of reactive Monte Carlo in a first-principles context. The algorithm samples in a modified NVT ensemble in which the volume, temperature, and total number of atoms of a given type are held fixed, but molecular composition is allowed to evolve through stochastic variation of chemical connectivity. We also discuss general features of the method, as well as techniques needed to enhance the efficiency of Boltzmann sampling. Finally, we compare the results of simulation of NH3 to those of ab initio molecular dynamics (AIMD). Furthermore, we find that there are regions of state space formore » which RxMC sampling is much more efficient than AIMD due to the “rare-event” character of chemical reactions.« less
Monte Carlo simulation of the hysteresis phenomena on ferromagnetic nanotubes.
Salazar-Enríquez, C D; Restrepo, J; Restrepo-Parra, E
2012-06-01
In this work the hysteretic properties of single wall ferromagnetic nanotubes were studied. Hysteresis loops were computed on the basis of a classical Heisenberg model involving nearest neighbor interactions and using a Monte Carlo method implemented with a single spin movement Metropolis dynamics. Nanotubes with square and hexagonal unit cells were studied varying their diameter, temperature and magneto-crystalline anisotropy. Effects of the diameter were found stronger in the square unit cell magnetic nanotubes (SMNTs) than in the hexagonal unit cell magnetic nanotubes (HMNTs). The ferromagnetic behavior was observed in SMNTs at higher temperature than in HMNTs. Moreover in both cases, SMNTs and HMNTs, the magneto-crystalline anisotropy in the longitudinal direction showed a linear correspondence with the coercive field.
Monte Carlo study of Dirac semimetals phase diagram
NASA Astrophysics Data System (ADS)
Braguta, V. V.; Katsnelson, M. I.; Kotov, A. Yu.; Nikolaev, A. A.
2016-11-01
In this paper the phase diagram of Dirac semimetals is studied within a lattice Monte Carlo simulation. In particular, we concentrate on the dynamical chiral symmetry breaking which results in a semimetal-insulator transition. Using numerical simulation, we determine the values of the critical coupling constant of the semimetal-insulator transition for different values of the anisotropy of the Fermi velocity. This measurement allows us to draw a tentative phase diagram for Dirac semimetals. It turns out that within the Dirac model with Coulomb interaction both Na3Bi and Cd3As2 , known experimentally to be Dirac semimetals, would lie deep in the insulating region of the phase diagram. This result probably shows a decisive role of screening of the interelectron interaction in real materials, similar to the situation in graphene.
OBJECT KINETIC MONTE CARLO SIMULATIONS OF RADIATION DAMAGE IN TUNGSTEN
Nandipati, Giridhar; Setyawan, Wahyu; Heinisch, Howard L.; Roche, Kenneth J.; Kurtz, Richard J.; Wirth, Brian D.
2015-04-16
We used our recently developed lattice-based object kinetic Monte Carlo code; KSOME [1] to carryout simulations of radiation damage in bulk tungsten at temperatures of 300, and 2050 K for various dose rates. Displacement cascades generated from molecular dynamics (MD) simulations for PKA energies at 60, 75 and 100 keV provided residual point defect distributions. It was found that the number density of vacancies in the simulation box does not change with dose rate while the number density of vacancy clusters slightly decreases with dose rate indicating that bigger clusters are formed at larger dose rates. At 300 K, although the average vacancy cluster size increases slightly, the vast majority of vacancies exist as mono-vacancies. At 2050 K no accumulation of defects was observed during irradiation over a wide range of dose rates for all PKA energies studied in this work.
bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport
Ryan, Benjamin R; Dolence, Joshua C.; Gammie, Charles F.
2015-06-25
We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and tomore » a slowly accreting Kerr black hole in axisymmetry.« less
bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport
Ryan, Benjamin R; Dolence, Joshua C.; Gammie, Charles F.
2015-06-25
We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and to a slowly accreting Kerr black hole in axisymmetry.
NOTE: Monte Carlo simulation of RapidArc radiotherapy delivery
NASA Astrophysics Data System (ADS)
Bush, K.; Townson, R.; Zavgorodni, S.
2008-10-01
RapidArc radiotherapy technology from Varian Medical Systems is one of the most complex delivery systems currently available, and achieves an entire intensity-modulated radiation therapy (IMRT) treatment in a single gantry rotation about the patient. Three dynamic parameters can be continuously varied to create IMRT dose distributions—the speed of rotation, beam shaping aperture and delivery dose rate. Modeling of RapidArc technology was incorporated within the existing Vancouver Island Monte Carlo (VIMC) system (Zavgorodni et al 2007 Radiother. Oncol. 84 S49, 2008 Proc. 16th Int. Conf. on Medical Physics). This process was named VIMC-Arc and has become an efficient framework for the verification of RapidArc treatment plans. VIMC-Arc is a fully automated system that constructs the Monte Carlo (MC) beam and patient models from a standard RapidArc DICOM dataset, simulates radiation transport, collects the resulting dose and converts the dose into DICOM format for import back into the treatment planning system (TPS). VIMC-Arc accommodates multiple arc IMRT deliveries and models gantry rotation as a series of segments with dynamic MLC motion within each segment. Several verification RapidArc plans were generated by the Eclipse TPS on a water-equivalent cylindrical phantom and re-calculated using VIMC-Arc. This includes one 'typical' RapidArc plan, one plan for dual arc treatment and one plan with 'avoidance' sectors. One RapidArc plan was also calculated on a DICOM patient CT dataset. Statistical uncertainty of MC simulations was kept within 1%. VIMC-Arc produced dose distributions that matched very closely to those calculated by the anisotropic analytical algorithm (AAA) that is used in Eclipse. All plans also demonstrated better than 1% agreement of the dose at the isocenter. This demonstrates the capabilities of our new MC system to model all dosimetric features required for RapidArc dose calculations.
Monte Carlo simulation of RapidArc radiotherapy delivery.
Bush, K; Townson, R; Zavgorodni, S
2008-10-07
RapidArc radiotherapy technology from Varian Medical Systems is one of the most complex delivery systems currently available, and achieves an entire intensity-modulated radiation therapy (IMRT) treatment in a single gantry rotation about the patient. Three dynamic parameters can be continuously varied to create IMRT dose distributions-the speed of rotation, beam shaping aperture and delivery dose rate. Modeling of RapidArc technology was incorporated within the existing Vancouver Island Monte Carlo (VIMC) system (Zavgorodni et al 2007 Radiother. Oncol. 84 S49, 2008 Proc. 16th Int. Conf. on Medical Physics). This process was named VIMC-Arc and has become an efficient framework for the verification of RapidArc treatment plans. VIMC-Arc is a fully automated system that constructs the Monte Carlo (MC) beam and patient models from a standard RapidArc DICOM dataset, simulates radiation transport, collects the resulting dose and converts the dose into DICOM format for import back into the treatment planning system (TPS). VIMC-Arc accommodates multiple arc IMRT deliveries and models gantry rotation as a series of segments with dynamic MLC motion within each segment. Several verification RapidArc plans were generated by the Eclipse TPS on a water-equivalent cylindrical phantom and re-calculated using VIMC-Arc. This includes one 'typical' RapidArc plan, one plan for dual arc treatment and one plan with 'avoidance' sectors. One RapidArc plan was also calculated on a DICOM patient CT dataset. Statistical uncertainty of MC simulations was kept within 1%. VIMC-Arc produced dose distributions that matched very closely to those calculated by the anisotropic analytical algorithm (AAA) that is used in Eclipse. All plans also demonstrated better than 1% agreement of the dose at the isocenter. This demonstrates the capabilities of our new MC system to model all dosimetric features required for RapidArc dose calculations.
Zhang, Jeff L.; Conlin, Chris C.; Carlston, Kristi; Xie, Luke; Kim, Daniel; Morrell, Glen; Morton, Kathryn; Lee, Vivian S.
2016-01-01
Dynamic contrast-enhanced (DCE) MRI is widely used for the measurement of tissue perfusion and to assess organ function. MR renography, which is acquired using a DCE sequence, can measure renal perfusion, filtration and concentrating ability. Optimization of the DCE acquisition protocol is important for the minimization of the error propagation from the acquired signals to the estimated parameters, thus improving the precision of the parameters. Critical to the optimization of contrast-enhanced T1-weighted protocols is the balance of the T1-shortening effect across the range of gadolinium (Gd) contrast concentration in the tissue of interest. In this study, we demonstrate a Monte Carlo simulation approach for the optimization of DCE MRI, in which a saturation-recovery T1-weighted gradient echo sequence is simulated and the impact of injected dose (D) and time delay (TD, for saturation recovery) is tested. The results show that high D and/or high TD cause saturation of the peak arterial signals and lead to an overestimation of renal plasma flow (RPF) and glomerular filtration rate (GFR). However, the use of low TD (e.g. 100 ms) and low D leads to similar errors in RPF and GFR, because of the Rician bias in the pre-contrast arterial signals. Our patient study including 22 human subjects compared TD values of 100 and 300 ms after the injection of 4 mL of Gd contrast for MR renography. At TD = 100 ms, we computed an RPF value of 157.2 ± 51.7 mL/min and a GFR of 33.3 ± 11.6 mL/min. These results were all significantly higher than the parameter estimates at TD = 300 ms: RPF = 143.4 ± 48.8 mL/min (p = 0.0006) and GFR = 30.2 ± 11.5 mL/min (p = 0.0015). In conclusion, appropriate optimization of the DCE MRI protocol using simulation can effectively improve the precision and, potentially, the accuracy of the measured parameters. PMID:27200499
Xu, Zuwei; Zhao, Haibo Zheng, Chuguang
2015-01-15
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are
Schabel, Matthias C; Fluckiger, Jacob U; DiBella, Edward V R
2010-08-21
Widespread adoption of quantitative pharmacokinetic modeling methods in conjunction with dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) has led to increased recognition of the importance of obtaining accurate patient-specific arterial input function (AIF) measurements. Ideally, DCE-MRI studies use an AIF directly measured in an artery local to the tissue of interest, along with measured tissue concentration curves, to quantitatively determine pharmacokinetic parameters. However, the numerous technical and practical difficulties associated with AIF measurement have made the use of population-averaged AIF data a popular, if sub-optimal, alternative to AIF measurement. In this work, we present and characterize a new algorithm for determining the AIF solely from the measured tissue concentration curves. This Monte Carlo blind estimation (MCBE) algorithm estimates the AIF from the subsets of D concentration-time curves drawn from a larger pool of M candidate curves via nonlinear optimization, doing so for multiple (Q) subsets and statistically averaging these repeated estimates. The MCBE algorithm can be viewed as a generalization of previously published methods that employ clustering of concentration-time curves and only estimate the AIF once. Extensive computer simulations were performed over physiologically and experimentally realistic ranges of imaging and tissue parameters, and the impact of choosing different values of D and Q was investigated. We found the algorithm to be robust, computationally efficient and capable of accurately estimating the AIF even for relatively high noise levels, long sampling intervals and low diversity of tissue curves. With the incorporation of bootstrapping initialization, we further demonstrated the ability to blindly estimate AIFs that deviate substantially in shape from the population-averaged initial guess. Pharmacokinetic parameter estimates for K(trans), k(ep), v(p) and v(e) all showed relative biases and
NASA Astrophysics Data System (ADS)
Xu, Zuwei; Zhao, Haibo; Zheng, Chuguang
2015-01-01
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance-rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are
An unbiased Hessian representation for Monte Carlo PDFs.
Carrazza, Stefano; Forte, Stefano; Kassabov, Zahari; Latorre, José Ignacio; Rojo, Juan
We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for the determination of the optimal basis. We validate the methodology by first showing that it faithfully reproduces a native Monte Carlo PDF set (NNPDF3.0), and then, that if applied to Hessian PDF set (MMHT14) which was transformed into a Monte Carlo set, it gives back the starting PDFs with minimal information loss. We then show that, when applied to a large Monte Carlo PDF set obtained as combination of several underlying sets, the methodology leads to a Hessian representation in terms of a rather smaller set of parameters (MC-H PDFs), thereby providing an alternative implementation of the recently suggested Meta-PDF idea and a Hessian version of the recently suggested PDF compression algorithm (CMC-PDFs). The mc2hessian conversion code is made publicly available together with (through LHAPDF6) a Hessian representations of the NNPDF3.0 set, and the MC-H PDF set.
Frequency domain optical tomography using a Monte Carlo perturbation method
NASA Astrophysics Data System (ADS)
Yamamoto, Toshihiro; Sakamoto, Hiroki
2016-04-01
A frequency domain Monte Carlo method is applied to near-infrared optical tomography, where an intensity-modulated light source with a given modulation frequency is used to reconstruct optical properties. The frequency domain reconstruction technique allows for better separation between the scattering and absorption properties of inclusions, even for ill-posed inverse problems, due to cross-talk between the scattering and absorption reconstructions. The frequency domain Monte Carlo calculation for light transport in an absorbing and scattering medium has thus far been analyzed mostly for the reconstruction of optical properties in simple layered tissues. This study applies a Monte Carlo calculation algorithm, which can handle complex-valued particle weights for solving a frequency domain transport equation, to optical tomography in two-dimensional heterogeneous tissues. The Jacobian matrix that is needed to reconstruct the optical properties is obtained by a first-order "differential operator" technique, which involves less variance than the conventional "correlated sampling" technique. The numerical examples in this paper indicate that the newly proposed Monte Carlo method provides reconstructed results for the scattering and absorption coefficients that compare favorably with the results obtained from conventional deterministic or Monte Carlo methods.
Monte Carlo Calculations of Polarized Microwave Radiation Emerging from Cloud Structures
NASA Technical Reports Server (NTRS)
Kummerow, Christian; Roberti, Laura
1998-01-01
The last decade has seen tremendous growth in cloud dynamical and microphysical models that are able to simulate storms and storm systems with very high spatial resolution, typically of the order of a few kilometers. The fairly realistic distributions of cloud and hydrometeor properties that these models generate has in turn led to a renewed interest in the three-dimensional microwave radiative transfer modeling needed to understand the effect of cloud and rainfall inhomogeneities upon microwave observations. Monte Carlo methods, and particularly backwards Monte Carlo methods have shown themselves to be very desirable due to the quick convergence of the solutions. Unfortunately, backwards Monte Carlo methods are not well suited to treat polarized radiation. This study reviews the existing Monte Carlo methods and presents a new polarized Monte Carlo radiative transfer code. The code is based on a forward scheme but uses aliasing techniques to keep the computational requirements equivalent to the backwards solution. Radiative transfer computations have been performed using a microphysical-dynamical cloud model and the results are presented together with the algorithm description.
Monte Carlo dose calculations in advanced radiotherapy
NASA Astrophysics Data System (ADS)
Bush, Karl Kenneth
The remarkable accuracy of Monte Carlo (MC) dose calculation algorithms has led to the widely accepted view that these methods should and will play a central role in the radiotherapy treatment verification and planning of the future. The advantages of using MC clinically are particularly evident for radiation fields passing through inhomogeneities, such as lung and air cavities, and for small fields, including those used in today's advanced intensity modulated radiotherapy techniques. Many investigators have reported significant dosimetric differences between MC and conventional dose calculations in such complex situations, and have demonstrated experimentally the unmatched ability of MC calculations in modeling charged particle disequilibrium. The advantages of using MC dose calculations do come at a cost. The nature of MC dose calculations require a highly detailed, in-depth representation of the physical system (accelerator head geometry/composition, anatomical patient geometry/composition and particle interaction physics) to allow accurate modeling of external beam radiation therapy treatments. To perform such simulations is computationally demanding and has only recently become feasible within mainstream radiotherapy practices. In addition, the output of the accelerator head simulation can be highly sensitive to inaccuracies within a model that may not be known with sufficient detail. The goal of this dissertation is to both improve and advance the implementation of MC dose calculations in modern external beam radiotherapy. To begin, a novel method is proposed to fine-tune the output of an accelerator model to better represent the measured output. In this method an intensity distribution of the electron beam incident on the model is inferred by employing a simulated annealing algorithm. The method allows an investigation of arbitrary electron beam intensity distributions and is not restricted to the commonly assumed Gaussian intensity. In a second component of
Benchmarking of Proton Transport in Super Monte Carlo Simulation Program
NASA Astrophysics Data System (ADS)
Wang, Yongfeng; Li, Gui; Song, Jing; Zheng, Huaqing; Sun, Guangyao; Hao, Lijuan; Wu, Yican
2014-06-01
The Monte Carlo (MC) method has been traditionally applied in nuclear design and analysis due to its capability of dealing with complicated geometries and multi-dimensional physics problems as well as obtaining accurate results. The Super Monte Carlo Simulation Program (SuperMC) is developed by FDS Team in China for fusion, fission, and other nuclear applications. The simulations of radiation transport, isotope burn-up, material activation, radiation dose, and biology damage could be performed using SuperMC. Complicated geometries and the whole physical process of various types of particles in broad energy scale can be well handled. Bi-directional automatic conversion between general CAD models and full-formed input files of SuperMC is supported by MCAM, which is a CAD/image-based automatic modeling program for neutronics and radiation transport simulation. Mixed visualization of dynamical 3D dataset and geometry model is supported by RVIS, which is a nuclear radiation virtual simulation and assessment system. Continuous-energy cross section data from hybrid evaluated nuclear data library HENDL are utilized to support simulation. Neutronic fixed source and critical design parameters calculates for reactors of complex geometry and material distribution based on the transport of neutron and photon have been achieved in our former version of SuperMC. Recently, the proton transport has also been intergrated in SuperMC in the energy region up to 10 GeV. The physical processes considered for proton transport include electromagnetic processes and hadronic processes. The electromagnetic processes include ionization, multiple scattering, bremsstrahlung, and pair production processes. Public evaluated data from HENDL are used in some electromagnetic processes. In hadronic physics, the Bertini intra-nuclear cascade model with exitons, preequilibrium model, nucleus explosion model, fission model, and evaporation model are incorporated to treat the intermediate energy nuclear
A practical Monte Carlo MU verification tool for IMRT quality assurance.
Fan, J; Li, J; Chen, L; Stathakis, S; Luo, W; Du Plessis, F; Xiong, W; Yang, J; Ma, C-M
2006-05-21
Quality assurance (QA) for intensity-modulated radiation therapy (IMRT) treatment planning and beam delivery, using ionization chamber measurements and film dosimetry in a phantom, is time consuming. The Monte Carlo method is the most accurate method for radiotherapy dose calculation. However, a major drawback of Monte Carlo dose calculation as currently implemented is its slow speed. The goal of this work is to bring the efficiency of Monte Carlo into a practical range by developing a fast Monte Carlo monitor unit (MU) verification tool for IMRT. A special estimator for dose at a point called the point detector has been used in this research. The point detector uses the next event estimation (NEE) method to calculate the photon energy fluence at a point of interest and then converts it to collision kerma by the mass energy absorption coefficient assuming the presence of transient charged particle equilibrium. The MU verification tool has been validated by comparing the calculation results with measurements. It can be used for both patient dose verification and phantom QA calculation. The dynamic leaf-sequence log file is used to rebuild the actual MLC leaf sequence in order to predict the dose actually received by the patient. Dose calculations for 20 patient plans have been performed using the point detector method. Results were compared with direct Monte Carlo simulations using EGS4/MCSIM, which is a well-benchmarked Monte Carlo code. The results between the point detector and MCSIM agreed to within 2%. A factor of 20 speedup can be achieved with the point detector method compared with direct Monte Carlo simulations.
A practical Monte Carlo MU verification tool for IMRT quality assurance
NASA Astrophysics Data System (ADS)
Fan, J.; Li, J.; Chen, L.; Stathakis, S.; Luo, W.; Du Plessis, F.; Xiong, W.; Yang, J.; Ma, C.-M.
2006-05-01
Quality assurance (QA) for intensity-modulated radiation therapy (IMRT) treatment planning and beam delivery, using ionization chamber measurements and film dosimetry in a phantom, is time consuming. The Monte Carlo method is the most accurate method for radiotherapy dose calculation. However, a major drawback of Monte Carlo dose calculation as currently implemented is its slow speed. The goal of this work is to bring the efficiency of Monte Carlo into a practical range by developing a fast Monte Carlo monitor unit (MU) verification tool for IMRT. A special estimator for dose at a point called the point detector has been used in this research. The point detector uses the next event estimation (NEE) method to calculate the photon energy fluence at a point of interest and then converts it to collision kerma by the mass energy absorption coefficient assuming the presence of transient charged particle equilibrium. The MU verification tool has been validated by comparing the calculation results with measurements. It can be used for both patient dose verification and phantom QA calculation. The dynamic leaf-sequence log file is used to rebuild the actual MLC leaf sequence in order to predict the dose actually received by the patient. Dose calculations for 20 patient plans have been performed using the point detector method. Results were compared with direct Monte Carlo simulations using EGS4/MCSIM, which is a well-benchmarked Monte Carlo code. The results between the point detector and MCSIM agreed to within 2%. A factor of 20 speedup can be achieved with the point detector method compared with direct Monte Carlo simulations.
A Monte Carlo investigation of the Hamiltonian mean field model
NASA Astrophysics Data System (ADS)
Pluchino, Alessandro; Andronico, Giuseppe; Rapisarda, Andrea
2005-04-01
We present a Monte Carlo numerical investigation of the Hamiltonian mean field (HMF) model. We begin by discussing canonical Metropolis Monte Carlo calculations, in order to check the caloric curve of the HMF model and study finite size effects. In the second part of the paper, we present numerical simulations obtained by means of a modified Monte Carlo procedure with the aim to test the stability of those states at minimum temperature and zero magnetization (homogeneous Quasi stationary states), which exist in the condensed phase of the model just below the critical point. For energy densities smaller than the limiting value U∼0.68, we find that these states are unstable confirming a recent result on the Vlasov stability analysis applied to the HMF model.
Monte Carlo simulation in statistical physics: an introduction
NASA Astrophysics Data System (ADS)
Binder, K., Heermann, D. W.
Monte Carlo Simulation in Statistical Physics deals with the computer simulation of many-body systems in condensed-matter physics and related fields of physics, chemistry and beyond, to traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, probability distributions are calculated, allowing the estimation of the thermodynamic properties of various systems. This book describes the theoretical background to several variants of these Monte Carlo methods and gives a systematic presentation from which newcomers can learn to perform such simulations and to analyze their results. This fourth edition has been updated and a new chapter on Monte Carlo simulation of quantum-mechanical problems has been added. To help students in their work a special web server has been installed to host programs and discussion groups (http://wwwcp.tphys.uni-heidelberg.de). Prof. Binder was the winner of the Berni J. Alder CECAM Award for Computational Physics 2001.
Monte Carlo simulation of laser attenuation characteristics in fog
NASA Astrophysics Data System (ADS)
Wang, Hong-Xia; Sun, Chao; Zhu, You-zhang; Sun, Hong-hui; Li, Pan-shi
2011-06-01
Based on the Mie scattering theory and the gamma size distribution model, the scattering extinction parameter of spherical fog-drop is calculated. For the transmission attenuation of the laser in the fog, a Monte Carlo simulation model is established, and the impact of attenuation ratio on visibility and field angle is computed and analysed using the program developed by MATLAB language. The results of the Monte Carlo method in this paper are compared with the results of single scattering method. The results show that the influence of multiple scattering need to be considered when the visibility is low, and single scattering calculations have larger errors. The phenomenon of multiple scattering can be interpreted more better when the Monte Carlo is used to calculate the attenuation ratio of the laser transmitting in the fog.
Classical Perturbation Theory for Monte Carlo Studies of System Reliability
Lewins, Jeffrey D.
2001-03-15
A variational principle for a Markov system allows the derivation of perturbation theory for models of system reliability, with prospects of extension to generalized Markov processes of a wide nature. It is envisaged that Monte Carlo or stochastic simulation will supply the trial functions for such a treatment, which obviates the standard difficulties of direct analog Monte Carlo perturbation studies. The development is given in the specific mode for first- and second-order theory, using an example with known analytical solutions. The adjoint equation is identified with the importance function and a discussion given as to how both the forward and backward (adjoint) fields can be obtained from a single Monte Carlo study, with similar interpretations for the additional functions required by second-order theory. Generalized Markov models with age-dependence are identified as coming into the scope of this perturbation theory.
BACKWARD AND FORWARD MONTE CARLO METHOD IN POLARIZED RADIATIVE TRANSFER
Yong, Huang; Guo-Dong, Shi; Ke-Yong, Zhu
2016-03-20
In general, the Stocks vector cannot be calculated in reverse in the vector radiative transfer. This paper presents a novel backward and forward Monte Carlo simulation strategy to study the vector radiative transfer in the participated medium. A backward Monte Carlo process is used to calculate the ray trajectory and the endpoint of the ray. The Stocks vector is carried out by a forward Monte Carlo process. A one-dimensional graded index semi-transparent medium was presented as the physical model and the thermal emission consideration of polarization was studied in the medium. The solution process to non-scattering, isotropic scattering, and the anisotropic scattering medium, respectively, is discussed. The influence of the optical thickness and albedo on the Stocks vector are studied. The results show that the U, V-components of the apparent Stocks vector are very small, but the Q-component of the apparent Stocks vector is relatively larger, which cannot be ignored.
Tool for Rapid Analysis of Monte Carlo Simulations
NASA Technical Reports Server (NTRS)
Restrepo, Carolina; McCall, Kurt E.; Hurtado, John E.
2011-01-01
Designing a spacecraft, or any other complex engineering system, requires extensive simulation and analysis work. Oftentimes, the large amounts of simulation data generated are very di cult and time consuming to analyze, with the added risk of overlooking potentially critical problems in the design. The authors have developed a generic data analysis tool that can quickly sort through large data sets and point an analyst to the areas in the data set that cause specific types of failures. The Tool for Rapid Analysis of Monte Carlo simulations (TRAM) has been used in recent design and analysis work for the Orion vehicle, greatly decreasing the time it takes to evaluate performance requirements. A previous version of this tool was developed to automatically identify driving design variables in Monte Carlo data sets. This paper describes a new, parallel version, of TRAM implemented on a graphical processing unit, and presents analysis results for NASA's Orion Monte Carlo data to demonstrate its capabilities.
Monte Carlo tests of the ELIPGRID-PC algorithm
Davidson, J.R.
1995-04-01
The standard tool for calculating the probability of detecting pockets of contamination called hot spots has been the ELIPGRID computer code of Singer and Wickman. The ELIPGRID-PC program has recently made this algorithm available for an IBM{reg_sign} PC. However, no known independent validation of the ELIPGRID algorithm exists. This document describes a Monte Carlo simulation-based validation of a modified version of the ELIPGRID-PC code. The modified ELIPGRID-PC code is shown to match Monte Carlo-calculated hot-spot detection probabilities to within {plus_minus}0.5% for 319 out of 320 test cases. The one exception, a very thin elliptical hot spot located within a rectangular sampling grid, differed from the Monte Carlo-calculated probability by about 1%. These results provide confidence in the ability of the modified ELIPGRID-PC code to accurately predict hot-spot detection probabilities within an acceptable range of error.
SPQR: a Monte Carlo reactor kinetics code. [LMFBR
Cramer, S.N.; Dodds, H.L.
1980-02-01
The SPQR Monte Carlo code has been developed to analyze fast reactor core accident problems where conventional methods are considered inadequate. The code is based on the adiabatic approximation of the quasi-static method. This initial version contains no automatic material motion or feedback. An existing Monte Carlo code is used to calculate the shape functions and the integral quantities needed in the kinetics module. Several sample problems have been devised and analyzed. Due to the large statistical uncertainty associated with the calculation of reactivity in accident simulations, the results, especially at later times, differ greatly from deterministic methods. It was also found that in large uncoupled systems, the Monte Carlo method has difficulty in handling asymmetric perturbations.
Photon beam description in PEREGRINE for Monte Carlo dose calculations
Cox, L. J., LLNL
1997-03-04
Goal of PEREGRINE is to provide capability for accurate, fast Monte Carlo calculation of radiation therapy dose distributions for routine clinical use and for research into efficacy of improved dose calculation. An accurate, efficient method of describing and sampling radiation sources is needed, and a simple, flexible solution is provided. The teletherapy source package for PEREGRINE, coupled with state-of-the-art Monte Carlo simulations of treatment heads, makes it possible to describe any teletherapy photon beam to the precision needed for highly accurate Monte Carlo dose calculations in complex clinical configurations that use standard patient modifiers such as collimator jaws, wedges, blocks, and/or multi-leaf collimators. Generic beam descriptions for a class of treatment machines can readily be adjusted to yield dose calculation to match specific clinical sites.
Implementation of Monte Carlo Simulations for the Gamma Knife System
NASA Astrophysics Data System (ADS)
Xiong, W.; Huang, D.; Lee, L.; Feng, J.; Morris, K.; Calugaru, E.; Burman, C.; Li, J.; Ma, C.-M.
2007-06-01
Currently the Gamma Knife system is accompanied with a treatment planning system, Leksell GammaPlan (LGP) which is a standard, computer-based treatment planning system for Gamma Knife radiosurgery. In LGP, the dose calculation algorithm does not consider the scatter dose contributions and the inhomogeneity effect due to the skull and air cavities. To improve the dose calculation accuracy, Monte Carlo simulations have been implemented for the Gamma Knife planning system. In this work, the 201 Cobalt-60 sources in the Gamma Knife unit are considered to have the same activity. Each Cobalt-60 source is contained in a cylindric stainless steel capsule. The particle phase space information is stored in four beam data files, which are collected in the inner sides of the 4 treatment helmets, after the Cobalt beam passes through the stationary and helmet collimators. Patient geometries are rebuilt from patient CT data. Twenty two Patients are included in the Monte Carlo simulation for this study. The dose is calculated using Monte Carlo in both homogenous and inhomogeneous geometries with identical beam parameters. To investigate the attenuation effect of the skull bone the dose in a 16cm diameter spherical QA phantom is measured with and without a 1.5mm Lead-covering and also simulated using Monte Carlo. The dose ratios with and without the 1.5mm Lead-covering are 89.8% based on measurements and 89.2% according to Monte Carlo for a 18mm-collimator Helmet. For patient geometries, the Monte Carlo results show that although the relative isodose lines remain almost the same with and without inhomogeneity corrections, the difference in the absolute dose is clinically significant. The average inhomogeneity correction is (3.9 ± 0.90) % for the 22 patients investigated. These results suggest that the inhomogeneity effect should be considered in the dose calculation for Gamma Knife treatment planning.
Parallel Monte Carlo Simulation for control system design
NASA Technical Reports Server (NTRS)
Schubert, Wolfgang M.
1995-01-01
The research during the 1993/94 academic year addressed the design of parallel algorithms for stochastic robustness synthesis (SRS). SRS uses Monte Carlo simulation to compute probabilities of system instability and other design-metric violations. The probabilities form a cost function which is used by a genetic algorithm (GA). The GA searches for the stochastic optimal controller. The existing sequential algorithm was analyzed and modified to execute in a distributed environment. For this, parallel approaches to Monte Carlo simulation and genetic algorithms were investigated. Initial empirical results are available for the KSR1.
A review of best practices for Monte Carlo criticality calculations
Brown, Forrest B
2009-01-01
Monte Carlo methods have been used to compute k{sub eff} and the fundamental mode eigenfunction of critical systems since the 1950s. While such calculations have become routine using standard codes such as MCNP and SCALE/KENO, there still remain 3 concerns that must be addressed to perform calculations correctly: convergence of k{sub eff} and the fission distribution, bias in k{sub eff} and tally results, and bias in statistics on tally results. This paper provides a review of the fundamental problems inherent in Monte Carlo criticality calculations. To provide guidance to practitioners, suggested best practices for avoiding these problems are discussed and illustrated by examples.
Monte Carlo Simulations of Phosphate Polyhedron Connectivity in Glasses
ALAM,TODD M.
1999-12-21
Monte Carlo simulations of phosphate tetrahedron connectivity distributions in alkali and alkaline earth phosphate glasses are reported. By utilizing a discrete bond model, the distribution of next-nearest neighbor connectivities between phosphate polyhedron for random, alternating and clustering bonding scenarios was evaluated as a function of the relative bond energy difference. The simulated distributions are compared to experimentally observed connectivities reported for solid-state two-dimensional exchange and double-quantum NMR experiments of phosphate glasses. These Monte Carlo simulations demonstrate that the polyhedron connectivity is best described by a random distribution in lithium phosphate and calcium phosphate glasses.
PEPSI — a Monte Carlo generator for polarized leptoproduction
NASA Astrophysics Data System (ADS)
Mankiewicz, L.; Schäfer, A.; Veltri, M.
1992-09-01
We describe PEPSI (Polarized Electron Proton Scattering Interactions), a Monte Carlo program for polarized deep inelastic leptoproduction mediated by electromagnetic interaction, and explain how to use it. The code is a modification of the LEPTO 4.3 Lund Monte Carlo for unpolarized scattering. The hard virtual gamma-parton scattering is generated according to the polarization-dependent QCD cross-section of the first order in α S. PEPSI requires the standard polarization-independent JETSET routines to simulate the fragmentation into final hadrons.
A Monte Carlo method for combined segregation and linkage analysis
Guo, S.W. ); Thompson, E.A. )
1992-11-01
The authors introduce a Monte Carlo approach to combined segregation and linkage analysis of a quantitative trait observed in an extended pedigree. In conjunction with the Monte Carlo method of likelihood-ratio evaluation proposed by Thompson and Guo, the method provides for estimation and hypothesis testing. The greatest attraction of this approach is its ability to handle complex genetic models and large pedigrees. Two examples illustrate the practicality of the method. One is of simulated data on a large pedigree; the other is a reanalysis of published data previously analyzed by other methods. 40 refs, 5 figs., 5 tabs.
Markov chain Monte Carlo linkage analysis of complex quantitative phenotypes.
Hinrichs, A; Reich, T
2001-01-01
We report a Markov chain Monte Carlo analysis of the five simulated quantitative traits in Genetic Analysis Workshop 12 using the Loki software. Our objectives were to determine the efficacy of the Markov chain Monte Carlo method and to test a new scoring technique. Our initial blind analysis, on replicate 42 (the "best replicate") successfully detected four out of the five disease loci and found no false positives. A power analysis shows that the software could usually detect 4 of the 10 trait/gene combinations at an empirical point-wise p-value of 1.5 x 10(-4).
Novel Quantum Monte Carlo Approaches for Quantum Liquids
NASA Astrophysics Data System (ADS)
Rubenstein, Brenda M.
Quantum Monte Carlo methods are a powerful suite of techniques for solving the quantum many-body problem. By using random numbers to stochastically sample quantum properties, QMC methods are capable of studying low-temperature quantum systems well beyond the reach of conventional deterministic techniques. QMC techniques have likewise been indispensible tools for augmenting our current knowledge of superfluidity and superconductivity. In this thesis, I present two new quantum Monte Carlo techniques, the Monte Carlo Power Method and Bose-Fermi Auxiliary-Field Quantum Monte Carlo, and apply previously developed Path Integral Monte Carlo methods to explore two new phases of quantum hard spheres and hydrogen. I lay the foundation for a subsequent description of my research by first reviewing the physics of quantum liquids in Chapter One and the mathematics behind Quantum Monte Carlo algorithms in Chapter Two. I then discuss the Monte Carlo Power Method, a stochastic way of computing the first several extremal eigenvalues of a matrix too memory-intensive to be stored and therefore diagonalized. As an illustration of the technique, I demonstrate how it can be used to determine the second eigenvalues of the transition matrices of several popular Monte Carlo algorithms. This information may be used to quantify how rapidly a Monte Carlo algorithm is converging to the equilibrium probability distribution it is sampling. I next present the Bose-Fermi Auxiliary-Field Quantum Monte Carlo algorithm. This algorithm generalizes the well-known Auxiliary-Field Quantum Monte Carlo algorithm for fermions to bosons and Bose-Fermi mixtures. Despite some shortcomings, the Bose-Fermi Auxiliary-Field Quantum Monte Carlo algorithm represents the first exact technique capable of studying Bose-Fermi mixtures of any size in any dimension. In Chapter Six, I describe a new Constant Stress Path Integral Monte Carlo algorithm for the study of quantum mechanical systems under high pressures. While
Complexity of Monte Carlo and deterministic dose-calculation methods.
Börgers, C
1998-03-01
Grid-based deterministic dose-calculation methods for radiotherapy planning require the use of six-dimensional phase space grids. Because of the large number of phase space dimensions, a growing number of medical physicists appear to believe that grid-based deterministic dose-calculation methods are not competitive with Monte Carlo methods. We argue that this conclusion may be premature. Our results do suggest, however, that finite difference or finite element schemes with orders of accuracy greater than one will probably be needed if such methods are to compete well with Monte Carlo methods for dose calculations.
Hybrid Monte Carlo/deterministic methods for radiation shielding problems
NASA Astrophysics Data System (ADS)
Becker, Troy L.
For the past few decades, the most common type of deep-penetration (shielding) problem simulated using Monte Carlo methods has been the source-detector problem, in which a response is calculated at a single location in space. Traditionally, the nonanalog Monte Carlo methods used to solve these problems have required significant user input to generate and sufficiently optimize the biasing parameters necessary to obtain a statistically reliable solution. It has been demonstrated that this laborious task can be replaced by automated processes that rely on a deterministic adjoint solution to set the biasing parameters---the so-called hybrid methods. The increase in computational power over recent years has also led to interest in obtaining the solution in a region of space much larger than a point detector. In this thesis, we propose two methods for solving problems ranging from source-detector problems to more global calculations---weight windows and the Transform approach. These techniques employ sonic of the same biasing elements that have been used previously; however, the fundamental difference is that here the biasing techniques are used as elements of a comprehensive tool set to distribute Monte Carlo particles in a user-specified way. The weight window achieves the user-specified Monte Carlo particle distribution by imposing a particular weight window on the system, without altering the particle physics. The Transform approach introduces a transform into the neutron transport equation, which results in a complete modification of the particle physics to produce the user-specified Monte Carlo distribution. These methods are tested in a three-dimensional multigroup Monte Carlo code. For a basic shielding problem and a more realistic one, these methods adequately solved source-detector problems and more global calculations. Furthermore, they confirmed that theoretical Monte Carlo particle distributions correspond to the simulated ones, implying that these methods
Parton distribution functions in Monte Carlo factorisation scheme
NASA Astrophysics Data System (ADS)
Jadach, S.; Płaczek, W.; Sapeta, S.; Siódmok, A.; Skrzypek, M.
2016-12-01
A next step in development of the KrkNLO method of including complete NLO QCD corrections to hard processes in a LO parton-shower Monte Carlo is presented. It consists of a generalisation of the method, previously used for the Drell-Yan process, to Higgs-boson production. This extension is accompanied with the complete description of parton distribution functions in a dedicated, Monte Carlo factorisation scheme, applicable to any process of production of one or more colour-neutral particles in hadron-hadron collisions.
Towards Fast, Scalable Hard Particle Monte Carlo Simulations on GPUs
NASA Astrophysics Data System (ADS)
Anderson, Joshua A.; Irrgang, M. Eric; Glaser, Jens; Harper, Eric S.; Engel, Michael; Glotzer, Sharon C.
2014-03-01
Parallel algorithms for Monte Carlo simulations of thermodynamic ensembles of particles have received little attention because of the inherent serial nature of the statistical sampling. We discuss the implementation of Monte Carlo for arbitrary hard shapes in HOOMD-blue, a GPU-accelerated particle simulation tool, to enable million particle simulations in a field where thousands is the norm. In this talk, we discuss our progress on basic parallel algorithms, optimizations that maximize GPU performance, and communication patterns for scaling to multiple GPUs. Research applications include colloidal assembly and other uses in materials design, biological aggregation, and operations research.
Kinetic Monte Carlo method applied to nucleic acid hairpin folding.
Sauerwine, Ben; Widom, Michael
2011-12-01
Kinetic Monte Carlo on coarse-grained systems, such as nucleic acid secondary structure, is advantageous for being able to access behavior at long time scales, even minutes or hours. Transition rates between coarse-grained states depend upon intermediate barriers, which are not directly simulated. We propose an Arrhenius rate model and an intermediate energy model that incorporates the effects of the barrier between simulated states without enlarging the state space itself. Applying our Arrhenius rate model to DNA hairpin folding, we demonstrate improved agreement with experiment compared to the usual kinetic Monte Carlo model. Further improvement results from including rigidity of single-stranded stacking.
NASA Astrophysics Data System (ADS)
Schabel, Matthias C.; DiBella, Edward V. R.; Jensen, Randy L.; Salzman, Karen L.
2010-08-01
Accurate quantification of pharmacokinetic model parameters in tracer kinetic imaging experiments requires correspondingly accurate determination of the arterial input function (AIF). Despite significant effort expended on methods of directly measuring patient-specific AIFs in modalities as diverse as dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), dynamic positron emission tomography (PET), and perfusion computed tomography (CT), fundamental and technical difficulties have made consistent and reliable achievement of that goal elusive. Here, we validate a new algorithm for AIF determination, the Monte Carlo blind estimation (MCBE) method (which is described in detail and characterized by extensive simulations in a companion paper), by comparing AIFs measured in DCE-MRI studies of eight brain tumor patients with results of blind estimation. Blind AIFs calculated with the MCBE method using a pool of concentration-time curves from a region of normal brain tissue were found to be quite similar to the measured AIFs, with statistically significant decreases in fit residuals observed in six of eight patients. Biases between the blind and measured pharmacokinetic parameters were the dominant source of error. Averaged over all eight patients, the mean biases were +7% in K trans, 0% in kep, -11% in vp and +10% in ve. Corresponding uncertainties (median absolute deviation from the best fit line) were 0.0043 min-1 in K trans, 0.0491 min-1 in kep, 0.29% in vp and 0.45% in ve. The use of a published population-averaged AIF resulted in larger mean biases in three of the four parameters (-23% in K trans, -22% in kep, -63% in vp), with the bias in ve unchanged, and led to larger uncertainties in all four parameters (0.0083 min-1 in K trans, 0.1038 min-1 in kep, 0.31% in vp and 0.95% in ve). When blind AIFs were calculated from a region of tumor tissue, statistically significant decreases in fit residuals were observed in all eight patients despite larger
NASA Astrophysics Data System (ADS)
Antipov, Andrey E.; Dong, Qiaoyuan; Kleinhenz, Joseph; Cohen, Guy; Gull, Emanuel
2017-02-01
We generalize the recently developed inchworm quantum Monte Carlo method to the full Keldysh contour with forward, backward, and equilibrium branches to describe the dynamics of strongly correlated impurity problems with time-dependent parameters. We introduce a method to compute Green's functions, spectral functions, and currents for inchworm Monte Carlo and show how systematic error assessments in real time can be obtained. We then illustrate the capabilities of the algorithm with a study of the behavior of quantum impurities after an instantaneous voltage quench from a thermal equilibrium state.
Monte Carlo Modeling of Thin Film Deposition: Factors that Influence 3D Islands
Gilmer, G H; Dalla Torre, J; Baumann, F H; Diaz de la Rubia, T
2002-01-04
In this paper we discuss the use of atomistic Monte Carlo simulations to predict film microstructure evolution. We discuss physical vapor deposition, and are primarily concerned with films that are formed by the nucleation and coalescence of 3D islands. Multi-scale modeling is used in the sense that information obtained from molecular dynamics and first principles calculations provide atomic interaction energies, surface and grain boundary properties and diffusion rates for use in the Monte Carlo model. In this paper, we discuss some fundamental issues associated with thin film formation, together with an assessment of the sensitivity of the film morphology to the deposition conditions and materials properties.
Cluster Monte Carlo and numerical mean field analysis for the water liquid-liquid phase transition
NASA Astrophysics Data System (ADS)
Mazza, Marco G.; Stokely, Kevin; Strekalova, Elena G.; Stanley, H. Eugene; Franzese, Giancarlo
2009-04-01
Using Wolff's cluster Monte Carlo simulations and numerical minimization within a mean field approach, we study the low temperature phase diagram of water, adopting a cell model that reproduces the known properties of water in its fluid phases. Both methods allow us to study the thermodynamic behavior of water at temperatures, where other numerical approaches - both Monte Carlo and molecular dynamics - are seriously hampered by the large increase of the correlation times. The cluster algorithm also allows us to emphasize that the liquid-liquid phase transition corresponds to the percolation transition of tetrahedrally ordered water molecules.
Quantum Monte Carlo Methods for First Principles Simulation of Liquid Water
ERIC Educational Resources Information Center
Gergely, John Robert
2009-01-01
Obtaining an accurate microscopic description of water structure and dynamics is of great interest to molecular biology researchers and in the physics and quantum chemistry simulation communities. This dissertation describes efforts to apply quantum Monte Carlo methods to this problem with the goal of making progress toward a fully "ab initio"…
Monte Carlo Analysis of Quantum Transport and Fluctuations in Semiconductors.
1986-02-18
methods to quantum transport within the Liouville formulation. The second part concerns with fluctuations of carrier velocities and energies both in...interactions) on the transport properties. Keywords: Monte Carlo; Charge Transport; Quantum Transport ; Fluctuations; Semiconductor Physics; Master Equation...The present report contains technical matter related to the research performed on two different subjects. The first part concerns with quantum
Monte Carlo simulation by computer for life-cycle costing
NASA Technical Reports Server (NTRS)
Gralow, F. H.; Larson, W. J.
1969-01-01
Prediction of behavior and support requirements during the entire life cycle of a system enables accurate cost estimates by using the Monte Carlo simulation by computer. The system reduces the ultimate cost to the procuring agency because it takes into consideration the costs of initial procurement, operation, and maintenance.
MODELING LEACHING OF VIRUSES BY THE MONTE CARLO METHOD
A predictive screening model was developed for fate and transport
of viruses in the unsaturated zone. A database of input parameters
allowed Monte Carlo analysis with the model. The resulting kernel
densities of predicted attenuation during percolation indicated very ...
The Metropolis Monte Carlo Method in Statistical Physics
NASA Astrophysics Data System (ADS)
Landau, David P.
2003-11-01
A brief overview is given of some of the advances in statistical physics that have been made using the Metropolis Monte Carlo method. By complementing theory and experiment, these have increased our understanding of phase transitions and other phenomena in condensed matter systems. A brief description of a new method, commonly known as "Wang-Landau sampling," will also be presented.
Quantum Monte Carlo simulation of topological phase transitions
NASA Astrophysics Data System (ADS)
Yamamoto, Arata; Kimura, Taro
2016-12-01
We study the electron-electron interaction effects on topological phase transitions by the ab initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.
The Use of Monte Carlo Techniques to Teach Probability.
ERIC Educational Resources Information Center
Newell, G. J.; MacFarlane, J. D.
1985-01-01
Presents sports-oriented examples (cricket and football) in which Monte Carlo methods are used on microcomputers to teach probability concepts. Both examples include computer programs (with listings) which utilize the microcomputer's random number generator. Instructional strategies, with further challenges to help students understand the role of…
Error estimations and their biases in Monte Carlo eigenvalue calculations
Ueki, Taro; Mori, Takamasa; Nakagawa, Masayuki
1997-01-01
In the Monte Carlo eigenvalue calculation of neutron transport, the eigenvalue is calculated as the average of multiplication factors from cycles, which are called the cycle k{sub eff}`s. Biases in the estimators of the variance and intercycle covariances in Monte Carlo eigenvalue calculations are analyzed. The relations among the real and apparent values of variances and intercycle covariances are derived, where real refers to a true value that is calculated from independently repeated Monte Carlo runs and apparent refers to the expected value of estimates from a single Monte Carlo run. Next, iterative methods based on the foregoing relations are proposed to estimate the standard deviation of the eigenvalue. The methods work well for the cases in which the ratios of the real to apparent values of variances are between 1.4 and 3.1. Even in the case where the foregoing ratio is >5, >70% of the standard deviation estimates fall within 40% from the true value.
Diffuse photon density wave measurements and Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Kuzmin, Vladimir L.; Neidrauer, Michael T.; Diaz, David; Zubkov, Leonid A.
2015-10-01
Diffuse photon density wave (DPDW) methodology is widely used in a number of biomedical applications. Here, we present results of Monte Carlo simulations that employ an effective numerical procedure based upon a description of radiative transfer in terms of the Bethe-Salpeter equation. A multifrequency noncontact DPDW system was used to measure aqueous solutions of intralipid at a wide range of source-detector separation distances, at which the diffusion approximation of the radiative transfer equation is generally considered to be invalid. We find that the signal-noise ratio is larger for the considered algorithm in comparison with the conventional Monte Carlo approach. Experimental data are compared to the Monte Carlo simulations using several values of scattering anisotropy and to the diffusion approximation. Both the Monte Carlo simulations and diffusion approximation were in very good agreement with the experimental data for a wide range of source-detector separations. In addition, measurements with different wavelengths were performed to estimate the size and scattering anisotropy of scatterers.
Calculating coherent pair production with Monte Carlo methods
Bottcher, C.; Strayer, M.R.
1989-01-01
We discuss calculations of the coherent electromagnetic pair production in ultra-relativistic hadron collisions. This type of production, in lowest order, is obtained from three diagrams which contain two virtual photons. We discuss simple Monte Carlo methods for evaluating these classes of diagrams without recourse to involved algebraic reduction schemes. 19 refs., 11 figs.
A Monte Carlo simulation of a supersaturated sodium chloride solution
NASA Astrophysics Data System (ADS)
Schwendinger, Michael G.; Rode, Bernd M.
1989-03-01
A simulation of a supersaturated sodium chloride solution with the Monte Carlo statistical thermodynamic method is reported. The water-water interactions are described by the Matsuoka-Clementi-Yoshimine (MCY) potential, while the ion-water potentials have been derived from ab initio calculations. Structural features of the solution have been evaluated, special interest being focused on possible precursors of nucleation.
Monte Carlo capabilities of the SCALE code system
Rearden, Bradley T.; Petrie, Jr., Lester M.; Peplow, Douglas E.; ...
2014-09-12
SCALE is a broadly used suite of tools for nuclear systems modeling and simulation that provides comprehensive, verified and validated, user-friendly capabilities for criticality safety, reactor physics, radiation shielding, and sensitivity and uncertainty analysis. For more than 30 years, regulators, licensees, and research institutions around the world have used SCALE for nuclear safety analysis and design. SCALE provides a “plug-and-play” framework that includes three deterministic and three Monte Carlo radiation transport solvers that can be selected based on the desired solution, including hybrid deterministic/Monte Carlo simulations. SCALE includes the latest nuclear data libraries for continuous-energy and multigroup radiation transport asmore » well as activation, depletion, and decay calculations. SCALE’s graphical user interfaces assist with accurate system modeling, visualization, and convenient access to desired results. SCALE 6.2 will provide several new capabilities and significant improvements in many existing features, especially with expanded continuous-energy Monte Carlo capabilities for criticality safety, shielding, depletion, and sensitivity and uncertainty analysis. Finally, an overview of the Monte Carlo capabilities of SCALE is provided here, with emphasis on new features for SCALE 6.2.« less
Monte Carlo capabilities of the SCALE code system
Rearden, Bradley T.; Petrie, Jr., Lester M.; Peplow, Douglas E.; Bekar, Kursat B.; Wiarda, Dorothea; Celik, Cihangir; Perfetti, Christopher M.; Ibrahim, Ahmad M.; Hart, S. W. D.; Dunn, Michael E.; Marshall, William J.
2014-09-12
SCALE is a broadly used suite of tools for nuclear systems modeling and simulation that provides comprehensive, verified and validated, user-friendly capabilities for criticality safety, reactor physics, radiation shielding, and sensitivity and uncertainty analysis. For more than 30 years, regulators, licensees, and research institutions around the world have used SCALE for nuclear safety analysis and design. SCALE provides a “plug-and-play” framework that includes three deterministic and three Monte Carlo radiation transport solvers that can be selected based on the desired solution, including hybrid deterministic/Monte Carlo simulations. SCALE includes the latest nuclear data libraries for continuous-energy and multigroup radiation transport as well as activation, depletion, and decay calculations. SCALE’s graphical user interfaces assist with accurate system modeling, visualization, and convenient access to desired results. SCALE 6.2 will provide several new capabilities and significant improvements in many existing features, especially with expanded continuous-energy Monte Carlo capabilities for criticality safety, shielding, depletion, and sensitivity and uncertainty analysis. Finally, an overview of the Monte Carlo capabilities of SCALE is provided here, with emphasis on new features for SCALE 6.2.
CMS Monte Carlo production operations in a distributed computing environment
Mohapatra, A.; Lazaridis, C.; Hernandez, J.M.; Caballero, J.; Hof, C.; Kalinin, S.; Flossdorf, A.; Abbrescia, M.; De Filippis, N.; Donvito, G.; Maggi, G.; /Bari U. /INFN, Bari /INFN, Pisa /Vrije U., Brussels /Brussels U. /Imperial Coll., London /CERN /Princeton U. /Fermilab
2008-01-01
Monte Carlo production for the CMS experiment is carried out in a distributed computing environment; the goal of producing 30M simulated events per month in the first half of 2007 has been reached. A brief overview of the production operations and statistics is presented.
Bayesian internal dosimetry calculations using Markov Chain Monte Carlo.
Miller, G; Martz, H F; Little, T T; Guilmette, R
2002-01-01
A new numerical method for solving the inverse problem of internal dosimetry is described. The new method uses Markov Chain Monte Carlo and the Metropolis algorithm. Multiple intake amounts, biokinetic types, and times of intake are determined from bioassay data by integrating over the Bayesian posterior distribution. The method appears definitive, but its application requires a large amount of computing time.
Play It Again: Teaching Statistics with Monte Carlo Simulation
ERIC Educational Resources Information Center
Sigal, Matthew J.; Chalmers, R. Philip
2016-01-01
Monte Carlo simulations (MCSs) provide important information about statistical phenomena that would be impossible to assess otherwise. This article introduces MCS methods and their applications to research and statistical pedagogy using a novel software package for the R Project for Statistical Computing constructed to lessen the often steep…
Observations on variational and projector Monte Carlo methods.
Umrigar, C J
2015-10-28
Variational Monte Carlo and various projector Monte Carlo (PMC) methods are presented in a unified manner. Similarities and differences between the methods and choices made in designing the methods are discussed. Both methods where the Monte Carlo walk is performed in a discrete space and methods where it is performed in a continuous space are considered. It is pointed out that the usual prescription for importance sampling may not be advantageous depending on the particular quantum Monte Carlo method used and the observables of interest, so alternate prescriptions are presented. The nature of the sign problem is discussed for various versions of PMC methods. A prescription for an exact PMC method in real space, i.e., a method that does not make a fixed-node or similar approximation and does not have a finite basis error, is presented. This method is likely to be practical for systems with a small number of electrons. Approximate PMC methods that are applicable to larger systems and go beyond the fixed-node approximation are also discussed.
Automated Monte Carlo Simulation of Proton Therapy Treatment Plans.
Verburg, Joost Mathijs; Grassberger, Clemens; Dowdell, Stephen; Schuemann, Jan; Seco, Joao; Paganetti, Harald
2016-12-01
Simulations of clinical proton radiotherapy treatment plans using general purpose Monte Carlo codes have been proven to be a valuable tool for basic research and clinical studies. They have been used to benchmark dose calculation methods, to study radiobiological effects, and to develop new technologies such as in vivo range verification methods. Advancements in the availability of computational power have made it feasible to perform such simulations on large sets of patient data, resulting in a need for automated and consistent simulations. A framework called MCAUTO was developed for this purpose. Both passive scattering and pencil beam scanning delivery are supported. The code handles the data exchange between the treatment planning system and the Monte Carlo system, which requires not only transfer of plan and imaging information but also translation of institutional procedures, such as output factor definitions. Simulations are performed on a high-performance computing infrastructure. The simulation methods were designed to use the full capabilities of Monte Carlo physics models, while also ensuring consistency in the approximations that are common to both pencil beam and Monte Carlo dose calculations. Although some methods need to be tailored to institutional planning systems and procedures, the described procedures show a general road map that can be easily translated to other systems.
Monte Carlo method for magnetic impurities in metals
NASA Technical Reports Server (NTRS)
Hirsch, J. E.; Fye, R. M.
1986-01-01
The paper discusses a Monte Carlo algorithm to study properties of dilute magnetic alloys; the method can treat a small number of magnetic impurities interacting wiith the conduction electrons in a metal. Results for the susceptibility of a single Anderson impurity in the symmetric case show the expected universal behavior at low temperatures. Some results for two Anderson impurities are also discussed.
An Overview of the Monte Carlo Methods, Codes, & Applications Group
Trahan, Travis John
2016-08-30
This report sketches the work of the Group to deliver first-principle Monte Carlo methods, production quality codes, and radiation transport-based computational and experimental assessments using the codes MCNP and MCATK for such applications as criticality safety, non-proliferation, nuclear energy, nuclear threat reduction and response, radiation detection and measurement, radiation health protection, and stockpile stewardship.
Parallel Monte Carlo simulation of multilattice thin film growth
NASA Astrophysics Data System (ADS)
Shu, J. W.; Lu, Qin; Wong, Wai-on; Huang, Han-chen
2001-07-01
This paper describe a new parallel algorithm for the multi-lattice Monte Carlo atomistic simulator for thin film deposition (ADEPT), implemented on parallel computer using the PVM (Parallel Virtual Machine) message passing library. This parallel algorithm is based on domain decomposition with overlapping and asynchronous communication. Multiple lattices are represented by a single reference lattice through one-to-one mappings, with resulting computational demands being comparable to those in the single-lattice Monte Carlo model. Asynchronous communication and domain overlapping techniques are used to reduce the waiting time and communication time among parallel processors. Results show that the algorithm is highly efficient with large number of processors. The algorithm was implemented on a parallel machine with 50 processors, and it is suitable for parallel Monte Carlo simulation of thin film growth with either a distributed memory parallel computer or a shared memory machine with message passing libraries. In this paper, the significant communication time in parallel MC simulation of thin film growth is effectively reduced by adopting domain decomposition with overlapping between sub-domains and asynchronous communication among processors. The overhead of communication does not increase evidently and speedup shows an ascending tendency when the number of processor increases. A near linear increase in computing speed was achieved with number of processors increases and there is no theoretical limit on the number of processors to be used. The techniques developed in this work are also suitable for the implementation of the Monte Carlo code on other parallel systems.
Monte Carlo methods for multidimensional integration for European option pricing
NASA Astrophysics Data System (ADS)
Todorov, V.; Dimov, I. T.
2016-10-01
In this paper, we illustrate examples of highly accurate Monte Carlo and quasi-Monte Carlo methods for multiple integrals related to the evaluation of European style options. The idea is that the value of the option is formulated in terms of the expectation of some random variable; then the average of independent samples of this random variable is used to estimate the value of the option. First we obtain an integral representation for the value of the option using the risk neutral valuation formula. Then with an appropriations change of the constants we obtain a multidimensional integral over the unit hypercube of the corresponding dimensionality. Then we compare a specific type of lattice rules over one of the best low discrepancy sequence of Sobol for numerical integration. Quasi-Monte Carlo methods are compared with Adaptive and Crude Monte Carlo techniques for solving the problem. The four approaches are completely different thus it is a question of interest to know which one of them outperforms the other for evaluation multidimensional integrals in finance. Some of the advantages and disadvantages of the developed algorithms are discussed.
Monte Carlo study of the atmospheric spread function
NASA Technical Reports Server (NTRS)
Pearce, W. A.
1986-01-01
Monte Carlo radiative transfer simulations are used to study the atmospheric spread function appropriate to satellite-based sensing of the earth's surface. The parameters which are explored include the nadir angle of view, the size distribution of the atmospheric aerosol, and the aerosol vertical profile.
Diffuse photon density wave measurements and Monte Carlo simulations.
Kuzmin, Vladimir L; Neidrauer, Michael T; Diaz, David; Zubkov, Leonid A
2015-10-01
Diffuse photon density wave (DPDW) methodology is widely used in a number of biomedical applications. Here, we present results of Monte Carlo simulations that employ an effective numerical procedure based upon a description of radiative transfer in terms of the Bethe–Salpeter equation. A multifrequency noncontact DPDW system was used to measure aqueous solutions of intralipid at a wide range of source–detector separation distances, at which the diffusion approximation of the radiative transfer equation is generally considered to be invalid. We find that the signal–noise ratio is larger for the considered algorithm in comparison with the conventional Monte Carlo approach. Experimental data are compared to the Monte Carlo simulations using several values of scattering anisotropy and to the diffusion approximation. Both the Monte Carlo simulations and diffusion approximation were in very good agreement with the experimental data for a wide range of source–detector separations. In addition, measurements with different wavelengths were performed to estimate the size and scattering anisotropy of scatterers.
Monte Carlo Approach for Reliability Estimations in Generalizability Studies.
ERIC Educational Resources Information Center
Dimitrov, Dimiter M.
A Monte Carlo approach is proposed, using the Statistical Analysis System (SAS) programming language, for estimating reliability coefficients in generalizability theory studies. Test scores are generated by a probabilistic model that considers the probability for a person with a given ability score to answer an item with a given difficulty…
Testing Dependent Correlations with Nonoverlapping Variables: A Monte Carlo Simulation
ERIC Educational Resources Information Center
Silver, N. Clayton; Hittner, James B.; May, Kim
2004-01-01
The authors conducted a Monte Carlo simulation of 4 test statistics or comparing dependent correlations with no variables in common. Empirical Type 1 error rates and power estimates were determined for K. Pearson and L. N. G. Filon's (1898) z, O. J. Dunn and V. A. Clark's (1969) z, J. H. Steiger's (1980) original modification of Dunn and Clark's…
Exploring Mass Perception with Markov Chain Monte Carlo
ERIC Educational Resources Information Center
Cohen, Andrew L.; Ross, Michael G.
2009-01-01
Several previous studies have examined the ability to judge the relative mass of objects in idealized collisions. With a newly developed technique of psychological Markov chain Monte Carlo sampling (A. N. Sanborn & T. L. Griffiths, 2008), this work explores participants; perceptions of different collision mass ratios. The results reveal…
Monte Carlo Estimation of the Electric Field in Stellarators
NASA Astrophysics Data System (ADS)
Bauer, F.; Betancourt, O.; Garabedian, P.; Ng, K. C.
1986-10-01
The BETA computer codes have been developed to study ideal magnetohydrodynamic equilibrium and stability of stellarators and to calculate neoclassical transport for electrons as well as ions by the Monte Carlo method. In this paper a numerical procedure is presented to select resonant terms in the electric potential so that the distribution functions and confinement times of the ions and electrons become indistinguishable.
Impact of random numbers on parallel Monte Carlo application
Pandey, Ras B.
2002-10-22
A number of graduate students are involved at various level of research in this project. We investigate the basic issues in materials using Monte Carlo simulations with specific interest in heterogeneous materials. Attempts have been made to seek collaborations with the DOE laboratories. Specific details are given.
Improved geometry representations for Monte Carlo radiation transport.
Martin, Matthew Ryan
2004-08-01
ITS (Integrated Tiger Series) permits a state-of-the-art Monte Carlo solution of linear time-integrated coupled electron/photon radiation transport problems with or without the presence of macroscopic electric and magnetic fields of arbitrary spatial dependence. ITS allows designers to predict product performance in radiation environments.
SABRINA: an interactive solid geometry modeling program for Monte Carlo
West, J.T.
1985-01-01
SABRINA is a fully interactive three-dimensional geometry modeling program for MCNP. In SABRINA, a user interactively constructs either body geometry, or surface geometry models, and interactively debugs spatial descriptions for the resulting objects. This enhanced capability significantly reduces the effort in constructing and debugging complicated three-dimensional geometry models for Monte Carlo Analysis.
A Monte Carlo photocurrent/photoemission computer program
NASA Technical Reports Server (NTRS)
Chadsey, W. L.; Ragona, C.
1972-01-01
A Monte Carlo computer program was developed for the computation of photocurrents and photoemission in gamma (X-ray)-irradiated materials. The program was used for computation of radiation-induced surface currents on space vehicles and the computation of radiation-induced space charge environments within space vehicles.
On a full Monte Carlo approach to quantum mechanics
NASA Astrophysics Data System (ADS)
Sellier, J. M.; Dimov, I.
2016-12-01
The Monte Carlo approach to numerical problems has shown to be remarkably efficient in performing very large computational tasks since it is an embarrassingly parallel technique. Additionally, Monte Carlo methods are well known to keep performance and accuracy with the increase of dimensionality of a given problem, a rather counterintuitive peculiarity not shared by any known deterministic method. Motivated by these very peculiar and desirable computational features, in this work we depict a full Monte Carlo approach to the problem of simulating single- and many-body quantum systems by means of signed particles. In particular we introduce a stochastic technique, based on the strategy known as importance sampling, for the computation of the Wigner kernel which, so far, has represented the main bottleneck of this method (it is equivalent to the calculation of a multi-dimensional integral, a problem in which complexity is known to grow exponentially with the dimensions of the problem). The introduction of this stochastic technique for the kernel is twofold: firstly it reduces the complexity of a quantum many-body simulation from non-linear to linear, secondly it introduces an embarassingly parallel approach to this very demanding problem. To conclude, we perform concise but indicative numerical experiments which clearly illustrate how a full Monte Carlo approach to many-body quantum systems is not only possible but also advantageous. This paves the way towards practical time-dependent, first-principle simulations of relatively large quantum systems by means of affordable computational resources.
Dark Photon Monte Carlo at SeaQuest
NASA Astrophysics Data System (ADS)
Hicks, Caleb; SeaQuest/E906 Collaboration
2016-09-01
Fermi National Laboratory's E906/SeaQuest is an experiment primarily designed to study the ratio of anti-down to anti-up quarks in the nucleon quark sea as a function of Bjorken x. SeaQuest's measurement is obtained by measuring the muon pairs produced by the Drell-Yan process. The experiment can also search for muon pair vertices past the target and beam dump, which would be a signature of Dark Photon decay. It is therefore necessary to run Monte Carlo simulations to determine how a changed Z vertex affects the detection and distribution of muon pairs using SeaQuest's detectors. SeaQuest has an existing Monte Carlo program that has been used for simulations of the Drell-Yan process as well as J/psi decay and other processes. The Monte Carlo program was modified to use a fixed Z vertex when generating muon pairs. Events were then generated with varying Z vertices and the resulting simulations were then analyzed. This work is focuses on the results of the Monte Carlo simulations and the effects on Dark Photon detection. This research was supported by US DOE MENP Grant DE-FG02-03ER41243.
Parallel canonical Monte Carlo simulations through sequential updating of particles
NASA Astrophysics Data System (ADS)
O'Keeffe, C. J.; Orkoulas, G.
2009-04-01
In canonical Monte Carlo simulations, sequential updating of particles is equivalent to random updating due to particle indistinguishability. In contrast, in grand canonical Monte Carlo simulations, sequential implementation of the particle transfer steps in a dense grid of distinct points in space improves both the serial and the parallel efficiency of the simulation. The main advantage of sequential updating in parallel canonical Monte Carlo simulations is the reduction in interprocessor communication, which is usually a slow process. In this work, we propose a parallelization method for canonical Monte Carlo simulations via domain decomposition techniques and sequential updating of particles. Each domain is further divided into a middle and two outer sections. Information exchange is required after the completion of the updating of the outer regions. During the updating of the middle section, communication does not occur unless a particle moves out of this section. Results on two- and three-dimensional Lennard-Jones fluids indicate a nearly perfect improvement in parallel efficiency for large systems.
Parallel canonical Monte Carlo simulations through sequential updating of particles.
O'Keeffe, C J; Orkoulas, G
2009-04-07
In canonical Monte Carlo simulations, sequential updating of particles is equivalent to random updating due to particle indistinguishability. In contrast, in grand canonical Monte Carlo simulations, sequential implementation of the particle transfer steps in a dense grid of distinct points in space improves both the serial and the parallel efficiency of the simulation. The main advantage of sequential updating in parallel canonical Monte Carlo simulations is the reduction in interprocessor communication, which is usually a slow process. In this work, we propose a parallelization method for canonical Monte Carlo simulations via domain decomposition techniques and sequential updating of particles. Each domain is further divided into a middle and two outer sections. Information exchange is required after the completion of the updating of the outer regions. During the updating of the middle section, communication does not occur unless a particle moves out of this section. Results on two- and three-dimensional Lennard-Jones fluids indicate a nearly perfect improvement in parallel efficiency for large systems.
A Variational Monte Carlo Approach to Atomic Structure
ERIC Educational Resources Information Center
Davis, Stephen L.
2007-01-01
The practicality and usefulness of variational Monte Carlo calculations to atomic structure are demonstrated. It is found to succeed in quantitatively illustrating electron shielding, effective nuclear charge, l-dependence of the orbital energies, and singlet-tripetenergy splitting and ionization energy trends in atomic structure theory.
Determining MTF of digital detector system with Monte Carlo simulation
NASA Astrophysics Data System (ADS)
Jeong, Eun Seon; Lee, Hyung Won; Nam, Sang Hee
2005-04-01
We have designed a detector based on a-Se(amorphous Selenium) and done simulation the detector with Monte Carlo method. We will apply the cascaded linear system theory to determine the MTF for whole detector system. For direct comparison with experiment, we have simulated 139um pixel pitch and used simulated X-ray tube spectrum.
A Monte Carlo Approach for Adaptive Testing with Content Constraints
ERIC Educational Resources Information Center
Belov, Dmitry I.; Armstrong, Ronald D.; Weissman, Alexander
2008-01-01
This article presents a new algorithm for computerized adaptive testing (CAT) when content constraints are present. The algorithm is based on shadow CAT methodology to meet content constraints but applies Monte Carlo methods and provides the following advantages over shadow CAT: (a) lower maximum item exposure rates, (b) higher utilization of the…
Monte Carlo Capabilities of the SCALE Code System
NASA Astrophysics Data System (ADS)
Rearden, B. T.; Petrie, L. M.; Peplow, D. E.; Bekar, K. B.; Wiarda, D.; Celik, C.; Perfetti, C. M.; Ibrahim, A. M.; Hart, S. W. D.; Dunn, M. E.
2014-06-01
SCALE is a widely used suite of tools for nuclear systems modeling and simulation that provides comprehensive, verified and validated, user-friendly capabilities for criticality safety, reactor physics, radiation shielding, and sensitivity and uncertainty analysis. For more than 30 years, regulators, licensees, and research institutions around the world have used SCALE for nuclear safety analysis and design. SCALE provides a "plug-and-play" framework that includes three deterministic and three Monte Carlo radiation transport solvers that can be selected based on the desired solution, including hybrid deterministic/Monte Carlo simulations. SCALE includes the latest nuclear data libraries for continuous-energy and multigroup radiation transport as well as activation, depletion, and decay calculations. SCALE's graphical user interfaces assist with accurate system modeling, visualization, and convenient access to desired results. SCALE 6.2, to be released in 2014, will provide several new capabilities and significant improvements in many existing features, especially with expanded continuous-energy Monte Carlo capabilities for criticality safety, shielding, depletion, and sensitivity and uncertainty analysis. An overview of the Monte Carlo capabilities of SCALE is provided here, with emphasis on new features for SCALE 6.2.
Self-evolving atomistic kinetic Monte Carlo simulations of defects in materials
Xu, Haixuan; Beland, Laurent K.; Stoller, Roger E.; Osetskiy, Yury N.
2015-01-29
The recent development of on-the-fly atomistic kinetic Monte Carlo methods has led to an increased amount attention on the methods and their corresponding capabilities and applications. In this review, the framework and current status of Self-Evolving Atomistic Kinetic Monte Carlo (SEAKMC) are discussed. SEAKMC particularly focuses on defect interaction and evolution with atomistic details without assuming potential defect migration/interaction mechanisms and energies. The strength and limitation of using an active volume, the key concept introduced in SEAKMC, are discussed. Potential criteria for characterizing an active volume are discussed and the influence of active volume size on saddle point energies is illustrated. A procedure starting with a small active volume followed by larger active volumes was found to possess higher efficiency. Applications of SEAKMC, ranging from point defect diffusion, to complex interstitial cluster evolution, to helium interaction with tungsten surfaces, are summarized. A comparison of SEAKMC with molecular dynamics and conventional object kinetic Monte Carlo is demonstrated. Overall, SEAKMC is found to be complimentary to conventional molecular dynamics, especially when the harmonic approximation of transition state theory is accurate. However it is capable of reaching longer time scales than molecular dynamics and it can be used to systematically increase the accuracy of other methods such as object kinetic Monte Carlo. Furthermore, the challenges and potential development directions are also outlined.
Self-evolving atomistic kinetic Monte Carlo simulations of defects in materials
Xu, Haixuan; Beland, Laurent K.; Stoller, Roger E.; ...
2015-01-29
The recent development of on-the-fly atomistic kinetic Monte Carlo methods has led to an increased amount attention on the methods and their corresponding capabilities and applications. In this review, the framework and current status of Self-Evolving Atomistic Kinetic Monte Carlo (SEAKMC) are discussed. SEAKMC particularly focuses on defect interaction and evolution with atomistic details without assuming potential defect migration/interaction mechanisms and energies. The strength and limitation of using an active volume, the key concept introduced in SEAKMC, are discussed. Potential criteria for characterizing an active volume are discussed and the influence of active volume size on saddle point energies ismore » illustrated. A procedure starting with a small active volume followed by larger active volumes was found to possess higher efficiency. Applications of SEAKMC, ranging from point defect diffusion, to complex interstitial cluster evolution, to helium interaction with tungsten surfaces, are summarized. A comparison of SEAKMC with molecular dynamics and conventional object kinetic Monte Carlo is demonstrated. Overall, SEAKMC is found to be complimentary to conventional molecular dynamics, especially when the harmonic approximation of transition state theory is accurate. However it is capable of reaching longer time scales than molecular dynamics and it can be used to systematically increase the accuracy of other methods such as object kinetic Monte Carlo. Furthermore, the challenges and potential development directions are also outlined.« less
Uncertainties in ozone concentrations predicted with a Lagrangian photochemical air quality model have been estimated using Bayesian Monte Carlo (BMC) analysis. Bayesian Monte Carlo analysis provides a means of combining subjective "prior" uncertainty estimates developed ...
Incorporation of Monte-Carlo Computer Techniques into Science and Mathematics Education.
ERIC Educational Resources Information Center
Danesh, Iraj
1987-01-01
Described is a Monte-Carlo method for modeling physical systems with a computer. Also discussed are ways to incorporate Monte-Carlo simulation techniques for introductory science and mathematics teaching and also for enriching computer and simulation courses. (RH)
Fast Monte Carlo for radiation therapy: the PEREGRINE Project
Hartmann Siantar, C.L.; Bergstrom, P.M.; Chandler, W.P.; Cox, L.J.; Daly, T.P.; Garrett, D.; House, R.K.; Moses, E.I.; Powell, C.L.; Patterson, R.W.; Schach von Wittenau, A.E.
1997-11-11
The purpose of the PEREGRINE program is to bring high-speed, high- accuracy, high-resolution Monte Carlo dose calculations to the desktop in the radiation therapy clinic. PEREGRINE is a three- dimensional Monte Carlo dose calculation system designed specifically for radiation therapy planning. It provides dose distributions from external beams of photons, electrons, neutrons, and protons as well as from brachytherapy sources. Each external radiation source particle passes through collimator jaws and beam modifiers such as blocks, compensators, and wedges that are used to customize the treatment to maximize the dose to the tumor. Absorbed dose is tallied in the patient or phantom as Monte Carlo simulation particles are followed through a Cartesian transport mesh that has been manually specified or determined from a CT scan of the patient. This paper describes PEREGRINE capabilities, results of benchmark comparisons, calculation times and performance, and the significance of Monte Carlo calculations for photon teletherapy. PEREGRINE results show excellent agreement with a comprehensive set of measurements for a wide variety of clinical photon beam geometries, on both homogeneous and heterogeneous test samples or phantoms. PEREGRINE is capable of calculating >350 million histories per hour for a standard clinical treatment plan. This results in a dose distribution with voxel standard deviations of <2% of the maximum dose on 4 million voxels with 1 mm resolution in the CT-slice plane in under 20 minutes. Calculation times include tracking particles through all patient specific beam delivery components as well as the patient. Most importantly, comparison of Monte Carlo dose calculations with currently-used algorithms reveal significantly different dose distributions for a wide variety of treatment sites, due to the complex 3-D effects of missing tissue, tissue heterogeneities, and accurate modeling of the radiation source.
Global Monte Carlo Simulation with High Order Polynomial Expansions
William R. Martin; James Paul Holloway; Kaushik Banerjee; Jesse Cheatham; Jeremy Conlin
2007-12-13
The functional expansion technique (FET) was recently developed for Monte Carlo simulation. The basic idea of the FET is to expand a Monte Carlo tally in terms of a high order expansion, the coefficients of which can be estimated via the usual random walk process in a conventional Monte Carlo code. If the expansion basis is chosen carefully, the lowest order coefficient is simply the conventional histogram tally, corresponding to a flat mode. This research project studied the applicability of using the FET to estimate the fission source, from which fission sites can be sampled for the next generation. The idea is that individual fission sites contribute to expansion modes that may span the geometry being considered, possibly increasing the communication across a loosely coupled system and thereby improving convergence over the conventional fission bank approach used in most production Monte Carlo codes. The project examined a number of basis functions, including global Legendre polynomials as well as “local” piecewise polynomials such as finite element hat functions and higher order versions. The global FET showed an improvement in convergence over the conventional fission bank approach. The local FET methods showed some advantages versus global polynomials in handling geometries with discontinuous material properties. The conventional finite element hat functions had the disadvantage that the expansion coefficients could not be estimated directly but had to be obtained by solving a linear system whose matrix elements were estimated. An alternative fission matrix-based response matrix algorithm was formulated. Studies were made of two alternative applications of the FET, one based on the kernel density estimator and one based on Arnoldi’s method of minimized iterations. Preliminary results for both methods indicate improvements in fission source convergence. These developments indicate that the FET has promise for speeding up Monte Carlo fission source
Svatos, M.; Zankowski, C.; Bednarz, B.
2016-01-01
Purpose: The future of radiation therapy will require advanced inverse planning solutions to support single-arc, multiple-arc, and “4π” delivery modes, which present unique challenges in finding an optimal treatment plan over a vast search space, while still preserving dosimetric accuracy. The successful clinical implementation of such methods would benefit from Monte Carlo (MC) based dose calculation methods, which can offer improvements in dosimetric accuracy when compared to deterministic methods. The standard method for MC based treatment planning optimization leverages the accuracy of the MC dose calculation and efficiency of well-developed optimization methods, by precalculating the fluence to dose relationship within a patient with MC methods and subsequently optimizing the fluence weights. However, the sequential nature of this implementation is computationally time consuming and memory intensive. Methods to reduce the overhead of the MC precalculation have been explored in the past, demonstrating promising reductions of computational time overhead, but with limited impact on the memory overhead due to the sequential nature of the dose calculation and fluence optimization. The authors propose an entirely new form of “concurrent” Monte Carlo treat plan optimization: a platform which optimizes the fluence during the dose calculation, reduces wasted computation time being spent on beamlets that weakly contribute to the final dose distribution, and requires only a low memory footprint to function. In this initial investigation, the authors explore the key theoretical and practical considerations of optimizing fluence in such a manner. Methods: The authors present a novel derivation and implementation of a gradient descent algorithm that allows for optimization during MC particle transport, based on highly stochastic information generated through particle transport of very few histories. A gradient rescaling and renormalization algorithm, and the
NASA Astrophysics Data System (ADS)
Goldman, Saul
1983-10-01
A method we call energy-scaled displacement Monte Carlo (ESDMC) whose purpose is to improve sampling efficiency and thereby speed up convergence rates in Monte Carlo calculations is presented. The method involves scaling the maximum displacement a particle may make on a trial move to the particle's configurational energy. The scaling is such that on the average, the most stable particles make the smallest moves and the most energetic particles the largest moves. The method is compared to Metropolis Monte Carlo (MMC) and Force Bias Monte Carlo of (FBMC) by applying all three methods to a dense Lennard-Jones fluid at two temperatures, and to hot ST2 water. The functions monitored as the Markov chains developed were, for the Lennard-Jones case: melting, radial distribution functions, internal energies, and heat capacities. For hot ST2 water, we monitored energies and heat capacities. The results suggest that ESDMC samples configuration space more efficiently than either MMC or FBMC in these systems for the biasing parameters used here. The benefit from using ESDMC seemed greatest for the Lennard-Jones systems.
Mukumoto, Nobutaka; Tsujii, Katsutomo; Saito, Susumu; Yasunaga, Masayoshi; Takegawa, Hidek; Yamamoto, Tokihiro; Numasaki, Hodaka; Teshima, Teruki
2009-10-01
Purpose: To develop an infrastructure for the integrated Monte Carlo verification system (MCVS) to verify the accuracy of conventional dose calculations, which often fail to accurately predict dose distributions, mainly due to inhomogeneities in the patient's anatomy, for example, in lung and bone. Methods and Materials: The MCVS consists of the graphical user interface (GUI) based on a computational environment for radiotherapy research (CERR) with MATLAB language. The MCVS GUI acts as an interface between the MCVS and a commercial treatment planning system to import the treatment plan, create MC input files, and analyze MC output dose files. The MCVS consists of the EGSnrc MC codes, which include EGSnrc/BEAMnrc to simulate the treatment head and EGSnrc/DOSXYZnrc to calculate the dose distributions in the patient/phantom. In order to improve computation time without approximations, an in-house cluster system was constructed. Results: The phase-space data of a 6-MV photon beam from a Varian Clinac unit was developed and used to establish several benchmarks under homogeneous conditions. The MC results agreed with the ionization chamber measurements to within 1%. The MCVS GUI could import and display the radiotherapy treatment plan created by the MC method and various treatment planning systems, such as RTOG and DICOM-RT formats. Dose distributions could be analyzed by using dose profiles and dose volume histograms and compared on the same platform. With the cluster system, calculation time was improved in line with the increase in the number of central processing units (CPUs) at a computation efficiency of more than 98%. Conclusions: Development of the MCVS was successful for performing MC simulations and analyzing dose distributions.
Boyle, Paul M; Houchens, Brent C; Kim, Albert S
2013-06-01
Pressure-driven flow through a channel with membrane walls is modeled for high particulate volume fractions of 10%. Particle transport is influenced by Brownian diffusion, shear-induced diffusion, and convection due to the axial crossflow. The particles are also subject to electrostatic double layer repulsion and van der Waals attraction, from both particle-particle and particle-membrane interactions. Force Bias Monte Carlo (FBMC) simulations predict the deposition of the particles onto the membranes, where both hydrodynamics and the change in particle potentials determine the probability that a proposed move is accepted. The particle volume fraction is used to determine an apparent local viscosity observed by the continuum flow. As particles migrate, the crossflow velocity field evolves in quasi-steady fashion with each time instance appearing fully developed in the downstream direction. Particles subject to combined hydrodynamic and electric effects (electrostatic double layer repulsion and van der Waals attraction) reach a more stable steady-state as compared to systems with only hydrodynamic effects considered. As expected, at higher crossflow Reynolds numbers more particles remain in the crossflow free stream.
Predicting the orientation of protein G B1 on hydrophobic surfaces using Monte Carlo simulations
Harrison, Elisa T.; Weidner, Tobias; Castner, David G.; Interlandi, Gianluca
2016-01-01
A Monte Carlo algorithm was developed to predict the most likely orientations of protein G B1, an immunoglobulin G (IgG) antibody-binding domain of protein G, adsorbed onto a hydrophobic surface. At each Monte Carlo step, the protein was rotated and translated as a rigid body. The assumption about rigidity was supported by quartz crystal microbalance with dissipation monitoring experiments, which indicated that protein G B1 adsorbed on a polystyrene surface with its native structure conserved and showed that its IgG antibody-binding activity was retained. The Monte Carlo simulations predicted that protein G B1 is likely adsorbed onto a hydrophobic surface in two different orientations, characterized as two mutually exclusive sets of amino acids contacting the surface. This was consistent with sum frequency generation (SFG) vibrational spectroscopy results. In fact, theoretical SFG spectra calculated from an equal combination of the two predicted orientations exhibited reasonable agreement with measured spectra of protein G B1 on polystyrene surfaces. Also, in explicit solvent molecular dynamics simulations, protein G B1 maintained its predicted orientation in three out of four runs. This work shows that using a Monte Carlo approach can provide an accurate estimate of a protein orientation on a hydrophobic surface, which complements experimental surface analysis techniques and provides an initial system to study the interaction between a protein and a surface in molecular dynamics simulations. PMID:27923271
MONITOR- MONTE CARLO INVESTIGATION OF TRAJECTORY OPERATIONS AND REQUIREMENTS
NASA Technical Reports Server (NTRS)
Glass, A. B.
1994-01-01
The Monte Carlo Investigation of Trajectory Operations and Requirements (MONITOR) program was developed to perform spacecraft mission maneuver simulations for geosynchronous, single maneuver, and comet encounter type trajectories. MONITOR is a multifaceted program which enables the modeling of various orbital sequences and missions, the generation of Monte Carlo simulation statistics, and the parametric scanning of user requested variables over specified intervals. The MONITOR program has been used primarily to study geosynchronous missions and has the capability to model Space Shuttle deployed satellite trajectories. The ability to perform a Monte Carlo error analysis of user specified orbital parameters using predicted maneuver execution errors can make MONITOR a significant part of any mission planning and analysis system. The MONITOR program can be executed in four operational modes. In the first mode, analytic state covariance matrix propagation is performed using state transition matrices for the coasting and powered burn phases of the trajectory. A two-body central force field is assumed throughout the analysis. Histograms of the final orbital elements and other state dependent variables may be evaluated by a Monte Carlo analysis. In the second mode, geosynchronous missions can be simulated from parking orbit injection through station acquisition. A two-body central force field is assumed throughout the simulation. Nominal mission studies can be conducted; however, the main use of this mode lies in evaluating the behavior of pertinent orbital trajectory parameters by making use of a Monte Carlo analysis. In the third mode, MONITOR performs parametric scans of user-requested variables for a nominal mission. Various orbital sequences may be specified; however, primary use is devoted to geosynchronous missions. A maximum of five variables may be scanned at a time. The fourth mode simulates a mission from orbit injection through comet encounter with optional
Kernel density estimator methods for Monte Carlo radiation transport
NASA Astrophysics Data System (ADS)
Banerjee, Kaushik
In this dissertation, the Kernel Density Estimator (KDE), a nonparametric probability density estimator, is studied and used to represent global Monte Carlo (MC) tallies. KDE is also employed to remove the singularities from two important Monte Carlo tallies, namely point detector and surface crossing flux tallies. Finally, KDE is also applied to accelerate the Monte Carlo fission source iteration for criticality problems. In the conventional MC calculation histograms are used to represent global tallies which divide the phase space into multiple bins. Partitioning the phase space into bins can add significant overhead to the MC simulation and the histogram provides only a first order approximation to the underlying distribution. The KDE method is attractive because it can estimate MC tallies in any location within the required domain without any particular bin structure. Post-processing of the KDE tallies is sufficient to extract detailed, higher order tally information for an arbitrary grid. The quantitative and numerical convergence properties of KDE tallies are also investigated and they are shown to be superior to conventional histograms as well as the functional expansion tally developed by Griesheimer. Monte Carlo point detector and surface crossing flux tallies are two widely used tallies but they suffer from an unbounded variance. As a result, the central limit theorem can not be used for these tallies to estimate confidence intervals. By construction, KDE tallies can be directly used to estimate flux at a point but the variance of this point estimate does not converge as 1/N, which is not unexpected for a point quantity. However, an improved approach is to modify both point detector and surface crossing flux tallies directly by using KDE within a variance reduction approach by taking advantage of the fact that KDE estimates the underlying probability density function. This methodology is demonstrated by several numerical examples and demonstrates that
Monte Carlo simulation of particle acceleration at astrophysical shocks
NASA Technical Reports Server (NTRS)
Campbell, Roy K.
1989-01-01
A Monte Carlo code was developed for the simulation of particle acceleration at astrophysical shocks. The code is implemented in Turbo Pascal on a PC. It is modularized and structured in such a way that modification and maintenance are relatively painless. Monte Carlo simulations of particle acceleration at shocks follow the trajectories of individual particles as they scatter repeatedly across the shock front, gaining energy with each crossing. The particles are assumed to scatter from magnetohydrodynamic (MHD) turbulence on both sides of the shock. A scattering law is used which is related to the assumed form of the turbulence, and the particle and shock parameters. High energy cosmic ray spectra derived from Monte Carlo simulations have observed power law behavior just as the spectra derived from analytic calculations based on a diffusion equation. This high energy behavior is not sensitive to the scattering law used. In contrast with Monte Carlo calculations diffusive calculations rely on the initial injection of supra-thermal particles into the shock environment. Monte Carlo simulations are the only known way to describe the extraction of particles directly from the thermal pool. This was the triumph of the Monte Carlo approach. The question of acceleration efficiency is an important one in the shock acceleration game. The efficiency of shock waves efficient to account for the observed flux of high energy galactic cosmic rays was examined. The efficiency of the acceleration process depends on the thermal particle pick-up and hence the low energy scattering in detail. One of the goals is the self-consistent derivation of the accelerated particle spectra and the MHD turbulence spectra. Presumably the upstream turbulence, which scatters the particles so they can be accelerated, is excited by the streaming accelerated particles and the needed downstream turbulence is convected from the upstream region. The present code is to be modified to include a better
An efficient approach to ab initio Monte Carlo simulation.
Leiding, Jeff; Coe, Joshua D
2014-01-21
We present a Nested Markov chain Monte Carlo (NMC) scheme for building equilibrium averages based on accurate potentials such as density functional theory. Metropolis sampling of a reference system, defined by an inexpensive but approximate potential, was used to substantially decorrelate configurations at which the potential of interest was evaluated, thereby dramatically reducing the number needed to build ensemble averages at a given level of precision. The efficiency of this procedure was maximized on-the-fly through variation of the reference system thermodynamic state (characterized here by its inverse temperature β(0)), which was otherwise unconstrained. Local density approximation results are presented for shocked states of argon at pressures from 4 to 60 GPa, where-depending on the quality of the reference system potential-acceptance probabilities were enhanced by factors of 1.2-28 relative to unoptimized NMC. The optimization procedure compensated strongly for reference potential shortcomings, as evidenced by significantly higher speedups when using a reference potential of lower quality. The efficiency of optimized NMC is shown to be competitive with that of standard ab initio molecular dynamics in the canonical ensemble.
Advances in the application of diffusion Monte Carlo to solids
NASA Astrophysics Data System (ADS)
Shulenburger, L.; Mattsson, T. R.
2014-03-01
The need for high fidelity electronic structure calculations has catalyzed an explosion in the development of new techniques. Improvements in DFT functionals, many body perturbation theory and dynamical mean field theory are starting to make significant headway towards reaching the accuracy required for a true predictive capability. One technique that is undergoing a resurgence is diffusion Monte Carlo (DMC). The early calculations with this method were of unquestionable accuracy (providing a valuable reference for DFT functionals) but were largely limited to model systems because of their high computational cost. Algorithmic advances and improvements in computer power have reached the point where this is no longer an insurmountable obstacle. In this talk I will present a broad study of DMC applied to condensed matter (arXiv:1310.1047). We have shown excellent agreement for the bulk modulus and lattice constant of solids exhibiting several different types of binding, including ionic, covalent and van der Waals. We will discuss both the opportunities for application of this method as well as opportunities for further theoretical improvements. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's NNSA under Contract No. DE-AC04-94AL85000.
Towards overcoming the Monte Carlo sign problem with tensor networks
NASA Astrophysics Data System (ADS)
Bañuls, Mari Carmen; Cichy, Krzysztof; Ignacio Cirac, J.; Jansen, Karl; Kühn, Stefan; Saito, Hana
2017-03-01
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.
Monte Carlo simulation studies of diffusion in crowded environments
NASA Astrophysics Data System (ADS)
Nandigrami, Prithviraj; Grove, Brandy; Konya, Andrew; Selinger, Robin
Anomalous diffusion has been observed in protein solutions and other multi-component systems due to macromolecular crowding. Using Monte Carlo simulations, we investigate mechanisms that govern anomalous diffusive transport and pattern formation in a crowded mixture. We consider a multi-component lattice gas model with ``tracer'' molecules diffusing across a density gradient in a solution containing sticky ``crowder'' molecules that cluster to form dynamically evolving obstacles. The dependence of tracer flux on crowder density shows an intriguing re-entrant behavior as a function of temperature with three distinct temperature regimes. At high temperature, crowders segregate near the tracer sink but, for low enough overall crowder density, remain sufficiently disordered to allow continuous tracer flux. At intermediate temperature, crowders segregate and block tracer flux entirely, giving rise to complex pattern formation. At low temperature, crowders aggregate to form small, slowly diffusing obstacles. The resulting tracer flux shows scaling behavior near the percolation threshold, analogous to the scenario when the obstacles are fixed and randomly distributed. Our simulations predict distinct quantitative dependence of tracer flux on crowder density in these temperature limits.
Hopping electron model with geometrical frustration: kinetic Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Terao, Takamichi
2016-09-01
The hopping electron model on the Kagome lattice was investigated by kinetic Monte Carlo simulations, and the non-equilibrium nature of the system was studied. We have numerically confirmed that aging phenomena are present in the autocorrelation function C ({t,tW )} of the electron system on the Kagome lattice, which is a geometrically frustrated lattice without any disorder. The waiting-time distributions p(τ ) of hopping electrons of the system on Kagome lattice has been also studied. It is confirmed that the profile of p (τ ) obtained at lower temperatures obeys the power-law behavior, which is a characteristic feature of continuous time random walk of electrons. These features were also compared with the characteristics of the Coulomb glass model, used as a model of disordered thin films and doped semiconductors. This work represents an advance in the understanding of the dynamics of geometrically frustrated systems and will serve as a basis for further studies of these physical systems.
MARKOV CHAIN MONTE CARLO POSTERIOR SAMPLING WITH THE HAMILTONIAN METHOD
K. HANSON
2001-02-01
The Markov Chain Monte Carlo technique provides a means for drawing random samples from a target probability density function (pdf). MCMC allows one to assess the uncertainties in a Bayesian analysis described by a numerically calculated posterior distribution. This paper describes the Hamiltonian MCMC technique in which a momentum variable is introduced for each parameter of the target pdf. In analogy to a physical system, a Hamiltonian H is defined as a kinetic energy involving the momenta plus a potential energy {var_phi}, where {var_phi} is minus the logarithm of the target pdf. Hamiltonian dynamics allows one to move along trajectories of constant H, taking large jumps in the parameter space with relatively few evaluations of {var_phi} and its gradient. The Hamiltonian algorithm alternates between picking a new momentum vector and following such trajectories. The efficiency of the Hamiltonian method for multidimensional isotropic Gaussian pdfs is shown to remain constant at around 7% for up to several hundred dimensions. The Hamiltonian method handles correlations among the variables much better than the standard Metropolis algorithm. A new test, based on the gradient of {var_phi}, is proposed to measure the convergence of the MCMC sequence.
Design of composite laminates by a Monte Carlo method
NASA Astrophysics Data System (ADS)
Fang, Chin; Springer, George S.
1993-01-01
A Monte Carlo procedure was developed for optimizing symmetric fiber reinforced composite laminates such that the weight is minimum and the Tsai-Wu strength failure criterion is satisfied in each ply. The laminate may consist of several materials including an idealized core, and may be subjected to several sets of combined in-plane and bending loads. The procedure yields the number of plies, the fiber orientation, and the material of each ply and the material and thickness of the core. A user friendly computer code was written for performing the numerical calculations. Laminates optimized by the code were compared to laminates resulting from existing optimization methods. These comparisons showed that the present Monte Carlo procedure is a useful and efficient tool for the design of composite laminates.
Monte Carlo Ground State Energy for Trapped Boson Systems
NASA Astrophysics Data System (ADS)
Rudd, Ethan; Mehta, N. P.
2012-06-01
Diffusion Monte Carlo (DMC) and Green's Function Monte Carlo (GFMC) algorithms were implemented to obtain numerical approximations for the ground state energies of systems of bosons in a harmonic trap potential. Gaussian pairwise particle interactions of the form V0e^-|ri-rj|^2/r0^2 were implemented in the DMC code. These results were verified for small values of V0 via a first-order perturbation theory approximation for which the N-particle matrix element evaluated to N2 V0(1 + 1/r0^2)^3/2. By obtaining the scattering length from the 2-body potential in the perturbative regime (V0φ 1), ground state energy results were compared to modern renormalized models by P.R. Johnson et. al, New J. Phys. 11, 093022 (2009).
Application of Monte Carlo simulations to improve basketball shooting strategy
NASA Astrophysics Data System (ADS)
Min, Byeong June
2016-10-01
The underlying physics of basketball shooting seems to be a straightforward example of Newtonian mechanics that can easily be traced by using numerical methods. However, a human basketball player does not make use of all the possible basketball trajectories. Instead, a basketball player will build up a database of successful shots and select the trajectory that has the greatest tolerance to the small variations of the real world. We simulate the basketball player's shooting training as a Monte Carlo sequence to build optimal shooting strategies, such as the launch speed and angle of the basketball, and whether to take a direct shot or a bank shot, as a function of the player's court position and height. The phase-space volume Ω that belongs to the successful launch velocities generated by Monte Carlo simulations is then used as the criterion to optimize a shooting strategy that incorporates not only mechanical, but also human, factors.
A tetrahedron-based inhomogeneous Monte Carlo optical simulator.
Shen, H; Wang, G
2010-02-21
Optical imaging has been widely applied in preclinical and clinical applications. Fifteen years ago, an efficient Monte Carlo program 'MCML' was developed for use with multi-layered turbid media and has gained popularity in the field of biophotonics. Currently, there is an increasingly pressing need for simulating tools more powerful than MCML in order to study light propagation phenomena in complex inhomogeneous objects, such as the mouse. Here we report a tetrahedron-based inhomogeneous Monte Carlo optical simulator (TIM-OS) to address this issue. By modeling an object as a tetrahedron-based inhomogeneous finite-element mesh, TIM-OS can determine the photon-triangle interaction recursively and rapidly. In numerical simulation, we have demonstrated the correctness and efficiency of TIM-OS.
Radiotherapy Monte Carlo simulation using cloud computing technology.
Poole, C M; Cornelius, I; Trapp, J V; Langton, C M
2012-12-01
Cloud computing allows for vast computational resources to be leveraged quickly and easily in bursts as and when required. Here we describe a technique that allows for Monte Carlo radiotherapy dose calculations to be performed using GEANT4 and executed in the cloud, with relative simulation cost and completion time evaluated as a function of machine count. As expected, simulation completion time decreases as 1/n for n parallel machines, and relative simulation cost is found to be optimal where n is a factor of the total simulation time in hours. Using the technique, we demonstrate the potential usefulness of cloud computing as a solution for rapid Monte Carlo simulation for radiotherapy dose calculation without the need for dedicated local computer hardware as a proof of principal.
Monte Carlo Simulations of Arterial Imaging with Optical Coherence Tomography
Amendt, P.; Estabrook, K.; Everett, M.; London, R.A.; Maitland, D.; Zimmerman, G.; Colston, B.; da Silva, L.; Sathyam, U.
2000-02-01
The laser-tissue interaction code LATIS [London et al., Appl. Optics 36, 9068 ( 1998)] is used to analyze photon scattering histories representative of optical coherence tomography (OCT) experiment performed at Lawrence Livermore National Laboratory. Monte Carlo photonics with Henyey-Greenstein anisotropic scattering is implemented and used to simulate signal discrimination of intravascular structure. An analytic model is developed and used to obtain a scaling law relation for optimization of the OCT signal and to validate Monte Carlo photonics. The appropriateness of the Henyey-Greenstein phase function is studied by direct comparison with more detailed Mie scattering theory using an ensemble of spherical dielectric scatterers. Modest differences are found between the two prescriptions for describing photon angular scattering in tissue. In particular, the Mie scattering phase functions provide less overall reflectance signal but more signal contrast compared to the Henyey-Greenstein formulation.
Large-cell Monte Carlo renormalization of irreversible growth processes
NASA Technical Reports Server (NTRS)
Nakanishi, H.; Family, F.
1985-01-01
Monte Carlo sampling is applied to a recently formulated direct-cell renormalization method for irreversible, disorderly growth processes. Large-cell Monte Carlo renormalization is carried out for various nonequilibrium problems based on the formulation dealing with relative probabilities. Specifically, the method is demonstrated by application to the 'true' self-avoiding walk and the Eden model of growing animals for d = 2, 3, and 4 and to the invasion percolation problem for d = 2 and 3. The results are asymptotically in agreement with expectations; however, unexpected complications arise, suggesting the possibility of crossovers, and in any case, demonstrating the danger of using small cells alone, because of the very slow convergence as the cell size b is extrapolated to infinity. The difficulty of applying the present method to the diffusion-limited-aggregation model, is commented on.
Estimation of beryllium ground state energy by Monte Carlo simulation
Kabir, K. M. Ariful; Halder, Amal
2015-05-15
Quantum Monte Carlo method represent a powerful and broadly applicable computational tool for finding very accurate solution of the stationary Schrödinger equation for atoms, molecules, solids and a variety of model systems. Using variational Monte Carlo method we have calculated the ground state energy of the Beryllium atom. Our calculation are based on using a modified four parameters trial wave function which leads to good result comparing with the few parameters trial wave functions presented before. Based on random Numbers we can generate a large sample of electron locations to estimate the ground state energy of Beryllium. Our calculation gives good estimation for the ground state energy of the Beryllium atom comparing with the corresponding exact data.
Monte Carlo methods for light propagation in biological tissues.
Vinckenbosch, Laura; Lacaux, Céline; Tindel, Samy; Thomassin, Magalie; Obara, Tiphaine
2015-11-01
Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis-Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang-Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg-Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurements.
Monte Carlo Methods in ICF (LIRPP Vol. 13)
NASA Astrophysics Data System (ADS)
Zimmerman, George B.
2016-10-01
Monte Carlo methods appropriate to simulate the transport of x-rays, neutrons, ions and electrons in Inertial Confinement Fusion targets are described and analyzed. The Implicit Monte Carlo method of x-ray transport handles symmetry within indirect drive ICF hohlraums well, but can be improved SOX in efficiency by angular biasing the x-rays towards the fuel capsule. Accurate simulation of thermonuclear burn and burn diagnostics involves detailed particle source spectra, charged particle ranges, inflight reaction kinematics, corrections for bulk and thermal Doppler effects and variance reduction to obtain adequate statistics for rare events. It is found that the effects of angular Coulomb scattering must be included in models of charged particle transport through heterogeneous materials.
Monte Carlo modeling of coherent scattering: Influence of interference
Leliveld, C.J.; Maas, J.G.; Bom, V.R.; Eijk, C.W.E. van
1996-12-01
In this study, the authors present Monte Carlo (MC) simulation results for the intensity and angular distribution of scattered radiation from cylindrical absorbers. For coherent scattering the authors have taken into account the effects of interference by using new molecular form factor data for the AAPM plastic materials and water. The form factor data were compiled from X-ray diffraction measurements. The new data have been implemented in the authors` Electron Gamma Shower (EGS4) Monte Carlo system. The hybrid MC simulation results show a significant influence on the intensity and the angular distribution of coherently scattered photons. They conclude that MC calculations are significantly in error when interference effects are ignored in the model for coherent scattering. Especially for simulation studies of scattered radiation in collimated geometries, where small angle scattering will prevail, the coherent scatter contribution is highly overestimated when conventional form factor data are used.
Monte Carlo analysis of satellite debris footprint dispersion
NASA Technical Reports Server (NTRS)
Rao, P. P.; Woeste, M. A.
1979-01-01
A comprehensive study is performed to investigate satellite debris impact point dispersion using a combination of Monte Carlo statistical analysis and parametric methods. The Monte Carlo technique accounts for nonlinearities in the entry point dispersion, which is represented by a covariance matrix of position and velocity errors. Because downrange distance of impact is a monotonic function of debris ballistic coefficient, a parametric method is useful for determining dispersion boundaries. The scheme is applied in the present analysis to estimate the Skylab footprint dispersions for a controlled reentry. A significant increase in the footprint dispersion is noticed for satellite breakup above a 200,000-ft altitude. A general discussion of the method used for analysis is presented together with some typical results obtained for the Skylab deboost mission, which was designed before NASA abandoned plans for a Skylab controlled reentry.
Condensed Matter Applications of Quantum Monte Carlo at the Petascale
NASA Astrophysics Data System (ADS)
Ceperley, David
2014-03-01
Applications of the Quantum Monte Carlo method have a number of advantages allowing them to be useful for high performance computation. The method scales well in particle number, can treat complex systems with weak or strong correlation including disordered systems, and large thermal and zero point effects of the nuclei. The methods are adaptable to a variety of computer architectures and have multiple parallelization strategies. Most errors are under control so that increases in computer resources allow a systematic increase in accuracy. We will discuss a number of recent applications of Quantum Monte Carlo including dense hydrogen and transition metal systems and suggest future directions. Support from DOE grants DE-FG52-09NA29456, SCIDAC DE-SC0008692, the Network for Ab Initio Many-Body Methods and INCITE allocation.
Computer Monte Carlo simulation in quantitative resource estimation
Root, D.H.; Menzie, W.D.; Scott, W.A.
1992-01-01
The method of making quantitative assessments of mineral resources sufficiently detailed for economic analysis is outlined in three steps. The steps are (1) determination of types of deposits that may be present in an area, (2) estimation of the numbers of deposits of the permissible deposit types, and (3) combination by Monte Carlo simulation of the estimated numbers of deposits with the historical grades and tonnages of these deposits to produce a probability distribution of the quantities of contained metal. Two examples of the estimation of the number of deposits (step 2) are given. The first example is for mercury deposits in southwestern Alaska and the second is for lode tin deposits in the Seward Peninsula. The flow of the Monte Carlo simulation program is presented with particular attention to the dependencies between grades and tonnages of deposits and between grades of different metals in the same deposit. ?? 1992 Oxford University Press.
Mammography X-Ray Spectra Simulated with Monte Carlo
Vega-Carrillo, H. R.; Gonzalez, J. Ramirez; Manzanares-Acuna, E.; Hernandez-Davila, V. M.; Villasana, R. Hernandez; Mercado, G. A.
2008-08-11
Monte Carlo calculations have been carried out to obtain the x-ray spectra of various target-filter combinations for a mammography unit. Mammography is widely used to diagnose breast cancer. Further to Mo target with Mo filter combination, Rh/Rh, Mo/Rh, Mo/Al, Rh/Al, and W/Rh are also utilized. In this work Monte Carlo calculations, using MCNP 4C code, were carried out to estimate the x-ray spectra produced when a beam of 28 keV electrons did collide with Mo, Rh and W targets. Resulting x-ray spectra show characteristic x-rays and continuous bremsstrahlung. Spectra were also calculated including filters.
Monte Carlo Strategies for Selecting Parameter Values in Simulation Experiments.
Leigh, Jessica W; Bryant, David
2015-09-01
Simulation experiments are used widely throughout evolutionary biology and bioinformatics to compare models, promote methods, and test hypotheses. The biggest practical constraint on simulation experiments is the computational demand, particularly as the number of parameters increases. Given the extraordinary success of Monte Carlo methods for conducting inference in phylogenetics, and indeed throughout the sciences, we investigate ways in which Monte Carlo framework can be used to carry out simulation experiments more efficiently. The key idea is to sample parameter values for the experiments, rather than iterate through them exhaustively. Exhaustive analyses become completely infeasible when the number of parameters gets too large, whereas sampled approaches can fare better in higher dimensions. We illustrate the framework with applications to phylogenetics and genetic archaeology.
Lattice-switch Monte Carlo: the fcc—bcc problem
NASA Astrophysics Data System (ADS)
Underwood, T. L.; Ackland, G. J.
2015-09-01
Lattice-switch Monte Carlo is an efficient method for calculating the free energy difference between two solid phases, or a solid and a fluid phase. Here, we provide a brief introduction to the method, and list its applications since its inception. We then describe a lattice switch for the fcc and bcc phases based on the Bain orientation relationship. Finally, we present preliminary results regarding our application of the method to the fcc and bcc phases in the Lennard-Jones system. Our initial calculations reveal that the bcc phase is unstable, quickly degenerating into some as yet undetermined metastable solid phase. This renders conventional lattice-switch Monte Carlo intractable for this phase. Possible solutions to this problem are discussed.
Fast Off-Lattice Monte Carlo Simulations with Soft Potentials
NASA Astrophysics Data System (ADS)
Zong, Jing; Yang, Delian; Yin, Yuhua; Zhang, Xinghua; Wang, Qiang (David)
2011-03-01
Fast off-lattice Monte Carlo simulations with soft repulsive potentials that allow particle overlapping give orders of magnitude faster/better sampling of the configurational space than conventional molecular simulations with hard-core repulsions (such as the hard-sphere or Lennard-Jones repulsion). Here we present our fast off-lattice Monte Carlo simulations ranging from small-molecule soft spheres and liquid crystals to polymeric systems including homopolymers and rod-coil diblock copolymers. The simulation results are compared with various theories based on the same Hamiltonian as in the simulations (thus without any parameter-fitting) to quantitatively reveal the consequences of approximations in these theories. Q. Wang and Y. Yin, J. Chem. Phys., 130, 104903 (2009).
Quantum Monte Carlo calculations with chiral effective field theory interactions.
Gezerlis, A; Tews, I; Epelbaum, E; Gandolfi, S; Hebeler, K; Nogga, A; Schwenk, A
2013-07-19
We present the first quantum Monte Carlo (QMC) calculations with chiral effective field theory (EFT) interactions. To achieve this, we remove all sources of nonlocality, which hamper the inclusion in QMC calculations, in nuclear forces to next-to-next-to-leading order. We perform auxiliary-field diffusion Monte Carlo (AFDMC) calculations for the neutron matter energy up to saturation density based on local leading-order, next-to-leading order, and next-to-next-to-leading order nucleon-nucleon interactions. Our results exhibit a systematic order-by-order convergence in chiral EFT and provide nonperturbative benchmarks with theoretical uncertainties. For the softer interactions, perturbative calculations are in excellent agreement with the AFDMC results. This work paves the way for QMC calculations with systematic chiral EFT interactions for nuclei and nuclear matter, for testing the perturbativeness of different orders, and allows for matching to lattice QCD results by varying the pion mass.
Drag coefficient modeling for grace using Direct Simulation Monte Carlo
NASA Astrophysics Data System (ADS)
Mehta, Piyush M.; McLaughlin, Craig A.; Sutton, Eric K.
2013-12-01
Drag coefficient is a major source of uncertainty in predicting the orbit of a satellite in low Earth orbit (LEO). Computational methods like the Test Particle Monte Carlo (TPMC) and Direct Simulation Monte Carlo (DSMC) are important tools in accurately computing physical drag coefficients. However, the methods are computationally expensive and cannot be employed real time. Therefore, modeling of the physical drag coefficient is required. This work presents a technique of developing parameterized drag coefficients models using the DSMC method. The technique is validated by developing a model for the Gravity Recovery and Climate Experiment (GRACE) satellite. Results show that drag coefficients computed using the developed model for GRACE agree to within 1% with those computed using DSMC.
Fixed-node diffusion Monte Carlo method for lithium systems
NASA Astrophysics Data System (ADS)
Rasch, K. M.; Mitas, L.
2015-07-01
We study lithium systems over a range of a number of atoms, specifically atomic anion, dimer, metallic cluster, and body-centered-cubic crystal, using the fixed-node diffusion Monte Carlo method. The focus is on analysis of the fixed-node errors of each system, and for that purpose we test several orbital sets in order to provide the most accurate nodal hypersurfaces. The calculations include both core and valence electrons in order to avoid any possible impact by pseudopotentials. To quantify the fixed-node errors, we compare our results to other highly accurate calculations, and wherever available, to experimental observations. The results for these Li systems show that the fixed-node diffusion Monte Carlo method achieves accurate total energies, recovers 96 -99 % of the correlation energy, and estimates binding energies with errors bounded by 0.1 eV /at .
Accelerated Monte Carlo simulations with restricted Boltzmann machines
NASA Astrophysics Data System (ADS)
Huang, Li; Wang, Lei
2017-01-01
Despite their exceptional flexibility and popularity, Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and techniques from the machine learning community. We fit the unnormalized probability of the physical model to a feed-forward neural network and reinterpret the architecture as a restricted Boltzmann machine. Then, exploiting its feature detection ability, we utilize the restricted Boltzmann machine to propose efficient Monte Carlo updates to speed up the simulation of the original physical system. We implement these ideas for the Falicov-Kimball model and demonstrate an improved acceptance ratio and autocorrelation time near the phase transition point.
Sign problem and Monte Carlo calculations beyond Lefschetz thimbles
Alexandru, Andrei; Basar, Gokce; Bedaque, Paulo F.; Ridgway, Gregory W.; Warrington, Neill C.
2016-05-10
We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action (“Lefschetz thimble”). We describe a family of such manifolds that interpolate between the tangent space at one critical point (where the sign problem is milder compared to the real plane but in some cases still severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). As a result, we exemplify this approach using a simple 0+1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefschetz thimbles was elusive.
Sign problem and Monte Carlo calculations beyond Lefschetz thimbles
Alexandru, Andrei; Basar, Gokce; Bedaque, Paulo F.; ...
2016-05-10
We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action (“Lefschetz thimble”). We describe a family of such manifolds that interpolate between the tangent space at one critical point (where the sign problem is milder compared to the real plane but in some cases still severe) and the union of relevant thimbles (where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling). As a result, we exemplify this approach using amore » simple 0+1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefschetz thimbles was elusive.« less
Adaptive kinetic Monte Carlo simulation of methanol decomposition on Cu(100)
Xu, Lijun; Mei, Donghai; Henkelman, Graeme A.
2009-12-31
The adaptive kinetic Monte Carlo method was used to calculate the dynamics of methanol decomposition on Cu(100) at room temperature over a time scale of minutes. Mechanisms of reaction were found using min-mode following saddle point searches based upon forces and energies from density functional theory. Rates of reaction were calculated with harmonic transition state theory. The dynamics followed a pathway from CH3-OH, CH3-O, CH2-O, CH-O and finally C-O. Our calculations confirm that methanol decomposition starts with breaking the O-H bond followed by breaking C-H bonds in the dehydrogenated intermediates until CO is produced. The bridge site on the Cu(100) surface is the active site for scissoring chemical bonds. Reaction intermediates are mobile on the surface which allows them to find this active reaction site. This study illustrates how the adaptive kinetic Monte Carlo method can model the dynamics of surface chemistry from first principles.
Overy, Catherine; Blunt, N. S.; Shepherd, James J.; Booth, George H.; Cleland, Deidre; Alavi, Ali
2014-12-28
Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.
Overy, Catherine; Booth, George H; Blunt, N S; Shepherd, James J; Cleland, Deidre; Alavi, Ali
2014-12-28
Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems.
Nedea, S V; van Steenhoven, A A; Markvoort, A J; Spijker, P; Giordano, D
2014-05-01
The influence of gas-surface interactions of a dilute gas confined between two parallel walls on the heat flux predictions is investigated using a combined Monte Carlo (MC) and molecular dynamics (MD) approach. The accommodation coefficients are computed from the temperature of incident and reflected molecules in molecular dynamics and used as effective coefficients in Maxwell-like boundary conditions in Monte Carlo simulations. Hydrophobic and hydrophilic wall interactions are studied, and the effect of the gas-surface interaction potential on the heat flux and other characteristic parameters like density and temperature is shown. The heat flux dependence on the accommodation coefficient is shown for different fluid-wall mass ratios. We find that the accommodation coefficient is increasing considerably when the mass ratio is decreased. An effective map of the heat flux depending on the accommodation coefficient is given and we show that MC heat flux predictions using Maxwell boundary conditions based on the accommodation coefficient give good results when compared to pure molecular dynamics heat predictions. The accommodation coefficients computed for a dilute gas for different gas-wall interaction parameters and mass ratios are transferred to compute the heat flux predictions for a dense gas. Comparison of the heat fluxes derived using explicit MD, MC with Maxwell-like boundary conditions based on the accommodation coefficients, and pure Maxwell boundary conditions are discussed. A map of the heat flux dependence on the accommodation coefficients for a dense gas, and the effective accommodation coefficients for different gas-wall interactions are given. In the end, this approach is applied to study the gas-surface interactions of argon and xenon molecules on a platinum surface. The derived accommodation coefficients are compared with values of experimental results.
Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo
NASA Astrophysics Data System (ADS)
Garcia, Alejandro L.; Bell, John B.; Crutchfield, William Y.; Alder, Berni J.
1999-09-01
Adaptive mesh and algorithm refinement (AMAR) embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement (AMR) hierarchy. The coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of AMR. Direct simulation Monte Carlo (DSMC) is used as the particle algorithm embedded within a Godunov-type compressible Navier-Stokes solver. Several examples are presented and compared with purely continuum calculations.
Monte Carlo calculation of patient organ doses from computed tomography.
Oono, Takeshi; Araki, Fujio; Tsuduki, Shoya; Kawasaki, Keiichi
2014-01-01
In this study, we aimed to evaluate quantitatively the patient organ dose from computed tomography (CT) using Monte Carlo calculations. A multidetector CT unit (Aquilion 16, TOSHIBA Medical Systems) was modeled with the GMctdospp (IMPS, Germany) software based on the EGSnrc Monte Carlo code. The X-ray spectrum and the configuration of the bowtie filter for the Monte Carlo modeling were determined from the chamber measurements for the half-value layer (HVL) of aluminum and the dose profile (off-center ratio, OCR) in air. The calculated HVL and OCR were compared with measured values for body irradiation with 120 kVp. The Monte Carlo-calculated patient dose distribution was converted to the absorbed dose measured by a Farmer chamber with a (60)Co calibration factor at the center of a CT water phantom. The patient dose was evaluated from dose-volume histograms for the internal organs in the pelvis. The calculated Al HVL was in agreement within 0.3% with the measured value of 5.2 mm. The calculated dose profile in air matched the measured value within 5% in a range of 15 cm from the central axis. The mean doses for soft tissues were 23.5, 23.8, and 27.9 mGy for the prostate, rectum, and bladder, respectively, under exposure conditions of 120 kVp, 200 mA, a beam pitch of 0.938, and beam collimation of 32 mm. For bones of the femur and pelvis, the mean doses were 56.1 and 63.6 mGy, respectively. The doses for bone increased by up to 2-3 times that of soft tissue, corresponding to the ratio of their mass-energy absorption coefficients.
Monte Carlo simulation of virtual Compton scattering below pion threshold
NASA Astrophysics Data System (ADS)
Janssens, P.; Van Hoorebeke, L.; Fonvieille, H.; D'Hose, N.; Bertin, P. Y.; Bensafa, I.; Degrande, N.; Distler, M.; Di Salvo, R.; Doria, L.; Friedrich, J. M.; Friedrich, J.; Hyde-Wright, Ch.; Jaminion, S.; Kerhoas, S.; Laveissière, G.; Lhuillier, D.; Marchand, D.; Merkel, H.; Roche, J.; Tamas, G.; Vanderhaeghen, M.; Van de Vyver, R.; Van de Wiele, J.; Walcher, Th.
2006-10-01
This paper describes the Monte Carlo simulation developed specifically for the Virtual Compton Scattering (VCS) experiments below pion threshold that have been performed at MAMI and JLab. This simulation generates events according to the (Bethe-Heitler + Born) cross-section behaviour and takes into account all relevant resolution-deteriorating effects. It determines the "effective" solid angle for the various experimental settings which are used for the precise determination of the photon electroproduction absolute cross-section.
Towards a Revised Monte Carlo Neutral Particle Surface Interaction Model
D.P. Stotler
2005-06-09
The components of the neutral- and plasma-surface interaction model used in the Monte Carlo neutral transport code DEGAS 2 are reviewed. The idealized surfaces and processes handled by that model are inadequate for accurately simulating neutral transport behavior in present day and future fusion devices. We identify some of the physical processes missing from the model, such as mixed materials and implanted hydrogen, and make some suggestions for improving the model.
Procedure for Adapting Direct Simulation Monte Carlo Meshes
NASA Technical Reports Server (NTRS)
Woronowicz, Michael S.; Wilmoth, Richard G.; Carlson, Ann B.; Rault, Didier F. G.
1992-01-01
A technique is presented for adapting computational meshes used in the G2 version of the direct simulation Monte Carlo method. The physical ideas underlying the technique are discussed, and adaptation formulas are developed for use on solutions generated from an initial mesh. The effect of statistical scatter on adaptation is addressed, and results demonstrate the ability of this technique to achieve more accurate results without increasing necessary computational resources.
Instantaneous GNSS attitude determination: A Monte Carlo sampling approach
NASA Astrophysics Data System (ADS)
Sun, Xiucong; Han, Chao; Chen, Pei
2017-04-01
A novel instantaneous GNSS ambiguity resolution approach which makes use of only single-frequency carrier phase measurements for ultra-short baseline attitude determination is proposed. The Monte Carlo sampling method is employed to obtain the probability density function of ambiguities from a quaternion-based GNSS-attitude model and the LAMBDA method strengthened with a screening mechanism is then utilized to fix the integer values. Experimental results show that 100% success rate could be achieved for ultra-short baselines.
Improved numerical techniques for processing Monte Carlo thermal scattering data
Schmidt, E; Rose, P
1980-01-01
As part of a Thermal Benchmark Validation Program sponsored by the Electric Power Research Institute (EPRI), the National Nuclear Data Center has been calculating thermal reactor lattices using the SAM-F Monte Carlo Computer Code. As part of this program a significant improvement has been made in the adequacy of the numerical procedures used to process the thermal differential scattering cross sections for hydrogen bound in H/sub 2/O.
Monte Carlo Methods and Applications for the Nuclear Shell Model
Dean, D.J.; White, J.A.
1998-08-10
The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sd-pf-shell nuclei, a discussion of electron-capture rates in pf-shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare earth systems.
Monte Carlo calculations for r-process nucleosynthesis
Mumpower, Matthew Ryan
2015-11-12
A Monte Carlo framework is developed for exploring the impact of nuclear model uncertainties on the formation of the heavy elements. Mass measurements tightly constrain the macroscopic sector of FRDM2012. For r-process nucleosynthesis, it is necessary to understand the microscopic physics of the nuclear model employed. A combined approach of measurements and a deeper understanding of the microphysics is thus warranted to elucidate the site of the r-process.
Monte Carlo simulation of the ELIMED beamline using Geant4
NASA Astrophysics Data System (ADS)
Pipek, J.; Romano, F.; Milluzzo, G.; Cirrone, G. A. P.; Cuttone, G.; Amico, A. G.; Margarone, D.; Larosa, G.; Leanza, R.; Petringa, G.; Schillaci, F.; Scuderi, V.
2017-03-01
In this paper, we present a Geant4-based Monte Carlo application for ELIMED beamline [1-6] simulation, including its features and several preliminary results. We have developed the application to aid the design of the beamline, to estimate various beam characteristics, and to assess the amount of secondary radiation. In future, an enhanced version of this application will support the beamline users when preparing their experiments.
Monte Carlo approach to nuclei and nuclear matter
Fantoni, Stefano; Gandolfi, Stefano; Illarionov, Alexey Yu.; Schmidt, Kevin E.; Pederiva, Francesco
2008-10-13
We report on the most recent applications of the Auxiliary Field Diffusion Monte Carlo (AFDMC) method. The equation of state (EOS) for pure neutron matter in both normal and BCS phase and the superfluid gap in the low-density regime are computed, using a realistic Hamiltonian containing the Argonne AV8' plus Urbana IX three-nucleon interaction. Preliminary results for the EOS of isospin-asymmetric nuclear matter are also presented.
Monte Carlo Simulations: Number of Iterations and Accuracy
2015-07-01
Monte Carlo, confidence interval, central limit theorem, number of iterations, Wilson score method, Wald method, normal probability plot 16. SECURITY...Iterations 16 6. Conclusions 17 7. References and Notes 20 Appendix. MATLAB Code to Produce a Normal Probability Plot for Data in Array A 23...for normality can be performed to quantify the confidence level of a normality assumption. The basic idea of an NPP is to plot the sample data in
Monte Carlo verification of IMRT treatment plans on grid.
Gómez, Andrés; Fernández Sánchez, Carlos; Mouriño Gallego, José Carlos; López Cacheiro, Javier; González Castaño, Francisco J; Rodríguez-Silva, Daniel; Domínguez Carrera, Lorena; González Martínez, David; Pena García, Javier; Gómez Rodríguez, Faustino; González Castaño, Diego; Pombar Cameán, Miguel
2007-01-01
The eIMRT project is producing new remote computational tools for helping radiotherapists to plan and deliver treatments. The first available tool will be the IMRT treatment verification using Monte Carlo, which is a computational expensive problem that can be executed remotely on a GRID. In this paper, the current implementation of this process using GRID and SOA technologies is presented, describing the remote execution environment and the client.
Mcfast, a Parameterized Fast Monte Carlo for Detector Studies
NASA Astrophysics Data System (ADS)
Boehnlein, Amber S.
McFast is a modularized and parameterized fast Monte Carlo program which is designed to generate physics analysis information for different detector configurations and subdetector designs. McFast is based on simple geometrical object definitions and includes hit generation, parameterized track generation, vertexing, a muon system, electromagnetic calorimetry, and trigger framework for physics studies. Auxiliary tools include a geometry editor, visualization, and an i/o system.
Direct Monte Carlo Simulations of Hypersonic Viscous Interactions Including Separation
NASA Technical Reports Server (NTRS)
Moss, James N.; Rault, Didier F. G.; Price, Joseph M.
1993-01-01
Results of calculations obtained using the direct simulation Monte Carlo method for Mach 25 flow over a control surface are presented. The numerical simulations are for a 35-deg compression ramp at a low-density wind-tunnel test condition. Calculations obtained using both two- and three-dimensional solutions are reviewed, and a qualitative comparison is made with the oil flow pictures highlight separation and three-dimensional flow structure.
Distributional monte carlo methods for the boltzmann equation
NASA Astrophysics Data System (ADS)
Schrock, Christopher R.
Stochastic particle methods (SPMs) for the Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) technique, have gained popularity for the prediction of flows in which the assumptions behind the continuum equations of fluid mechanics break down; however, there are still a number of issues that make SPMs computationally challenging for practical use. In traditional SPMs, simulated particles may possess only a single velocity vector, even though they may represent an extremely large collection of actual particles. This limits the method to converge only in law to the Boltzmann solution. This document details the development of new SPMs that allow the velocity of each simulated particle to be distributed. This approach has been termed Distributional Monte Carlo (DMC). A technique is described which applies kernel density estimation to Nanbu's DSMC algorithm. It is then proven that the method converges not just in law, but also in solution for Linfinity(R 3) solutions of the space homogeneous Boltzmann equation. This provides for direct evaluation of the velocity density function. The derivation of a general Distributional Monte Carlo method is given which treats collision interactions between simulated particles as a relaxation problem. The framework is proven to converge in law to the solution of the space homogeneous Boltzmann equation, as well as in solution for Linfinity(R3) solutions. An approach based on the BGK simplification is presented which computes collision outcomes deterministically. Each technique is applied to the well-studied Bobylev-Krook-Wu solution as a numerical test case. Accuracy and variance of the solutions are examined as functions of various simulation parameters. Significantly improved accuracy and reduced variance are observed in the normalized moments for the Distributional Monte Carlo technique employing discrete BGK collision modeling.
Testing trivializing maps in the Hybrid Monte Carlo algorithm
Engel, Georg P.; Schaefer, Stefan
2011-01-01
We test a recent proposal to use approximate trivializing maps in a field theory to speed up Hybrid Monte Carlo simulations. Simulating the CPN−1 model, we find a small improvement with the leading order transformation, which is however compensated by the additional computational overhead. The scaling of the algorithm towards the continuum is not changed. In particular, the effect of the topological modes on the autocorrelation times is studied. PMID:21969733
Monte Carlo simulation for kinetic chemotaxis model: An application to the traveling population wave
NASA Astrophysics Data System (ADS)
Yasuda, Shugo
2017-02-01
A Monte Carlo simulation of chemotactic bacteria is developed on the basis of the kinetic model and is applied to a one-dimensional traveling population wave in a microchannel. In this simulation, the Monte Carlo method, which calculates the run-and-tumble motions of bacteria, is coupled with a finite volume method to calculate the macroscopic transport of the chemical cues in the environment. The simulation method can successfully reproduce the traveling population wave of bacteria that was observed experimentally and reveal the microscopic dynamics of bacterium coupled with the macroscopic transports of the chemical cues and bacteria population density. The results obtained by the Monte Carlo method are also compared with the asymptotic solution derived from the kinetic chemotaxis equation in the continuum limit, where the Knudsen number, which is defined by the ratio of the mean free path of bacterium to the characteristic length of the system, vanishes. The validity of the Monte Carlo method in the asymptotic behaviors for small Knudsen numbers is numerically verified.
Monte Carlo simulation of electrodeposition of copper: a multistep free energy calculation.
Harinipriya, S; Subramanian, Venkat R
2008-04-03
Electrodeposition of copper (Cu) involves length scales of a micrometer or even less. Several theoretical techniques such as continuum Monte Carlo, kinetic Monte Carlo (KMC), and molecular dynamics have been used for simulating this problem. However the multiphenomena characteristics of the problem pose a challenge for an efficient simulation algorithm. Traditional KMC methods are slow, especially when modeling surface diffusion with large number of particles and frequent particle jumps. Parameter estimation involving thousands of KMC runs is very time-consuming. Thus a less time-consuming and novel multistep continuum Monte Carlo simulation is carried out to evaluate the step wise free energy change in the process of electrochemical copper deposition. The procedure involves separate Monte Carlo codes employing different random number criterion (using hydrated radii, bare radii, hydration number of the species, redox potentials, etc.) to obtain the number of species (CuCl(2) or CuSO(4) or Cu as the case may be) and in turn the free energy. The effect of concentration of electrolyte, influence of electric field and presence of chloride ions on the free energy change for the processes is studied. The rate determining step for the process of electrodeposition of copper from CuCl(2) and CuSO(4) is also determined.
CloudMC: a cloud computing application for Monte Carlo simulation.
Miras, H; Jiménez, R; Miras, C; Gomà, C
2013-04-21
This work presents CloudMC, a cloud computing application-developed in Windows Azure®, the platform of the Microsoft® cloud-for the parallelization of Monte Carlo simulations in a dynamic virtual cluster. CloudMC is a web application designed to be independent of the Monte Carlo code in which the simulations are based-the simulations just need to be of the form: input files → executable → output files. To study the performance of CloudMC in Windows Azure®, Monte Carlo simulations with penelope were performed on different instance (virtual machine) sizes, and for different number of instances. The instance size was found to have no effect on the simulation runtime. It was also found that the decrease in time with the number of instances followed Amdahl's law, with a slight deviation due to the increase in the fraction of non-parallelizable time with increasing number of instances. A simulation that would have required 30 h of CPU on a single instance was completed in 48.6 min when executed on 64 instances in parallel (speedup of 37 ×). Furthermore, the use of cloud computing for parallel computing offers some advantages over conventional clusters: high accessibility, scalability and pay per usage. Therefore, it is strongly believed that cloud computing will play an important role in making Monte Carlo dose calculation a reality in future clinical practice.
Valence-bond quantum Monte Carlo algorithms defined on trees.
Deschner, Andreas; Sørensen, Erik S
2014-09-01
We present a class of algorithms for performing valence-bond quantum Monte Carlo of quantum spin models. Valence-bond quantum Monte Carlo is a projective T=0 Monte Carlo method based on sampling of a set of operator strings that can be viewed as forming a treelike structure. The algorithms presented here utilize the notion of a worm that moves up and down this tree and changes the associated operator string. In quite general terms, we derive a set of equations whose solutions correspond to a whole class of algorithms. As specific examples of this class of algorithms, we focus on two cases. The bouncing worm algorithm, for which updates are always accepted by allowing the worm to bounce up and down the tree, and the driven worm algorithm, where a single parameter controls how far up the tree the worm reaches before turning around. The latter algorithm involves only a single bounce where the worm turns from going up the tree to going down. The presence of the control parameter necessitates the introduction of an acceptance probability for the update.
Comparison of deterministic and Monte Carlo methods in shielding design.
Oliveira, A D; Oliveira, C
2005-01-01
In shielding calculation, deterministic methods have some advantages and also some disadvantages relative to other kind of codes, such as Monte Carlo. The main advantage is the short computer time needed to find solutions while the disadvantages are related to the often-used build-up factor that is extrapolated from high to low energies or with unknown geometrical conditions, which can lead to significant errors in shielding results. The aim of this work is to investigate how good are some deterministic methods to calculating low-energy shielding, using attenuation coefficients and build-up factor corrections. Commercial software MicroShield 5.05 has been used as the deterministic code while MCNP has been used as the Monte Carlo code. Point and cylindrical sources with slab shield have been defined allowing comparison between the capability of both Monte Carlo and deterministic methods in a day-by-day shielding calculation using sensitivity analysis of significant parameters, such as energy and geometrical conditions.
A New Approach to Monte Carlo Simulations in Statistical Physics
NASA Astrophysics Data System (ADS)
Landau, David P.
2002-08-01
Monte Carlo simulations [1] have become a powerful tool for the study of diverse problems in statistical/condensed matter physics. Standard methods sample the probability distribution for the states of the system, most often in the canonical ensemble, and over the past several decades enormous improvements have been made in performance. Nonetheless, difficulties arise near phase transitions-due to critical slowing down near 2nd order transitions and to metastability near 1st order transitions, and these complications limit the applicability of the method. We shall describe a new Monte Carlo approach [2] that uses a random walk in energy space to determine the density of states directly. Once the density of states is known, all thermodynamic properties can be calculated. This approach can be extended to multi-dimensional parameter spaces and should be effective for systems with complex energy landscapes, e.g., spin glasses, protein folding models, etc. Generalizations should produce a broadly applicable optimization tool. 1. A Guide to Monte Carlo Simulations in Statistical Physics, D. P. Landau and K. Binder (Cambridge U. Press, Cambridge, 2000). 2. Fugao Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001); Phys. Rev. E64, 056101-1 (2001).
Autocorrelation and Dominance Ratio in Monte Carlo Criticality Calculations
Ueki, Taro; Brown, Forrest B.; Parsons, D. Kent; Kornreich, Drew E.
2003-11-15
The cycle-to-cycle correlation (autocorrelation) in Monte Carlo criticality calculations is analyzed concerning the dominance ratio of fission kernels. The mathematical analysis focuses on how the eigenfunctions of a fission kernel decay if operated on by the cycle-to-cycle error propagation operator of the Monte Carlo stationary source distribution. The analytical results obtained can be summarized as follows: When the dominance ratio of a fission kernel is close to unity, autocorrelation of the k-effective tallies is weak and may be negligible, while the autocorrelation of the source distribution is strong and decays slowly. The practical implication is that when one analyzes a critical reactor with a large dominance ratio by Monte Carlo methods, the confidence interval estimation of the fission rate and other quantities at individual locations must account for the strong autocorrelation. Numerical results are presented for sample problems with a dominance ratio of 0.85-0.99, where Shannon and relative entropies are utilized to exclude the influence of initial nonstationarity.
VARIANCE ESTIMATION IN DOMAIN DECOMPOSED MONTE CARLO EIGENVALUE CALCULATIONS
Mervin, Brenden T; Maldonado, G. Ivan; Mosher, Scott W; Evans, Thomas M; Wagner, John C
2012-01-01
The number of tallies performed in a given Monte Carlo calculation is limited in most modern Monte Carlo codes by the amount of memory that can be allocated on a single processor. By using domain decomposition, the calculation is now limited by the total amount of memory available on all processors, allowing for significantly more tallies to be performed. However, decomposing the problem geometry introduces significant issues with the way tally statistics are conventionally calculated. In order to deal with the issue of calculating tally variances in domain decomposed environments for the Shift hybrid Monte Carlo code, this paper presents an alternative approach for reactor scenarios in which an assumption is made that once a particle leaves a domain, it does not reenter the domain. Particles that reenter the domain are instead treated as separate independent histories. This assumption introduces a bias that inevitably leads to under-prediction of the calculated variances for tallies within a few mean free paths of the domain boundaries. However, through the use of different decomposition strategies, primarily overlapping domains, the negative effects of such an assumption can be significantly reduced to within reasonable levels.
Improved diffusion coefficients generated from Monte Carlo codes
Herman, B. R.; Forget, B.; Smith, K.; Aviles, B. N.
2013-07-01
Monte Carlo codes are becoming more widely used for reactor analysis. Some of these applications involve the generation of diffusion theory parameters including macroscopic cross sections and diffusion coefficients. Two approximations used to generate diffusion coefficients are assessed using the Monte Carlo code MC21. The first is the method of homogenization; whether to weight either fine-group transport cross sections or fine-group diffusion coefficients when collapsing to few-group diffusion coefficients. The second is a fundamental approximation made to the energy-dependent P1 equations to derive the energy-dependent diffusion equations. Standard Monte Carlo codes usually generate a flux-weighted transport cross section with no correction to the diffusion approximation. Results indicate that this causes noticeable tilting in reconstructed pin powers in simple test lattices with L2 norm error of 3.6%. This error is reduced significantly to 0.27% when weighting fine-group diffusion coefficients by the flux and applying a correction to the diffusion approximation. Noticeable tilting in reconstructed fluxes and pin powers was reduced when applying these corrections. (authors)
Accelerating Monte Carlo power studies through parametric power estimation.
Ueckert, Sebastian; Karlsson, Mats O; Hooker, Andrew C
2016-04-01
Estimating the power for a non-linear mixed-effects model-based analysis is challenging due to the lack of a closed form analytic expression. Often, computationally intensive Monte Carlo studies need to be employed to evaluate the power of a planned experiment. This is especially time consuming if full power versus sample size curves are to be obtained. A novel parametric power estimation (PPE) algorithm utilizing the theoretical distribution of the alternative hypothesis is presented in this work. The PPE algorithm estimates the unknown non-centrality parameter in the theoretical distribution from a limited number of Monte Carlo simulation and estimations. The estimated parameter linearly scales with study size allowing a quick generation of the full power versus study size curve. A comparison of the PPE with the classical, purely Monte Carlo-based power estimation (MCPE) algorithm for five diverse pharmacometric models showed an excellent agreement between both algorithms, with a low bias of less than 1.2 % and higher precision for the PPE. The power extrapolated from a specific study size was in a very good agreement with power curves obtained with the MCPE algorithm. PPE represents a promising approach to accelerate the power calculation for non-linear mixed effect models.
Monte Carlo simulations of particle acceleration at oblique shocks
NASA Technical Reports Server (NTRS)
Baring, Matthew G.; Ellison, Donald C.; Jones, Frank C.
1994-01-01
The Fermi shock acceleration mechanism may be responsible for the production of high-energy cosmic rays in a wide variety of environments. Modeling of this phenomenon has largely focused on plane-parallel shocks, and one of the most promising techniques for its study is the Monte Carlo simulation of particle transport in shocked fluid flows. One of the principal problems in shock acceleration theory is the mechanism and efficiency of injection of particles from the thermal gas into the accelerated population. The Monte Carlo technique is ideally suited to addressing the injection problem directly, and previous applications of it to the quasi-parallel Earth bow shock led to very successful modeling of proton and heavy ion spectra, as well as other observed quantities. Recently this technique has been extended to oblique shock geometries, in which the upstream magnetic field makes a significant angle Theta(sub B1) to the shock normal. Spectral resutls from test particle Monte Carlo simulations of cosmic-ray acceleration at oblique, nonrelativistic shocks are presented. The results show that low Mach number shocks have injection efficiencies that are relatively insensitive to (though not independent of) the shock obliquity, but that there is a dramatic drop in efficiency for shocks of Mach number 30 or more as the obliquity increases above 15 deg. Cosmic-ray distributions just upstream of the shock reveal prominent bumps at energies below the thermal peak; these disappear far upstream but might be observable features close to astrophysical shocks.
Progress on coupling UEDGE and Monte-Carlo simulation codes
Rensink, M.E.; Rognlien, T.D.
1996-08-28
Our objective is to develop an accurate self-consistent model for plasma and neutral sin the edge of tokamak devices such as DIII-D and ITER. The tow-dimensional fluid model in the UEDGE code has been used successfully for simulating a wide range of experimental plasma conditions. However, when the neutral mean free path exceeds the gradient scale length of the background plasma, the validity of the diffusive and inertial fluid models in UEDGE is questionable. In the long mean free path regime, neutrals can be accurately and efficiently described by a Monte Carlo neutrals model. Coupling of the fluid plasma model in UEDGE with a Monte Carlo neutrals model should improve the accuracy of our edge plasma simulations. The results described here used the EIRENE Monte Carlo neutrals code, but since information is passed to and from the UEDGE plasma code via formatted test files, any similar neutrals code such as DEGAS2 or NIMBUS could, in principle, be used.
Estimating return period of landslide triggering by Monte Carlo simulation
NASA Astrophysics Data System (ADS)
Peres, D. J.; Cancelliere, A.
2016-10-01
Assessment of landslide hazard is a crucial step for landslide mitigation planning. Estimation of the return period of slope instability represents a quantitative method to map landslide triggering hazard on a catchment. The most common approach to estimate return periods consists in coupling a triggering threshold equation, derived from an hydrological and slope stability process-based model, with a rainfall intensity-duration-frequency (IDF) curve. Such a traditional approach generally neglects the effect of rainfall intensity variability within events, as well as the variability of initial conditions, which depend on antecedent rainfall. We propose a Monte Carlo approach for estimating the return period of shallow landslide triggering which enables to account for both variabilities. Synthetic hourly rainfall-landslide data generated by Monte Carlo simulations are analysed to compute return periods as the mean interarrival time of a factor of safety less than one. Applications are first conducted to map landslide triggering hazard in the Loco catchment, located in highly landslide-prone area of the Peloritani Mountains, Sicily, Italy. Then a set of additional simulations are performed in order to evaluate the traditional IDF-based method by comparison with the Monte Carlo one. Results show that return period is affected significantly by variability of both rainfall intensity within events and of initial conditions, and that the traditional IDF-based approach may lead to an overestimation of the return period of landslide triggering, or, in other words, a non-conservative assessment of landslide hazard.