Stabilized multilevel Monte Carlo method for stiff stochastic differential equations
Abdulle, Assyr Blumenthal, Adrian
2013-10-15
A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates because of the time step restriction to resolve the fastest scales that prevents to exploit all the levels of the MLMC approach. We show that by switching to explicit stabilized stochastic methods and balancing the stabilization procedure simultaneously with the hierarchical sampling strategy of MLMC methods, the computational cost for stiff systems is significantly reduced, while keeping the computational algorithm fully explicit and easy to implement. Numerical experiments on linear and nonlinear stochastic differential equations and on a stochastic partial differential equation illustrate the performance of the stabilized MLMC method and corroborate our theoretical findings.
Quantum Monte Carlo with a stochastic Poisson solver
NASA Astrophysics Data System (ADS)
Das, Dyutiman
Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually QMC has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall QMC scheme. We have developed a modified "Walk On Spheres" (WOS) algorithm using Green's function techniques, which can efficiently account for the interaction energy of walker configurations, typical of QMC algorithms. This stochastically obtained potential can be easily incorporated within popular QMC techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo(DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor. Then we apply this method to calculate the singlet-triplet splitting in a realistic heterostructure device. We also outline some other prospective applications for spherical quantum dots where the dielectric mismatch becomes an important issue for the addition energy spectrum.
Optimization of Monte Carlo transport simulations in stochastic media
Liang, C.; Ji, W.
2012-07-01
This paper presents an accurate and efficient approach to optimize radiation transport simulations in a stochastic medium of high heterogeneity, like the Very High Temperature Gas-cooled Reactor (VHTR) configurations packed with TRISO fuel particles. Based on a fast nearest neighbor search algorithm, a modified fast Random Sequential Addition (RSA) method is first developed to speed up the generation of the stochastic media systems packed with both mono-sized and poly-sized spheres. A fast neutron tracking method is then developed to optimize the next sphere boundary search in the radiation transport procedure. In order to investigate their accuracy and efficiency, the developed sphere packing and neutron tracking methods are implemented into an in-house continuous energy Monte Carlo code to solve an eigenvalue problem in VHTR unit cells. Comparison with the MCNP benchmark calculations for the same problem indicates that the new methods show considerably higher computational efficiency. (authors)
Longitudinal functional principal component modeling via Stochastic Approximation Monte Carlo
Martinez, Josue G.; Liang, Faming; Zhou, Lan; Carroll, Raymond J.
2010-01-01
The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented. PMID:20689648
Franke, B. C.; Prinja, A. K.
2013-07-01
The stochastic Galerkin method (SGM) is an intrusive technique for propagating data uncertainty in physical models. The method reduces the random model to a system of coupled deterministic equations for the moments of stochastic spectral expansions of result quantities. We investigate solving these equations using the Monte Carlo technique. We compare the efficiency with brute-force Monte Carlo evaluation of uncertainty, the non-intrusive stochastic collocation method (SCM), and an intrusive Monte Carlo implementation of the stochastic collocation method. We also describe the stability limitations of our SGM implementation. (authors)
Monte Carlo Hybrid Applied to Binary Stochastic Mixtures
Keady, K. P.
2008-08-11
The purpose of this set of codes isto use an inexpensive, approximate deterministic flux distribution to generate weight windows, wihich will then be used to bound particle weights for the Monte Carlo code run. The process is not automated; the user must run the deterministic code and use the output file as a command-line argument for the Monte Carlo code. Two sets of text input files are included as test problems/templates.
Stochastic resonance phenomenon in Monte Carlo simulations of silver adsorbed on gold
NASA Astrophysics Data System (ADS)
Gimenez, María Cecilia
2016-03-01
The possibility of observing the stochastic resonance phenomenon was analyzed by means of Monte Carlo simulations of silver adsorbed on 100 gold surfaces. The coverage degree was studied as a function of the periodical variation of the chemical potential. The signal-noise relationship was studied as a function of the amplitude and frequency of chemical potential and temperature. When this value is plotted as a function of temperature, a maximum is found, indicating the possible presence of stochastic resonance.
Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application
Blunt, N. S. Kersten, J. A. F.; Smart, Simon D.; Spencer, J. S.; Booth, George H.; Alavi, Ali
2015-05-14
We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.
Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application.
Blunt, N S; Smart, Simon D; Kersten, J A F; Spencer, J S; Booth, George H; Alavi, Ali
2015-05-14
We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable. PMID:25978883
A Hybrid Monte Carlo-Deterministic Method for Global Binary Stochastic Medium Transport Problems
Keady, K P; Brantley, P
2010-03-04
Global deep-penetration transport problems are difficult to solve using traditional Monte Carlo techniques. In these problems, the scalar flux distribution is desired at all points in the spatial domain (global nature), and the scalar flux typically drops by several orders of magnitude across the problem (deep-penetration nature). As a result, few particle histories may reach certain regions of the domain, producing a relatively large variance in tallies in those regions. Implicit capture (also known as survival biasing or absorption suppression) can be used to increase the efficiency of the Monte Carlo transport algorithm to some degree. A hybrid Monte Carlo-deterministic technique has previously been developed by Cooper and Larsen to reduce variance in global problems by distributing particles more evenly throughout the spatial domain. This hybrid method uses an approximate deterministic estimate of the forward scalar flux distribution to automatically generate weight windows for the Monte Carlo transport simulation, avoiding the necessity for the code user to specify the weight window parameters. In a binary stochastic medium, the material properties at a given spatial location are known only statistically. The most common approach to solving particle transport problems involving binary stochastic media is to use the atomic mix (AM) approximation in which the transport problem is solved using ensemble-averaged material properties. The most ubiquitous deterministic model developed specifically for solving binary stochastic media transport problems is the Levermore-Pomraning (L-P) model. Zimmerman and Adams proposed a Monte Carlo algorithm (Algorithm A) that solves the Levermore-Pomraning equations and another Monte Carlo algorithm (Algorithm B) that is more accurate as a result of improved local material realization modeling. Recent benchmark studies have shown that Algorithm B is often significantly more accurate than Algorithm A (and therefore the L-P model) for deep penetration problems such as examined in this paper. In this research, we investigate the application of a variant of the hybrid Monte Carlo-deterministic method proposed by Cooper and Larsen to global deep penetration problems involving binary stochastic media. To our knowledge, hybrid Monte Carlo-deterministic methods have not previously been applied to problems involving a stochastic medium. We investigate two approaches for computing the approximate deterministic estimate of the forward scalar flux distribution used to automatically generate the weight windows. The first approach uses the atomic mix approximation to the binary stochastic medium transport problem and a low-order discrete ordinates angular approximation. The second approach uses the Levermore-Pomraning model for the binary stochastic medium transport problem and a low-order discrete ordinates angular approximation. In both cases, we use Monte Carlo Algorithm B with weight windows automatically generated from the approximate forward scalar flux distribution to obtain the solution of the transport problem.
Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm
NASA Astrophysics Data System (ADS)
Takaishi, Tetsuya
2013-04-01
The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. We perform the HMC simulations of the SV model for two liquid stock returns traded on the Tokyo Stock Exchange and measure the volatilities of those stock returns. Then we calculate the accuracy of the volatility measurement using the realized volatility as a proxy of the true volatility and compare the SV model with the GARCH model which is one of other volatility models. Using the accuracy calculated with the realized volatility we find that empirically the SV model performs better than the GARCH model.
Bayesian estimation of realized stochastic volatility model by Hybrid Monte Carlo algorithm
NASA Astrophysics Data System (ADS)
Takaishi, Tetsuya
2014-03-01
The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integrator. We also find that the autocorrelation time of the volatility variables sampled by the HMCA is very short. Thus it is concluded that the HMCA with the 2MNI is an efficient algorithm for parameter estimations of the RSV model.
Can Markov chain Monte Carlo be usefully applied to stochastic processes with hidden birth times?
NASA Astrophysics Data System (ADS)
Renshaw, Eric; Gibson, Gavin J.
1998-12-01
This paper examines the power of Markov chain Monte Carlo methods to tackle the `inverse' problem of stochastic population modelling. Namely, given a partial series of event-time observations, believed governed by a known process, what range of model parameters might plausibly explain it? This problem is first introduced in the simple context of an immigration-death process, in which only deaths are recorded, and is then extended through the introduction of birth, standard and power-law logistic growth, and an `odd-even effects' quantum optics model. The results show that simple Metropolis Hastings samplers can be applied to provide useful information on models containing a high degree of complexity. Specific problems highlighted include: the potentially poor mixing qualities of simple Metropolis Hastings samplers; and, that heavily non-symmetric full likelihood surfaces may inflict substantial bias on their associated marginal distributions.
A Monte Carlo simulation based inverse propagation method for stochastic model updating
NASA Astrophysics Data System (ADS)
Bao, Nuo; Wang, Chunjie
2015-08-01
This paper presents an efficient stochastic model updating method based on statistical theory. Significant parameters have been selected implementing the F-test evaluation and design of experiments, and then the incomplete fourth-order polynomial response surface model (RSM) has been developed. Exploiting of the RSM combined with Monte Carlo simulation (MCS), reduces the calculation amount and the rapid random sampling becomes possible. The inverse uncertainty propagation is given by the equally weighted sum of mean and covariance matrix objective functions. The mean and covariance of parameters are estimated synchronously by minimizing the weighted objective function through hybrid of particle-swarm and Nelder-Mead simplex optimization method, thus the better correlation between simulation and test is achieved. Numerical examples of a three degree-of-freedom mass-spring system under different conditions and GARTEUR assembly structure validated the feasibility and effectiveness of the proposed method.
Stochastic Monte-Carlo Markov Chain Inversions on Models Regionalized Using Receiver Functions
NASA Astrophysics Data System (ADS)
Larmat, C. S.; Maceira, M.; Kato, Y.; Bodin, T.; Calo, M.; Romanowicz, B. A.; Chai, C.; Ammon, C. J.
2014-12-01
There is currently a strong interest in stochastic approaches to seismic modeling - versus deterministic methods such as gradient methods - due to the ability of these methods to better deal with highly non-linear problems. Another advantage of stochastic methods is that they allow the estimation of the a posteriori probability distribution of the derived parameters, meaning the envisioned Bayesian inversion of Tarantola allowing the quantification of the solution error. The cost to pay of stochastic methods is that they require testing thousands of variations of each unknown parameter and their associated weights to ensure reliable probabilistic inferences. Even with the best High-Performance Computing resources available, 3D stochastic full waveform modeling at the regional scale still remains out-of-reach. We are exploring regionalization as one way to reduce the dimension of the parameter space, allowing the identification of areas in the models that can be treated as one block in a subsequent stochastic inversion. Regionalization is classically performed through the identification of tectonic or structural elements. Lekic & Romanowicz (2011) proposed a new approach with a cluster analysis of the tomographic velocity models instead. Here we present the results of a clustering analysis on the P-wave receiver-functions used in the subsequent inversion. Different clustering algorithms and quality of clustering are tested for different datasets of North America and China. Preliminary results with the kmean clustering algorithm show that an interpolated receiver function wavefield (Chai et al., GRL, in review) improve the agreement with the geological and tectonic regions of North America compared to the traditional approach of stacked receiver functions. After regionalization, 1D profile for each region is stochastically inferred using a parallelized code based on Monte-Carlo Markov Chains (MCMC), and modeling surfacewave-dispersion and receiver-functions observations. The parameters of the inversion are the elastic properties, the thickness and the number of isotropic layers. We will present preliminary results and compare them to results obtained from a different regionalizationbased on a tomographic model (Calo et al., 2013).
Energy Science and Technology Software Center (ESTSC)
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.
NASA Astrophysics Data System (ADS)
Franke, Brian C.; Kensek, Ronald P.; Prinja, Anil K.
2014-06-01
Stochastic-media simulations require numerous boundary crossings. We consider two Monte Carlo electron transport approaches and evaluate accuracy with numerous material boundaries. In the condensed-history method, approximations are made based on infinite-medium solutions for multiple scattering over some track length. Typically, further approximations are employed for material-boundary crossings where infinite-medium solutions become invalid. We have previously explored an alternative "condensed transport" formulation, a Generalized Boltzmann-Fokker-Planck GBFP method, which requires no special boundary treatment but instead uses approximations to the electron-scattering cross sections. Some limited capabilities for analog transport and a GBFP method have been implemented in the Integrated Tiger Series (ITS) codes. Improvements have been made to the condensed history algorithm. The performance of the ITS condensed-history and condensed-transport algorithms are assessed for material-boundary crossings. These assessments are made both by introducing artificial material boundaries and by comparison to analog Monte Carlo simulations.
Energy Science and Technology Software Center (ESTSC)
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.
Stochastic method for accommodation of equilibrating basins in kinetic Monte Carlo simulations
Van Siclen, Clinton D
2007-02-01
A computationally simple way to accommodate "basins" of trapping states in standard kinetic Monte Carlo simulations is presented. By assuming the system is effectively equilibrated in the basin, the residence time (time spent in the basin before escape) and the probabilities for transition to states outside the basin may be calculated. This is demonstrated for point defect diffusion over a periodic grid of sites containing a complex basin.
NASA Astrophysics Data System (ADS)
Shimizu, Noritaka; Mizusaki, Takahiro; Kaneko, Kazunari
2013-06-01
We propose a new variational Monte Carlo (VMC) approach based on the Krylov subspace for large-scale shell-model calculations. A random walker in the VMC is formulated with the M-scheme representation, and samples a small number of configurations from a whole Hilbert space stochastically. This VMC framework is demonstrated in the shell-model calculations of 48Cr and 60Zn, and we discuss its relation to a small number of Lanczos iterations. By utilizing the wave function obtained by the conventional particle-hole-excitation truncation as an initial state, this VMC approach provides us with a sequence of systematically improved results.
Monte Carlo methods on advanced computer architectures
Martin, W.R.
1991-12-31
Monte Carlo methods describe a wide class of computational methods that utilize random numbers to perform a statistical simulation of a physical problem, which itself need not be a stochastic process. For example, Monte Carlo can be used to evaluate definite integrals, which are not stochastic processes, or may be used to simulate the transport of electrons in a space vehicle, which is a stochastic process. The name Monte Carlo came about during the Manhattan Project to describe the new mathematical methods being developed which had some similarity to the games of chance played in the casinos of Monte Carlo. Particle transport Monte Carlo is just one application of Monte Carlo methods, and will be the subject of this review paper. Other applications of Monte Carlo, such as reliability studies, classical queueing theory, molecular structure, the study of phase transitions, or quantum chromodynamics calculations for basic research in particle physics, are not included in this review. The reference by Kalos is an introduction to general Monte Carlo methods and references to other applications of Monte Carlo can be found in this excellent book. For the remainder of this paper, the term Monte Carlo will be synonymous to particle transport Monte Carlo, unless otherwise noted. 60 refs., 14 figs., 4 tabs.
NASA Astrophysics Data System (ADS)
Jin, Shengye; Tamura, Masayuki
2013-10-01
Monte Carlo Ray Tracing (MCRT) method is a versatile application for simulating radiative transfer regime of the Solar - Atmosphere - Landscape system. Moreover, it can be used to compute the radiation distribution over a complex landscape configuration, as an example like a forest area. Due to its robustness to the complexity of the 3-D scene altering, MCRT method is also employed for simulating canopy radiative transfer regime as the validation source of other radiative transfer models. In MCRT modeling within vegetation, one basic step is the canopy scene set up. 3-D scanning application was used for representing canopy structure as accurately as possible, but it is time consuming. Botanical growth function can be used to model the single tree growth, but cannot be used to express the impaction among trees. L-System is also a functional controlled tree growth simulation model, but it costs large computing memory. Additionally, it only models the current tree patterns rather than tree growth during we simulate the radiative transfer regime. Therefore, it is much more constructive to use regular solid pattern like ellipsoidal, cone, cylinder etc. to indicate single canopy. Considering the allelopathy phenomenon in some open forest optical images, each tree in its own `domain' repels other trees. According to this assumption a stochastic circle packing algorithm is developed to generate the 3-D canopy scene in this study. The canopy coverage (%) and the tree amount (N) of the 3-D scene are declared at first, similar to the random open forest image. Accordingly, we randomly generate each canopy radius (rc). Then we set the circle central coordinate on XY-plane as well as to keep circles separate from each other by the circle packing algorithm. To model the individual tree, we employ the Ishikawa's tree growth regressive model to set the tree parameters including DBH (dt), tree height (H). However, the relationship between canopy height (Hc) and trunk height (Ht) is unclear to us. We assume the proportion between Hc and Ht as a random number in the interval from 2.0 to 3.0. De Wit's sphere leaf angle distribution function was used within the canopy for acceleration. Finally, we simulate the open forest albedo using MCRT method. The MCRT algorithm of this study is summarized as follows (1) Initialize the photon with a position (r0), source direction (Ω0) and intensity (I0), respectively. (2) Simulate the free path (s) of a photon under the condition of (r', Ω, I') in the canopy. (3) Calculate the new position of the photon r=r +sΩ'. (4) Determine the new scattering direction (Ω)after collision at, r and then calculate the new intensity I = ΥL(ΩL,Ω'-->Ω)I'.(5) Accumulate the intensity I of a photon escaping from the top boundary of the 3-D Scene, otherwise redo from step (2), until I is smaller than a threshold. (6) Repeat from step (1), for each photon. We testify the model on four different simulated open forests and the effectiveness of the model is demonstrated in details.
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.
A stochastic Markov chain approach for tennis: Monte Carlo simulation and modeling
NASA Astrophysics Data System (ADS)
Aslam, Kamran
This dissertation describes the computational formulation of probability density functions (pdfs) that facilitate head-to-head match simulations in tennis along with ranking systems developed from their use. A background on the statistical method used to develop the pdfs , the Monte Carlo method, and the resulting rankings are included along with a discussion on ranking methods currently being used both in professional sports and in other applications. Using an analytical theory developed by Newton and Keller in [34] that defines a tennis player's probability of winning a game, set, match and single elimination tournament, a computational simulation has been developed in Matlab that allows further modeling not previously possible with the analytical theory alone. Such experimentation consists of the exploration of non-iid effects, considers the concept the varying importance of points in a match and allows an unlimited number of matches to be simulated between unlikely opponents. The results of these studies have provided pdfs that accurately model an individual tennis player's ability along with a realistic, fair and mathematically sound platform for ranking them.
NASA Astrophysics Data System (ADS)
Zhang, Yue; Sun, Xian; Thiele, Antje; Hinz, Stefan
2015-10-01
Synthetic aperture radar (SAR) systems, such as TanDEM-X, TerraSAR-X and Cosmo-SkyMed, acquire imagery with high spatial resolution (HR), making it possible to observe objects in urban areas with high detail. In this paper, we propose a new top-down framework for three-dimensional (3D) building reconstruction from HR interferometric SAR (InSAR) data. Unlike most methods proposed before, we adopt a generative model and utilize the reconstruction process by maximizing a posteriori estimation (MAP) through Monte Carlo methods. The reason for this strategy refers to the fact that the noisiness of SAR images calls for a thorough prior model to better cope with the inherent amplitude and phase fluctuations. In the reconstruction process, according to the radar configuration and the building geometry, a 3D building hypothesis is mapped to the SAR image plane and decomposed to feature regions such as layover, corner line, and shadow. Then, the statistical properties of intensity, interferometric phase and coherence of each region are explored respectively, and are included as region terms. Roofs are not directly considered as they are mixed with wall into layover area in most cases. When estimating the similarity between the building hypothesis and the real data, the prior, the region term, together with the edge term related to the contours of layover and corner line, are taken into consideration. In the optimization step, in order to achieve convergent reconstruction outputs and get rid of local extrema, special transition kernels are designed. The proposed framework is evaluated on the TanDEM-X dataset and performs well for buildings reconstruction.
Cramer, S.N.
1984-01-01
The MORSE code is a large general-use multigroup Monte Carlo code system. Although no claims can be made regarding its superiority in either theoretical details or Monte Carlo techniques, MORSE has been, since its inception at ORNL in the late 1960s, the most widely used Monte Carlo radiation transport code. The principal reason for this popularity is that MORSE is relatively easy to use, independent of any installation or distribution center, and it can be easily customized to fit almost any specific need. Features of the MORSE code are described.
Shell model Monte Carlo methods
Koonin, S.E.; Dean, D.J.
1996-10-01
We review quantum Monte Carlo methods for dealing with large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; resultant path integral is evaluated stochastically. We first discuss the motivation, formalism, and implementation of such Shell Model Monte Carlo methods. There then follows a sampler of results and insights obtained from a number of applications. These include the ground state and thermal properties of pf-shell nuclei, thermal behavior of {gamma}-soft nuclei, and calculation of double beta-decay matrix elements. Finally, prospects for further progress in such calculations are discussed. 87 refs.
NASA Astrophysics Data System (ADS)
Kalos, M. H.
2010-01-01
Computation now plays an essential role in science, especially in theoretical physics. The greater depth of our understanding of physical phenomena and the need to predict the behavior of complex devices demands a level of analysis that purely mathematical methods cannot meet. Monte Carlo methods offer some of the most powerful approaches to computation. They permit a simple transcription of a random process into a computer code. Alternatively, they give the only accurate approach to the many-dimensional problems of theoretical physics. I will describe a number of complementary approaches for Monte Carlo methods in treating diverse systems.
Viral load and stochastic mutation in a Monte Carlo simulation of HIV
NASA Astrophysics Data System (ADS)
Ruskin, H. J.; Pandey, R. B.; Liu, Y.
2002-08-01
Viral load is examined, as a function of primary viral growth factor ( Pg) and mutation, through a computer simulation model for HIV immune response. Cell-mediated immune response is considered on a cubic lattice with four cell types: macrophage ( M), helper ( H), cytotoxic ( C), and virus ( V). Rule-based interactions are used with random sequential update of the binary cellular states. The relative viral load (the concentration of virus with respect to helper cells) is found to increase with the primary viral growth factor above a critical value ( Pc), leading to a phase transition from immuno-competent to immuno-deficient state. The critical growth factor ( Pc) seems to depend on mobility and mutation. The stochastic growth due to mutation is found to depend non-monotonically on the relative viral load, with a maximum at a characteristic load which is lower for stronger viral growth.
2010-01-01
Background Although many infections that are transmissible from person to person are acquired through direct contact between individuals, a minority, notably pulmonary tuberculosis (TB), measles and influenza are known to be spread by the airborne route. Airborne infections pose a particular threat to susceptible individuals whenever they are placed together with the index case in confined spaces. With this in mind, waiting areas of healthcare facilities present a particular challenge, since large numbers of people, some of whom may have underlying conditions which predispose them to infection, congregate in such spaces and can be exposed to an individual who may be shedding potentially pathogenic microorganisms. It is therefore important to understand the risks posed by infectious individuals in waiting areas, so that interventions can be developed to minimise the spread of airborne infections. Method A stochastic Monte Carlo model was constructed to analyse the transmission of airborne infection in a hypothetical 132 m3 hospital waiting area in which occupancy levels, waiting times and ventilation rate can all be varied. In the model the Gammaitoni-Nucci equation was utilized to predict probability of susceptible individuals becoming infected. The model was used to assess the risk of transmission of three infectious diseases, TB, influenza and measles. In order to allow for stochasticity a random number generator was applied to the variables in the model and a total of 10000 individual simulations were undertaken. The mean quanta production rates used in the study were 12.7, 100 and 570 per hour for TB, influenza and measles, respectively. Results The results of the study revealed the mean probability of acquiring a TB infection during a 30-minute stay in the waiting area to be negligible (i.e. 0.0034), while that for influenza was an order of magnitude higher at 0.0262. By comparison the mean probability of acquiring a measles infection during the same period was 0.1349. If the duration of the stay was increased to 60 minutes then these values increased to 0.0087, 0.0662 and 0.3094, respectively. Conclusion Under normal circumstances the risk of acquiring a TB infection during a visit to a hospital waiting area is minimal. Likewise the risks associated with the transmission of influenza, although an order of magnitude greater than those for TB, are relatively small. By comparison, the risks associated with measles are high. While the installation of air disinfection may be beneficial, when seeking to prevent the transmission of airborne viral infection it is important to first minimize waiting times and the number of susceptible individuals present before turning to expensive technological solutions. PMID:20727178
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.
NASA Astrophysics Data System (ADS)
Nissenbaum, Daniel; Lin, Hsin; Barbiellini, Bernardo; Bansil, Arun
2009-03-01
To study the performance of the Stochastic Gradient Approximation (SGA) for variational Quantum Monte Carlo methods, we have considered lithium nano-clusters [1] described by Hartree-Fock wavefunctions multiplied by two-body Jastrow factors with a single variational parameter b. Even when the system size increases, we have shown the feasibility of obtaining an accurate value of b that minimizes the energy without an explicit calculation of the energy itself. The present SGA algorithm is so efficient because an analytic gradient formula is used and because the statistical noise in the gradient is smaller than in the energy [2]. Interestingly, in this scheme the absolute value of the gradient is less important than the sign of the gradient. Work supported in part by U.S. DOE. [1] D. Nissenbaum et al., Phys. Rev. B 76, 033412 (2007). [2] A. Harju, J. Low. Temp. Phys. 140, 181 (2005).
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
Reactive canonical Monte Carlo
NASA Astrophysics Data System (ADS)
Johnson, J. Karl; Panagiotopoulos, Athanassios Z.; Gubbins, Keith E.
A new simulation technique is developed for calculating the properties of chemically reactive and associating (hydrogen bonding, charge transfer) systems. We call this new method reactive canonical Monte Carlo (RCMC). In contrast to previous methods for treating chemical reactions, this algorithm is applicable to reactions involving a change in mole number. Stoichiometrically balanced reactions are attempted in the forward and reverse directions to achieve chemical equilibrium. The transition probabilities do not depend on the chemical potentials or chemical potential differences of any of the components. We also extend RCMC to work in concert with the isothermal-isobaric ensemble for simulating chemical reactions at constant pressure, and with the Gibbs ensemble for simultaneous calculation of phase and chemical equilibria. Association is treated as a chemical reaction in the RCMC formalism. Results are presented for dimerization of simple model associating fluids. In contrast to previous methods, the reactive Gibbs ensemble can be used to calculate phase equilibrium for associating fluids with very strong bonding sites. RCMC simulations are performed for nitric oxide dimerization and results are compared with available experimental data in the liquid phase. Agreement with experiment is excellent. Results for a vapour phase simulation are also in remarkable agreement with estimates based on second virial coefficient data.
Isotropic Monte Carlo Grain Growth
Energy Science and Technology Software Center (ESTSC)
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.
Bieda, Bogusław
2014-05-15
The purpose of the paper is to present the results of application of stochastic approach based on Monte Carlo (MC) simulation for life cycle inventory (LCI) data of Mittal Steel Poland (MSP) complex in Kraków, Poland. In order to assess the uncertainty, the software CrystalBall® (CB), which is associated with Microsoft® Excel spreadsheet model, is used. The framework of the study was originally carried out for 2005. The total production of steel, coke, pig iron, sinter, slabs from continuous steel casting (CSC), sheets from hot rolling mill (HRM) and blast furnace gas, collected in 2005 from MSP was analyzed and used for MC simulation of the LCI model. In order to describe random nature of all main products used in this study, normal distribution has been applied. The results of the simulation (10,000 trials) performed with the use of CB consist of frequency charts and statistical reports. The results of this study can be used as the first step in performing a full LCA analysis in the steel industry. Further, it is concluded that the stochastic approach is a powerful method for quantifying parameter uncertainty in LCA/LCI studies and it can be applied to any steel industry. The results obtained from this study can help practitioners and decision-makers in the steel production management. PMID:24290145
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.
Khromov, K. Yu.; Vaks, V. G. Zhuravlev, I. A.
2013-02-15
The previously developed ab initio model and the kinetic Monte Carlo method (KMCM) are used to simulate precipitation in a number of iron-copper alloys with different copper concentrations x and temperatures T. The same simulations are also made using an improved version of the previously suggested stochastic statistical method (SSM). The results obtained enable us to make a number of general conclusions about the dependences of the decomposition kinetics in Fe-Cu alloys on x and T. We also show that the SSM usually describes the precipitation kinetics in good agreement with the KMCM, and using the SSM in conjunction with the KMCM allows extending the KMC simulations to the longer evolution times. The results of simulations seem to agree with available experimental data for Fe-Cu alloys within statistical errors of simulations and the scatter of experimental results. Comparison of simulation results with experiments for some multicomponent Fe-Cu-based alloys allows making certain conclusions about the influence of alloying elements in these alloys on the precipitation kinetics at different stages of evolution.
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 performing a variety of functions, (b) the water resource system of Athens comprising four reservoirs and many aqueducts, and (c) a human-modified inadequately measured basin in which the parameter fitting of a hydrological model is sought.
Monte Carlo calculations of nuclei
Pieper, S.C.
1997-10-01
Nuclear many-body calculations have the complication of strong spin- and isospin-dependent potentials. In these lectures the author discusses the variational and Green`s function Monte Carlo techniques that have been developed to address this complication, and presents a few results.
Is Monte Carlo embarrassingly parallel?
Hoogenboom, J. E.
2012-07-01
Monte Carlo is often stated as being embarrassingly parallel. However, running a Monte Carlo calculation, especially a reactor criticality calculation, in parallel using tens of processors shows a serious limitation in speedup and the execution time may even increase beyond a certain number of processors. In this paper the main causes of the loss of efficiency when using many processors are analyzed using a simple Monte Carlo program for criticality. The basic mechanism for parallel execution is MPI. One of the bottlenecks turn out to be the rendez-vous points in the parallel calculation used for synchronization and exchange of data between processors. This happens at least at the end of each cycle for fission source generation in order to collect the full fission source distribution for the next cycle and to estimate the effective multiplication factor, which is not only part of the requested results, but also input to the next cycle for population control. Basic improvements to overcome this limitation are suggested and tested. Also other time losses in the parallel calculation are identified. Moreover, the threading mechanism, which allows the parallel execution of tasks based on shared memory using OpenMP, is analyzed in detail. Recommendations are given to get the maximum efficiency out of a parallel Monte Carlo calculation. (authors)
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 Technical Reports Server (NTRS)
Parrish, R. V.; Dieudonne, J. E.; Filippas, T. A.
1971-01-01
An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.
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…
NASA Technical Reports Server (NTRS)
Bell, Thomas L.; Abdullah, A.; Martin, Russell L.; North, Gerald R.
1990-01-01
Estimates of monthly average rainfall based on satellite observations from a low earth orbit will differ from the true monthly average because the satellite observes a given area only intermittently. This sampling error inherent in satellite monitoring of rainfall would occur even if the satellite instruments could measure rainfall perfectly. The size of this error is estimated for a satellite system being studied at NASA, the Tropical Rainfall Measuring Mission (TRMM). First, the statistical description of rainfall on scales from 1 to 1000 km is examined in detail, based on rainfall data from the Global Atmospheric Research Project Atlantic Tropical Experiment (GATE). A TRMM-like satellite is flown over a two-dimensional time-evolving simulation of rainfall using a stochastic model with statistics tuned to agree with GATE statistics. The distribution of sampling errors found from many months of simulated observations is found to be nearly normal, even though the distribution of area-averaged rainfall is far from normal. For a range of orbits likely to be employed in TRMM, sampling error is found to be less than 10 percent of the mean for rainfall averaged over a 500 x 500 sq km area.
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 Schrdinger 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 pairing orbitals are presented and their nodal properties are tested in calculations of first row atoms and molecules. Finally, backflow "dressed" coordinates are introduced as another possibility for capturing correlation effects and for decreasing the fixed-node bias.
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.
A Monte Carlo primer for health physicists.
Turner, J E; Wright, H A; Hamm, R N
1985-06-01
The basic ideas and principles of Monte Carlo calculations are presented in the form of a "primer" for health physicists. A simple integral with a known answer is evaluated by two different Monte Carlo approaches. Random numbers, which underlie Monte Carlo work, are discussed, and a sample table of random numbers generated by a hand calculator is presented. Monte Carlo calculations of dose and linear energy transfer (LET) from 100-keV neutrons incident on a tissue slab are discussed. The random-number table is used in a hand calculation of the initial sequence of events for a 100-keV neutron entering the slab. Some pitfalls in Monte Carlo work are described. While this primer addresses mainly the "bare bones" of Monte Carlo, a final section briefly describes some of the more sophisticated techniques used in practice to reduce variance and computing time. PMID:3997524
Monte Carlo primer for health physicists
Turner, J.E.; Wright, H.A.; Hamm, R.N.
1985-06-01
The basic ideas and principles of Monte Carlo calculations are presented in the form of a primer for health physicists. A simple integral with a known answer is evaluated by two different Monte Carlo approaches. Random number, which underlie Monte Carlo work, are discussed, and a sample table of random numbers generated by a hand calculator is presented. Monte Carlo calculations of dose and linear energy transfer (LET) from 100-keV neutrons incident on a tissue slab are discussed. The random-number table is used in a hand calculation of the initial sequence of events for a 100-keV neutron entering the slab. Some pitfalls in Monte Carlo work are described. While this primer addresses mainly the bare bones of Monte Carlo, a final section briefly describes some of the more sophisticated techniques used in practice to reduce variance and computing time.
A Monte Carlo primer for health physicists.
TOXLINE Toxicology Bibliographic Information
Turner JE; Wright HA; Hamm RN
1985-06-01
The basic ideas and principles of Monte Carlo calculations are presented in the form of a "primer" for health physicists. A simple integral with a known answer is evaluated by two different Monte Carlo approaches. Random numbers, which underlie Monte Carlo work, are discussed, and a sample table of random numbers generated by a hand calculator is presented. Monte Carlo calculations of dose and linear energy transfer (LET) from 100-keV neutrons incident on a tissue slab are discussed. The random-number table is used in a hand calculation of the initial sequence of events for a 100-keV neutron entering the slab. Some pitfalls in Monte Carlo work are described. While this primer addresses mainly the "bare bones" of Monte Carlo, a final section briefly describes some of the more sophisticated techniques used in practice to reduce variance and computing time.
Present status of vectorized Monte Carlo
Brown, F.B.
1987-01-01
Monte Carlo applications have traditionally been limited by the large amounts of computer time required to produce acceptably small statistical uncertainties, so the immediate benefit of vectorization is an increase in either the number of jobs completed or the number of particles processed per job, typically by one order of magnitude or more. This results directly in improved engineering design analyses, since Monte Carlo methods are used as standards for correcting more approximate methods. The relatively small number of vectorized programs is a consequence of the newness of vectorized Monte Carlo, the difficulties of nonportability, and the very large development effort required to rewrite or restructure Monte Carlo codes for vectorization. Based on the successful efforts to date, it may be concluded that Monte Carlo vectorization will spread to increasing numbers of codes and applications. The possibility of multitasking provides even further motivation for vectorizing Monte Carlo, since the step from vector to multitasked vector is relatively straightforward.
1-D EQUILIBRIUM DISCRETE DIFFUSION MONTE CARLO
T. EVANS; ET AL
2000-08-01
We present a new hybrid Monte Carlo method for 1-D equilibrium diffusion problems in which the radiation field coexists with matter in local thermodynamic equilibrium. This method, the Equilibrium Discrete Diffusion Monte Carlo (EqDDMC) method, combines Monte Carlo particles with spatially discrete diffusion solutions. We verify the EqDDMC method with computational results from three slab problems. The EqDDMC method represents an incremental step toward applying this hybrid methodology to non-equilibrium diffusion, where it could be simultaneously coupled to Monte Carlo transport.
Uncertainty Propagation with Fast Monte Carlo Techniques
NASA Astrophysics Data System (ADS)
Rochman, D.; van der Marck, S. C.; Koning, A. J.; Sjöstrand, H.; Zwermann, W.
2014-04-01
Two new and faster Monte Carlo methods for the propagation of nuclear data uncertainties in Monte Carlo nuclear simulations are presented (the "Fast TMC" and "Fast GRS" methods). They are addressing the main drawback of the original Total Monte Carlo method (TMC), namely the necessary large time multiplication factor compared to a single calculation. With these new methods, Monte Carlo simulations can now be accompanied with uncertainty propagation (other than statistical), with small additional calculation time. The new methods are presented and compared with the TMC methods for criticality benchmarks.
Monte Carlo surface flux tallies
Favorite, Jeffrey A
2010-11-19
Particle fluxes on surfaces are difficult to calculate with Monte Carlo codes because the score requires a division by the surface-crossing angle cosine, and grazing angles lead to inaccuracies. We revisit the standard practice of dividing by half of a cosine 'cutoff' for particles whose surface-crossing cosines are below the cutoff. The theory behind this approximation is sound, but the application of the theory to all possible situations does not account for two implicit assumptions: (1) the grazing band must be symmetric about 0, and (2) a single linear expansion for the angular flux must be applied in the entire grazing band. These assumptions are violated in common circumstances; for example, for separate in-going and out-going flux tallies on internal surfaces, and for out-going flux tallies on external surfaces. In some situations, dividing by two-thirds of the cosine cutoff is more appropriate. If users were able to control both the cosine cutoff and the substitute value, they could use these parameters to make accurate surface flux tallies. The procedure is demonstrated in a test problem in which Monte Carlo surface fluxes in cosine bins are converted to angular fluxes and compared with the results of a discrete ordinates calculation.
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. PMID:27081724
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 telescope performance modeling
NASA Astrophysics Data System (ADS)
Hubbard, Robert P.; Oschmann, Jacobus M., Jr.
2004-09-01
We describe and demonstrate a telescope performance model based on Monte Carlo simulations. As a specific example, we apply this method to our delivered image quality error budgets for the Advanced Technology Solar Telescope (ATST). The ATST site survey database provides us with probability distributions for parameters that affect image quality, like wind velocity and Fried"s seeing parameter. The histograms characterizing these parameters can be sampled many times randomly to yield fact-based predictions of system performance. From this we are able to estimate the fraction of the time that a given site will meet or exceed the performance goals of the telescope. The calculations are performed using Crystal Ball, an after-market add-in for Microsoft Excel marketed by Decisioneering, Inc. of Denver Colorado.
Summarizing Monte Carlo Results in Methodological Research.
ERIC Educational Resources Information Center
Harwell, Michael R.
Monte Carlo studies of statistical tests are prominently featured in the methodological research literature. Unfortunately, the information from these studies does not appear to have significantly influenced methodological practice in educational and psychological research. One reason is that Monte Carlo studies lack an overarching theory to guide
Summarizing Monte Carlo Results in Methodological Research.
ERIC Educational Resources Information Center
Harwell, Michael R.
1992-01-01
A methodological framework is provided for quantitatively integrating Type I error rates and power values for Monte Carlo studies. An example is given using Monte Carlo studies of a test of equality of variances, and the importance of relating metanalytic results to exact statistical theory is emphasized. (SLD)
Optimization of the Fixed Node Energy in Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Lin, Chang; Ceperley, David
1998-03-01
Good wave functions play an important role in Fixed-Node Quantum Monte Carlo simulations. Typical wave function optimization methods minimize the energy or variance within Variational Monte Carlo. We present a method to minimize the fixed node energy directly in Diffusion Monte Carlo(DMC). The fixed node energy, together with its derivatives with respect to the variational parameters in the wave function, is calculated. The derivative information is used to dynamically optimize variational parameters during a single DMC run using the Stochastic Gradient Approximation (SGA) method. We give results for the Be atom with a single variational parameter, and the Li2 molecule, with multiple parameters. (One of the Authors, C.L. would like to thank Claudia Filippi for providing a good Li2 wave function and many valuable discussions.)
Application of Monte Carlo simulation for three-dimensional flows
NASA Astrophysics Data System (ADS)
Scheurlen, M.; Noll, B.; Wittig, S.
1992-02-01
A Monte Carlo technique is outlined for the simulation of the transport of a joint scalar probability density function (PDF). The discretization of the partial differential equations is based on a finite volume approximation. The problem of frozen solutions is addressed if the number of stochastic elements is limited. Non-adiabatic boundary conditions are discussed if the energy equation is solved by a Monte Carlo simulation. The Monte Carlo simulation is compared with deterministic calculations and with an experiment in a three dimensional non-isothermal non-reacting jet mixing flow. The results of the simulation agree very well with the experiment and the deterministic calculations. However, the computer time and storage requirements for a three dimensional simulation of the transport of a single scalar PDF increases dramatically in comparison to deterministic calculations. The results also indicate the need for a simulation procedure that is free of numerical diffusion.
Monte Carlo approaches to light nuclei
Carlson, J.
1990-01-01
Significant progress has been made recently in the application of Monte Carlo methods to the study of light nuclei. We review new Green's function Monte Carlo results for the alpha particle, Variational Monte Carlo studies of {sup 16}O, and methods for low-energy scattering and transitions. Through these calculations, a coherent picture of the structure and electromagnetic properties of light nuclei has arisen. In particular, we examine the effect of the three-nucleon interaction and the importance of exchange currents in a variety of experimentally measured properties, including form factors and capture cross sections. 29 refs., 7 figs.
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.
Monte Carlo Transport for Electron Thermal Transport
NASA Astrophysics Data System (ADS)
Chenhall, Jeffrey; Cao, Duc; Moses, Gregory
2015-11-01
The iSNB (implicit Schurtz Nicolai Busquet multigroup electron thermal transport method of Cao et al. is adapted into a Monte Carlo transport method in order to better model the effects of non-local behavior. The end goal is a hybrid transport-diffusion method that combines Monte Carlo Transport with a discrete diffusion Monte Carlo (DDMC). The hybrid method will combine the efficiency of a diffusion method in short mean free path regions with the accuracy of a transport method in long mean free path regions. The Monte Carlo nature of the approach allows the algorithm to be massively parallelized. Work to date on the method will be presented. This work was supported by Sandia National Laboratory - Albuquerque and the University of Rochester Laboratory for Laser Energetics.
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.
Multiple-time-stepping generalized hybrid Monte Carlo methods
NASA Astrophysics Data System (ADS)
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.
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.
A Guide to Monte Carlo Simulations in Statistical Physics
NASA Astrophysics Data System (ADS)
Landau, David P.; Binder, Kurt
2014-11-01
1. Introduction; 2. Some necessary background; 3. Simple sampling Monte Carlo methods; 4. Importance sampling Monte Carlo methods; 5. More on importance sampling Monte Carlo methods for lattice systems; 6. Off-lattice models; 7. Reweighting methods; 8. Quantum Monte Carlo methods; 9. Monte Carlo renormalization group methods; 10. Non-equilibrium and irreversible processes; 11. Lattice gauge models: a brief introduction; 12. A brief review of other methods of computer simulation; 13. Monte Carlo simulations at the periphery of physics and beyond; 14. Monte Carlo studies of biological molecules; 15. Outlook; Appendix: listing of programs mentioned in the text; Index.
A Guide to Monte Carlo Simulations in Statistical Physics
NASA Astrophysics Data System (ADS)
Landau, David P.; Binder, Kurt
2013-11-01
Preface; 1. Introduction; 2. Some necessary background; 3. Simple sampling Monte Carlo methods; 4. Importance sampling Monte Carlo methods; 5. More on importance sampling Monte Carlo methods of lattice systems; 6. Off-lattice models; 7. Reweighting methods; 8. Quantum Monte Carlo methods; 9. Monte Carlo renormalization group methods; 10. Non-equilibrium and irreversible processes; 11. Lattice gauge models: a brief introduction; 12. A brief review of other methods of computer simulation; 13. Monte Carlo simulations at the periphery of physics and beyond; 14. Monte Carlo studies of biological molecules; 15. Outlook; Appendix; Index.
A Guide to Monte Carlo Simulations in Statistical Physics
NASA Astrophysics Data System (ADS)
Landau, David P.; Binder, Kurt
2009-09-01
Preface; 1. Introduction; 2. Some necessary background; 3. Simple sampling Monte Carlo methods; 4. Importance sampling Monte Carlo methods; 5. More on importance sampling Monte Carlo methods of lattice systems; 6. Off-lattice models; 7. Reweighting methods; 8. Quantum Monte Carlo methods; 9. Monte Carlo renormalization group methods; 10. Non-equilibrium and irreversible processes; 11. Lattice gauge models: a brief introduction; 12. A brief review of other methods of computer simulation; 13. Monte Carlo simulations at the periphery of physics and beyond; 14. Monte Carlo studies of biological molecules; 15. Outlook; Appendix; Index.
Quantum Monte Carlo simulations of complex Hamiltonians
NASA Astrophysics Data System (ADS)
Rousseau, Valery; Hettiarachchilage, Kalani; Tam, Ka-Ming; Moreno, Juana; Jarrell, Mark
2013-03-01
In the last two decades there have been tremendous advances in boson Quantum Monte Carlo methods, which allow for solving more and more complex Hamiltonians. In particular, it is now possible to simulate Hamiltonians that include terms that couple an arbitrary number of sites and/or particles, such as six-site ring-exchange terms. These ring-exchange interactions are crucial for the study of quantum fluctuations on highly frustrated systems. We illustrate how the Stochastic Green Function algorithm with Global Space-Time Update can easily simulate such complex systems, and present some results for a highly non-trivial model of bosons in a pyrochlore crystal with six-site ring-exchange terms. This work is supported by NSF OISE-0952300 (KH, VGR and JM) and by DOE SciDAC grant DE-FC02-06ER25792 (KMT and MJ). This work used the Extreme Science and Engineer- ing Discovery Environment (XSEDE), which is sup- ported by the National Science Foundation
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 spatially low-order kernel, the fundamental eigenvector of which should converge faster than that of continuous kernel. We can then redistribute the fission bank to match the fundamental fission matrix eigenvector, effectively eliminating all higher modes. For all computations here biasing is not used, with the intention of comparing the unaltered, conventional Monte Carlo process with the fission matrix results. The source convergence of standard Monte Carlo criticality calculations are, to some extent, always subject to the characteristics of the problem. This method seeks to partially eliminate this problem-dependence by directly calculating the spatial coupling. The primary cost of this, which has prevented widespread use since its inception [2,3,4], is the extra storage required. To account for the coupling of all N spatial regions to every other region requires storing N{sup 2} values. For realistic problems, where a fine resolution is required for the suppression of discretization error, the storage becomes inordinate. Two factors lead to a renewed interest here: the larger memory available on modern computers and the development of a better storage scheme based on physical intuition. When the distance between source and fission events is short compared with the size of the entire system, saving memory by accounting for only local coupling introduces little extra error. We can gain other information from directly tallying the fission kernel: higher eigenmodes and eigenvalues. Conventional Monte Carlo cannot calculate this data - here we have a way to get new information for multiplying systems. In Ref. [5], higher mode eigenfunctions are analyzed for a three-region 1-dimensional problem and 2-dimensional homogenous problem. We analyze higher modes for more realistic problems. There is also the question of practical use of this information; here we examine a way of using eigenmode information to address the negative confidence interval bias due to inter-cycle correlation. We apply this method mainly to four problems: 2D pressurized water reactor (PWR) [6], 3D Kord Smith Challenge [7], OECD - Nuclear Energy Agency (NEA) source convergence benchmark fuel storage vault [8], and Advanced Test Reactor (ATR) [9]. We see excellent source convergence acceleration for the most difficult problems: the 3D Kord Smith Challenge and fuel storage vault. Additionally, we examine higher eigenmode results for all these problems. Using part of the eigenvalue spectrum for a one-group 1D problem, we find confidence interval correction factors that are improvements over existing corrections [10].
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 the eventual hope is to apply this algorithm to the exploration of yet unidentified high-pressure, low-temperature phases of hydrogen, I employ this algorithm to determine whether or not quantum hard spheres can form a low-temperature bcc solid if exchange is not taken into account. In the final chapter of this thesis, I use Path Integral Monte Carlo once again to explore whether glassy para-hydrogen exhibits superfluidity. Physicists have long searched for ways to coax hydrogen into becoming a superfluid. I present evidence that, while glassy hydrogen does not crystallize at the temperatures at which hydrogen might become a superfluid, it nevertheless does not exhibit superfluidity. This is because the average binding energy per p-H2 molecule poses a severe barrier to exchange regardless of whether the system is crystalline. All in all, this work extends the reach of Quantum Monte Carlo methods to new systems and brings the power of existing methods to bear on new problems. Portions of this work have been published in Rubenstein, PRE (2010) and Rubenstein, PRA (2012) [167;169]. Other papers not discussed here published during my Ph.D. include Rubenstein, BPJ (2008) and Rubenstein, PRL (2012) [166;168]. The work in Chapters 6 and 7 is currently unpublished. [166] Brenda M. Rubenstein, Ivan Coluzza, and Mark A. Miller. Controlling the folding and substrate-binding of proteins using polymer brushes. Physical Review Letters, 108(20):208104, May 2012. [167] Brenda M. Rubenstein, J.E. Gubernatis, and J.D. Doll. Comparative monte carlo efficiency by monte carlo analysis. Physical Review E, 82(3):036701, September 2010. [168] Brenda M. Rubenstein and Laura J. Kaufman. The role of extracellular matrix in glioma invasion: A cellular potts model approach. Biophysical Journal, 95(12):5661-- 5680, December 2008. [169] Brenda M. Rubenstein, Shiwei Zhang, and David R. Reichman. Finite-temperature auxiliary-field quantum monte carlo for bose-fermi mixtures. Physical Review A, 86(5):053606, November 2012.
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
Exploring pseudo- and chaotic random Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Blais, J. A. Rod; Zhang, Zhan
2011-07-01
Computer simulations are an increasingly important area of geoscience research and development. At the core of stochastic or Monte Carlo simulations are the random number sequences that are assumed to be distributed with specific characteristics. Computer-generated random numbers, uniformly distributed on (0, 1), can be very different depending on the selection of pseudo-random number (PRN) or chaotic random number (CRN) generators. In the evaluation of some definite integrals, the resulting error variances can even be of different orders of magnitude. Furthermore, practical techniques for variance reduction such as importance sampling and stratified sampling can be applied in most Monte Carlo simulations and significantly improve the results. A comparative analysis of these strategies has been carried out for computational applications in planar and spatial contexts. Based on these experiments, and on some practical examples of geodetic direct and inverse problems, conclusions and recommendations concerning their performance and general applicability are included.
Exploring Various Monte Carlo Simulations for Geoscience Applications
NASA Astrophysics Data System (ADS)
Blais, R.
2010-12-01
Computer simulations are increasingly important in geoscience research and development. At the core of stochastic or Monte Carlo simulations are the random number sequences that are assumed to be distributed with specific characteristics. Computer generated random numbers, uniformly distributed on (0, 1), can be very different depending on the selection of pseudo-random number (PRN), or chaotic random number (CRN) generators. Equidistributed quasi-random numbers (QRNs) can also be used in Monte Carlo simulations. In the evaluation of some definite integrals, the resulting error variances can even be of different orders of magnitude. Furthermore, practical techniques for variance reduction such as Importance Sampling and Stratified Sampling can be implemented to significantly improve the results. A comparative analysis of these strategies has been carried out for computational applications in planar and spatial contexts. Based on these experiments, and on examples of geodetic applications of gravimetric terrain corrections and gravity inversion, conclusions and recommendations concerning their performance and general applicability are included.
Exponential distributed time-delay nonlinear models: Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Cáceres, Manuel O.; Rojas R., Christian D.
2014-09-01
The stochastic dynamics toward the final attractor in an exponential distributed time-delay nonlinear model is studied, in the small noise approximation. The passage time statistic for this non-Markovian type of system has been worked out using Monte Carlo simulations. We report the mean first passage time
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.
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
Fast quantum Monte Carlo on a GPU
NASA Astrophysics Data System (ADS)
Lutsyshyn, Y.
2015-02-01
We present a scheme for the parallelization of quantum Monte Carlo method on graphical processing units, focusing on variational Monte Carlo simulation of bosonic systems. We use asynchronous execution schemes with shared memory persistence, and obtain an excellent utilization of the accelerator. The CUDA code is provided along with a package that simulates liquid helium-4. The program was benchmarked on several models of Nvidia GPU, including Fermi GTX560 and M2090, and the Kepler architecture K20 GPU. Special optimization was developed for the Kepler cards, including placement of data structures in the register space of the Kepler GPUs. Kepler-specific optimization is discussed.
Monte Carlo simulation of scenario probability distributions
Glaser, R.
1996-10-23
Suppose a scenario of interest can be represented as a series of events. A final result R may be viewed then as the intersection of three events, A, B, and C. The probability of the result P(R) in this case is the product P(R) = P(A) P(B {vert_bar} A) P(C {vert_bar} A {intersection} B). An expert may be reluctant to estimate P(R) as a whole yet agree to supply his notions of the component probabilities in the form of prior distributions. Each component prior distribution may be viewed as the stochastic characterization of the expert`s uncertainty regarding the true value of the component probability. Mathematically, the component probabilities are treated as independent random variables and P(R) as their product; the induced prior distribution for P(R) is determined which characterizes the expert`s uncertainty regarding P(R). It may be both convenient and adequate to approximate the desired distribution by Monte Carlo simulation. Software has been written for this task that allows a variety of component priors that experts with good engineering judgment might feel comfortable with. The priors are mostly based on so-called likelihood classes. The software permits an expert to choose for a given component event probability one of six types of prior distributions, and the expert specifies the parameter value(s) for that prior. Each prior is unimodal. The expert essentially decides where the mode is, how the probability is distributed in the vicinity of the mode, and how rapidly it attenuates away. Limiting and degenerate applications allow the expert to be vague or precise.
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 demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discrete-sectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.
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 demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discrete-sectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.
Linked coupled cluster Monte Carlo.
Franklin, R S T; Spencer, J S; Zoccante, A; Thom, A J W
2016-01-28
We consider a new formulation of the stochastic coupled cluster method in terms of the similarity transformed Hamiltonian. We show that improvement in the granularity with which the wavefunction is represented results in a reduction in the critical population required to correctly sample the wavefunction for a range of systems and excitation levels and hence leads to a substantial reduction in the computational cost. This development has the potential to substantially extend the range of the method, enabling it to be used to treat larger systems with excitation levels not easily accessible with conventional deterministic methods. PMID:26827206
Linked coupled cluster Monte Carlo
NASA Astrophysics Data System (ADS)
Franklin, R. S. T.; Spencer, J. S.; Zoccante, A.; Thom, A. J. W.
2016-01-01
We consider a new formulation of the stochastic coupled cluster method in terms of the similarity transformed Hamiltonian. We show that improvement in the granularity with which the wavefunction is represented results in a reduction in the critical population required to correctly sample the wavefunction for a range of systems and excitation levels and hence leads to a substantial reduction in the computational cost. This development has the potential to substantially extend the range of the method, enabling it to be used to treat larger systems with excitation levels not easily accessible with conventional deterministic methods.
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.
Computer system for Monte Carlo experimentation
Grier, D.A.
1986-01-01
A new computer system for Monte Carlo Experimentation is presented. The new system speeds and simplifies the process of coding and preparing a Monte Carlo Experiment; it also encourages the proper design of Monte Carlo Experiments, and the careful analysis of the experimental results. A new functional language is the core of this system. Monte Carlo Experiments, and their experimental designs, are programmed in this new language; those programs are compiled into Fortran output. The Fortran output is then compiled and executed. The experimental results are analyzed with a standard statistics package such as Si, Isp, or Minitab or with a user-supplied program. Both the experimental results and the experimental design may be directly loaded into the workspace of those packages. The new functional language frees programmers from many of the details of programming an experiment. Experimental designs such as factorial, fractional factorial, or latin square are easily described by the control structures and expressions of the language. Specific mathematical modes are generated by the routines of the language.
Coded aperture optimization using Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Martineau, A.; Rocchisani, J. M.; Moretti, J. L.
2010-04-01
Coded apertures using Uniformly Redundant Arrays (URA) have been unsuccessfully evaluated for two-dimensional and three-dimensional imaging in Nuclear Medicine. The images reconstructed from coded projections contain artifacts and suffer from poor spatial resolution in the longitudinal direction. We introduce a Maximum-Likelihood Expectation-Maximization (MLEM) algorithm for three-dimensional coded aperture imaging which uses a projection matrix calculated by Monte Carlo simulations. The aim of the algorithm is to reduce artifacts and improve the three-dimensional spatial resolution in the reconstructed images. Firstly, we present the validation of GATE (Geant4 Application for Emission Tomography) for Monte Carlo simulations of a coded mask installed on a clinical gamma camera. The coded mask modelling was validated by comparison between experimental and simulated data in terms of energy spectra, sensitivity and spatial resolution. In the second part of the study, we use the validated model to calculate the projection matrix with Monte Carlo simulations. A three-dimensional thyroid phantom study was performed to compare the performance of the three-dimensional MLEM reconstruction with conventional correlation method. The results indicate that the artifacts are reduced and three-dimensional spatial resolution is improved with the Monte Carlo-based MLEM reconstruction.
Parallel processing Monte Carlo radiation transport codes
McKinney, G.W.
1994-02-01
Issues related to distributed-memory multiprocessing as applied to Monte Carlo radiation transport are discussed. Measurements of communication overhead are presented for the radiation transport code MCNP which employs the communication software package PVM, and average efficiency curves are provided for a homogeneous virtual machine.
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)
Krylov-Projected Quantum Monte Carlo Method.
Blunt, N S; Alavi, Ali; Booth, George H
2015-07-31
We present an approach to the calculation of arbitrary spectral, thermal, and excited state properties within the full configuration interaction quzantum Monte Carlo framework. This is achieved via an unbiased projection of the Hamiltonian eigenvalue problem into a space of stochastically sampled Krylov vectors, thus, enabling the calculation of real-frequency spectral and thermal properties and avoiding explicit analytic continuation. We use this approach to calculate temperature-dependent properties and one- and two-body spectral functions for various Hubbard models, as well as isolated excited states in ab initio systems. PMID:26274406
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.
Baker, R.S.; Filippone, W.F. . Dept. of Nuclear and Energy Engineering); Alcouffe, R.E. )
1991-01-01
The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S{sub N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S{sub N} regions are fully coupled in the sense that no assumption is made about geometrical separation of decoupling. The fully coupled Monte Carlo/S{sub N} technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S{sub N} calculation is to be performed. The Monte Carlo and S{sub N} regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and group sources. The hybrid method provides a new method of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S{sub N} is well suited for by itself. The fully coupled Monte Carlo/S{sub N} method has been implemented in the S{sub N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and group sources, and linkage subroutines to carry out the interface flux iterations. The common angular boundary fluxes are included in the S{sub N} code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating the S{sub N} calculations. The Monte Carlo routines have been successfully vectorized, with approximately a factor of five increases in speed over the nonvectorized version. The hybrid method is capable of solving forward, inhomogeneous source problems in X-Y and R-Z geometries. This capability now includes mulitigroup problems involving upscatter and fission in non-highly multiplying systems. 8 refs., 8 figs., 1 tab.
NASA Astrophysics Data System (ADS)
Sabelfeld, K. K.
2015-09-01
A stochastic algorithm for simulation of fluctuation-induced kinetics of H2 formation on grain surfaces is suggested as a generalization of the technique developed in our recent studies [1] where this method was developed to describe the annihilation of spatially separate electrons and holes in a disordered semiconductor. The stochastic model is based on the spatially inhomogeneous, nonlinear integro-differential Smoluchowski equations with random source term. In this paper we derive the general system of Smoluchowski type equations for the formation of H2 from two hydrogen atoms on the surface of interstellar dust grains with physisorption and chemisorption sites. We focus in this study on the spatial distribution, and numerically investigate the segregation in the case of a source with a continuous generation in time and randomly distributed in space. The stochastic particle method presented is based on a probabilistic interpretation of the underlying process as a stochastic Markov process of interacting particle system in discrete but randomly progressed time instances. The segregation is analyzed through the correlation analysis of the vector random field of concentrations which appears to be isotropic in space and stationary in time.
Path integral Monte Carlo and the electron gas
NASA Astrophysics Data System (ADS)
Brown, Ethan W.
Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational principle inherent in the path integral Monte Carlo method to optimize the nodal surface. By using a ansatz resembling a free particle density matrix, we make a unique connection between a nodal effective mass and the traditional effective mass of many-body quantum theory. We then propose and test several alternate nodal ansatzes and apply them to single atomic systems. Finally, we propose a method to tackle the sign problem head on, by leveraging the relatively simple structure of permutation space. Using this method, we find we can perform exact simulations this of the electron gas and 3He that were previously impossible.
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.
Monte Carlo-based tail exponent estimator
NASA Astrophysics Data System (ADS)
Barunik, Jozef; Vacha, Lukas
2010-11-01
In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations, we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce a Monte Carlo-based method of estimation for the tail exponent. Our proposed method is not sensitive to the choice of tail size and works well also on small data samples. The new estimator also gives unbiased results with symmetrical confidence intervals. Finally, we demonstrate the power of our estimator on the international world stock market indices. On the two separate periods of 2002-2005 and 2006-2009, we estimate the tail exponent.
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. PMID:26226927
Quantum Monte Carlo calculations for carbon nanotubes
NASA Astrophysics Data System (ADS)
Luu, Thomas; Lähde, Timo A.
2016-04-01
We show how lattice quantum Monte Carlo can be applied to the electronic properties of carbon nanotubes in the presence of strong electron-electron correlations. We employ the path-integral formalism and use methods developed within the lattice QCD community for our numerical work. Our lattice Hamiltonian is closely related to the hexagonal Hubbard model augmented by a long-range electron-electron interaction. We apply our method to the single-quasiparticle spectrum of the (3,3) armchair nanotube configuration, and consider the effects of strong electron-electron correlations. Our approach is equally applicable to other nanotubes, as well as to other carbon nanostructures. We benchmark our Monte Carlo calculations against the two- and four-site Hubbard models, where a direct numerical solution is feasible.
Monte Carlo simulation of Touschek effect.
Xiao, A.; Borland, M.; Accelerator Systems Division
2010-07-30
We present a Monte Carlo method implementation in the code elegant for simulating Touschek scattering effects in a linac beam. The local scattering rate and the distribution of scattered electrons can be obtained from the code either for a Gaussian-distributed beam or for a general beam whose distribution function is given. In addition, scattered electrons can be tracked through the beam line and the local beam-loss rate and beam halo information recorded.
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.
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.
Monte Carlo simulation of Alaska wolf survival
NASA Astrophysics Data System (ADS)
Feingold, S. J.
1996-02-01
Alaskan wolves live in a harsh climate and are hunted intensively. Penna's biological aging code, using Monte Carlo methods, has been adapted to simulate wolf survival. It was run on the case in which hunting causes the disruption of wolves' social structure. Social disruption was shown to increase the number of deaths occurring at a given level of hunting. For high levels of social disruption, the population did not survive.
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.
The CCFM Monte Carlo generator CASCADE
NASA Astrophysics Data System (ADS)
Jung, H.
2002-02-01
CASCADE is a full hadron level Monte Carlo event generator for ep, γp and p p¯ processes, which uses the CCFM evolution equation for the initial state cascade in a backward evolution approach supplemented with off-shell matrix elements for the hard scattering. A detailed program description is given, with emphasis on parameters the user wants to change and common block variables which completely specify the generated events.
Monte Carlo simulations of muon production
Palmer, R.B.; Gallardo, J.C.; Fernow, R.C.; Torun, Y.; Neuffer, D.; Winn, D.
1995-03-01
Muon production requirements for a muon collider are presented. Production of muons from pion decay is studied. Lithium lenses and solenoids are considered for focusing pions from a target, and for matching the pions into a decay channel. Pion decay channels of alternating quadrupoles and long solenoids are compared. Monte Carlo simulations are presented for production of {pi} {yields} {mu} by protons over a wide energy range, and criteria for choosing the best proton energy are discussed.
An introduction to Monte Carlo methods
NASA Astrophysics Data System (ADS)
Walter, J.-C.; Barkema, G. T.
2015-01-01
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform an exact enumeration. The main principles of Monte Carlo simulations are ergodicity and detailed balance. The Ising model is a lattice spin system with nearest neighbor interactions that is appropriate to illustrate different examples of Monte Carlo simulations. It displays a second order phase transition between disordered (high temperature) and ordered (low temperature) phases, leading to different strategies of simulations. The Metropolis algorithm and the Glauber dynamics are efficient at high temperature. Close to the critical temperature, where the spins display long range correlations, cluster algorithms are more efficient. We introduce the rejection free (or continuous time) algorithm and describe in details an interesting alternative representation of the Ising model using graphs instead of spins with the so-called Worm algorithm. We conclude with an important discussion of the dynamical effects such as thermalization and correlation time.
Numerical reproducibility for implicit Monte Carlo simulations
Cleveland, M.; Brunner, T.; Gentile, N.
2013-07-01
We describe and compare different approaches for achieving numerical reproducibility in photon Monte Carlo simulations. Reproducibility is desirable for code verification, testing, and debugging. Parallelism creates a unique problem for achieving reproducibility in Monte Carlo simulations because it changes the order in which values are summed. This is a numerical problem because double precision arithmetic is not associative. In [1], a way of eliminating this roundoff error using integer tallies was described. This approach successfully achieves reproducibility at the cost of lost accuracy by rounding double precision numbers to fewer significant digits. This integer approach, and other extended reproducibility techniques, are described and compared in this work. Increased precision alone is not enough to ensure reproducibility of photon Monte Carlo simulations. A non-arbitrary precision approaches required a varying degree of rounding to achieve reproducibility. For the problems investigated in this work double precision global accuracy was achievable by using 100 bits of precision or greater on all unordered sums which where subsequently rounded to double precision at the end of every time-step. (authors)
Filippone, W.L.; Baker, R.S.
1990-12-31
The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S{sub N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S{sub N} regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S{sub N} is well suited for by themselves. The fully coupled Monte Carlo/S{sub N} technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S{sub N} calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary S{sub N} region. The Monte Carlo and S{sub N} regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the S{sub N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and volumetric sources, and linkage subrountines to carry out the interface flux iterations. The common angular boundary fluxes are included in the S{sub N} code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating S{sub N} calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. However, the routines have been successfully vectorized, with approximately a factor of five increase in speed over the non-vectorized version.
Ballarini, F; Biaggi, M; Merzagora, M; Ottolenghi, A; Dingfelder, M; Friedland, W; Jacob, P; Paretzke, H G
2000-09-01
A new physical module for the biophysical simulation code PARTRAC has recently been developed, based on newly derived electron inelastic-scattering cross-sections in liquid water. In the present work, two modules of PARTRAC describing the production, diffusion and interaction of chemical species were developed with the specific purpose of quantifying the role of the uncertainties in the parameters controlling the early stages of liquid water radiolysis. A set of values for such parameters was identified, and time-dependent yields and frequency distributions of chemical species produced by electrons of different energies were calculated. The calculated yields were in good agreement with available data and simulations, thus confirming the reliability of the code. As the primary-electron energy decreases down to 1 keV, the *OH decay kinetics were found to get faster, reflecting variations in the spatial distribution of the initial energy depositions. In agreement with analogous works, an opposite trend was found for energies of a few hundred eV, due to the very small number of species involved. The spreading effects shown at long times by *OH frequency distributions following 1 keV irradiation were found to be essentially due to stochastic aspects of the chemical stage, whereas for 1 MeV tracks the physical and pre-chemical stages also were found to play a significant role. Relevant differences in the calculated e(aq) -yields were found by coupling the physics of PARTRAC with descriptions of the pre-chemical and chemical stages adopted in different models. This indicates a strict interrelation of the various stages, and thus a strong dependence of the parameter values on the assumptions made for the preceding and subsequent stages of the process. Although equally acceptable results can be obtained starting from different assumptions, it is necessary to keep control of such uncertainties, since they can significantly influence the modeling of radical attack on DNA and, more generally, radiobiological damage estimation. This study confirms the need for new, independently derived data on specific steps of water radiolysis, to be included in comprehensive biophysical simulation codes. PMID:11095148
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.
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.
A Monte Carlo algorithm for degenerate plasmas
Turrell, A.E. Sherlock, M.; Rose, S.J.
2013-09-15
A procedure for performing Monte Carlo calculations of plasmas with an arbitrary level of degeneracy is outlined. It has possible applications in inertial confinement fusion and astrophysics. Degenerate particles are initialised according to the Fermi–Dirac distribution function, and scattering is via a Pauli blocked binary collision approximation. The algorithm is tested against degenerate electron–ion equilibration, and the degenerate resistivity transport coefficient from unmagnetised first order transport theory. The code is applied to the cold fuel shell and alpha particle equilibration problem of inertial confinement fusion.
Modulated pulse bathymetric lidar Monte Carlo simulation
NASA Astrophysics Data System (ADS)
Luo, Tao; Wang, Yabo; Wang, Rong; Du, Peng; Min, Xia
2015-10-01
A typical modulated pulse bathymetric lidar system is investigated by simulation using a modulated pulse lidar simulation system. In the simulation, the return signal is generated by Monte Carlo method with modulated pulse propagation model and processed by mathematical tools like cross-correlation and digital filter. Computer simulation results incorporating the modulation detection scheme reveal a significant suppression of the water backscattering signal and corresponding target contrast enhancement. More simulation experiments are performed with various modulation and reception variables to investigate the effect of them on the bathymetric system performance.
Monte Carlo simulation of the enantioseparation process
NASA Astrophysics Data System (ADS)
Bustos, V. A.; Acosta, G.; Gomez, M. R.; Pereyra, V. D.
2012-09-01
By means of Monte Carlo simulation, a study of enantioseparation by capillary electrophoresis has been carried out. A simplified system consisting of two enantiomers S (R) and a selector chiral C, which reacts with the enantiomers to form complexes RC (SC), has been considered. The dependence of Δμ (enantioseparation) with the concentration of chiral selector and with temperature have been analyzed by simulation. The effect of the binding constant and the charge of the complexes are also analyzed. The results are qualitatively satisfactory, despite the simplicity of the model.
Diffusion quantum Monte Carlo for molecules
Lester, W.A. Jr.
1986-07-01
A quantum mechanical Monte Carlo method has been used for the treatment of molecular problems. The imaginary-time Schroedinger equation written with a shift in zero energy (E/sub T/ - V(R)) can be interpreted as a generalized diffusion equation with a position-dependent rate or branching term. Since diffusion is the continuum limit of a random walk, one may simulate the Schroedinger equation with a function psi (note, not psi/sup 2/) as a density of ''walks.'' The walks undergo an exponential birth and death as given by the rate term. 16 refs., 2 tabs.
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. PMID:26274310
Monte Carlo simulation in Fourier space
NASA Astrophysics Data System (ADS)
Trster, Andreas
2008-07-01
In the context of solving the long-standing problem of computing Landau-Ginzburg free energies including gradient corrections for the ? model, we recently introduced a new Monte Carlo algorithm for lattice spin systems based exclusively on Fourier amplitudes of the underlying spin configurations [A. Trster, Phys. Rev. B 76 (2007) 012402]. In the present paper we shall provide additional information on the motivation, main ideas and constructions underlying the algorithm. Also we discuss important details of its construction with emphasis on an analysis of its scaling behavior with system size.
Monte Carlo radiation transport¶llelism
Cox, L. J.; Post, S. E.
2002-01-01
This talk summarizes the main aspects of the LANL ASCI Eolus project and its major unclassified code project, MCNP. The MCNP code provide a state-of-the-art Monte Carlo radiation transport to approximately 3000 users world-wide. Almost all hardware platforms are supported because we strictly adhere to the FORTRAN-90/95 standard. For parallel processing, MCNP uses a mixture of OpenMp combined with either MPI or PVM (shared and distributed memory). This talk summarizes our experiences on various platforms using MPI with and without OpenMP. These platforms include PC-Windows, Intel-LINUX, BlueMountain, Frost, ASCI-Q and others.
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.
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.
Reverse Monte Carlo simulation of liquid water
NASA Astrophysics Data System (ADS)
Jedlovszky, P.; Bak, I.; Plinks, G.
1994-04-01
Reverse Monte Carlo simulation of liquid water has been carried out on the basis of partial pair correlation functions determined by Soper and Phillips. The configurations obtained from this simulation were analyzed in detail. The results were compared with those obtained from molecular dynamics (MD) simulation in order to interpret the differences between the experimental and the MD partial pair correlation function sets. By evaluating the experimental data we found a more distorted geometry of the hydrogen bonds, and also that a significant fraction of the nearest-neighbour molecules distributes randomly rather than tetrahedrally around a central water molecule.
Monte Carlo simulations of muon production
Palmer, R.B.; Gallardo, J.C.; Fernow, R.C.; Torun, Y.; Neuffer, D.; Winn, D.
1996-01-01
Muon production requirements for a muon collider are presented. Production of muons from pion decay is studied. Lithium lenses and solenoids are considered for focussing pions from a target, and for matching the pions into a decay channel. Pion decay channels of alternating quadrupoles and long solenoids are compared. Monte Carlo simulations are presented for production of {pi}{r_arrow}{mu} by protons over a wide energy range, and criteria for choosing the best proton energy are discussed. {copyright} {ital 1995 American Institute of Physics.}
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.
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.
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.
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.
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.
Reverse Monte Carlo modeling in confined systems
Sánchez-Gil, V.; Noya, E. G.; Lomba, E.
2014-01-14
An extension of the well established Reverse Monte Carlo (RMC) method for modeling systems under close confinement has been developed. The method overcomes limitations induced by close confinement in systems such as fluids adsorbed in microporous materials. As a test of the method, we investigate a model system of {sup 36}Ar adsorbed into two zeolites with significantly different pore sizes: Silicalite-I (a pure silica form of ZSM-5 zeolite, characterized by relatively narrow channels forming a 3D network) at partial and full loadings and siliceous Faujasite (which exhibits relatively wide channels and large cavities). The model systems are simulated using grand canonical Monte Carlo and, in each case, its structure factor is used as input for the proposed method, which shows a rapid convergence and yields an adsorbate microscopic structure in good agreement with that of the model system, even to the level of three body correlations, when these are induced by the confining media. The application to experimental systems is straightforward incorporating factors such as the experimental resolution and appropriate q-sampling, along the lines of previous experiences of RMC modeling of powder diffraction data including Bragg and diffuse scattering.
Reverse Monte Carlo modeling in confined systems.
Sánchez-Gil, V; Noya, E G; Lomba, E
2014-01-14
An extension of the well established Reverse Monte Carlo (RMC) method for modeling systems under close confinement has been developed. The method overcomes limitations induced by close confinement in systems such as fluids adsorbed in microporous materials. As a test of the method, we investigate a model system of (36)Ar adsorbed into two zeolites with significantly different pore sizes: Silicalite-I (a pure silica form of ZSM-5 zeolite, characterized by relatively narrow channels forming a 3D network) at partial and full loadings and siliceous Faujasite (which exhibits relatively wide channels and large cavities). The model systems are simulated using grand canonical Monte Carlo and, in each case, its structure factor is used as input for the proposed method, which shows a rapid convergence and yields an adsorbate microscopic structure in good agreement with that of the model system, even to the level of three body correlations, when these are induced by the confining media. The application to experimental systems is straightforward incorporating factors such as the experimental resolution and appropriate q-sampling, along the lines of previous experiences of RMC modeling of powder diffraction data including Bragg and diffuse scattering. PMID:24437893
Feedback-optimized parallel tempering Monte Carlo
NASA Astrophysics Data System (ADS)
Katzgraber, Helmut G.; Trebst, Simon; Huse, David A.; Troyer, Matthias
2006-03-01
We introduce an algorithm for systematically improving the efficiency of parallel tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that optimizes the simulated statistical ensemble in generalized broad-histogram Monte Carlo simulations. Conventionally, a temperature set is chosen in such a way that the acceptance rates for replica swaps between adjacent temperatures are independent of the temperature and large enough to ensure frequent swaps. In this paper, we show that by choosing the temperatures with a modified version of the optimized ensemble feedback method we can minimize the round-trip times between the lowest and highest temperatures which effectively increases the efficiency of the parallel tempering algorithm. In particular, the density of temperatures in the optimized temperature set increases at the 'bottlenecks' of the simulation, such as phase transitions. In turn, the acceptance rates are now temperature dependent in the optimized temperature ensemble. We illustrate the feedback-optimized parallel tempering algorithm by studying the two-dimensional Ising ferromagnet and the two-dimensional fully frustrated Ising model, and briefly discuss possible feedback schemes for systems that require configurational averages, such as spin glasses.
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.
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.
Simple Monte Carlo model for crowd dynamics
NASA Astrophysics Data System (ADS)
Piazza, Francesco
2010-08-01
In this paper, we introduce a simple Monte Carlo method for simulating the dynamics of a crowd. Within our model a collection of hard-disk agents is subjected to a series of two-stage steps, implying (i) the displacement of one specific agent followed by (ii) a rearrangement of the rest of the group through a Monte Carlo dynamics. The rules for the combined steps are determined by the specific setting of the granular flow, so that our scheme should be easily adapted to describe crowd dynamics issues of many sorts, from stampedes in panic scenarios to organized flow around obstacles or through bottlenecks. We validate our scheme by computing the serving times statistics of a group of agents crowding to be served around a desk. In the case of a size homogeneous crowd, we recover intuitive results prompted by physical sense. However, as a further illustration of our theoretical framework, we show that heterogeneous systems display a less obvious behavior, as smaller agents feature shorter serving times. Finally, we analyze our results in the light of known properties of nonequilibrium hard-disk fluids and discuss general implications of our model.
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,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, 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-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
Monte Carlo radiative transfer in protoplanetary disks
NASA Astrophysics Data System (ADS)
Pinte, C.; Ménard, F.; Duchêne, G.; Bastien, P.
2006-12-01
Aims.We present a new continuum 3D radiative transfer code, MCFOST, based on a Monte-Carlo method. MCFOST can be used to calculate (i) monochromatic images in scattered light and/or thermal emission; (ii) polarisation maps; (iii) interferometric visibilities; (iv) spectral energy distributions; and (v) dust temperature distributions of protoplanetary disks. Methods: .Several improvements to the standard Monte Carlo method are implemented in MCFOST to increase efficiency and reduce convergence time, including wavelength distribution adjustments, mean intensity calculations, and an adaptive sampling of the radiation field. The reliability and efficiency of the code are tested against a previously-defined benchmark, using a 2D disk configuration. No significant difference (no more than 10% and usually much less) is found between the temperatures and SEDs calculated by MCFOST and by other codes included in the benchmark. Results: . A study of the lowest disk mass detectable by Spitzer, around young stars, is presented and the colours of "representative" parametric disks compared to recent IRAC and MIPS Spitzer colours of solar-like young stars located in nearby star-forming regions.
The MCNPX Monte Carlo Radiation Transport Code
Waters, Laurie S.; McKinney, Gregg W.; Durkee, Joe W.; Fensin, Michael L.; Hendricks, John S.; James, Michael R.; Johns, Russell C.; Pelowitz, Denise B.
2007-03-19
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 MCNP4c 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.
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 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.
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.
Composite biasing in Monte Carlo radiative transfer
NASA Astrophysics Data System (ADS)
Baes, Maarten; Gordon, Karl D.; Lunttila, Tuomas; Bianchi, Simone; Camps, Peter; Juvela, Mika; Kuiper, Rolf
2016-05-01
Biasing or importance sampling is a powerful technique in Monte Carlo radiative transfer, and can be applied in different forms to increase the accuracy and efficiency of simulations. One of the drawbacks of the use of biasing is the potential introduction of large weight factors. We discuss a general strategy, composite biasing, to suppress the appearance of large weight factors. We use this composite biasing approach for two different problems faced by current state-of-the-art Monte Carlo radiative transfer codes: the generation of photon packages from multiple components, and the penetration of radiation through high optical depth barriers. In both cases, the implementation of the relevant algorithms is trivial and does not interfere with any other optimisation techniques. Through simple test models, we demonstrate the general applicability, accuracy and efficiency of the composite biasing approach. In particular, for the penetration of high optical depths, the gain in efficiency is spectacular for the specific problems that we consider: in simulations with composite path length stretching, high accuracy results are obtained even for simulations with modest numbers of photon packages, while simulations without biasing cannot reach convergence, even with a huge number of photon packages.
Kinetic Monte Carlo with fields: diffusion in heterogeneous systems
NASA Astrophysics Data System (ADS)
Caro, Jose Alfredo
2011-03-01
It is commonly perceived that to achieve breakthrough scientific discoveries in the 21st century an integration of world leading experimental capabilities with theory, computational modeling and high performance computer simulations is necessary. Lying between the atomic and the macro scales, the meso scale is crucial for advancing materials research. Deterministic methods result computationally too heavy to cover length and time scales relevant for this scale. Therefore, stochastic approaches are one of the options of choice. In this talk I will describe recent progress in efficient parallelization schemes for Metropolis and kinetic Monte Carlo [1-2], and the combination of these ideas into a new hybrid Molecular Dynamics-kinetic Monte Carlo algorithm developed to study the basic mechanisms taking place in diffusion in concentrated alloys under the action of chemical and stress fields, incorporating in this way the actual driving force emerging from chemical potential gradients. Applications are shown on precipitation and segregation in nanostructured materials. Work in collaboration with E. Martinez, LANL, and with B. Sadigh, P. Erhart and A. Stukowsky, LLNL. Supported by the Center for Materials at Irradiation and Mechanical Extremes, an Energy Frontier Research Center funded by the U.S. Department of Energy (Award # 2008LANL1026) at Los Alamos National Laboratory
Importance sampling based direct simulation Monte Carlo method
NASA Astrophysics Data System (ADS)
Vedula, Prakash; Otten, Dustin
2010-11-01
We propose a novel and efficient approach, termed as importance sampling based direct simulation Monte Carlo (ISDSMC), for prediction of nonequilibrium flows via solution of the Boltzmann equation. Besides leading to a reduction in computational cost, ISDSMC also results in a reduction in statistical scatter compared to conventional direct simulation Monte Carlo (DSMC) and hence appears to be potentially useful for prediction of a variety of flows, especially where the signal to noise ratio is small (e.g. microflows) . In this particle in cell approach, the computational particles are initially assigned weights (or importance) based on constraints on generalized moments of velocity. Solution of the Boltzmann equation is achieved by use of (i) a streaming operator which streams the computational particles and (ii) a collision operator where the representative collision pairs are selected stochastically based on particle weights via an acceptance-rejection algorithm. Performance of ISDSMC approach is evaluated using analysis of three canonical microflows, namely (i) thermal Couette flow, (ii) velocity-slip Couette flow and (iii) Poiseulle flow. Our results based on ISDSMC indicate good agreement with those obtained from conventional DSMC methods. The potential advantages of this (ISDSMC) approach to granular flows will also be demonstrated using simulations of homogeneous relaxation of a granular gas.
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 published papers, 15 invited talks and lectures nationally and internationally. My former graduate student and postdoc Dr. Michal Bajdich, who was supported byt this grant, is currently a postdoc with ORNL in the group of Dr. F. Reboredo and Dr. P. Kent and is using the developed tools in a number of DOE projects. The QWalk package has become a truly important research tool used by the electronic structure community and has attracted several new developers in other research groups. Our tools use several types of correlated wavefunction approaches, variational, diffusion and reptation methods, large-scale optimization methods for wavefunctions and enables to calculate energy differences such as cohesion, electronic gaps, but also densities and other properties, using multiple runs one can obtain equations of state for given structures and beyond. Our codes use efficient numerical and Monte Carlo strategies (high accuracy numerical orbitals, multi-reference wave functions, highly accurate correlation factors, pairing orbitals, force biased and correlated sampling Monte Carlo), are robustly parallelized and enable to run on tens of thousands cores very efficiently. Our demonstration applications were focused on the challenging research problems in several fields of materials science such as transition metal solids. We note that our study of FeO solid was the first QMC calculation of transition metal oxides at high pressures.
Reactive Monte Carlo sampling with an ab initio potential.
Leiding, Jeff; Coe, Joshua D
2016-05-01
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 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). We find that there are regions of state space for which RxMC sampling is much more efficient than AIMD due to the "rare-event" character of chemical reactions. PMID:27155627
Reactive Monte Carlo sampling with an ab initio potential
NASA Astrophysics Data System (ADS)
Leiding, Jeff; Coe, Joshua D.
2016-05-01
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 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). We find that there are regions of state space for which RxMC sampling is much more efficient than AIMD due to the "rare-event" character of chemical reactions.
Accelerating particle-in-cell simulations using multilevel Monte Carlo
NASA Astrophysics Data System (ADS)
Ricketson, Lee
2015-11-01
Particle-in-cell (PIC) simulations have been an important tool in understanding plasmas since the dawn of the digital computer. Much more recently, the multilevel Monte Carlo (MLMC) method has accelerated particle-based simulations of a variety of systems described by stochastic differential equations (SDEs), from financial portfolios to porous media flow. The fundamental idea of MLMC is to perform correlated particle simulations using a hierarchy of different time steps, and to use these correlations for variance reduction on the fine-step result. This framework is directly applicable to the Langevin formulation of Coulomb collisions, as demonstrated in previous work, but in order to apply to PIC simulations of realistic scenarios, MLMC must be generalized to incorporate self-consistent evolution of the electromagnetic fields. We present such a generalization, with rigorous results concerning its accuracy and efficiency. We present examples of the method in the collisionless, electrostatic context, and discuss applications and extensions for the future.
Normality of Monte Carlo criticality eigenfunction decomposition coefficients
Toth, B. E.; Martin, W. R.; Griesheimer, D. P.
2013-07-01
A proof is presented, which shows that after a single Monte Carlo (MC) neutron transport power method iteration without normalization, the coefficients of an eigenfunction decomposition of the fission source density are normally distributed when using analog or implicit capture MC. Using a Pearson correlation coefficient test, the proof is corroborated by results from a uniform slab reactor problem, and those results also suggest that the coefficients are normally distributed with normalization. The proof and numerical test results support the application of earlier work on the convergence of eigenfunctions under stochastic operators. Knowledge of the Gaussian shape of decomposition coefficients allows researchers to determine an appropriate level of confidence in the distribution of fission sites taken from a MC simulation. This knowledge of the shape of the probability distributions of decomposition coefficients encourages the creation of new predictive convergence diagnostics. (authors)
Theory and Applications of Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Deible, Michael John
With the development of peta-scale computers and exa-scale only a few years away, the quantum Monte Carlo (QMC) method, with favorable scaling and inherent parrallelizability, is poised to increase its impact on the electronic structure community. The most widely used variation of QMC is the diffusion Monte Carlo (DMC) method. The accuracy of the DMC method is only limited by the trial wave function that it employs. The effect of the trial wave function is studied here by initially developing correlation-consistent Gaussian basis sets for use in DMC calculations. These basis sets give a low variance in variance Monte Carlo calculations and improved convergence in DMC. The orbital type used in the trial wave function is then investigated, and it is shown that Brueckner orbitals result in a DMC energy comparable to a DMC energy with orbitals from density functional theory and significantly lower than orbitals from Hartree-Fock theory. Three large weakly interacting systems are then studied; a water-16 isomer, a methane clathrate, and a carbon dioxide clathrate. The DMC method is seen to be in good agreement with MP2 calculations and provides reliable benchmarks. Several strongly correlated systems are then studied. An H4 model system that allows for a fine tuning of the multi-configurational character of the wave function shows when the accuracy of the DMC method with a single Slater-determinant trial function begins to deviate from multi-reference benchmarks. The weakly interacting face-to-face ethylene dimer is studied with and without a rotation around the pi bond, which is used to increase the multi-configurational nature of the wave function. This test shows that the effect of a multi-configurational wave function in weakly interacting systems causes DMC with a single Slater-determinant to be unable to achieve sub-chemical accuracy. The beryllium dimer is studied, and it is shown that a very large determinant expansion is required for DMC to predict a binding energy that is in close agreement with experiment. Finally, water interacting with increasingly large acenes is studied, as is the benzene and anthracene dimer. Deviations from benchmarks are discussed.
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.
Monte Carlo simulations in Nuclear Medicine
Loudos, George K.
2007-11-26
Molecular imaging technologies provide unique abilities to localise signs of disease before symptoms appear, assist in drug testing, optimize and personalize therapy, and assess the efficacy of treatment regimes for different types of cancer. Monte Carlo simulation packages are used as an important tool for the optimal design of detector systems. In addition they have demonstrated potential to improve image quality and acquisition protocols. Many general purpose (MCNP, Geant4, etc) or dedicated codes (SimSET etc) have been developed aiming to provide accurate and fast results. Special emphasis will be given to GATE toolkit. The GATE code currently under development by the OpenGATE collaboration is the most accurate and promising code for performing realistic simulations. The purpose of this article is to introduce the non expert reader to the current status of MC simulations in nuclear medicine and briefly provide examples of current simulated systems, and present future challenges that include simulation of clinical studies and dosimetry applications.
Monte Carlo simulations in Nuclear Medicine
NASA Astrophysics Data System (ADS)
Loudos, George K.
2007-11-01
Molecular imaging technologies provide unique abilities to localise signs of disease before symptoms appear, assist in drug testing, optimize and personalize therapy, and assess the efficacy of treatment regimes for different types of cancer. Monte Carlo simulation packages are used as an important tool for the optimal design of detector systems. In addition they have demonstrated potential to improve image quality and acquisition protocols. Many general purpose (MCNP, Geant4, etc) or dedicated codes (SimSET etc) have been developed aiming to provide accurate and fast results. Special emphasis will be given to GATE toolkit. The GATE code currently under development by the OpenGATE collaboration is the most accurate and promising code for performing realistic simulations. The purpose of this article is to introduce the non expert reader to the current status of MC simulations in nuclear medicine and briefly provide examples of current simulated systems, and present future challenges that include simulation of clinical studies and dosimetry applications.
Configurational temperature: Verification of Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Butler, B. D.; Ayton, Gary; Jepps, Owen G.; Evans, Denis J.
1998-10-01
A new diagnostic that is useful for checking the algorithmic correctness of Monte Carlo computer programs is presented. The check is made by comparing the Boltzmann temperature, which is input to the program and used to accept or reject moves, with a configurational temperature kBTconfig=|∇qΦ|2/∇q2Φ. Here, Φ is the potential energy of the system and ∇q represents the dimensionless gradient operator with respect to the particle positions q. We show, using a simulation of Lennard-Jones particles, that the configurational temperature rapidly and accurately tracks changes made to the input temperature even when the system is not in global thermodynamic equilibrium. Coding and/or algorithm errors can be detected by checking that the input temperature and Tconfig agree. The effects of system size and continuity of Φ and its first derivative on Tconfig are also discussed.
Monte Carlo renormalization group Calculations for polymers
NASA Astrophysics Data System (ADS)
Muthukumar, M.
1983-02-01
A simple method based on Wilson's renormalization group ideas is applied to calculate the dynamical critical exponent z for polymer chains in different dynamical regimes. It is shown that the Doi-Edwards reptating chain does not belong to the same dynamical universality class as the Rouse chain. The earlier results based on ɛ(4 - d, d ˜ space dimensionality) expansion for chains with excluded volume effect are recovered without any ɛ expansion. When combined with the Monte Carlo techniques, this method results in a simple scheme for calculating the static and dynamic exponents for a polymer chain with a prescribed dynamics. Numerical results suggest that the slithering snake model of Wall and Mandel for the dynamics is in a different dynamic universality class than the Rouse chain.
Vectorization of Monte Carlo particle transport
Burns, P.J.; Christon, M.; Schweitzer, R.; Lubeck, O.M.; Wasserman, H.J.; Simmons, M.L.; Pryor, D.V. . Computer Center; Los Alamos National Lab., NM; Supercomputing Research Center, Bowie, MD )
1989-01-01
Fully vectorized versions of the Los Alamos National Laboratory benchmark code Gamteb, a Monte Carlo photon transport algorithm, were developed for the Cyber 205/ETA-10 and Cray X-MP/Y-MP architectures. Single-processor performance measurements of the vector and scalar implementations were modeled in a modified Amdahl's Law that accounts for additional data motion in the vector code. The performance and implementation strategy of the vector codes are related to architectural features of each machine. Speedups between fifteen and eighteen for Cyber 205/ETA-10 architectures, and about nine for CRAY X-MP/Y-MP architectures are observed. The best single processor execution time for the problem was 0.33 seconds on the ETA-10G, and 0.42 seconds on the CRAY Y-MP. 32 refs., 12 figs., 1 tab.
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.
Monte Carlo Exploration of Warped Higgsless Models
Hewett, J
2004-07-06
We have performed a detailed Monte Carlo exploration of the parameter space for a warped Higgsless model of electroweak symmetry breaking in 5 dimensions. This model is based on the SU(2)L x SU(2){sub R} x U(1){sub B-L} gauge group in an AdS{sub 5} bulk with arbitrary gauge kinetic terms on both the Planck and TeV branes. Constraints arising from precision electroweak measurements and collider data are found to be relatively easy to satisfy. We show, however, that the additional requirement of perturbative unitarity up to the cut-off, {approx} 10 TeV, in W{sub L}{sup +}W{sub L}{sup -} elastic scattering in the absence of dangerous tachyons eliminates all models. If successful models of this class exist, they must be highly fine-tuned.
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.
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 simulation of ferroelectric domain growth
NASA Astrophysics Data System (ADS)
Li, B. L.; Liu, X. P.; Fang, F.; Zhu, J. L.; Liu, J.-M.
2006-01-01
The kinetics of two-dimensional isothermal domain growth in a quenched ferroelectric system is investigated using Monte Carlo simulation based on a realistic Ginzburg-Landau ferroelectric model with cubic-tetragonal (square-rectangle) phase transitions. The evolution of the domain pattern and domain size with annealing time is simulated, and the stability of trijunctions and tetrajunctions of domain walls is analyzed. It is found that in this much realistic model with strong dipole alignment anisotropy and long-range Coulomb interaction, the powerlaw for normal domain growth still stands applicable. Towards the late stage of domain growth, both the average domain area and reciprocal density of domain wall junctions increase linearly with time, and the one-parameter dynamic scaling of the domain growth is demonstrated.
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.
Monte Carlo simulation of radiating reentry flows
NASA Technical Reports Server (NTRS)
Taylor, Jeff C.; Carlson, Ann B.; Hassan, H. A.
1993-01-01
The Direct Simulation Monte Carlo (DSMC) method is applied to a radiating, hypersonic, axisymmetric flow over a blunt body in the near continuum regime. The ability of the method to predict the flowfield radiation and the radiative heating is investigated for flow over the Project Fire II configuration at 11.36 kilometers per second at an altitude of 76.42 kilometers. Two methods that differ in the manner in which they treat ionization and estimate electronic excitation are employed. The calculated results are presented and compared with both experimental data and solutions where radiation effects were not included. Differences in the results are discussed. Both methods ignore self absorption and, as a result, overpredict measured radiative heating.
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 andmore » experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.« less
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.
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.
abcpmc: Approximate Bayesian Computation for Population Monte-Carlo code
NASA Astrophysics Data System (ADS)
Akeret, Joel
2015-04-01
abcpmc is a Python Approximate Bayesian Computing (ABC) Population Monte Carlo (PMC) implementation based on Sequential Monte Carlo (SMC) with Particle Filtering techniques. It is extendable with k-nearest neighbour (KNN) or optimal local covariance matrix (OLCM) pertubation kernels and has built-in support for massively parallelized sampling on a cluster using MPI.
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
Variance and efficiency in Monte Carlo transport calculations
NASA Astrophysics Data System (ADS)
Lux, Iván
1980-09-01
Recent developments in Monte Carlo variance and efficiency analysis are summarized. Sufficient conditions are given under which the variance of a Monte Carlo game is less than that of another. The efficiencies of the ELP method and a game with survival biasing and Russian roulette are treated.
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…
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…
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…
Accelerated GPU based SPECT Monte Carlo simulations.
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, (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 efficiency of SPECT imaging simulations. PMID:27163656
Monte Carlo approaches to effective field theories
Carlson, J. ); Schmidt, K.E. . Dept. of Physics)
1991-01-01
In this paper, we explore the application of continuum Monte Carlo methods to effective field theory models. Effective field theories, in this context, are those in which a Fock space decomposition of the state is useful. These problems arise both in nuclear and condensed matter physica. In nuclear physics, much work has been done on effective field theories of mesons and baryons. While the theories are not fundamental, they should be able to describe nuclear properties at low energy and momentum scales. After describing the methods, we solve two simple scalar field theory problems; the polaron and two nucleons interacting through scalar meson exchange. The methods presented here are rather straightforward extensions of methods used to solve quantum mechanics problems. Monte Carlo methods are used to avoid the truncation inherent in a Tamm-Dancoff approach and its associated difficulties. Nevertheless, the methods will be most valuable when the Fock space decomposition of the states is useful. Hence, while they are not intended for ab initio studies of QCD, they may prove valuable in studies of light nuclei, or for systems of interacting electrons and phonons. In these problems a Fock space decomposition can be used to reduce the number of degrees of freedom and to retain the rotational symmetries exactly. The problems we address here are comparatively simple, but offer useful initial tests of the method. We present results for the polaron and two non-relativistic nucleons interacting through scalar meson exchange. In each case, it is possible to integrate out the boson degrees of freedom exactly, and obtain a retarded form of the action that depends only upon the fermion paths. Here we keep the explicit bosons, though, since we would like to retain information about the boson components of the states and it will be necessary to keep these components in order to treat non-scalar of interacting bosonic fields.
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.
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.
A hybrid Monte Carlo and response matrix Monte Carlo method in criticality calculation
Li, Z.; Wang, K.
2012-07-01
Full core calculations are very useful and important in reactor physics analysis, especially in computing the full core power distributions, optimizing the refueling strategies and analyzing the depletion of fuels. To reduce the computing time and accelerate the convergence, a method named Response Matrix Monte Carlo (RMMC) method based on analog Monte Carlo simulation was used to calculate the fixed source neutron transport problems in repeated structures. To make more accurate calculations, we put forward the RMMC method based on non-analog Monte Carlo simulation and investigate the way to use RMMC method in criticality calculations. Then a new hybrid RMMC and MC (RMMC+MC) method is put forward to solve the criticality problems with combined repeated and flexible geometries. This new RMMC+MC method, having the advantages of both MC method and RMMC method, can not only increase the efficiency of calculations, also simulate more complex geometries rather than repeated structures. Several 1-D numerical problems are constructed to test the new RMMC and RMMC+MC method. The results show that RMMC method and RMMC+MC method can efficiently reduce the computing time and variations in the calculations. Finally, the future research directions are mentioned and discussed at the end of this paper to make RMMC method and RMMC+MC method more powerful. (authors)
Crossing the mesoscale no-mans land via parallel kinetic Monte Carlo.
Garcia Cardona, Cristina; Webb, Edmund Blackburn, III; Wagner, Gregory John; Tikare, Veena; Holm, Elizabeth Ann; Plimpton, Steven James; Thompson, Aidan Patrick; Slepoy, Alexander; Zhou, Xiao Wang; Battaile, Corbett Chandler; Chandross, Michael Evan
2009-10-01
The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.
Simple geometry optimization with Variational Quantum Monte Carlo method
NASA Astrophysics Data System (ADS)
Nissenbaum, Dan
2005-03-01
Stochastic optimization methods may be combined with Quantum Monte Carlo (QMC) integration to obtain a computational scheme for treating many body wavefunctions suitable for addressing modern problems in nanoscale physics. In this connection, we are investigating the range of applicability of the Stochastic Gradient Approximation (SGA) technique [1]. The SGA possesses the important advantage that the updating of the electronic variational parameters and the nuclear coordinates can be carried out simultaneously and without an explicit determination of the total energy for each geometry. We present illustrative results using simple variational functions for describing the hydrogen molecule, the lithium dimer, and the neutral and charged Li4 clusters. We computed highly accurate potential energy surfaces on a fine grid in order to test the efficacy of the SGA in locating the energy minima in the parameter space. Work supported in part by the USDOE.[1] A. Harju, B. Barbiellini, S. Siljamä'ki, R.M. Nieminen, and G. Ortiz, Phys. Rev. Lett. 79, 1173 (1997).
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.
Recent advances and future prospects for Monte Carlo
Brown, Forrest B
2010-01-01
The history of Monte Carlo methods is closely linked to that of computers: The first known Monte Carlo program was written in 1947 for the ENIAC; a pre-release of the first Fortran compiler was used for Monte Carlo In 1957; Monte Carlo codes were adapted to vector computers in the 1980s, clusters and parallel computers in the 1990s, and teraflop systems in the 2000s. Recent advances include hierarchical parallelism, combining threaded calculations on multicore processors with message-passing among different nodes. With the advances In computmg, Monte Carlo codes have evolved with new capabilities and new ways of use. Production codes such as MCNP, MVP, MONK, TRIPOLI and SCALE are now 20-30 years old (or more) and are very rich in advanced featUres. The former 'method of last resort' has now become the first choice for many applications. Calculations are now routinely performed on office computers, not just on supercomputers. Current research and development efforts are investigating the use of Monte Carlo methods on FPGAs. GPUs, and many-core processors. Other far-reaching research is exploring ways to adapt Monte Carlo methods to future exaflop systems that may have 1M or more concurrent computational processes.
Continuous-time quantum Monte Carlo impurity solvers
NASA Astrophysics Data System (ADS)
Gull, Emanuel; Werner, Philipp; Fuchs, Sebastian; Surer, Brigitte; Pruschke, Thomas; Troyer, Matthias
2011-04-01
Continuous-time quantum Monte Carlo impurity solvers are algorithms that sample the partition function of an impurity model using diagrammatic Monte Carlo techniques. The present paper describes codes that implement the interaction expansion algorithm originally developed by Rubtsov, Savkin, and Lichtenstein, as well as the hybridization expansion method developed by Werner, Millis, Troyer, et al. These impurity solvers are part of the ALPS-DMFT application package and are accompanied by an implementation of dynamical mean-field self-consistency equations for (single orbital single site) dynamical mean-field problems with arbitrary densities of states. Program summaryProgram title: dmft Catalogue identifier: AEIL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: ALPS LIBRARY LICENSE version 1.1 No. of lines in distributed program, including test data, etc.: 899 806 No. of bytes in distributed program, including test data, etc.: 32 153 916 Distribution format: tar.gz Programming language: C++ Operating system: The ALPS libraries have been tested on the following platforms and compilers: Linux with GNU Compiler Collection (g++ version 3.1 and higher), and Intel C++ Compiler (icc version 7.0 and higher) MacOS X with GNU Compiler (g++ Apple-version 3.1, 3.3 and 4.0) IBM AIX with Visual Age C++ (xlC version 6.0) and GNU (g++ version 3.1 and higher) compilers Compaq Tru64 UNIX with Compq C++ Compiler (cxx) SGI IRIX with MIPSpro C++ Compiler (CC) HP-UX with HP C++ Compiler (aCC) Windows with Cygwin or coLinux platforms and GNU Compiler Collection (g++ version 3.1 and higher) RAM: 10 MB-1 GB Classification: 7.3 External routines: ALPS [1], BLAS/LAPACK, HDF5 Nature of problem: (See [2].) Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self-energy and local correlation functions. Solution method: Quantum impurity models require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms for which we present implementations here meet this challenge. Continuous-time quantum impurity methods are based on partition function expansions of quantum impurity models that are stochastically sampled to all orders using diagrammatic quantum Monte Carlo techniques. For a review of quantum impurity models and their applications and of continuous-time quantum Monte Carlo methods for impurity models we refer the reader to [2]. Additional comments: Use of dmft requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. Running time: 60 s-8 h per iteration.
Quantum Monte Carlo Algorithms for Diagrammatic Vibrational Structure Calculations
NASA Astrophysics Data System (ADS)
Hermes, Matthew; Hirata, So
2015-06-01
Convergent hierarchies of theories for calculating many-body vibrational ground and excited-state wave functions, such as Møller-Plesset perturbation theory or coupled cluster theory, tend to rely on matrix-algebraic manipulations of large, high-dimensional arrays of anharmonic force constants, tasks which require large amounts of computer storage space and which are very difficult to implement in a parallel-scalable fashion. On the other hand, existing quantum Monte Carlo (QMC) methods for vibrational wave functions tend to lack robust techniques for obtaining excited-state energies, especially for large systems. By exploiting analytical identities for matrix elements of position operators in a harmonic oscillator basis, we have developed stochastic implementations of the size-extensive vibrational self-consistent field (MC-XVSCF) and size-extensive vibrational Møller-Plesset second-order perturbation (MC-XVMP2) theories which do not require storing the potential energy surface (PES). The programmable equations of MC-XVSCF and MC-XVMP2 take the form of a small number of high-dimensional integrals evaluated using Metropolis Monte Carlo techniques. The associated integrands require independent evaluations of only the value, not the derivatives, of the PES at many points, a task which is trivial to parallelize. However, unlike existing vibrational QMC methods, MC-XVSCF and MC-XVMP2 can calculate anharmonic frequencies directly, rather than as a small difference between two noisy total energies, and do not require user-selected coordinates or nodal surfaces. MC-XVSCF and MC-XVMP2 can also directly sample the PES in a given approximation without analytical or grid-based approximations, enabling us to quantify the errors induced by such approximations.
Variance reduction in Monte Carlo analysis of rarefied gas diffusion.
NASA Technical Reports Server (NTRS)
Perlmutter, M.
1972-01-01
The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.
Accurate rotational barrier calculations with diffusion quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Klahm, Sebastian; Lüchow, Arne
2014-04-01
Accurate quantum Monte Carlo, MP2, coupled cluster, and DFT calculations of rotational barriers of several small molecules are presented. With the diffusion quantum Monte Carlo method (DMC) excellent agreement with experimental barriers is obtained except for the gauche-gauche barriers of n-butane and ethylmethylether. It is argued that these two experimental values might be erroneous. Additionally, barriers calculated with the more efficient variational quantum Monte Carlo method (VMC) are presented. The VMC barriers are less accurate than the DMC results, but it is demonstrated that accurate barriers can be obtained with sophisticated Jastrow correlation functions.
Discrete Diffusion Monte Carlo for Electron Thermal Transport
NASA Astrophysics Data System (ADS)
Chenhall, Jeffrey; Cao, Duc; Wollaeger, Ryan; Moses, Gregory
2014-10-01
The iSNB (implicit Schurtz Nicolai Busquet electron thermal transport method of Cao et al. is adapted to a Discrete Diffusion Monte Carlo (DDMC) solution method for eventual inclusion in a hybrid IMC-DDMC (Implicit Monte Carlo) method. The hybrid method will combine the efficiency of a diffusion method in short mean free path regions with the accuracy of a transport method in long mean free path regions. The Monte Carlo nature of the approach allows the algorithm to be massively parallelized. Work to date on the iSNB-DDMC method will be presented. This work was supported by Sandia National Laboratory - Albuquerque.
A radiating shock evaluated using Implicit Monte Carlo Diffusion
Cleveland, M.; Gentile, N.
2013-07-01
Implicit Monte Carlo [1] (IMC) has been shown to be very expensive when used to evaluate a radiation field in opaque media. Implicit Monte Carlo Diffusion (IMD) [2], which evaluates a spatial discretized diffusion equation using a Monte Carlo algorithm, can be used to reduce the cost of evaluating the radiation field in opaque media [2]. This work couples IMD to the hydrodynamics equations to evaluate opaque diffusive radiating shocks. The Lowrie semi-analytic diffusive radiating shock benchmark[a] is used to verify our implementation of the coupled system of equations. (authors)
Monte Carlo Production Management at CMS
NASA Astrophysics Data System (ADS)
Boudoul, G.; Franzoni, G.; Norkus, A.; Pol, A.; Srimanobhas, P.; Vlimant, J.-R.
2015-12-01
The analysis of the LHC data at the Compact Muon Solenoid (CMS) experiment requires the production of a large number of simulated events. During the RunI of LHC (20102012), CMS has produced over 12 Billion simulated events, organized in approximately sixty different campaigns each emulating specific detector conditions and LHC running conditions (pile up). In order to aggregate the information needed for the configuration and prioritization of the events production, assure the book-keeping of all the processing requests placed by the physics analysis groups, and to interface with the CMS production infrastructure, the web- based service Monte Carlo Management (McM) has been developed and put in production in 2013. McM is based on recent server infrastructure technology (CherryPy + AngularJS) and relies on a CouchDB database back-end. This contribution covers the one and half year of operational experience managing samples of simulated events for CMS, the evolution of its functionalities and the extension of its capability to monitor the status and advancement of the events production.
Multideterminant Wave Functions in Quantum Monte Carlo.
Morales, Miguel A; McMinis, Jeremy; Clark, Bryan K; Kim, Jeongnim; Scuseria, Gustavo E
2012-07-10
Quantum Monte Carlo (QMC) methods have received considerable attention over past decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with the number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multideterminant expansions in QMC and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistry methods like MP2, CCSD(T), and various DFT approximations, the QMC results show a marked improvement over all of them. In fact, only the explicitly correlated CCSD(T) method with a large basis set produces more accurate results. Further developments in trial wave functions and algorithmic improvements appear promising for rendering QMC as the benchmark standard in large electronic systems. PMID:26588949
Monte Carlo Investigation of Quark Gluon Plasma
NASA Astrophysics Data System (ADS)
Hunt-Isaak, Ian
2015-10-01
The Quark Gluon Plasma (QGP) is a hot, dense state of matter in which the Quarks and Gluons which make up Hadrons are freed hypothesized to be similar to the conditions of the very early universe. The QGP can be generated via the collision of Heavy Ions, Lead (Pb) for this work, at ultrarelativistc velocities. However in QGP is short lived so it cannot be investigated by external probes. Instead internal probes such as jets are used, jets are sprays of particles from a hard scattering of quarks and gluons. It is expected that Proton-Proton (pp) collisions do not generate a QGP so by comparing jet observable in PbPb and pp collisions, we can gain information about the medium. Through comparison of Monte Carlo simulations to data, information about medium can be deduced. For this work a framework to run
Commensurabilities between ETNOs: a Monte Carlo survey
NASA Astrophysics Data System (ADS)
de la Fuente Marcos, C.; de la Fuente Marcos, R.
2016-04-01
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.
Accelerated Monte Carlo Methods for Coulomb Collisions
NASA Astrophysics Data System (ADS)
Rosin, Mark; Ricketson, Lee; Dimits, Andris; Caflisch, Russel; Cohen, Bruce
2014-03-01
We present a new highly efficient multi-level Monte Carlo (MLMC) simulation algorithm for Coulomb collisions in a plasma. The scheme, initially developed and used successfully for applications in financial mathematics, is applied here to kinetic plasmas for the first time. The method is based on a Langevin treatment of the Landau-Fokker-Planck equation and has a rich history derived from the works of Einstein and Chandrasekhar. The MLMC scheme successfully reduces the computational cost of achieving an RMS error ɛ in the numerical solution to collisional plasma problems from (ɛ-3) - for the standard state-of-the-art Langevin and binary collision algorithms - to a theoretically optimal (ɛ-2) scaling, when used in conjunction with an underlying Milstein discretization to the Langevin equation. In the test case presented here, the method accelerates simulations by factors of up to 100. We summarize the scheme, present some tricks for improving its efficiency yet further, and discuss the method's range of applicability. Work performed for US DOE by LLNL under contract DE-AC52- 07NA27344 and by UCLA under grant DE-FG02-05ER25710.
Monte Carlo Model of Mercury's Sodium Exosphere
NASA Astrophysics Data System (ADS)
Killen, Rosemary; Vervack, Ronald; Mouawad, Nelly; Crider, Dana, , Dr
Mercury's sodium exosphere has been observed via ground-based, high-resolution optical telescopes since its discovery in 1985, and the processes behind the observed high temporal and spatial variability are still controversial after two decades of study. We have therefore undertaken a systematic modeling effort using a Monte Carlo technique to simulate the sources and sinks of the exosphere under various conditions. The assumed source processes are photonstimulated desorption (PSD), impact vaporization and ion sputtering. We assume that PSD is directly proportional to the incoming solar UV flux with a small temperature dependence, that impact vaporization by micrometeorites is uniform, and that ion sputtering depends on the assumed flux and energy of incoming ions, which can be set arbitrarily in the model. The interaction of atoms with the surface is set by two parameters that determine the probability of sticking and the exchange of energy with the surface. Loss is by Jeans escape, sticking at the surface, and photo-ionization. We currently do not track ions in this code nor the reemission of particles that stick to the surface. We present results for simulations at perihelion, aphelion, and true anomaly angles 63 and 297 degrees (where radiation pressure is greatest and the radial velocity of the planet with respect to the sun is positive and negative, respectively). These simulations will provide a basis for the interpretation of both ground-based and spacecraft data.
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
Measuring Berry curvature with quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Kolodrubetz, Michael
2014-01-01
The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric properties of a quantum ground state manifold. While Berry curvature has been well studied in the regimes of few-body physics and noninteracting particles, its use in the regime of strong interactions is hindered by the lack of numerical methods to solve for it. In this paper I fill this gap by implementing a quantum Monte Carlo method to solve for the Berry curvature, based on interpreting Berry curvature as a leading correction to imaginary time ramps. I demonstrate my algorithm using the transverse-field Ising model in one and two dimensions, the latter of which is nonintegrable. Despite the fact that the Berry curvature gives information about the phase of the wave function, I show that the algorithm has no sign or phase problem for standard sign-problem-free Hamiltonians. My algorithm scales similarly to conventional methods as a function of system size and energy gap, and therefore should prove a valuable tool in investigating the quantum geometry of many-body systems.
Monte Carlo models of dust coagulation
NASA Astrophysics Data System (ADS)
Zsom, Andras
2010-10-01
The thesis deals with the first stage of planet formation, namely dust coagulation from micron to millimeter sizes in circumstellar disks. For the first time, we collect and compile the recent laboratory experiments on dust aggregates into a collision model that can be implemented into dust coagulation models. We put this model into a Monte Carlo code that uses representative particles to simulate dust evolution. Simulations are performed using three different disk models in a local box (0D) located at 1 AU distance from the central star. We find that the dust evolution does not follow the previously assumed growth-fragmentation cycle, but growth is halted by bouncing before the fragmentation regime is reached. We call this the bouncing barrier which is an additional obstacle during the already complex formation process of planetesimals. The absence of the growth-fragmentation cycle and the halted growth has two important consequences for planet formation. 1) It is observed that disk atmospheres are dusty throughout their lifetime. Previous models concluded that the small, continuously produced fragments can keep the disk atmospheres dusty. We however show that small fragments are not produced because bouncing prevents fragmentation. 2) As particles do not reach the fragmentation barrier, their sizes are smaller compared to the sizes reached in previous dust models. We decided to investigate point 1) in more detail. A vertical column of a disk (1D) is modeled including the sedimentation of the particles. We find that already intermediate levels of turbulence can prevent particles settling to the midplane.
Finding Planet Nine: a Monte Carlo approach
NASA Astrophysics Data System (ADS)
de la Fuente Marcos, C.; de la Fuente Marcos, R.
2016-03-01
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 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 antialignment scenario. In addition and after studying the current statistics of ETNOs, a cautionary note on the robustness of the perihelia clustering is presented.
A Monte Carlo model for `jet quenching'
NASA Astrophysics Data System (ADS)
Zapp, Korinna; Ingelman, Gunnar; Rathsman, Johan; Stachel, Johanna; Wiedemann, Urs Achim
2009-04-01
We have developed the Monte Carlo simulation program Jewel 1.0 (Jet Evolution With Energy Loss), which interfaces a perturbative final-state parton shower with medium effects occurring in ultra-relativistic heavy-ion collisions. This is done by comparing for each jet fragment the probability of further perturbative splitting with the density-dependent probability of scattering with the medium. A simple hadronisation mechanism is included. In the absence of medium effects, we validate Jewel against a set of benchmark jet measurements. For elastic interactions with the medium, we characterise not only the medium-induced modification of the jet, but also the jet-induced modification of the medium. Our main physical result is the observation that collisional and radiative medium modifications lead to characteristic differences in the jet fragmentation pattern, which persist above a soft background cut. We argue that this should allow one to disentangle collisional and radiative parton energy loss mechanisms by measuring the n-jet fraction or a class of jet shape observables.
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.
Biofilm growth: a lattice Monte Carlo model
NASA Astrophysics Data System (ADS)
Tao, Yuguo; Slater, Gary
2011-03-01
Biofilms are complex colonies of bacteria that grow in contact with a wall, often in the presence of a flow. In the current work, biofilm growth is investigated using a new two-dimensional lattice Monte Carlo algorithm based on the Bond-Fluctuation Algorithm (BFA). One of the distinguishing characteristics of biofilms, the synthesis and physical properties of the extracellular polymeric substance (EPS) in which the cells are embedded, is explicitly taken into account. Cells are modelled as autonomous closed loops with well-defined mechanical and thermodynamic properties, while the EPS is modelled as flexible polymeric chains. This BFA model allows us to add biologically relevant features such as: the uptake of nutrients; cell growth, division and death; the production of EPS; cell maintenance and hibernation; the generation of waste and the impact of toxic molecules; cell mutation and evolution; cell motility. By tuning the structural, interactional and morphologic parameters of the model, the cell shapes as well as the growth and maturation of various types of biofilm colonies can be controlled.
NASA Technical Reports Server (NTRS)
Queen, Eric M.; Omara, Thomas M.
1990-01-01
A realization of a stochastic atmosphere model for use in simulations is presented. The model provides pressure, density, temperature, and wind velocity as a function of latitude, longitude, and altitude, and is implemented in a three degree of freedom simulation package. This implementation is used in the Monte Carlo simulation of an aeroassisted orbital transfer maneuver and results are compared to those of a more traditional approach.
Grover search algorithm with Rydberg-blockaded atoms: quantum Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Petrosyan, David; Saffman, Mark; Mølmer, Klaus
2016-05-01
We consider the Grover search algorithm implementation for a quantum register of size N={2}k using k (or k+1) microwave- and laser-driven Rydberg-blockaded atoms, following the proposal by Mølmer et al (2011 J. Phys. B 44 184016). We suggest some simplifications for the microwave and laser couplings, and analyze the performance of the algorithm for up to k = 4 multilevel atoms under realistic experimental conditions using quantum stochastic (Monte Carlo) wavefunction simulations.
Noise-induced instability in self-consistent Monte Carlo calculations
Lemons, D.S.; Lackman, J.; Jones, M.E.; Winske, D.
1995-12-01
We identify, analyze, and propose remedies for a numerical instability responsible for the growth or decay of sums that should be conserved in Monte Carlo simulations of stochastically interacting particles. ``Noisy`` sums with fluctuations proportional to 1/ {radical}{ital n} , where {ital n} is the number of particles in the simulation, provide feedback that drives the instability. Numerical illustrations of an energy loss or ``cooling`` instability in an Ornstein-Uhlenbeck process support our analysis. (c) 1995 The American Physical Society
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.
DETERMINING UNCERTAINTY IN PHYSICAL PARAMETER MEASUREMENTS BY MONTE CARLO SIMULATION
A statistical approach, often called Monte Carlo Simulation, has been used to examine propagation of error with measurement of several parameters important in predicting environmental transport of chemicals. These parameters are vapor pressure, water solubility, octanol-water par...
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.
Monte Carlo computations of the hadronic mass spectrum
Rebbi, C.
1982-01-01
This paper summarizes two talks presented at the Orbis Scientiae Meeting, 1982. Monte Carlo results on the mass gap (or glueball mass) and on the masses of the lightest quark-model hadrons are illustrated.
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)
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.
Shift: A Massively Parallel Monte Carlo Radiation Transport Package
Pandya, Tara M; Johnson, Seth R; Davidson, Gregory G; Evans, Thomas M; Hamilton, Steven P
2015-01-01
This paper discusses the massively-parallel Monte Carlo radiation transport package, Shift, developed at Oak Ridge National Laboratory. It reviews the capabilities, implementation, and parallel performance of this code package. Scaling results demonstrate very good strong and weak scaling behavior of the implemented algorithms. Benchmark results from various reactor problems show that Shift results compare well to other contemporary Monte Carlo codes and experimental results.
A Particle Population Control Method for Dynamic Monte Carlo
NASA Astrophysics Data System (ADS)
Sweezy, Jeremy; Nolen, Steve; Adams, Terry; Zukaitis, Anthony
2014-06-01
A general particle population control method has been derived from splitting and Russian Roulette for dynamic Monte Carlo particle transport. A well-known particle population control method, known as the particle population comb, has been shown to be a special case of this general method. This general method has been incorporated in Los Alamos National Laboratory's Monte Carlo Application Toolkit (MCATK) and examples of it's use are shown for both super-critical and sub-critical systems.
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.
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 this paper has proven useful in planning several Crew Exploration Vehicle parachute tests.
Neutron spectral unfolding using the Monte Carlo method
NASA Astrophysics Data System (ADS)
O'Brien, Keran; Sanna, Robert
A solution to the neutron unfolding problem, without approximation or a priori assumptions as to spectral shape, has been devised, based on the Monte Carlo method, and its rate of convergence derived. By application to synthesized measurements with controlled and varying levels of error, the effect of measurement error has been investigated. This Monte Carlo method has also been applied to experimental stray neutron data from measurements inside a reactor containment vessel.
Multiscale MonteCarlo equilibration: Pure Yang-Mills theory
Endres, Michael G.; Brower, Richard C.; Orginos, Kostas; Detmold, William; Pochinsky, Andrew V.
2015-12-29
In this study, 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.
SCALE Monte Carlo Eigenvalue Methods and New Advancements
Goluoglu, Sedat; Leppanen, Jaakko; Petrie Jr, Lester M; Dunn, Michael E
2010-01-01
SCALE code system is developed and maintained by Oak Ridge National Laboratory to perform criticality safety, reactor analysis, radiation shielding, and spent fuel characterization for nuclear facilities and transportation/storage package designs. SCALE is a modular code system that includes several codes which use either Monte Carlo or discrete ordinates solution methodologies for solving relevant neutral particle transport equations. This paper describes some of the key capabilities of the Monte Carlo criticality safety codes within the SCALE code system.
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.
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.
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. Phys. J. C 23 (2002) 311]. This program implements some of the more significant ones, enabling the simulation of central particle production through color singlet exchange between interacting protons or antiprotons. Method of solution: The Monte Carlo method is used to simulate all elementary 2→2 and 2→1 processes available in HERWIG. The color singlet exchanges implemented in DPEMC are implemented as functions reweighting the photon flux already present in HERWIG. Restriction on the complexity of the problem: The program relying extensively on HERWIG, the limitations are the same as in [G. Marchesini, B.R. Webber, G. Abbiendi, I.G. Knowles, M.H. Seymour, L. Stanco, Comput. Phys. Comm. 67 (1992) 465; G. Corcella, I.G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. Seymour, B. Webber, JHEP 0101 (2001) 010]. Typical running time: Approximate times on a 800 MHz Pentium III: 5-20 min per 10 000 unweighted events, depending on the process under consideration.
Monte Carlo study of microdosimetric diamond detectors.
Solevi, Paola; Magrin, Giulio; Moro, Davide; Mayer, Ramona
2015-09-21
Ion-beam therapy provides a high dose conformity and increased radiobiological effectiveness with respect to conventional radiation-therapy. Strict constraints on the maximum uncertainty on the biological weighted dose and consequently on the biological weighting factor require the determination of the radiation quality, defined as the types and energy spectra of the radiation at a specific point. However the experimental determination of radiation quality, in particular for an internal target, is not simple and the features of ion interactions and treatment delivery require dedicated and optimized detectors. Recently chemical vapor deposition (CVD) diamond detectors have been suggested as ion-beam therapy microdosimeters. Diamond detectors can be manufactured with small cross sections and thin shapes, ideal to cope with the high fluence rate. However the sensitive volume of solid state detectors significantly deviates from conventional microdosimeters, with a diameter that can be up to 1000 times the height. This difference requires a redefinition of the concept of sensitive thickness and a deep study of the secondary to primary radiation, of the wall effects and of the impact of the orientation of the detector with respect to the radiation field. The present work intends to study through Monte Carlo simulations the impact of the detector geometry on the determination of radiation quality quantities, in particular on the relative contribution of primary and secondary radiation. The dependence of microdosimetric quantities such as the unrestricted linear energy L and the lineal energy y are investigated for different detector cross sections, by varying the particle type (carbon ions and protons) and its energy. PMID:26309235
Monte Carlo simulations of the photospheric process
NASA Astrophysics Data System (ADS)
Santana, Rodolfo; Crumley, Patrick; Hernández, Roberto A.; Kumar, Pawan
2016-02-01
We present a Monte Carlo (MC) code we wrote to simulate the photospheric process and to study the photospheric spectrum above the peak energy. Our simulations were performed with a photon-to-electron ratio Nγ/Ne = 105, as determined by observations of the Gamma-ray Burst prompt emission. We searched an exhaustive parameter space to determine if the photospheric process can match the observed high-energy spectrum of the prompt emission. If we do not consider electron re-heating, we determined that the best conditions to produce the observed high-energy spectrum are low photon temperatures and high optical depths. However, for these simulations, the spectrum peaks at an energy below 300 keV by a factor of ˜10. For the cases we consider with higher photon temperatures and lower optical depths, we demonstrate that additional energy in the electrons is required to produce a power-law spectrum above the peak energy. By considering electron re-heating near the photosphere, the spectra for these simulations have a peak energy ˜300 keV and a power-law spectrum extending to at least 10 MeV with a spectral index consistent with the prompt emission observations. We also performed simulations for different values of Nγ/Ne and determined that the simulation results are very sensitive to Nγ/Ne. Lastly, in addition to Comptonizing a blackbody spectrum, we also simulate the Comptonization of a fν ∝ ν-1/2 fast cooled synchrotron spectrum. The spectrum for these simulations peaks at ˜104 keV, with a flat spectrum fν ∝ ν0 below the peak energy.
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.
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 study of microdosimetric diamond detectors
NASA Astrophysics Data System (ADS)
Solevi, Paola; Magrin, Giulio; Moro, Davide; Mayer, Ramona
2015-09-01
Ion-beam therapy provides a high dose conformity and increased radiobiological effectiveness with respect to conventional radiation-therapy. Strict constraints on the maximum uncertainty on the biological weighted dose and consequently on the biological weighting factor require the determination of the radiation quality, defined as the types and energy spectra of the radiation at a specific point. However the experimental determination of radiation quality, in particular for an internal target, is not simple and the features of ion interactions and treatment delivery require dedicated and optimized detectors. Recently chemical vapor deposition (CVD) diamond detectors have been suggested as ion-beam therapy microdosimeters. Diamond detectors can be manufactured with small cross sections and thin shapes, ideal to cope with the high fluence rate. However the sensitive volume of solid state detectors significantly deviates from conventional microdosimeters, with a diameter that can be up to 1000 times the height. This difference requires a redefinition of the concept of sensitive thickness and a deep study of the secondary to primary radiation, of the wall effects and of the impact of the orientation of the detector with respect to the radiation field. The present work intends to study through Monte Carlo simulations the impact of the detector geometry on the determination of radiation quality quantities, in particular on the relative contribution of primary and secondary radiation. The dependence of microdosimetric quantities such as the unrestricted linear energy L and the lineal energy y are investigated for different detector cross sections, by varying the particle type (carbon ions and protons) and its energy.
Monte carlo sampling of fission multiplicity.
Hendricks, J. S.
2004-01-01
Two new methods have been developed for fission multiplicity modeling in Monte Carlo calculations. The traditional method of sampling neutron multiplicity from fission is to sample the number of neutrons above or below the average. For example, if there are 2.7 neutrons per fission, three would be chosen 70% of the time and two would be chosen 30% of the time. For many applications, particularly {sup 3}He coincidence counting, a better estimate of the true number of neutrons per fission is required. Generally, this number is estimated by sampling a Gaussian distribution about the average. However, because the tail of the Gaussian distribution is negative and negative neutrons cannot be produced, a slight positive bias can be found in the average value. For criticality calculations, the result of rejecting the negative neutrons is an increase in k{sub eff} of 0.1% in some cases. For spontaneous fission, where the average number of neutrons emitted from fission is low, the error also can be unacceptably large. If the Gaussian width approaches the average number of fissions, 10% too many fission neutrons are produced by not treating the negative Gaussian tail adequately. The first method to treat the Gaussian tail is to determine a correction offset, which then is subtracted from all sampled values of the number of neutrons produced. This offset depends on the average value for any given fission at any energy and must be computed efficiently at each fission from the non-integrable error function. The second method is to determine a corrected zero point so that all neutrons sampled between zero and the corrected zero point are killed to compensate for the negative Gaussian tail bias. Again, the zero point must be computed efficiently at each fission. Both methods give excellent results with a negligible computing time penalty. It is now possible to include the full effects of fission multiplicity without the negative Gaussian tail bias.
Lattice Monte Carlo simulations of polymer melts.
Hsu, Hsiao-Ping
2014-12-21
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. PMID:25527957
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.
Quantum Monte Carlo Endstation for Petascale Computing
David Ceperley
2011-03-02
The major achievements enabled by QMC Endstation grant include * Performance improvement on clusters of x86 multi-core systems, especially on Cray XT systems * New and improved methods for the wavefunction optimizations * New forms of trial wavefunctions * Implementation of the full application on NVIDIA GPUs using CUDA The scaling studies of QMCPACK on large-scale systems show excellent parallel efficiency up to 216K cores on Jaguarpf (Cray XT5). The GPU implementation shows speedups of 10-15x over the CPU implementation on older generation of x86. We have implemented hybrid OpenMP/MPI scheme in QMC to take advantage of multi-core shared memory processors of petascale systems. Our hybrid scheme has several advantages over the standard MPI-only scheme. * Memory optimized: large read-only data to store one-body orbitals and other shared properties to represent the trial wave function and many-body Hamiltonian can be shared among threads, which reduces the memory footprint of a large-scale problem. * Cache optimized: the data associated with an active Walker are in cache during the compute-intensive drift-diffusion process and the operations on an Walker are optimized for cache reuse. Thread-local objects are used to ensure the data affinity to a thread. * Load balanced: Walkers in an ensemble are evenly distributed among threads and MPI tasks. The two-level parallelism reduces the population imbalance among MPI tasks and reduces the number of point-to-point communications of large messages (serialized objects) for the Walker exchange. * Communication optimized: the communication overhead, especially for the collective operations necessary to determine ET and measure the properties of an ensemble, is significantly lowered by using less MPI tasks. The multiple forms of parallelism afforded by QMC algorithms make them ideal candidates for acceleration in the many-core paradigm. We presented the results of our effort to port the QMCPACK simulation code to the NVIDIA 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 hydrogen on Ti(1,2)ethylene-nH2 using Diffusion Monte Carlo. This work has been started and is ongoing. We are studying systems involving 1 and 2 Ti bonding sites with up to 10 hydrogen molecules in numerous configurations. This work will establish a benchmark that will test the accuracy of density functional calculations and establish the feasibility of our methods for similar systems.
Lattice Monte Carlo simulation of Galilei variant anomalous diffusion
Guo, Gang; Bittig, Arne; Uhrmacher, Adelinde
2015-05-01
The observation of an increasing number of anomalous diffusion phenomena motivates the study to reveal the actual reason for such stochastic processes. When it is difficult to get analytical solutions or necessary to track the trajectory of particles, lattice Monte Carlo (LMC) simulation has been shown to be particularly useful. To develop such an LMC simulation algorithm for the Galilei variant anomalous diffusion, we derive explicit solutions for the conditional and unconditional first passage time (FPT) distributions with double absorbing barriers. According to the theory of random walks on lattices and the FPT distributions, we propose an LMC simulation algorithm and prove that such LMC simulation can reproduce both the mean and the mean square displacement exactly in the long-time limit. However, the error introduced in the second moment of the displacement diverges according to a power law as the simulation time progresses. We give an explicit criterion for choosing a small enough lattice step to limit the error within the specified tolerance. We further validate the LMC simulation algorithm and confirm the theoretical error analysis through numerical simulations. The numerical results agree with our theoretical predictions very well.
Monte Carlo simulations of intensity profiles for energetic particle propagation
NASA Astrophysics Data System (ADS)
Tautz, R. C.; Bolte, J.; Shalchi, A.
2016-02-01
Aims: Numerical test-particle simulations are a reliable and frequently used tool for testing analytical transport theories and predicting mean-free paths. The comparison between solutions of the diffusion equation and the particle flux is used to critically judge the applicability of diffusion to the stochastic transport of energetic particles in magnetized turbulence. Methods: A Monte Carlo simulation code is extended to allow for the generation of intensity profiles and anisotropy-time profiles. Because of the relatively low number density of computational particles, a kernel function has to be used to describe the spatial extent of each particle. Results: The obtained intensity profiles are interpreted as solutions of the diffusion equation by inserting the diffusion coefficients that have been directly determined from the mean-square displacements. The comparison shows that the time dependence of the diffusion coefficients needs to be considered, in particular the initial ballistic phase and the often subdiffusive perpendicular coefficient. Conclusions: It is argued that the perpendicular component of the distribution function is essential if agreement between the diffusion solution and the simulated flux is to be obtained. In addition, time-dependent diffusion can provide a better description than the classic diffusion equation only after the initial ballistic phase.
Probability Forecasting Using Monte Carlo Simulation
NASA Astrophysics Data System (ADS)
Duncan, M.; Frisbee, J.; Wysack, J.
2014-09-01
Space Situational Awareness (SSA) is defined as the knowledge and characterization of all aspects of space. SSA is now a fundamental and critical component of space operations. Increased dependence on our space assets has in turn lead to a greater need for accurate, near real-time knowledge of all space activities. With the growth of the orbital debris population, satellite operators are performing collision avoidance maneuvers more frequently. Frequent maneuver execution expends fuel and reduces the operational lifetime of the spacecraft. Thus the need for new, more sophisticated collision threat characterization methods must be implemented. The collision probability metric is used operationally to quantify the collision risk. The collision probability is typically calculated days into the future, so that high risk and potential high risk conjunction events are identified early enough to develop an appropriate course of action. As the time horizon to the conjunction event is reduced, the collision probability changes. A significant change in the collision probability will change the satellite mission stakeholder's course of action. So constructing a method for estimating how the collision probability will evolve improves operations by providing satellite operators with a new piece of information, namely an estimate or 'forecast' of how the risk will change as time to the event is reduced. Collision probability forecasting is a predictive process where the future risk of a conjunction event is estimated. The method utilizes a Monte Carlo simulation that produces a likelihood distribution for a given collision threshold. Using known state and state uncertainty information, the simulation generates a set possible trajectories for a given space object pair. Each new trajectory produces a unique event geometry at the time of close approach. Given state uncertainty information for both objects, a collision probability value can be computed for every trail. This yields a collision probability distribution given known, predicted uncertainty. This paper presents the details of the collision probability forecasting method. We examine various conjunction event scenarios and numerically demonstrate the utility of this approach in typical event scenarios. We explore the utility of a probability-based track scenario simulation that models expected tracking data frequency as the tasking levels are increased. The resulting orbital uncertainty is subsequently used in the forecasting algorithm.
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 on detectability. Coherent scatter analysis using a wide slot setup is promising as an enhancement for screening mammography. Unlike conventional mammography which depends on attenuation difference, coherent scatter imaging gives new information based on tissues typing. A combination of the two methods would yield high spatial resolution from the conventional mammography and high contrast from coherent scatter imaging.
Smith, Leon E.; Gesh, Christopher J.; Pagh, Richard T.; Miller, Erin A.; Shaver, Mark W.; Ashbaker, Eric D.; Batdorf, Michael T.; Ellis, J. E.; Kaye, William R.; McConn, Ronald J.; Meriwether, George H.; Ressler, Jennifer J.; Valsan, Andrei B.; Wareing, Todd A.
2008-10-31
Radiation transport modeling methods used in the radiation detection community fall into one of two broad categories: stochastic (Monte Carlo) and deterministic. Monte Carlo methods are typically the tool of choice for simulating gamma-ray spectrometers operating in homeland and national security settings (e.g. portal monitoring of vehicles or isotope identification using handheld devices), but deterministic codes that discretize the linear Boltzmann transport equation in space, angle, and energy offer potential advantages in computational efficiency for many complex radiation detection problems. This paper describes the development of a scenario simulation framework based on deterministic algorithms. Key challenges include: formulating methods to automatically define an energy group structure that can support modeling of gamma-ray spectrometers ranging from low to high resolution; combining deterministic transport algorithms (e.g. ray-tracing and discrete ordinates) to mitigate ray effects for a wide range of problem types; and developing efficient and accurate methods to calculate gamma-ray spectrometer response functions from the deterministic angular flux solutions. The software framework aimed at addressing these challenges is described and results from test problems that compare coupled deterministic-Monte Carlo methods and purely Monte Carlo approaches are provided.
NASA Astrophysics Data System (ADS)
Tonkin, Matthew; Doherty, John
2009-12-01
We describe a subspace Monte Carlo (SSMC) technique that reduces the burden of calibration-constrained Monte Carlo when undertaken with highly parameterized models. When Monte Carlo methods are used to evaluate the uncertainty in model outputs, ensuring that parameter realizations reproduce the calibration data requires many model runs to condition each realization. In the new SSMC approach, the model is first calibrated using a subspace regularization method, ideally the hybrid Tikhonov-TSVD "superparameter" approach described by Tonkin and Doherty (2005). Sensitivities calculated with the calibrated model are used to define the calibration null-space, which is spanned by parameter combinations that have no effect on simulated equivalents to available observations. Next, a stochastic parameter generator is used to produce parameter realizations, and for each a difference is formed between the stochastic parameters and the calibrated parameters. This difference is projected onto the calibration null-space and added to the calibrated parameters. If the model is no longer calibrated, parameter combinations that span the calibration solution space are reestimated while retaining the null-space projected parameter differences as additive values. The recalibration can often be undertaken using existing sensitivities, so that conditioning requires only a small number of model runs. Using synthetic and real-world model applications we demonstrate that the SSMC approach is general (it is not limited to any particular model or any particular parameterization scheme) and that it can rapidly produce a large number of conditioned parameter sets.
A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations
NASA Astrophysics Data System (ADS)
Jha, Prateek; Kuzovkov, Vladimir; Grzybowski, Bartosz; Olvera de La Cruz, Monica
2012-02-01
We have developed an off-lattice kinetic Monte Carlo simulation scheme for reaction-diffusion problems in soft matter systems. The definition of transition probabilities in the Monte Carlo scheme are taken identical to the transition rates in a renormalized master equation of the diffusion process and match that of the Glauber dynamics of Ising model. Our scheme provides several advantages over the Brownian dynamics technique for non-equilibrium simulations. Since particle displacements are accepted/rejected in a Monte Carlo fashion as opposed to moving particles following a stochastic equation of motion, nonphysical movements (e.g., violation of a hard core assumption) are not possible (these moves have zero acceptance). Further, the absence of a stochastic ``noise'' term resolves the computational difficulties associated with generating statistically independent trajectories with definitive mean properties. Finally, since the timestep is independent of the magnitude of the interaction forces, much longer time-steps can be employed than Brownian dynamics. We discuss the applications of this scheme for dynamic self-assembly of photo-switchable nanoparticles and dynamical problems in polymeric systems.
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 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 this dissertation the design, implementation and evaluation of a technique for reducing a latent variance inherent from the recycling of phase space particle tracks in a simulation is presented. In the technique a random azimuthal rotation about the beam's central axis is applied to each recycled particle, achieving a significant reduction of the latent variance. In a third component, the dissertation presents the first MC modeling of Varian's new RapidArc delivery system and a comparison of dose calculations with the Eclipse treatment planning system. A total of four arc plans are compared including an oropharynx patient phantom containing tissue inhomogeneities. Finally, in a step toward introducing MC dose calculation into the planning of treatments such as RapidArc, a technique is presented to feasibly generate and store a large set of MC calculated dose distributions. A novel 3-D dyadic multi-resolution (MR) decomposition algorithm is presented and the compressibility of the dose data using this algorithm is investigated. The presented MC beamlet generation method, in conjunction with the presented 3-D data MR decomposition, represents a viable means to introduce MC dose calculation in the planning and optimization stages of advanced radiotherapy.
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.
Quantum Monte Carlo simulations of tunneling in quantum adiabatic optimization
NASA Astrophysics Data System (ADS)
Brady, Lucas T.; van Dam, Wim
2016-03-01
We explore to what extent path-integral quantum Monte Carlo methods can efficiently simulate quantum adiabatic optimization algorithms during a quantum tunneling process. Specifically we look at symmetric cost functions defined over n bits with a single potential barrier that a successful quantum adiabatic optimization algorithm will have to tunnel through. The height and width of this barrier depend on n , and by tuning these dependencies, we can make the optimization algorithm succeed or fail in polynomial time. In this article we compare the strength of quantum adiabatic tunneling with that of path-integral quantum Monte Carlo methods. We find numerical evidence that quantum Monte Carlo algorithms will succeed in the same regimes where quantum adiabatic optimization succeeds.
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.
Skin image reconstruction using Monte Carlo based color generation
NASA Astrophysics Data System (ADS)
Aizu, Yoshihisa; Maeda, Takaaki; Kuwahara, Tomohiro; Hirao, Tetsuji
2010-11-01
We propose a novel method of skin image reconstruction based on color generation using Monte Carlo simulation of spectral reflectance in the nine-layered skin tissue model. The RGB image and spectral reflectance of human skin are obtained by RGB camera and spectrophotometer, respectively. The skin image is separated into the color component and texture component. The measured spectral reflectance is used to evaluate scattering and absorption coefficients in each of the nine layers which are necessary for Monte Carlo simulation. Various skin colors are generated by Monte Carlo simulation of spectral reflectance in given conditions for the nine-layered skin tissue model. The new color component is synthesized to the original texture component to reconstruct the skin image. The method is promising for applications in the fields of dermatology and cosmetics.
Vectorizing and macrotasking Monte Carlo neutral particle algorithms
Heifetz, D.B.
1987-04-01
Monte Carlo algorithms for computing neutral particle transport in plasmas have been vectorized and macrotasked. The techniques used are directly applicable to Monte Carlo calculations of neutron and photon transport, and Monte Carlo integration schemes in general. A highly vectorized code was achieved by calculating test flight trajectories in loops over arrays of flight data, isolating the conditional branches to as few a number of loops as possible. A number of solutions are discussed to the problem of gaps appearing in the arrays due to completed flights, which impede vectorization. A simple and effective implementation of macrotasking is achieved by dividing the calculation of the test flight profile among several processors. A tree of random numbers is used to ensure reproducible results. The additional memory required for each task may preclude using a larger number of tasks. In future machines, the limit of macrotasking may be possible, with each test flight, and split test flight, being a separate task.
Backward and Forward Monte Carlo Method in Polarized Radiative Transfer
NASA Astrophysics Data System (ADS)
Yong, Huang; Guo-Dong, Shi; Ke-Yong, Zhu
2016-03-01
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.
Willert, Jeffrey Park, H.
2014-11-01
In this article we explore the possibility of replacing Standard Monte Carlo (SMC) transport sweeps within a Moment-Based Accelerated Thermal Radiative Transfer (TRT) algorithm with a Residual Monte Carlo (RMC) formulation. Previous Moment-Based Accelerated TRT implementations have encountered trouble when stochastic noise from SMC transport sweeps accumulates over several iterations and pollutes the low-order system. With RMC we hope to significantly lower the build-up of statistical error at a much lower cost. First, we display encouraging results for a zero-dimensional test problem. Then, we demonstrate that we can achieve a lower degree of error in two one-dimensional test problems by employing an RMC transport sweep with multiple orders of magnitude fewer particles per sweep. We find that by reformulating the high-order problem, we can compute more accurate solutions at a fraction of the cost.
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.
Collective translational and rotational Monte Carlo moves for attractive particles
NASA Astrophysics Data System (ADS)
RÅ¯žička, Štěpán; Allen, Michael P.
2014-03-01
Virtual move Monte Carlo is a Monte Carlo (MC) cluster algorithm forming clusters via local energy gradients and approximating the collective kinetic or dynamic motion of attractive colloidal particles. We carefully describe, analyze, and test the algorithm. To formally validate the algorithm through highlighting its symmetries, we present alternative and compact ways of selecting and accepting clusters which illustrate the formal use of abstract concepts in the design of biased MC techniques: the superdetailed balance and the early rejection scheme. A brief and comprehensive summary of the algorithms is presented, which makes them accessible without needing to understand the details of the derivation.
Overview of the MCU Monte Carlo Software Package
NASA Astrophysics Data System (ADS)
Kalugin, M. A.; Oleynik, D. S.; Shkarovsky, D. A.
2014-06-01
MCU (Monte Carlo Universal) is a project on development and practical use of a universal computer code for simulation of particle transport (neutrons, photons, electrons, positrons) in three-dimensional systems by means of the Monte Carlo method. This paper provides the information on the current state of the project. The developed libraries of constants are briefly described, and the potentialities of the MCU-5 package modules and the executable codes compiled from them are characterized. Examples of important problems of reactor physics solved with the code are presented.
Enhancements for Multi-Player Monte-Carlo Tree Search
NASA Astrophysics Data System (ADS)
Nijssen, J. (Pim) A. M.; Winands, Mark H. M.
Monte-Carlo Tree Search (MCTS) is becoming increasingly popular for playing multi-player games. In this paper we propose two enhancements for MCTS in multi-player games: (1) Progressive History and (2) Multi-Player Monte-Carlo Tree Search Solver (MP-MCTS-Solver). We analyze the performance of these enhancements in two different multi-player games: Focus and Chinese Checkers. Based on the experimental results we conclude that Progressive History is a considerable improvement in both games and MP-MCTS-Solver, using the standard update rule, is a genuine improvement in Focus.
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.
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.
Bold Diagrammatic Monte Carlo for Fermionic and Fermionized Systems
NASA Astrophysics Data System (ADS)
Svistunov, Boris
2013-03-01
In three different fermionic cases--repulsive Hubbard model, resonant fermions, and fermionized spins-1/2 (on triangular lattice)--we observe the phenomenon of sign blessing: Feynman diagrammatic series features finite convergence radius despite factorial growth of the number of diagrams with diagram order. Bold diagrammatic Monte Carlo technique allows us to sample millions of skeleton Feynman diagrams. With the universal fermionization trick we can fermionize essentially any (bosonic, spin, mixed, etc.) lattice system. The combination of fermionization and Bold diagrammatic Monte Carlo yields a universal first-principle approach to strongly correlated lattice systems, provided the sign blessing is a generic fermionic phenomenon. Supported by NSF and DARPA
MonteCarlo Simulation of Coarse Grain Polymeric Systems
NASA Astrophysics Data System (ADS)
Detcheverry, François A.; Pike, Darin Q.; Nealey, Paul F.; Müller, Marcus; de Pablo, Juan J.
2009-05-01
We introduce a particle-based Monte Carlo formalism for the study of polymeric melts, where the interaction energy is given by a local density functional, as is done in traditional field-theoretic models. The method enables Monte Carlo simulations in arbitrary ensembles and direct calculation of free energies. We present results for the phase diagram and the critical point of a binary homopolymer blend. For a symmetric diblock copolymer, we compute the distribution of local stress in lamellae and locate the order-disorder transition.
Mesh Optimization for Monte Carlo-Based Optical Tomography
Edmans, Andrew; Intes, Xavier
2015-01-01
Mesh-based Monte Carlo techniques for optical imaging allow for accurate modeling of light propagation in complex biological tissues. Recently, they have been developed within an efficient computational framework to be used as a forward model in optical tomography. However, commonly employed adaptive mesh discretization techniques have not yet been implemented for Monte Carlo based tomography. Herein, we propose a methodology to optimize the mesh discretization and analytically rescale the associated Jacobian based on the characteristics of the forward model. We demonstrate that this method maintains the accuracy of the forward model even in the case of temporal data sets while allowing for significant coarsening or refinement of the mesh. PMID:26566523
A non-Monte Carlo approach to analyzing 1D Anderson localization in dispersive metamaterials
NASA Astrophysics Data System (ADS)
Kissel, Glen J.
2015-09-01
Monte Carlo simulations have long been used to study Anderson localization in models of one-dimensional random stacks. Because such simulations use substantial computational resources and because the randomness of random number generators for such simulations has been called into question, a non-Monte Carlo approach is of interest. This paper uses a non-Monte Carlo methodology, limited to discrete random variables, to determine the Lyapunov exponent, or its reciprocal, known as the localization length, for a one-dimensional random stack model, proposed by Asatryan, et al., consisting of various combinations of negative, imaginary and positive index materials that include the effects of dispersion and absorption, as well as off-axis incidence and polarization effects. Dielectric permittivity and magnetic permeability are the two variables randomized in the models. In the paper, Furstenberg's integral formula is used to calculate the Lyapunov exponent of an infinite product of random matrices modeling the one-dimensional stack. The integral formula requires integration with respect to the probability distribution of the randomized layer parameters, as well as integration with respect to the so-called invariant probability measure of the direction of the vector propagated by the long chain of random matrices. The non-Monte Carlo approach uses a numerical procedure of Froyland and Aihara which calculates the invariant measure as the left eigenvector of a certain sparse row-stochastic matrix, thus avoiding the use of any random number generator. The results show excellent agreement with the Monte Carlo generated simulations which make use of continuous random variables, while frequently providing reductions in computation 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.
Anomalous diffusion of a tethered membrane: a Monte Carlo investigation.
Popova, Hristina; Milchev, Andrey
2008-04-01
Using a continuum bead-spring Monte Carlo model, we study the anomalous diffusion dynamics of a self-avoiding tethered membrane by means of extensive computer simulations. We focus on the subdiffusive stochastic motion of the membrane's central node in the regime of flat membranes at temperatures above the membrane folding transition. While at times, larger than the characteristic membrane relaxation time tau(R) , the mean-square displacement of the center of mass of the sheet,
Observations on variational and projector Monte Carlo methods
NASA Astrophysics Data System (ADS)
Umrigar, C. J.
2015-10-01
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.
Present Status and Extensions of the Monte Carlo Performance Benchmark
NASA Astrophysics Data System (ADS)
Hoogenboom, J. Eduard; Petrovic, Bojan; Martin, William R.
2014-06-01
The NEA Monte Carlo Performance benchmark started in 2011 aiming to monitor over the years the abilities to perform a full-size Monte Carlo reactor core calculation with a detailed power production for each fuel pin with axial distribution. This paper gives an overview of the contributed results thus far. It shows that reaching a statistical accuracy of 1 % for most of the small fuel zones requires about 100 billion neutron histories. The efficiency of parallel execution of Monte Carlo codes on a large number of processor cores shows clear limitations for computer clusters with common type computer nodes. However, using true supercomputers the speedup of parallel calculations is increasing up to large numbers of processor cores. More experience is needed from calculations on true supercomputers using large numbers of processors in order to predict if the requested calculations can be done in a short time. As the specifications of the reactor geometry for this benchmark test are well suited for further investigations of full-core Monte Carlo calculations and a need is felt for testing other issues than its computational performance, proposals are presented for extending the benchmark to a suite of benchmark problems for evaluating fission source convergence for a system with a high dominance ratio, for coupling with thermal-hydraulics calculations to evaluate the use of different temperatures and coolant densities and to study the correctness and effectiveness of burnup calculations. Moreover, other contemporary proposals for a full-core calculation with realistic geometry and material composition will be discussed.
A Monte Carlo Investigation of Spuriously Inflated Regression Estimates.
ERIC Educational Resources Information Center
Jovick, Thomas D.
A Monte Carlo simulation was used to ascertain the degree of inflation that can occur in regression estimates when samples contain randomly occurring instances of a pattern among correlations called cooperative suppression. Ten thousand samples of scores on three variables were randomly drawn from a population in which the correlations among 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.
Probability Distributions of School Enrollment Predictions Using Monte Carlo Simulation
ERIC Educational Resources Information Center
Denham, Carolyn H.
1973-01-01
A major problem in most predictions of school enrollment is the forecaster's failure to express adequately his certainty or uncertainty in his estimates. Describes a method whereby a forecaster can prepare probability distributions of enrollment predictions. The Monte Carlo computer simulation calculates enrollments by the multivariable method,…
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.
Monte Carlo radiation transport: A revolution in science
Hendricks, J.
1993-04-01
When Enrico Fermi, Stan Ulam, Nicholas Metropolis, John von Neuman, and Robert Richtmyer invented the Monte Carlo method fifty years ago, little could they imagine the far-flung consequences, the international applications, and the revolution in science epitomized by their abstract mathematical method. The Monte Carlo method is used in a wide variety of fields to solve exact computational models approximately by statistical sampling. It is an alternative to traditional physics modeling methods which solve approximate computational models exactly by deterministic methods. Modern computers and improved methods, such as variance reduction, have enhanced the method to the point of enabling a true predictive capability in areas such as radiation or particle transport. This predictive capability has contributed to a radical change in the way science is done: design and understanding come from computations built upon experiments rather than being limited to experiments, and the computer codes doing the computations have become the repository for physics knowledge. The MCNP Monte Carlo computer code effort at Los Alamos is an example of this revolution. Physicians unfamiliar with physics details can design cancer treatments using physics buried in the MCNP computer code. Hazardous environments and hypothetical accidents can be explored. Many other fields, from underground oil well exploration to aerospace, from physics research to energy production, from safety to bulk materials processing, benefit from MCNP, the Monte Carlo method, and the revolution in science.
Bayesian Monte Carlo Method for Nuclear Data Evaluation
Koning, A.J.
2015-01-15
A Bayesian Monte Carlo method is outlined which allows a systematic evaluation of nuclear reactions using TALYS. The result will be either an EXFOR-weighted covariance matrix or a collection of random files, each accompanied by an experiment based weight.
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…
Quantum Monte Carlo simulation with a black hole
NASA Astrophysics Data System (ADS)
Benić, Sanjin; Yamamoto, Arata
2016-05-01
We perform quantum Monte Carlo simulations in the background of a classical black hole. The lattice discretized path integral is numerically calculated in the Schwarzschild metric and in its approximated metric. We study spontaneous symmetry breaking of a real scalar field theory. We observe inhomogeneous symmetry breaking induced by an inhomogeneous gravitational field.
Monte-carlo calculations for some problems of quantum mechanics
Novoselov, A. A. Pavlovsky, O. V.; Ulybyshev, M. V.
2012-09-15
The Monte-Carlo technique for the calculations of functional integral in two one-dimensional quantum-mechanical problems had been applied. The energies of the bound states in some potential wells were obtained using this method. Also some peculiarities in the calculation of the kinetic energy in the ground state had been studied.
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.
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…
Ordinal Hypothesis in ANOVA Designs: A Monte Carlo Study.
ERIC Educational Resources Information Center
Braver, Sanford L.; Sheets, Virgil L.
Numerous designs using analysis of variance (ANOVA) to test ordinal hypotheses were assessed using a Monte Carlo simulation. Each statistic was computed on each of over 10,000 random samples drawn from a variety of population conditions. The number of groups, population variance, and patterns of population means were varied. In the non-null…
Monte Carlo variance reduction using finite element adjoint weight windows
Shahdatullah, M. S.; Ziver, K.; Eaton, M. D.; Pain, C. C.; Goddard, A. J. H.
2006-07-01
The use of Monte Carlo variance reduction techniques is unavoidable on present day computers in obtaining numerical solutions in complex shielding, deep penetration or other radiation transport problems such as nuclear well logging and ex-core reactor core modeling etc. A deterministic variance reduction technique based on the finite element adjoint weight window (FEAWW) scheme is developed and applied in the well-known and widely used Monte Carlo radiation transport code MCNP. The scheme involves generating importance maps from the adjoint deterministic EVENT transport calculations which are then extracted and used as 'weight window lower bounds' suitable for acceleration of the forward Monte Carlo radiation transport calculations. The 'holy grail' of an automatic variance reduction technique is to provide a single method which provides systematic or nearly systematic ways to eliminate much of the user's intervention. The proposed method employs the adjoint solutions to the problem of interest which has been folded into the MCNP weight window scheme. The FEAWW method is tested on a number of complex deep penetration and neutron streaming problems and compared against the standard Monte Carlo generated variance reduction techniques with encouraging results. (authors)
Monte Carlo event generators for hadron-hadron collisions
Knowles, I.G.; Protopopescu, S.D.
1993-06-01
A brief review of Monte Carlo event generators for simulating hadron-hadron collisions is presented. Particular emphasis is placed on comparisons of the approaches used to describe physics elements and identifying their relative merits and weaknesses. This review summarizes a more detailed report.
Monte Carlo Simulations of Light Propagation in Apples
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper reports on the investigation of light propagation in fresh apples in the visible and short-wave near-infrared region using Monte Carlo simulations. Optical properties of ‘Golden Delicious’ apples were determined over the spectral range of 500-1100 nm using a hyperspectral imaging method, ...
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.
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…
Dynamic Structure Factor in BCC Helium from Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Arovas, Daniel; Gazit, Snir; Podolsky, Daniel; Auerbach, Assa; Nonne, Heloise
2014-03-01
An unexpected optic-like mode has been observed by inelastic neutron scattering in BCC Helium-4. We report on worm algorithm quantum Monte Carlo calculations of the dynamic structure factor in order to compare with experiment. A theoretical model based on a dynamical Landau-Ginzburg action is also analyzed. Israel Science Foundation, US-Israel Binational Science Foundation
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. PMID:26520496
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.
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
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 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
The Number of Iterations in Monte Carlo Studies of Robustness.
ERIC Educational Resources Information Center
Robey, Randall R.; Barcikowski, Robert S.
A recent survey of simulation studies concluded that an overwhelming majority of papers do not report a rationale for the number of iterations carried out in Monte Carlo robustness (MCR) experiments. The survey suggested that researchers might benefit from adopting a hypothesis testing strategy in the planning and reporting of simulation studies.…
Monte Carlo Radiation Analysis of a Spacecraft Radioisotope Power System
NASA Technical Reports Server (NTRS)
Wallace, M.
1994-01-01
A Monte Carlo statistical computer analysis was used to create neutron and photon radiation predictions for the General Purpose Heat Source Radioisotope Thermoelectric Generator (GPHS RTG). The GPHS RTG is being used on several NASA planetary missions. Analytical results were validated using measured health physics data.
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.
Efficient cosmological parameter estimation with Hamiltonian Monte Carlo technique
Hajian, Amir
2007-04-15
Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing, and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo (MCMC) technique built upon the basic principle of Hamiltonian mechanics. Hamiltonian dynamics allows the chain to move along trajectories of constant energy, taking large jumps in the parameter space with relatively inexpensive computations. This new technique improves the acceptance rate by a factor of 4 while reducing the correlations and boosts up the efficiency by almost a factor of D in a D-dimensional parameter space. Therefore shorter chains will be needed for a reliable parameter estimation comparing to a traditional MCMC chain yielding the same performance. Besides that, the HMC is well suited for sampling from non-Gaussian and curved distributions which are very hard to sample from using the traditional MCMC methods. The method is very simple to code and can be easily plugged into standard parameter estimation codes such as CosmoMC. In this paper we demonstrate how the HMC can be efficiently used in cosmological parameter estimation. Also we discuss possible ways of getting good estimates of the derivatives of (the log of) posterior which is needed for HMC.
Microbial contamination in poultry chillers estimated by Monte Carlo simulations
Technology Transfer Automated Retrieval System (TEKTRAN)
The risk of microbial contamination during poultry processing may be reduced by the operating characteristics of the chiller. The performance of air chillers and immersion chillers were compared in terms of pre-chill and post-chill contamination using Monte Carlo simulations. Three parameters were u...
Monte Carlo simulation of entry in the Martian atmosphere
NASA Technical Reports Server (NTRS)
Hash, David B.; Hassan, H. A.
1992-01-01
The Direct Simulation Monte Carlo method of Bird is used to investigate the characteristics of low density hypersonic flowfields for typical aerobrakes during Martian atmospheric entry. The method allows for both thermal and chemical nonequilibrium. Results are presented for a sixty-degree spherically blunt cone for various nose radii and altitudes.
A separable shadow Hamiltonian hybrid Monte Carlo method
NASA Astrophysics Data System (ADS)
Sweet, Christopher R.; Hampton, Scott S.; Skeel, Robert D.; Izaguirre, Jesús A.
2009-11-01
Hybrid Monte Carlo (HMC) is a rigorous sampling method that uses molecular dynamics (MD) as a global Monte Carlo move. The acceptance rate of HMC decays exponentially with system size. The shadow hybrid Monte Carlo (SHMC) was previously introduced to reduce this performance degradation by sampling instead from the shadow Hamiltonian defined for MD when using a symplectic integrator. SHMC's performance is limited by the need to generate momenta for the MD step from a nonseparable shadow Hamiltonian. We introduce the separable shadow Hamiltonian hybrid Monte Carlo (S2HMC) method based on a formulation of the leapfrog/Verlet integrator that corresponds to a separable shadow Hamiltonian, which allows efficient generation of momenta. S2HMC gives the acceptance rate of a fourth order integrator at the cost of a second-order integrator. Through numerical experiments we show that S2HMC consistently gives a speedup greater than two over HMC for systems with more than 4000 atoms for the same variance. By comparison, SHMC gave a maximum speedup of only 1.6 over HMC. S2HMC has the additional advantage of not requiring any user parameters beyond those of HMC. S2HMC is available in the program PROTOMOL 2.1. A Python version, adequate for didactic purposes, is also in MDL (http://mdlab.sourceforge.net/s2hmc).
Monitor unit calculation for Monte Carlo treatment planning
NASA Astrophysics Data System (ADS)
Ma, C.-M.; Price, R. A., Jr.; Li, J. S.; Chen, L.; Wang, L.; Fourkal, E.; Qin, L.; Yang, J.
2004-05-01
In this work, we investigate a formalism for monitor unit (MU) calculation in Monte Carlo based treatment planning. By relating MU to dose measured under reference calibration conditions (central axis, depth of dose maximum in water, 10 cm 10 cm field defined at 100 cm source-to-surface distance) our formalism determines the MU required for a treatment plan based on the prescription dose and Monte Carlo calculated dose distribution. Detailed descriptions and formulae are given for various clinical situations including conventional treatments and advanced techniques such as intensity-modulated radiotherapy (IMRT) and modulated electron radiotherapy (MERT). Analysis is made of the effects of source modelling, beam modifier simulation and patient dose calculation accuracy, all of which are important factors for absolute dose calculations using Monte Carlo simulations. We have tested the formalism through phantom measurements and the predicted MU values were consistent with measured values to within 2%. The formalism has been used for MU calculation and plan comparison for advanced treatment techniques such as MERT, extracranial stereotactic IMRT, MRI-based treatment planning and intensity-modulated laser-proton therapy studies. It is also used for absolute dose calculations using Monte Carlo simulations for treatment verification, which has become part of our comprehensive IMRT quality assurance programme.
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.
Calculating Potential Energy Curves with Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Powell, Andrew D.; Dawes, Richard
2014-06-01
Quantum Monte Carlo (QMC) is a computational technique that can be applied to the electronic Schrödinger equation for molecules. QMC methods such as Variational Monte Carlo (VMC) and Diffusion Monte Carlo (DMC) have demonstrated the capability of capturing large fractions of the correlation energy, thus suggesting their possible use for high-accuracy quantum chemistry calculations. QMC methods scale particularly well with respect to parallelization making them an attractive consideration in anticipation of next-generation computing architectures which will involve massive parallelization with millions of cores. Due to the statistical nature of the approach, in contrast to standard quantum chemistry methods, uncertainties (error-bars) are associated with each calculated energy. This study focuses on the cost, feasibility and practical application of calculating potential energy curves for small molecules with QMC methods. Trial wave functions were constructed with the multi-configurational self-consistent field (MCSCF) method from GAMESS-US.[1] The CASINO Monte Carlo quantum chemistry package [2] was used for all of the DMC calculations. An overview of our progress in this direction will be given. References: M. W. Schmidt et al. J. Comput. Chem. 14, 1347 (1993). R. J. Needs et al. J. Phys.: Condensed Matter 22, 023201 (2010).
Reagents for Electrophilic Amination: A Quantum Monte CarloStudy
Amador-Bedolla, Carlos; Salomon-Ferrer, Romelia; Lester Jr.,William A.; Vazquez-Martinez, Jose A.; Aspuru-Guzik, Alan
2006-11-01
Electroamination is an appealing synthetic strategy toconstruct carbon-nitrogen bonds. We explore the use of the quantum MonteCarlo method and a proposed variant of the electron-pair localizationfunction--the electron-pair localization function density--as a measureof the nucleophilicity of nitrogen lone-pairs as a possible screeningprocedure for electrophilic reagents.
Analysis and Monte Carlo simulation of near-terminal aircraft flight paths
NASA Technical Reports Server (NTRS)
Schiess, J. R.; Matthews, C. G.
1982-01-01
The flight paths of arriving and departing aircraft at an airport are stochastically represented. Radar data of the aircraft movements are used to decompose the flight paths into linear and curvilinear segments. Variables which describe the segments are derived, and the best fitting probability distributions of the variables, based on a sample of flight paths, are found. Conversely, given information on the probability distribution of the variables, generation of a random sample of flight paths in a Monte Carlo simulation is discussed. Actual flight paths at Dulles International Airport are analyzed and simulated.
Understanding and improving the efficiency of full configuration interaction quantum Monte Carlo.
Vigor, W A; Spencer, J S; Bearpark, M J; Thom, A J W
2016-03-01
Within full configuration interaction quantum Monte Carlo, we investigate how the statistical error behaves as a function of the parameters which control the stochastic sampling. We define the inefficiency as a measure of the statistical error per particle sampling the space and per time step and show there is a sizeable parameter regime where this is minimised. We find that this inefficiency increases sublinearly with Hilbert space size and can be reduced by localising the canonical Hartree-Fock molecular orbitals, suggesting that the choice of basis impacts the method beyond that of the sign problem. PMID:26957160
Understanding and improving the efficiency of full configuration interaction quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Vigor, W. A.; Spencer, J. S.; Bearpark, M. J.; Thom, A. J. W.
2016-03-01
Within full configuration interaction quantum Monte Carlo, we investigate how the statistical error behaves as a function of the parameters which control the stochastic sampling. We define the inefficiency as a measure of the statistical error per particle sampling the space and per time step and show there is a sizeable parameter regime where this is minimised. We find that this inefficiency increases sublinearly with Hilbert space size and can be reduced by localising the canonical Hartree-Fock molecular orbitals, suggesting that the choice of basis impacts the method beyond that of the sign problem.
Variational Quantum MonteCarlo Simulations with Tensor-Network States
NASA Astrophysics Data System (ADS)
Sandvik, A. W.; Vidal, G.
2007-11-01
We show that the formalism of tensor-network states, such as the matrix-product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of this approach by explicit MPS calculations for the transverse Ising chain with up to N=256 spins at criticality, using periodic boundary conditions and D×D matrices with D up to 48. The computational cost of our scheme formally scales as ND3, whereas standard MPS approaches and the related density matrix renormalization group method scale as ND5 and ND6, respectively, for periodic systems.
Accurate characterization of Monte Carlo calculated electron beams for radiotherapy.
Ma, C M; Faddegon, B A; Rogers, D W; Mackie, T R
1997-03-01
Monte Carlo studies of dose distributions in patients treated with radiotherapy electron beams would benefit from generalized models of clinical beams if such models introduce little error into the dose calculations. Methodology is presented for the design of beam models, including their evaluation in terms of how well they preserve the character of the clinical beam, and the effect of the beam models on the accuracy of dose distributions calculated with Monte Carlo. This methodology has been used to design beam models for electron beams from two linear accelerators, with either a scanned beam or a scattered beam. Monte Carlo simulations of the accelerator heads are done in which a record is kept of the particle phase-space, including the charge, energy, direction, and position of every particle that emerges from the treatment head, along with a tag regarding the details of the particle history. The character of the simulated beams are studied in detail and used to design various beam models from a simple point source to a sophisticated multiple-source model which treats particles from different parts of a linear accelerator as from different sub-sources. Dose distributions calculated using both the phase-space data and the multiple-source model agree within 2%, demonstrating that the model is adequate for the purpose of Monte Carlo treatment planning for the beams studied. Benefits of the beam models over phase-space data for dose calculation are shown to include shorter computation time in the treatment head simulation and a smaller disk space requirement, both of which impact on the clinical utility of Monte Carlo treatment planning. PMID:9089592
Adaptive sample map for Monte Carlo ray tracing
NASA Astrophysics Data System (ADS)
Teng, Jun; Luo, Lixin; Chen, Zhibo
2010-07-01
Monte Carlo ray tracing algorithm is widely used by production quality renderers to generate synthesized images in films and TV programs. Noise artifact exists in synthetic images generated by Monte Carlo ray tracing methods. In this paper, a novel noise artifact detection and noise level representation method is proposed. We first apply discrete wavelet transform (DWT) on a synthetic image; the high frequency sub-bands of the DWT result encode the noise information. The sub-bands coefficients are then combined to generate a noise level description of the synthetic image, which is called noise map in the paper. This noise map is then subdivided into blocks for robust noise level metric calculation. Increasing the samples per pixel in Monte Carlo ray tracer can reduce the noise of a synthetic image to visually unnoticeable level. A noise-to-sample number mapping algorithm is thus performed on each block of the noise map, higher noise value is mapped to larger sample number, and lower noise value is mapped to smaller sample number, the result of mapping is called sample map. Each pixel in a sample map can be used by Monte Carlo ray tracer to reduce the noise level in the corresponding block of pixels in a synthetic image. However, this block based scheme produces blocky artifact as appeared in video and image compression algorithms. We use Gaussian filter to smooth the sample map, the result is adaptive sample map (ASP). ASP serves two purposes in rendering process; its statistics information can be used as noise level metric in synthetic image, and it can also be used by a Monte Carlo ray tracer to refine the synthetic image adaptively in order to reduce the noise to unnoticeable level but with less rendering time than the brute force method.
Reconstruction of Human Monte Carlo Geometry from Segmented Images
NASA Astrophysics Data System (ADS)
Zhao, Kai; Cheng, Mengyun; Fan, Yanchang; Wang, Wen; Long, Pengcheng; Wu, Yican
2014-06-01
Human computational phantoms have been used extensively for scientific experimental analysis and experimental simulation. This article presented a method for human geometry reconstruction from a series of segmented images of a Chinese visible human dataset. The phantom geometry could actually describe detailed structure of an organ and could be converted into the input file of the Monte Carlo codes for dose calculation. A whole-body computational phantom of Chinese adult female has been established by FDS Team which is named Rad-HUMAN with about 28.8 billion voxel number. For being processed conveniently, different organs on images were segmented with different RGB colors and the voxels were assigned with positions of the dataset. For refinement, the positions were first sampled. Secondly, the large sums of voxels inside the organ were three-dimensional adjacent, however, there were not thoroughly mergence methods to reduce the cell amounts for the description of the organ. In this study, the voxels on the organ surface were taken into consideration of the mergence which could produce fewer cells for the organs. At the same time, an indexed based sorting algorithm was put forward for enhancing the mergence speed. Finally, the Rad-HUMAN which included a total of 46 organs and tissues was described by the cuboids into the Monte Carlo Monte Carlo Geometry for the simulation. The Monte Carlo geometry was constructed directly from the segmented images and the voxels was merged exhaustively. Each organ geometry model was constructed without ambiguity and self-crossing, its geometry information could represent the accuracy appearance and precise interior structure of the organs. The constructed geometry largely retaining the original shape of organs could easily be described into different Monte Carlo codes input file such as MCNP. Its universal property was testified and high-performance was experimentally verified
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.
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)
Accelerated rescaling of single Monte Carlo simulation runs with the Graphics Processing Unit (GPU)
Yang, Owen; Choi, Bernard
2013-01-01
Abstract: To interpret fiber-based and camera-based measurements of remitted light from biological tissues, researchers typically use analytical models, such as the diffusion approximation to light transport theory, or stochastic models, such as Monte Carlo modeling. To achieve rapid (ideally real-time) measurement of tissue optical properties, especially in clinical situations, there is a critical need to accelerate Monte Carlo simulation runs. In this manuscript, we report on our approach using the Graphics Processing Unit (GPU) to accelerate rescaling of single Monte Carlo runs to calculate rapidly diffuse reflectance values for different sets of tissue optical properties. We selected MATLAB to enable non-specialists in C and CUDA-based programming to use the generated open-source code. We developed a software package with four abstraction layers. To calculate a set of diffuse reflectance values from a simulated tissue with homogeneous optical properties, our rescaling GPU-based approach achieves a reduction in computation time of several orders of magnitude as compared to other GPU-based approaches. Specifically, our GPU-based approach generated a diffuse reflectance value in 0.08ms. The transfer time from CPU to GPU memory currently is a limiting factor with GPU-based calculations. However, for calculation of multiple diffuse reflectance values, our GPU-based approach still can lead to processing that is ~3400 times faster than other GPU-based approaches. PMID:24298424
NASA Astrophysics Data System (ADS)
Armas-Pérez, Julio C.; Londono-Hurtado, Alejandro; Guzmán, Orlando; Hernández-Ortiz, Juan P.; de Pablo, Juan J.
2015-07-01
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.
A Fast Monte Carlo Simulation for the International Linear Collider Detector
Furse, D.; /Georgia Tech
2005-12-15
The following paper contains details concerning the motivation for, implementation and performance of a Java-based fast Monte Carlo simulation for a detector designed to be used in the International Linear Collider. This simulation, presently included in the SLAC ILC group's org.lcsim package, reads in standard model or SUSY events in STDHEP file format, stochastically simulates the blurring in physics measurements caused by intrinsic detector error, and writes out an LCIO format file containing a set of final particles statistically similar to those that would have found by a full Monte Carlo simulation. In addition to the reconstructed particles themselves, descriptions of the calorimeter hit clusters and tracks that these particles would have produced are also included in the LCIO output. These output files can then be put through various analysis codes in order to characterize the effectiveness of a hypothetical detector at extracting relevant physical information about an event. Such a tool is extremely useful in preliminary detector research and development, as full simulations are extremely cumbersome and taxing on processor resources; a fast, efficient Monte Carlo can facilitate and even make possible detector physics studies that would be very impractical with the full simulation by sacrificing what is in many cases inappropriate attention to detail for valuable gains in time required for results.
A comparison of generalized hybrid Monte Carlo methods with and without momentum flip
Akhmatskaya, Elena; Bou-Rabee, Nawaf; Reich, Sebastian
2009-04-01
The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.
Cluster-Event Biasing in Monte Carlo Applications to Systems Reliability
Khazen, Michael; Dubi, Arie
2002-07-15
Estimation of the probabilities of rare events with significant consequences, e.g., disasters, is one of the most difficult problems in Monte Carlo applications to systems engineering and reliability. The Bernoulli-type estimator used in analog Monte Carlo is characterized by extremely high variance when applied to the estimation of rare events. Variance reduction methods are, therefore, of importance in this field.The present work suggests a parametric nonanalog probability measure based on the superposition of transition biasing and forced events biasing. The cluster-event model is developed providing an effective and reliable approximation for the second moment and the benefit along with a methodology of selecting near-optimal biasing parameters. Numerical examples show a considerable benefit when the method is applied to problems of particular difficulty for the analog Monte Carlo method.The suggested model is applicable for reliability assessment of stochastic networks of complicated topology and high redundancy with component-level repair (i.e., repair applied to an individual failed component while the system is operational)
Armas-Perez, Julio C.; Londono-Hurtado, Alejandro; Guzman, Orlando; Hernandez-Ortiz, Juan P.; de Pablo, Juan J.
2015-07-27
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.
Accelerated Monte Carlo Methods for Coulomb Collisions
NASA Astrophysics Data System (ADS)
Rosin, Mark; Dimits, Andris; Ricketson, Lee; Caflisch, Russel; Cohen, Bruce
2012-10-01
As an alternative to binary-collision models for simulating Coulomb collisions in the Fokker-Planck limit, we present a new numerical higher-order-accurate time integration scheme for Langevin-equation-based collisions. A Taylor-series expansion of the stochastic differential equations is used to improve upon the standard Euler time integration. Additional Milstein terms arise in the time-discretization due to both the velocity dependence of the diffusion coefficients, and the aggregation of angular deflections. We introduce an accurate, easily computable direct sampling method for the multidimensional terms -- an approximation to the double integral over products of Gaussian random processes. Including these terms improves the strong convergence of the time integration of the particle trajectories from O(δt1/2) to O(δt). This is useful as a both a first step towards direct higher-order weak schemes (for computing average quantities), and as a key component in a ``multi-level'' scheme that returns a computationally efficient estimate of averaged quantities. The latter is maximally efficient, in the asymptotic sense, when used with Milstein terms, and therefore the optimal choice of multi-level scheme. We present results showing both the improved strong convergence of the new integration method, and the increased efficiency multi-level scheme.
NASA Technical Reports Server (NTRS)
Ponomarev, Artem; Cucinotta, F.
2011-01-01
To create a generalized mechanistic model of DNA damage in human cells that will generate analytical and image data corresponding to experimentally observed DNA damage foci and will help to improve the experimental foci yields by simulating spatial foci patterns and resolving problems with quantitative image analysis. Material and Methods: The analysis of patterns of RIFs (radiation-induced foci) produced by low- and high-LET (linear energy transfer) radiation was conducted by using a Monte Carlo model that combines the heavy ion track structure with characteristics of the human genome on the level of chromosomes. The foci patterns were also simulated in the maximum projection plane for flat nuclei. Some data analysis was done with the help of image segmentation software that identifies individual classes of RIFs and colocolized RIFs, which is of importance to some experimental assays that assign DNA damage a dual phosphorescent signal. Results: The model predicts the spatial and genomic distributions of DNA DSBs (double strand breaks) and associated RIFs in a human cell nucleus for a particular dose of either low- or high-LET radiation. We used the model to do analyses for different irradiation scenarios. In the beam-parallel-to-the-disk-of-a-flattened-nucleus scenario we found that the foci appeared to be merged due to their high density, while, in the perpendicular-beam scenario, the foci appeared as one bright spot per hit. The statistics and spatial distribution of regions of densely arranged foci, termed DNA foci chains, were predicted numerically using this model. Another analysis was done to evaluate the number of ion hits per nucleus, which were visible from streaks of closely located foci. In another analysis, our image segmentaiton software determined foci yields directly from images with single-class or colocolized foci. Conclusions: We showed that DSB clustering needs to be taken into account to determine the true DNA damage foci yield, which helps to determine the DSB yield. Using the model analysis, a researcher can refine the DSB yield per nucleus per particle. We showed that purely geometric artifacts, present in the experimental images, can be analytically resolved with the model, and that the quantization of track hits and DSB yields can be provided to the experimentalists who use enumeration of radiation-induced foci in immunofluorescence experiments using proteins that detect DNA damage. An automated image segmentaiton software can prove useful in a faster and more precise object counting for colocolized foci images.
Monte Carlo simulation of particle acceleration at astrophysical shocks
NASA Astrophysics Data System (ADS)
Campbell, Roy K.
1989-09-01
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 description of particle scattering (pitch-angle instead of hard-sphere) and as iterative procedure for treating the self-excitation of the MHD turbulence.
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 description of particle scattering (pitch-angle instead of hard-sphere) and as iterative procedure for treating the self-excitation of the MHD turbulence.
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.
Müller, Florian Jenny, Patrick Meyer, Daniel W.
2013-10-01
Monte Carlo (MC) is a well known method for quantifying uncertainty arising for example in subsurface flow problems. Although robust and easy to implement, MC suffers from slow convergence. Extending MC by means of multigrid techniques yields the multilevel Monte Carlo (MLMC) method. MLMC has proven to greatly accelerate MC for several applications including stochastic ordinary differential equations in finance, elliptic stochastic partial differential equations and also hyperbolic problems. In this study, MLMC is combined with a streamline-based solver to assess uncertain two phase flow and Buckley–Leverett transport in random heterogeneous porous media. The performance of MLMC is compared to MC for a two dimensional reservoir with a multi-point Gaussian logarithmic permeability field. The influence of the variance and the correlation length of the logarithmic permeability on the MLMC performance is studied.
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations.
Arampatzis, Georgios; Katsoulakis, Markos A
2014-03-28
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-"coupled"- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code. PMID:24697425
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Arampatzis, Georgios; Katsoulakis, Markos A.
2014-03-01
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-"coupled"- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code.
NASA Astrophysics Data System (ADS)
Müller, Florian; Jenny, Patrick; Daniel, Meyer
2014-05-01
To a large extent, the flow and transport behaviour within a subsurface reservoir is governed by its permeability. Typically, permeability measurements of a subsurface reservoir are affordable at few spatial locations only. Due to this lack of information, permeability fields are preferably described by stochastic models rather than deterministically. A stochastic method is needed to asses the transition of the input uncertainty in permeability through the system of partial differential equations describing flow and transport to the output quantity of interest. Monte Carlo (MC) is an established method for quantifying uncertainty arising in subsurface flow and transport problems. Although robust and easy to implement, MC suffers from slow statistical convergence. To reduce the computational cost of MC, the multilevel Monte Carlo (MLMC) method was introduced. Instead of sampling a random output quantity of interest on the finest affordable grid as in case of MC, MLMC operates on a hierarchy of grids. If parts of the sampling process are successfully delegated to coarser grids where sampling is inexpensive, MLMC can dramatically outperform MC. MLMC has proven to accelerate MC for several applications including integration problems, stochastic ordinary differential equations in finance as well as stochastic elliptic and hyperbolic partial differential equations. In this study, MLMC is combined with a reservoir simulator to assess uncertain two phase (water/oil) flow and transport within a random permeability field. The performance of MLMC is compared to MC for a two-dimensional reservoir with a multi-point Gaussian logarithmic permeability field. It is found that MLMC yields significant speed-ups with respect to MC while providing results of essentially equal accuracy. This finding holds true not only for one specific Gaussian logarithmic permeability model but for a range of correlation lengths and variances.
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations
Arampatzis, Georgios; Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003 ; Katsoulakis, Markos A.
2014-03-28
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo (KMC). Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-“coupled”- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g., coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore, the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz–Kalos–Lebowitz algorithm's philosophy, where events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption, and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach. We also provide a complete implementation of the proposed sensitivity analysis algorithms, including various spatial KMC examples, in a supplementary MATLAB source code.
Monte Carlo simulation for PET scanners and shields.
Hasegawa, Tomoyuki; Michel, Christian; Murayama, Hideo; Yamaya, Taiga; Matsuura, Hajime; Tanada, Syuuji
2001-01-01
A Monte Carlo simulation code was developed for simulating PET scanners with the Monte Carlo program package GEANT. The present simulation code can handle not only conventional types of PET scanners, but also any complex detector systems with arbitrary geometrical configuration. All the relevant interactions of photons and electrons are taken into account in all the defined objects while optical tracking in the scintillation crystals is approximated by simple analytical simulation. In addition to basic PET scanner performance factors, such as sensitivity and scatter fraction, valuable but un-measurable information, such as photon trajectories and interaction position distribution, can be obtained and represented graphically in various ways. This simulation code has proved useful in analyzing the physics characteristics of existing commercial PET scanners and related shields, and in design studies of new PET scanners. PMID:12766303
grmonty: A MONTE CARLO CODE FOR RELATIVISTIC RADIATIVE TRANSPORT
Dolence, Joshua C.; Gammie, Charles F.; Leung, Po Kin; Moscibrodzka, Monika
2009-10-01
We describe a Monte Carlo radiative transport code intended for calculating spectra of hot, optically thin plasmas in full general relativity. The version we describe here is designed to model hot accretion flows in the Kerr metric and therefore incorporates synchrotron emission and absorption, and Compton scattering. The code can be readily generalized, however, to account for other radiative processes and an arbitrary spacetime. We describe a suite of test problems, and demonstrate the expected N {sup -1/2} convergence rate, where N is the number of Monte Carlo samples. Finally, we illustrate the capabilities of the code with a model calculation, a spectrum of the slowly accreting black hole Sgr A* based on data provided by a numerical general relativistic MHD model of the accreting plasma.
Rejection-free Monte Carlo scheme for anisotropic particles.
Sinkovits, Daniel W; Barr, Stephen A; Luijten, Erik
2012-04-14
We extend the geometric cluster algorithm [J. Liu and E. Luijten, Phys. Rev. Lett. 92, 035504 (2004)], a highly efficient, rejection-free Monte Carlo scheme for fluids and colloidal suspensions, to the case of anisotropic particles. This is made possible by adopting hyperspherical boundary conditions. A detailed derivation of the algorithm is presented, along with extensive implementation details as well as benchmark results. We describe how the quaternion notation is particularly suitable for the four-dimensional geometric operations employed in the algorithm. We present results for asymmetric Lennard-Jones dimers and for the Yukawa one-component plasma in hyperspherical geometry. The efficiency gain that can be achieved compared to conventional, Metropolis-type Monte Carlo simulations is investigated for rod-sphere mixtures as a function of rod aspect ratio, rod-sphere diameter ratio, and rod concentration. The effect of curved geometry on physical properties is addressed. PMID:22502505
Ab initio Monte Carlo investigation of small lithium clusters.
Srinivas, S.
1999-06-16
Structural and thermal properties of small lithium clusters are studied using ab initio-based Monte Carlo simulations. The ab initio scheme uses a Hartree-Fock/density functional treatment of the electronic structure combined with a jump-walking Monte Carlo sampling of nuclear configurations. Structural forms of Li{sub 8} and Li{sub 9}{sup +} clusters are obtained and their thermal properties analyzed in terms of probability distributions of the cluster potential energy, average potential energy and configurational heat capacity all considered as a function of the cluster temperature. Details of the gradual evolution with temperature of the structural forms sampled are examined. Temperatures characterizing the onset of structural changes and isomer coexistence are identified for both clusters.
A tetrahedron-based inhomogeneous Monte Carlo optical simulator
Shen, H; Wang, G
2010-01-01
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. PMID:20090182
Efficient, Automated Monte Carlo Methods for Radiation Transport
Kong, Rong; Ambrose, Martin; Spanier, Jerome
2012-01-01
Monte Carlo simulations provide an indispensible model for solving radiative transport problems, but their slow convergence inhibits their use as an everyday computational tool. In this paper, we present two new ideas for accelerating the convergence of Monte Carlo algorithms based upon an efficient algorithm that couples simulations of forward and adjoint transport equations. Forward random walks are first processed in stages, each using a fixed sample size, and information from stage k is used to alter the sampling and weighting procedure in stage k + 1. This produces rapid geometric convergence and accounts for dramatic gains in the efficiency of the forward computation. In case still greater accuracy is required in the forward solution, information from an adjoint simulation can be added to extend the geometric learning of the forward solution. The resulting new approach should find widespread use when fast, accurate simulations of the transport equation are needed. PMID:23226872
A standard timing benchmark for EGS4 Monte Carlo calculations.
Bielajew, A F; Rogers, D W
1992-01-01
A Fortran 77 Monte Carlo source code built from the EGS4 Monte Carlo code system has been used for timing benchmark purposes on 29 different computers. This code simulates the deposition of energy from an incident electron beam in a 3-D rectilinear geometry such as one would employ to model electron and photon transport through a series of CT slices. The benchmark forms a standalone system and does not require that the EGS4 system be installed. The Fortran source code may be ported to different architectures by modifying a few lines and only a moderate amount of CPU time is required ranging from about 5 h on PC/386/387 to a few seconds on a massively parallel supercomputer (a BBN TC2000 with 512 processors). PMID:1584121
Analytical band Monte Carlo analysis of electron transport in silicene
NASA Astrophysics Data System (ADS)
Yeoh, K. H.; Ong, D. S.; Ooi, C. H. Raymond; Yong, T. K.; Lim, S. K.
2016-06-01
An analytical band Monte Carlo (AMC) with linear energy band dispersion has been developed to study the electron transport in suspended silicene and silicene on aluminium oxide (Al2O3) substrate. We have calibrated our model against the full band Monte Carlo (FMC) results by matching the velocity-field curve. Using this model, we discover that the collective effects of charge impurity scattering and surface optical phonon scattering can degrade the electron mobility down to about 400 cm2 V‑1 s‑1 and thereafter it is less sensitive to the changes of charge impurity in the substrate and surface optical phonon. We also found that further reduction of mobility to ∼100 cm2 V‑1 s‑1 as experimentally demonstrated by Tao et al (2015 Nat. Nanotechnol. 10 227) can only be explained by the renormalization of Fermi velocity due to interaction with Al2O3 substrate.
Multiparticle moves in acceptance rate optimized Monte Carlo.
Neumann, Tobias; Danilov, Denis; Wenzel, Wolfgang
2015-11-15
Molecular Dynamics (MD) and Monte Carlo (MC) based simulation methods are widely used to investigate molecular and nanoscale structures and processes. While the investigation of systems in MD simulations is limited by very small time steps, MC methods are often stifled by low acceptance rates for moves that significantly perturb the system. In many Metropolis MC methods with hard potentials, the acceptance rate drops exponentially with the number of uncorrelated, simultaneously proposed moves. In this work, we discuss a multiparticle Acceptance Rate Optimized Monte Carlo approach (AROMoCa) to construct collective moves with near unit acceptance probability, while preserving detailed balance even for large step sizes. After an illustration of the protocol, we demonstrate that AROMoCa significantly accelerates MC simulations in four model systems in comparison to standard MC methods. AROMoCa can be applied to all MC simulations where a gradient of the potential is available and can help to significantly speed up molecular simulations. PMID:26459216
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. PMID:26362232
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.
The MCLIB library: Monte Carlo simulation of neutron scattering instruments
Seeger, P.A.
1995-09-01
Monte Carlo is a method to integrate over a large number of variables. Random numbers are used to select a value for each variable, and the integrand is evaluated. The process is repeated a large number of times and the resulting values are averaged. For a neutron transport problem, first select a neutron from the source distribution, and project it through the instrument using either deterministic or probabilistic algorithms to describe its interaction whenever it hits something, and then (if it hits the detector) tally it in a histogram representing where and when it was detected. This is intended to simulate the process of running an actual experiment (but it is much slower). This report describes the philosophy and structure of MCLIB, a Fortran library of Monte Carlo subroutines which has been developed for design of neutron scattering instruments. A pair of programs (LQDGEOM and MC{_}RUN) which use the library are shown as an example.
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. PMID:26012871
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.
Monte Carlo Integration Using Spatial Structure of Markov Random Field
NASA Astrophysics Data System (ADS)
Yasuda, Muneki
2015-03-01
Monte Carlo integration (MCI) techniques are important in various fields. In this study, a new MCI technique for Markov random fields (MRFs) is proposed. MCI consists of two successive parts: the first involves sampling using a technique such as the Markov chain Monte Carlo method, and the second involves an averaging operation using the obtained sample points. In the averaging operation, a simple sample averaging technique is often employed. The method proposed in this paper improves the averaging operation by addressing the spatial structure of the MRF and is mathematically guaranteed to statistically outperform standard MCI using the simple sample averaging operation. Moreover, the proposed method can be improved in a systematic manner and is numerically verified by numerical simulations using planar Ising models. In the latter part of this paper, the proposed method is applied to the inverse Ising problem and we observe that it outperforms the maximum pseudo-likelihood estimation.
Analytic results and weighted Monte Carlo simulations for CDO pricing
NASA Astrophysics Data System (ADS)
Stippinger, M.; Rácz, É.; Vető, B.; Bihary, Zs.
2012-02-01
We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically ˜ 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulas are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.
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.
Engineering local optimality in quantum Monte Carlo algorithms
Pollet, Lode . E-mail: pollet@itp.phys.ethz.ch; Houcke, Kris Van; Rombouts, Stefan M.A.
2007-08-10
Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic models. Both algorithms work in the grand-canonical ensemble and can have a winding number larger than zero. However, they retain a lot of intrinsic degrees of freedom which can be used to optimize the algorithm. We let us guide by the rigorous statements on the globally optimal form of Markov chain Monte Carlo simulations in order to devise a locally optimal formulation of the worm algorithm while incorporating ideas from the directed loop algorithm. We provide numerical examples for the soft-core Bose-Hubbard model and various spin-S models.
Bayesian Monte Carlo method for nuclear data evaluation
NASA Astrophysics Data System (ADS)
Koning, A. J.
2015-12-01
A Bayesian Monte Carlo method is outlined which allows a systematic evaluation of nuclear reactions using the nuclear model code TALYS and the experimental nuclear reaction database EXFOR. The method is applied to all nuclides at the same time. First, the global predictive power of TALYS is numerically assessed, which enables to set the prior space of nuclear model solutions. Next, the method gradually zooms in on particular experimental data per nuclide, until for each specific target nuclide its existing experimental data can be used for weighted Monte Carlo sampling. To connect to the various different schools of uncertainty propagation in applied nuclear science, the result will be either an EXFOR-weighted covariance matrix or a collection of random files, each accompanied by the EXFOR-based weight.
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.
Efficient, automated Monte Carlo methods for radiation transport
Kong Rong; Ambrose, Martin; Spanier, Jerome
2008-11-20
Monte Carlo simulations provide an indispensible model for solving radiative transport problems, but their slow convergence inhibits their use as an everyday computational tool. In this paper, we present two new ideas for accelerating the convergence of Monte Carlo algorithms based upon an efficient algorithm that couples simulations of forward and adjoint transport equations. Forward random walks are first processed in stages, each using a fixed sample size, and information from stage k is used to alter the sampling and weighting procedure in stage k+1. This produces rapid geometric convergence and accounts for dramatic gains in the efficiency of the forward computation. In case still greater accuracy is required in the forward solution, information from an adjoint simulation can be added to extend the geometric learning of the forward solution. The resulting new approach should find widespread use when fast, accurate simulations of the transport equation are needed.
Variance reduction for Fokker-Planck based particle Monte Carlo schemes
NASA Astrophysics Data System (ADS)
Gorji, M. Hossein; Andric, Nemanja; Jenny, Patrick
2015-08-01
Recently, Fokker-Planck based particle Monte Carlo schemes have been proposed and evaluated for simulations of rarefied gas flows [1-3]. In this paper, the variance reduction for particle Monte Carlo simulations based on the Fokker-Planck model is considered. First, deviational based schemes were derived and reviewed, and it is shown that these deviational methods are not appropriate for practical Fokker-Planck based rarefied gas flow simulations. This is due to the fact that the deviational schemes considered in this study lead either to instabilities in the case of two-weight methods or to large statistical errors if the direct sampling method is applied. Motivated by this conclusion, we developed a novel scheme based on correlated stochastic processes. The main idea here is to synthesize an additional stochastic process with a known solution, which is simultaneously solved together with the main one. By correlating the two processes, the statistical errors can dramatically be reduced; especially for low Mach numbers. To assess the methods, homogeneous relaxation, planar Couette and lid-driven cavity flows were considered. For these test cases, it could be demonstrated that variance reduction based on parallel processes is very robust and effective.
COMET-PE as an Alternative to Monte Carlo for Photon and Electron Transport
NASA Astrophysics Data System (ADS)
Hayward, Robert M.; Rahnema, Farzad
2014-06-01
Monte Carlo methods are a central component of radiotherapy treatment planning, shielding design, detector modeling, and other applications. Long calculation times, however, can limit the usefulness of these purely stochastic methods. The coarse mesh method for photon and electron transport (COMET-PE) provides an attractive alternative. By combining stochastic pre-computation with a deterministic solver, COMET-PE achieves accuracy comparable to Monte Carlo methods in only a fraction of the time. The method's implementation has been extended to 3D, and in this work, it is validated by comparison to DOSXYZnrc using a photon radiotherapy benchmark. The comparison demonstrates excellent agreement; of the voxels that received more than 10% of the maximum dose, over 97.3% pass a 2% / 2mm acceptance test and over 99.7% pass a 3% / 3mm test. Furthermore, the method is over an order of magnitude faster than DOSXYZnrc and is able to take advantage of both distributed-memory and shared-memory parallel architectures for increased performance.
MCSpearman: Monte Carlo error analyses of Spearman's rank test
NASA Astrophysics Data System (ADS)
Curran, Peter A.
2015-04-01
Spearman’s rank correlation test is commonly used in astronomy to discern whether a set of two variables are correlated or not. Unlike most other quantities quoted in astronomical literature, the Spearman’s rank correlation coefficient is generally quoted with no attempt to estimate the errors on its value. This code implements a number of Monte Carlo based methods to estimate the uncertainty on the Spearman’s rank correlation coefficient.
Monte Carlo simulation of photon-induced air showers
NASA Astrophysics Data System (ADS)
D'Ettorre Piazzoli, B.; di Sciascio, G.
1994-05-01
The EPAS code (Electron Photon-induced Air Showers) is a three-dimensional Monte Carlo simulation developed to study the properties of extensive air showers (EAS) generated by the interaction of high energy photons (or electrons) in the atmosphere. Results of the present simulation concern the longitudinal, lateral, temporal and angular distributions of electrons in atmospheric cascades initiated by photons of energies up to 10^3 TeV.
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.
The Hybrid Monte Carlo Algorithm and the chiral transition
NASA Astrophysics Data System (ADS)
Gupta, Rajan
1988-04-01
In this talk I describe tests of the Hybrid Monte Carlo Algorithm for QCD done in collaboration with Greg Kilcup and Stephen Sharpe. We find that the acceptance in the global Metropolis step for Staggered fermions can be tuned and kept large without having to make the step-size prohibitively small. We present results for the finite temperature transition on 4 4 and 4 × 6 3 lattices using this algorithm.
Regenerative Markov Chain Monte Carlo for any distribution.
Minh, D.
2012-01-01
While Markov chain Monte Carlo (MCMC) methods are frequently used for difficult calculations in a wide range of scientific disciplines, they suffer from a serious limitation: their samples are not independent and identically distributed. Consequently, estimates of expectations are biased if the initial value of the chain is not drawn from the target distribution. Regenerative simulation provides an elegant solution to this problem. In this article, we propose a simple regenerative MCMC algorithm to generate variates for any distribution
Monte Carlo approach to nuclei and nuclear matter
NASA Astrophysics Data System (ADS)
Fantoni, Stefano; Gandolfi, Stefano; Illarionov, Alexey Yu.; Schmidt, Kevin E.; Pederiva, Francesco
2008-10-01
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 lowdensity regime are computed, using a realistic Hamiltonian containing the Argonne AV8' plus Urbana IX threenucleon interaction. Preliminary results for the EOS of isospinasymmetric nuclear matter are also presented.
A new method for commissioning Monte Carlo treatment planning systems
NASA Astrophysics Data System (ADS)
Aljarrah, Khaled Mohammed
2005-11-01
The Monte Carlo method is an accurate method for solving numerical problems in different fields. It has been used for accurate radiation dose calculation for radiation treatment of cancer. However, the modeling of an individual radiation beam produced by a medical linear accelerator for Monte Carlo dose calculation, i.e., the commissioning of a Monte Carlo treatment planning system, has been the bottleneck for the clinical implementation of Monte Carlo treatment planning. In this study a new method has been developed to determine the parameters of the initial electron beam incident on the target for a clinical linear accelerator. The interaction of the initial electron beam with the accelerator target produces x-ray and secondary charge particles. After successive interactions in the linac head components, the x-ray photons and the secondary charge particles interact with the patient's anatomy and deliver dose to the region of interest. The determination of the initial electron beam parameters is important for estimating the delivered dose to the patients. These parameters, such as beam energy and radial intensity distribution, are usually estimated through a trial and error process. In this work an easy and efficient method was developed to determine these parameters. This was accomplished by comparing calculated 3D dose distributions for a grid of assumed beam energies and radii in a water phantom with measurements data. Different cost functions were studied to choose the appropriate function for the data comparison. The beam parameters were determined on the light of this method. Due to the assumption that same type of linacs are exactly the same in their geometries and only differ by the initial phase space parameters, the results of this method were considered as a source data to commission other machines of the same type.
Calculations of pair production by Monte Carlo methods
Bottcher, C.; Strayer, M.R.
1991-01-01
We describe some of the technical design issues associated with the production of particle-antiparticle pairs in very large accelerators. To answer these questions requires extensive calculation of Feynman diagrams, in effect multi-dimensional integrals, which we evaluate by Monte Carlo methods on a variety of supercomputers. We present some portable algorithms for generating random numbers on vector and parallel architecture machines. 12 refs., 14 figs.
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. PMID:17476053
Monte Carlo Study on Anomalous Carrier Diffusion in Inhomogeneous Semiconductors
NASA Astrophysics Data System (ADS)
Mori, N.; Hill, R. J. A.; Patan, A.; Eaves, L.
2015-10-01
We perform ensemble Monte Carlo simulations of electron diffusion in high mobility inhomogeneous InAs layers. Electrons move ballistically for short times while moving diffusively for sufficiently long times. We find that electrons show anomalous diffusion in the intermediate time domain. Our study suggests that electrons in inhomogeneous InAs could be used to experimentally explore generalized random walk phenomena, which, some studies assert, also occur naturally in the motion of animal foraging paths.
OBJECT KINETIC MONTE CARLO SIMULATIONS OF MICROSTRUCTURE EVOLUTION
Nandipati, Giridhar; Setyawan, Wahyu; Heinisch, Howard L.; Roche, Kenneth J.; Kurtz, Richard J.; Wirth, Brian D.
2013-09-30
The objective is to report the development of the flexible object kinetic Monte Carlo (OKMC) simulation code KSOME (kinetic simulation of microstructure evolution) which can be used to simulate microstructure evolution of complex systems under irradiation. In this report we briefly describe the capabilities of KSOME and present preliminary results for short term annealing of single cascades in tungsten at various primary-knock-on atom (PKA) energies and temperatures.
Variational Monte Carlo study of He-4 in two dimensions
NASA Astrophysics Data System (ADS)
Belic, A.; Fantoni, S.
1993-11-01
The study of the ground state of liquid and solid He-4 in two dimensions (2D) and at zero temperature, using Variational Monte Carlo (VMC) method, is presented. The trial wave functions used include the Shadow Wave Function (SWF) and the recently proposed Extended Shadow Wave Function (ESWF), and well as Jastrow (JWF), Jastrow-Nosanow (JNWF) and Jastrow+Triplet Wave Function (JTWF).
Variational Monte Carlo study of 4He in two dimensions
NASA Astrophysics Data System (ADS)
Be´, A.; Fantoni, S.
1994-02-01
The study of the ground state of liquid and solid 4He in two dimensions (2D) and at zero temperature, using Variational Monte Carlo (VMC) method, is presented. The trial wave functions used include the shadow wave function (SWF) and the recently proposed extended shadow wave function (ESWF), as well as Jastrow (JWF), Jastrow-Nosanow (JNWF) and Jastrow+Triplet wave function (JTWF).
Monte-Carlo simulation of heavy-ion collisions
NASA Astrophysics Data System (ADS)
Schenke, Bjrn; Jeon, Sangyong; Gale, Charles
2011-04-01
We present Monte-Carlo simulations for heavy-ion collisions combining PYTHIA and the McGill-AMY formalism to describe the evolution of hard partons in a soft background, modelled using hydrodynamic simulations. MARTINI generates full event configurations in the high pT region that take into account thermal QCD and QED effects as well as effects of the evolving medium. This way it is possible to perform detailed quantitative comparisons with experimental observables.
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.
Representation and simulation for pyrochlore lattice via Monte Carlo technique
NASA Astrophysics Data System (ADS)
Passos, André Luis; de Albuquerque, Douglas F.; Filho, João Batista Santos
2016-05-01
This work presents a representation of the Kagome and pyrochlore lattices using Monte Carlo simulation as well as some results of the critical properties. These lattices are composed corner sharing triangles and tetrahedrons respectively. The simulation was performed employing the Cluster Wolf Algorithm for the spin updates through the standard ferromagnetic Ising Model. The determination of the critical temperature and exponents was based on the Histogram Technique and the Finite-Size Scaling Theory.
Recent advances in the Mercury Monte Carlo particle transport code
Brantley, P. S.; Dawson, S. A.; McKinley, M. S.; O'Brien, M. J.; Stevens, D. E.; Beck, B. R.; Jurgenson, E. D.; Ebbers, C. A.; Hall, J. M.
2013-07-01
We review recent physics and computational science advances in the Mercury Monte Carlo particle transport code under development at Lawrence Livermore National Laboratory. We describe recent efforts to enable a nuclear resonance fluorescence capability in the Mercury photon transport. We also describe recent work to implement a probability of extinction capability into Mercury. We review the results of current parallel scaling and threading efforts that enable the code to run on millions of MPI processes. (authors)
Adaptive mesh and algorithm refinement using direct simulation Monte Carlo
Garcia, A.L.; Bell, J.B.; Crutchfield, W.Y.; Alder, B.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.
The All Particle Monte Carlo method: Atomic data files
Rathkopf, J.A.; Cullen, D.E.; Perkins, S.T.
1990-11-06
Development of the All Particle Method, a project to simulate the transport of particles via the Monte Carlo method, has proceeded on two fronts: data collection and algorithm development. In this paper we report on the status of the data libraries. The data collection is nearly complete with the addition of electron, photon, and atomic data libraries to the existing neutron, gamma ray, and charged particle libraries. The contents of these libraries are summarized.
Quantum MonteCarlo Calculations of Symmetric Nuclear Matter
NASA Astrophysics Data System (ADS)
Gandolfi, Stefano; Pederiva, Francesco; Fantoni, Stefano; Schmidt, Kevin E.
2007-03-01
We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon-nucleon interactions by means of auxiliary field diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and represents an important step forward towards a quantitative understanding of problems in nuclear structure and astrophysics.
Shell-model Monte Carlo calculations in nuclei
Dean, D.J. |
1998-11-01
The author`s research over the past few years has been in the area of the nuclear shell model solved not by diagonalization, but by integration. In what follows, the author describes the shell-model Monte Carlo (SMMC) method, and discusses two recent and interesting results obtained from theory. These include calculations of electron-capture rates in fp-shell nuclei, and pairing correlations in medium-mass nuclei near N = Z.
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.
Path integral Monte Carlo on a lattice: Extended states
NASA Astrophysics Data System (ADS)
O'Callaghan, Mark; Miller, Bruce N.
2014-04-01
The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and atoms are restricted to the sites of a one-dimensional lattice. A path integral formalism is developed within the context of the canonical ensemble in which the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. For the case of a free particle, analytical expressions for the energy, its fluctuations, and the qp-qp correlation function are derived and compared with the Monte Carlo simulations. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp for a periodic interaction potential, forcing the qp to occupy extended states. We consider a striped potential in one dimension, where every other lattice site is occupied by an atom with potential ɛ, and every other lattice site is empty. This potential serves as a stress test for the path integral formalism because of its rapid site-to-site variation. An analytical solution was determined in this case by utilizing Bloch's theorem due to the periodicity of the potential. Comparisons of the potential energy, the total energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the analytical calculations.
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. PMID:26934878
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. PMID:26374029
Path integral Monte Carlo on a lattice: extended states.
O'Callaghan, Mark; Miller, Bruce N
2014-04-01
The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and atoms are restricted to the sites of a one-dimensional lattice. A path integral formalism is developed within the context of the canonical ensemble in which the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. For the case of a free particle, analytical expressions for the energy, its fluctuations, and the qp-qp correlation function are derived and compared with the Monte Carlo simulations. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp for a periodic interaction potential, forcing the qp to occupy extended states. We consider a striped potential in one dimension, where every other lattice site is occupied by an atom with potential ε, and every other lattice site is empty. This potential serves as a stress test for the path integral formalism because of its rapid site-to-site variation. An analytical solution was determined in this case by utilizing Bloch's theorem due to the periodicity of the potential. Comparisons of the potential energy, the total energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the analytical calculations. PMID:24827210
Uncertainties in external dosimetry: analytical vs. Monte Carlo method.
Behrens, R
2010-03-01
Over the years, the International Commission on Radiological Protection (ICRP) and other organisations have formulated recommendations regarding uncertainty in occupational dosimetry. The most practical and widely accepted recommendations are the trumpet curves. To check whether routine dosemeters comply with them, a Technical Report on uncertainties issued by the International Electrotechnical Commission (IEC) can be used. In this report, the analytical method is applied to assess the uncertainty of a dosemeter fulfilling an IEC standard. On the other hand, the Monte Carlo method can be used to assess the uncertainty. In this work, a direct comparison of the analytical and the Monte Carlo methods is performed using the same input data. It turns out that the analytical method generally overestimates the uncertainty by about 10-30 %. Therefore, the results often do not comply with the recommendations of the ICRP regarding uncertainty. The results of the more realistic uncertainty evaluation using the Monte Carlo method usually comply with the recommendations of the ICRP. This is confirmed by results seen in regular tests in Germany. PMID:19942627
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)
Quantitative PET Imaging Using A Comprehensive Monte Carlo System Model
Southekal, S.; Vaska, P.; Southekal, s.; Purschke, M.L.; Schlyer, d.J.; Vaska, P.
2011-10-01
We present the complete image generation methodology developed for the RatCAP PET scanner, which can be extended to other PET systems for which a Monte Carlo-based system model is feasible. The miniature RatCAP presents a unique set of advantages as well as challenges for image processing, and a combination of conventional methods and novel ideas developed specifically for this tomograph have been implemented. The crux of our approach is a low-noise Monte Carlo-generated probability matrix with integrated corrections for all physical effects that impact PET image quality. The generation and optimization of this matrix are discussed in detail, along with the estimation of correction factors and their incorporation into the reconstruction framework. Phantom studies and Monte Carlo simulations are used to evaluate the reconstruction as well as individual corrections for random coincidences, photon scatter, attenuation, and detector efficiency variations in terms of bias and noise. Finally, a realistic rat brain phantom study reconstructed using this methodology is shown to recover >; 90% of the contrast for hot as well as cold regions. The goal has been to realize the potential of quantitative neuroreceptor imaging with the RatCAP.
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.
ALEPH2 - A general purpose Monte Carlo depletion code
Stankovskiy, A.; Van Den Eynde, G.; Baeten, P.; Trakas, C.; Demy, P. M.; Villatte, L.
2012-07-01
The Monte-Carlo burn-up code ALEPH is being developed at SCK-CEN since 2004. A previous version of the code implemented the coupling between the Monte Carlo transport (any version of MCNP or MCNPX) and the ' deterministic' depletion code ORIGEN-2.2 but had important deficiencies in nuclear data treatment and limitations inherent to ORIGEN-2.2. A new version of the code, ALEPH2, has several unique features making it outstanding among other depletion codes. The most important feature is full data consistency between steady-state Monte Carlo and time-dependent depletion calculations. The last generation general-purpose nuclear data libraries (JEFF-3.1.1, ENDF/B-VII and JENDL-4) are fully implemented, including special purpose activation, spontaneous fission, fission product yield and radioactive decay data. The built-in depletion algorithm allows to eliminate the uncertainties associated with obtaining the time-dependent nuclide concentrations. A predictor-corrector mechanism, calculation of nuclear heating, calculation of decay heat, decay neutron sources are available as well. The validation of the code on the results of REBUS experimental program has been performed. The ALEPH2 has shown better agreement with measured data than other depletion codes. (authors)
A semianalytic Monte Carlo code for modelling LIDAR measurements
NASA Astrophysics Data System (ADS)
Palazzi, Elisa; Kostadinov, Ivan; Petritoli, Andrea; Ravegnani, Fabrizio; Bortoli, Daniele; Masieri, Samuele; Premuda, Margherita; Giovanelli, Giorgio
2007-10-01
LIDAR (LIght Detection and Ranging) is an optical active remote sensing technology with many applications in atmospheric physics. Modelling of LIDAR measurements appears useful approach for evaluating the effects of various environmental variables and scenarios as well as of different measurement geometries and instrumental characteristics. In this regard a Monte Carlo simulation model can provide a reliable answer to these important requirements. A semianalytic Monte Carlo code for modelling LIDAR measurements has been developed at ISAC-CNR. The backscattered laser signal detected by the LIDAR system is calculated in the code taking into account the contributions due to the main atmospheric molecular constituents and aerosol particles through processes of single and multiple scattering. The contributions by molecular absorption, ground and clouds reflection are evaluated too. The code can perform simulations of both monostatic and bistatic LIDAR systems. To enhance the efficiency of the Monte Carlo simulation, analytical estimates and expected value calculations are performed. Artificial devices (such as forced collision, local forced collision, splitting and russian roulette) are moreover foreseen by the code, which can enable the user to drastically reduce the variance of the calculation.
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. PMID:25314561
Monte Carlo studies for medical imaging detector optimization
NASA Astrophysics Data System (ADS)
Fois, G. R.; Cisbani, E.; Garibaldi, F.
2016-02-01
This work reports on the Monte Carlo optimization studies of detection systems for Molecular Breast Imaging with radionuclides and Bremsstrahlung Imaging in nuclear medicine. Molecular Breast Imaging requires competing performances of the detectors: high efficiency and high spatial resolutions; in this direction, it has been proposed an innovative device which combines images from two different, and somehow complementary, detectors at the opposite sides of the breast. The dual detector design allows for spot compression and improves significantly the performance of the overall system if all components are well tuned, layout and processing carefully optimized; in this direction the Monte Carlo simulation represents a valuable tools. In recent years, Bremsstrahlung Imaging potentiality in internal radiotherapy (with beta-radiopharmaceuticals) has been clearly emerged; Bremsstrahlung Imaging is currently performed with existing detector generally used for single photon radioisotopes. We are evaluating the possibility to adapt an existing compact gamma camera and optimize by Monte Carlo its performance for Bremsstrahlung imaging with photons emitted by the beta- from 90 Y.
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.
Performance of quantum Monte Carlo for calculating molecular bond lengths.
Cleland, Deidre M; Per, Manolo C
2016-03-28
This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10(-3) Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10(-3) Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries. PMID:27036428
Chemical accuracy from quantum Monte Carlo for the benzene dimer
NASA Astrophysics Data System (ADS)
Azadi, Sam; Cohen, R. E.
2015-09-01
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 modelling of positron transport in real world applications
NASA Astrophysics Data System (ADS)
Marjanović, S.; Banković, A.; Šuvakov, M.; Petrović, Z. Lj
2014-05-01
Due to the unstable nature of positrons and their short lifetime, it is difficult to obtain high positron particle densities. This is why the Monte Carlo simulation technique, as a swarm method, is very suitable for modelling most of the current positron applications involving gaseous and liquid media. The ongoing work on the measurements of cross-sections for positron interactions with atoms and molecules and swarm calculations for positrons in gasses led to the establishment of good cross-section sets for positron interaction with gasses commonly used in real-world applications. Using the standard Monte Carlo technique and codes that can follow both low- (down to thermal energy) and high- (up to keV) energy particles, we are able to model different systems directly applicable to existing experimental setups and techniques. This paper reviews the results on modelling Surko-type positron buffer gas traps, application of the rotating wall technique and simulation of positron tracks in water vapor as a substitute for human tissue, and pinpoints the challenges in and advantages of applying Monte Carlo simulations to these systems.
MONTE CARLO ERROR ESTIMATION APPLIED TO NONDESTRUCTIVE ASSAY METHODS
R. ESTEP; ET AL
2000-06-01
Monte Carlo randomization of nuclear counting data into N replicate sets is the basis of a simple and effective method for estimating error propagation through complex analysis algorithms such as those using neural networks or tomographic image reconstructions. The error distributions of properly simulated replicate data sets mimic those of actual replicate measurements and can be used to estimate the std. dev. for an assay along with other statistical quantities. We have used this technique to estimate the standard deviation in radionuclide masses determined using the tomographic gamma scanner (TGS) and combined thermal/epithermal neutron (CTEN) methods. The effectiveness of this approach is demonstrated by a comparison of our Monte Carlo error estimates with the error distributions in actual replicate measurements and simulations of measurements. We found that the std. dev. estimated this way quickly converges to an accurate value on average and has a predictable error distribution similar to N actual repeat measurements. The main drawback of the Monte Carlo method is that N additional analyses of the data are required, which may be prohibitively time consuming with slow analysis algorithms.
Transient analysis of CML inverter using Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Galdin, Sylvie; Musalem, Franois-Xavier; Dollfus, Philippe; Mouis, Mireille; Hesto, Patrice
1996-02-01
Monte Carlo simulation of a complete CML gate composed of two submicron bipolar transistors has been performed. The gate delay time ?D is usually calculated, according to a widely-used formula, as a weighted sum of time constants deduced from the transistor small-signal parameters. In this paper we analyse the validity of this approach. The weighting factor values, used in the ?D expression are determined from this expression and transient Monte Carlo simulation results. Comparison between these results and those given in the literature shows that the best agreement is obtained if two conditions are fulfilled: the transit time used in the ?D expression is reduced to the intrinsic base transit time, and the access base resistance is limited to the extrinsic one. However, even in this case, the weighting factors associated with depletion capacitances are called into question by the Monte Carlo analysis. A set of weighting factor values is proposed, which leads to a discrepancy between the simulated and calculated ?D within 10%.
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.
On Monte Carlo Methods and Applications in Geoscience
NASA Astrophysics Data System (ADS)
Zhang, Z.; Blais, J.
2009-05-01
Monte Carlo methods are designed to study various deterministic problems using probabilistic approaches, and with computer simulations to explore much wider possibilities for the different algorithms. Pseudo- Random Number Generators (PRNGs) are based on linear congruences of some large prime numbers, while Quasi-Random Number Generators (QRNGs) provide low discrepancy sequences, both of which giving uniformly distributed numbers in (0,1). Chaotic Random Number Generators (CRNGs) give sequences of 'random numbers' satisfying some prescribed probabilistic density, often denser around the two corners of interval (0,1), but transforming this type of density to a uniform one is usually possible. Markov Chain Monte Carlo (MCMC), as indicated by its name, is associated with Markov Chain simulations. Basic descriptions of these random number generators will be given, and a comparative analysis of these four methods will be included based on their efficiencies and other characteristics. Some applications in geoscience using Monte Carlo simulations will be described, and a comparison of these algorithms will also be included with some concluding remarks.
Performance of quantum Monte Carlo for calculating molecular bond lengths
NASA Astrophysics Data System (ADS)
Cleland, Deidre M.; Per, Manolo C.
2016-03-01
This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10-3 Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10-3 Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.
Monte Carlo simulations of particle acceleration at oblique shocks
NASA Astrophysics Data System (ADS)
Baring, Matthew G.; Ellison, Donald C.; Jones, Frank C.
1994-02-01
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 ThetaB1 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.
Paul P.H. Wilson
2005-07-30
The development of Monte Carlo techniques for isotopic inventory analysis has been explored in order to facilitate the modeling of systems with flowing streams of material through varying neutron irradiation environments. This represents a novel application of Monte Carlo methods to a field that has traditionally relied on deterministic solutions to systems of first-order differential equations. The Monte Carlo techniques were based largely on the known modeling techniques of Monte Carlo radiation transport, but with important differences, particularly in the area of variance reduction and efficiency measurement. The software that was developed to implement and test these methods now provides a basis for validating approximate modeling techniques that are available to deterministic methodologies. The Monte Carlo methods have been shown to be effective in reproducing the solutions of simple problems that are possible using both stochastic and deterministic methods. The Monte Carlo methods are also effective for tracking flows of materials through complex systems including the ability to model removal of individual elements or isotopes in the system. Computational performance is best for flows that have characteristic times that are large fractions of the system lifetime. As the characteristic times become short, leading to thousands or millions of passes through the system, the computational performance drops significantly. Further research is underway to determine modeling techniques to improve performance within this range of problems. This report describes the technical development of Monte Carlo techniques for isotopic inventory analysis. The primary motivation for this solution methodology is the ability to model systems of flowing material being exposed to varying and stochastically varying radiation environments. The methodology was developed in three stages: analog methods which model each atom with true reaction probabilities (Section 2), non-analog methods which bias the probability distributions while adjusting atom weights to preserve a fair game (Section 3), and efficiency measures to provide local and global measures of the effectiveness of the non-analog methods (Section 4). Following this development, the MCise (Monte Carlo isotope simulation engine) software was used to explore the efficiency of different modeling techniques (Section 5).
Independent pixel and Monte Carlo estimates of stratocumulus albedo
NASA Technical Reports Server (NTRS)
Cahalan, Robert F.; Ridgway, William; Wiscombe, Warren J.; Gollmer, Steven; HARSHVARDHAN
1994-01-01
Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.
Monte Carlo investigation of electron beam relative output factors
NASA Astrophysics Data System (ADS)
Zhang, Geoffrey G.
One of the tasks in commissioning an electron accelerator in cancer clinics is to measure relative output factors (ROFs) versus various parameters such as applicator size (called applicator factors), cutout size (cutout factors) and air-gap size (gap factors) for various electron beam energies and applicator sizes. This kind of measurement takes a lot of time and labour. This thesis shows that Monte Carlo simulation offers an alternative to this task. With BEAM (Med. Phys. 22(1995)503-524), an EGS4 user- code, clinical accelerator electron beams are simulated and ROFs for a Siemens MD2 linear accelerator and a Varian Clinac 2100C accelerator are calculate The study shows that the Monte Carlo method is not only practical in clinics but also powerful in analyzing the related physics. The calculated ROFs agree within 1% with the measurements for most cases and 2% for all cases that have been studied, which is more than acceptable in clinical practice. The details of each component of the dose, such as dose from particles scattered off the photon-jaws and the applicator, the dose from contaminant photon, the dose from direct electrons, etc., are also analyzed. The study also explains quantitatively why the effective SSD (Source to Phantom Surface Distance) is often not the nominal reference SSD. For ROF measurements for small fields using an ion chamber, this study discusses the stopping- power ratio corrections due to changes in the depth of dose maximum as a function of field size and versus various accelerators. Since it handles ROF calculations for arbitrary fields, including square, rectangular, circular and irregular fields, in the same way, Monte Carlo is the simplest method to get ROFs compared to other algorithms. As the first step towards implementing Monte Carlo methods in clinical treatment planning, Monte Carlo calculations for electron beam ROFs can replace measurements in clinical practice. It takes about 6 hours of CPU time on a single Pentium Pro 200MHz computer to simulate an accelerator and additional 2 hours for each ROF.
Monte Carlo study of a Cyberknife stereotactic radiosurgery system
Araki, Fujio
2006-08-15
This study investigated small-field dosimetry for a Cyberknife stereotactic radiosurgery system using Monte Carlo simulations. The EGSnrc/BEAMnrc Monte Carlo code was used to simulate the Cyberknife treatment head, and the DOSXYZnrc code was implemented to calculate central axis depth-dose curves, off-axis dose profiles, and relative output factors for various circular collimator sizes of 5 to 60 mm. Water-to-air stopping power ratios necessary for clinical reference dosimetry of the Cyberknife system were also evaluated by Monte Carlo simulations. Additionally, a beam quality conversion factor, k{sub Q}, for the Cyberknife system was evaluated for cylindrical ion chambers with different wall material. The accuracy of the simulated beam was validated by agreement within 2% between the Monte Carlo calculated and measured central axis depth-dose curves and off-axis dose profiles. The calculated output factors were compared with those measured by a diode detector and an ion chamber in water. The diode output factors agreed within 1% with the calculated values down to a 10 mm collimator. The output factors with the ion chamber decreased rapidly for collimators below 20 mm. These results were confirmed by the comparison to those from Monte Carlo methods with voxel sizes and materials corresponding to both detectors. It was demonstrated that the discrepancy in the 5 and 7.5 mm collimators for the diode detector is due to the water nonequivalence of the silicon material, and the dose fall-off for the ion chamber is due to its large active volume against collimators below 20 mm. The calculated stopping power ratios of the 60 mm collimator from the Cyberknife system (without a flattening filter) agreed within 0.2% with those of a 10x10 cm{sup 2} field from a conventional linear accelerator with a heavy flattening filter and the incident electron energy, 6 MeV. The difference in the stopping power ratios between 5 and 60 mm collimators was within 0.5% at a 10 cm depth in water. Furthermore, k{sub Q} values for the Cyberknife system were in agreement within 0.3% with those of the conventional 6 MV-linear accelerator for the cylindrical ion chambers with different wall material.
NASA Astrophysics Data System (ADS)
Shepherd, James J.; López Ríos, Pablo; Needs, Richard J.; Drummond, Neil D.; Mohr, Jennifer A.-F.; Booth, George H.; Grüneis, Andreas; Kresse, Georg; Alavi, Ali
2013-03-01
Full configuration interaction quantum Monte Carlo1 (FCIQMC) and its initiator adaptation2 allow for exact solutions to the Schrödinger equation to be obtained within a finite-basis wavefunction ansatz. In this talk, we explore an application of FCIQMC to the homogeneous electron gas (HEG). In particular we use these exact finite-basis energies to compare with approximate quantum chemical calculations from the VASP code3. After removing the basis set incompleteness error by extrapolation4,5, we compare our energies with state-of-the-art diffusion Monte Carlo calculations from the CASINO package6. Using a combined approach of the two quantum Monte Carlo methods, we present the highest-accuracy thermodynamic (infinite-particle) limit energies for the HEG achieved to date. 1 G. H. Booth, A. Thom, and A. Alavi, J. Chem. Phys. 131, 054106 (2009). 2 D. Cleland, G. H. Booth, and A. Alavi, J. Chem. Phys. 132, 041103 (2010). 3 www.vasp.at (2012). 4 J. J. Shepherd, A. Grüneis, G. H. Booth, G. Kresse, and A. Alavi, Phys. Rev. B. 86, 035111 (2012). 5 J. J. Shepherd, G. H. Booth, and A. Alavi, J. Chem. Phys. 136, 244101 (2012). 6 R. Needs, M. Towler, N. Drummond, and P. L. Ríos, J. Phys.: Condensed Matter 22, 023201 (2010).
An automated variance reduction method for global Monte Carlo neutral particle transport problems
NASA Astrophysics Data System (ADS)
Cooper, Marc Andrew
A method to automatically reduce the variance in global neutral particle Monte Carlo problems by using a weight window derived from a deterministic forward solution is presented. This method reduces a global measure of the variance of desired tallies and increases its associated figure of merit. Global deep penetration neutron transport problems present difficulties for analog Monte Carlo. When the scalar flux decreases by many orders of magnitude, so does the number of Monte Carlo particles. This can result in large statistical errors. In conjunction with survival biasing, a weight window is employed which uses splitting and Russian roulette to restrict the symbolic weights of Monte Carlo particles. By establishing a connection between the scalar flux and the weight window, two important concepts are demonstrated. First, such a weight window can be constructed from a deterministic solution of a forward transport problem. Also, the weight window will distribute Monte Carlo particles in such a way to minimize a measure of the global variance. For Implicit Monte Carlo solutions of radiative transfer problems, an inefficient distribution of Monte Carlo particles can result in large statistical errors in front of the Marshak wave and at its leading edge. Again, the global Monte Carlo method is used, which employs a time-dependent weight window derived from a forward deterministic solution. Here, the algorithm is modified to enhance the number of Monte Carlo particles in the wavefront. Simulations show that use of this time-dependent weight window significantly improves the Monte Carlo calculation.
MCDE: a new Monte Carlo dose engine for IMRT.
Reynaert, N; De Smedt, B; Coghe, M; Paelinck, L; Van Duyse, B; De Gersem, W; De Wagter, C; De Neve, W; Thierens, H
2004-07-21
A new accurate Monte Carlo code for IMRT dose computations, MCDE (Monte Carlo dose engine), is introduced. MCDE is based on BEAMnrc/DOSXYZnrc and consequently the accurate EGSnrc electron transport. DOSXYZnrc is reprogrammed as a component module for BEAMnrc. In this way both codes are interconnected elegantly, while maintaining the BEAM structure and only minimal changes to BEAMnrc.mortran are necessary. The treatment head of the Elekta SLiplus linear accelerator is modelled in detail. CT grids consisting of up to 200 slices of 512 x 512 voxels can be introduced and up to 100 beams can be handled simultaneously. The beams and CT data are imported from the treatment planning system GRATIS via a DICOM interface. To enable the handling of up to 50 x 10(6) voxels the system was programmed in Fortran95 to enable dynamic memory management. All region-dependent arrays (dose, statistics, transport arrays) were redefined. A scoring grid was introduced and superimposed on the geometry grid, to be able to limit the number of scoring voxels. The whole system uses approximately 200 MB of RAM and runs on a PC cluster consisting of 38 1.0 GHz processors. A set of in-house made scripts handle the parallellization and the centralization of the Monte Carlo calculations on a server. As an illustration of MCDE, a clinical example is discussed and compared with collapsed cone convolution calculations. At present, the system is still rather slow and is intended to be a tool for reliable verification of IMRT treatment planning in the case of the presence of tissue inhomogeneities such as air cavities. PMID:15357203
Parallel Monte Carlo Synthetic Acceleration methods for discrete transport problems
NASA Astrophysics Data System (ADS)
Slattery, Stuart R.
This work researches and develops Monte Carlo Synthetic Acceleration (MCSA) methods as a new class of solution techniques for discrete neutron transport and fluid flow problems. Monte Carlo Synthetic Acceleration methods use a traditional Monte Carlo process to approximate the solution to the discrete problem as a means of accelerating traditional fixed-point methods. To apply these methods to neutronics and fluid flow and determine the feasibility of these methods on modern hardware, three complementary research and development exercises are performed. First, solutions to the SPN discretization of the linear Boltzmann neutron transport equation are obtained using MCSA with a difficult criticality calculation for a light water reactor fuel assembly used as the driving problem. To enable MCSA as a solution technique a group of modern preconditioning strategies are researched. MCSA when compared to conventional Krylov methods demonstrated improved iterative performance over GMRES by converging in fewer iterations when using the same preconditioning. Second, solutions to the compressible Navier-Stokes equations were obtained by developing the Forward-Automated Newton-MCSA (FANM) method for nonlinear systems based on Newton's method. Three difficult fluid benchmark problems in both convective and driven flow regimes were used to drive the research and development of the method. For 8 out of 12 benchmark cases, it was found that FANM had better iterative performance than the Newton-Krylov method by converging the nonlinear residual in fewer linear solver iterations with the same preconditioning. Third, a new domain decomposed algorithm to parallelize MCSA aimed at leveraging leadership-class computing facilities was developed by utilizing parallel strategies from the radiation transport community. The new algorithm utilizes the Multiple-Set Overlapping-Domain strategy in an attempt to reduce parallel overhead and add a natural element of replication to the algorithm. It was found that for the current implementation of MCSA, both weak and strong scaling improved on that observed for production implementations of Krylov methods.
Anisotropic seismic inversion using a multigrid Monte Carlo approach
NASA Astrophysics Data System (ADS)
Mewes, Armin; Kulessa, Bernd; McKinley, John D.; Binley, Andrew M.
2010-10-01
We propose a new approach for the inversion of anisotropic P-wave data based on Monte Carlo methods combined with a multigrid approach. Simulated annealing facilitates objective minimization of the functional characterizing the misfit between observed and predicted traveltimes, as controlled by the Thomsen anisotropy parameters (ɛ, δ). Cycling between finer and coarser grids enhances the computational efficiency of the inversion process, thus accelerating the convergence of the solution while acting as a regularization technique of the inverse problem. Multigrid perturbation samples the probability density function without the requirements for the user to adjust tuning parameters. This increases the probability that the preferred global, rather than a poor local, minimum is attained. Undertaking multigrid refinement and Monte Carlo search in parallel produces more robust convergence than does the initially more intuitive approach of completing them sequentially. We demonstrate the usefulness of the new multigrid Monte Carlo (MGMC) scheme by applying it to (a) synthetic, noise-contaminated data reflecting an isotropic subsurface of constant slowness, horizontally layered geologic media and discrete subsurface anomalies; and (b) a crosshole seismic data set acquired by previous authors at the Reskajeage test site in Cornwall, UK. Inverted distributions of slowness (s) and the Thomson anisotropy parameters (ɛ, δ) compare favourably with those obtained previously using a popular matrix-based method. Reconstruction of the Thomsen ɛ parameter is particularly robust compared to that of slowness and the Thomsen δ parameter, even in the face of complex subsurface anomalies. The Thomsen ɛ and δ parameters have enhanced sensitivities to bulk-fabric and fracture-based anisotropies in the TI medium at Reskajeage. Because reconstruction of slowness (s) is intimately linked to that ɛ and δ in the MGMC scheme, inverted images of phase velocity reflect the integrated effects of these two modes of anisotropy. The new MGMC technique thus promises to facilitate rapid inversion of crosshole P-wave data for seismic slownesses and the Thomsen anisotropy parameters, with minimal user input in the inversion process.
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 combination of Generalized Valence Bond wavefunctions, improved correlation functions, and stabilized weighting techniques for calculations run on graphics cards, represents a new way for using Quantum Monte Carlo to study arbitrarily sized molecules.
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
2014-07-01
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 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. PMID:25005287
Monte Carlo simulation of energy spectra for (123)I imaging.
Tanaka, Minoru; Uehara, Shuzo; Kojima, Akihiro; Matsumoto, Masanori
2007-08-01
(123)I is a radionuclide frequently used in nuclear medicine imaging. The image formed by the 159 keV photopeak includes a considerable scatter component due to high energy gamma-ray emission. In order to evaluate the fraction of scattered photons, a Monte Carlo simulation of a scintillation camera used for (123)I imaging was undertaken. The Monte Carlo code consists of two modules, the HEXAGON code modelled the collimator with a complex hexagonal geometry and the NAI code modelled the NaI detector system including the back compartment. The simulation was carried out for various types of collimators under two separate conditions of the source locations in air and in water. Energy spectra of (123)I for every pixel (matrix size = 256 x 256) were obtained by separating the unscattered from the scattered and the penetrated photons. The calculated energy spectra (cps MBq(-1) keV(-1)) agreed with the measured spectra with approximately 20% deviations for three different collimators. The difference of the sensitivities (cps MBq(-1)) for the window of 143-175 keV was less than 10% between the simulation and the experiment. The partial sensitivities for the scattered and the unscattered components were obtained. The simulated fraction of the unscattered photons to the total photons were 0.46 for LEHR, 0.54 for LEGP and 0.90 for MEGP for the 'in air' set-up, and 0.35, 0.40 and 0.68 for the 'in water' set-up, respectively. The Monte Carlo simulation presented in this work enabled us to investigate the design of a new collimator optimum for (123)I scintigraphy. PMID:17634641
NOTE: MCDE: a new Monte Carlo dose engine for IMRT
NASA Astrophysics Data System (ADS)
Reynaert, N.; DeSmedt, B.; Coghe, M.; Paelinck, L.; Van Duyse, B.; DeGersem, W.; DeWagter, C.; DeNeve, W.; Thierens, H.
2004-07-01
A new accurate Monte Carlo code for IMRT dose computations, MCDE (Monte Carlo dose engine), is introduced. MCDE is based on BEAMnrc/DOSXYZnrc and consequently the accurate EGSnrc electron transport. DOSXYZnrc is reprogrammed as a component module for BEAMnrc. In this way both codes are interconnected elegantly, while maintaining the BEAM structure and only minimal changes to BEAMnrc.mortran are necessary. The treatment head of the Elekta SLiplus linear accelerator is modelled in detail. CT grids consisting of up to 200 slices of 512 × 512 voxels can be introduced and up to 100 beams can be handled simultaneously. The beams and CT data are imported from the treatment planning system GRATIS via a DICOM interface. To enable the handling of up to 50 × 106 voxels the system was programmed in Fortran95 to enable dynamic memory management. All region-dependent arrays (dose, statistics, transport arrays) were redefined. A scoring grid was introduced and superimposed on the geometry grid, to be able to limit the number of scoring voxels. The whole system uses approximately 200 MB of RAM and runs on a PC cluster consisting of 38 1.0 GHz processors. A set of in-house made scripts handle the parallellization and the centralization of the Monte Carlo calculations on a server. As an illustration of MCDE, a clinical example is discussed and compared with collapsed cone convolution calculations. At present, the system is still rather slow and is intended to be a tool for reliable verification of IMRT treatment planning in the case of the presence of tissue inhomogeneities such as air cavities.
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.
Coupled Monte Carlo neutronics and thermal hydraulics for power reactors
Bernnat, W.; Buck, M.; Mattes, M.; Zwermann, W.; Pasichnyk, I.; Velkov, K.
2012-07-01
The availability of high performance computing resources enables more and more the use of detailed Monte Carlo models even for full core power reactors. The detailed structure of the core can be described by lattices, modeled by so-called repeated structures e.g. in Monte Carlo codes such as MCNP5 or MCNPX. For cores with mainly uniform material compositions, fuel and moderator temperatures, there is no problem in constructing core models. However, when the material composition and the temperatures vary strongly a huge number of different material cells must be described which complicate the input and in many cases exceed code or memory limits. The second problem arises with the preparation of corresponding temperature dependent cross sections and thermal scattering laws. Only if these problems can be solved, a realistic coupling of Monte Carlo neutronics with an appropriate thermal-hydraulics model is possible. In this paper a method for the treatment of detailed material and temperature distributions in MCNP5 is described based on user-specified internal functions which assign distinct elements of the core cells to material specifications (e.g. water density) and temperatures from a thermal-hydraulics code. The core grid itself can be described with a uniform material specification. The temperature dependency of cross sections and thermal neutron scattering laws is taken into account by interpolation, requiring only a limited number of data sets generated for different temperatures. Applications will be shown for the stationary part of the Purdue PWR benchmark using ATHLET for thermal- hydraulics and for a generic Modular High Temperature reactor using THERMIX for thermal- hydraulics. (authors)
CSnrc: Correlated sampling Monte Carlo calculations using EGSnrc
Buckley, Lesley A.; Kawrakow, I.; Rogers, D.W.O.
2004-12-01
CSnrc, a new user-code for the EGSnrc Monte Carlo system is described. This user-code improves the efficiency when calculating ratios of doses from similar geometries. It uses a correlated sampling variance reduction technique. CSnrc is developed from an existing EGSnrc user-code CAVRZnrc and improves upon the correlated sampling algorithm used in an earlier version of the code written for the EGS4 Monte Carlo system. Improvements over the EGS4 version of the algorithm avoid repetition of sections of particle tracks. The new code includes a rectangular phantom geometry not available in other EGSnrc cylindrical codes. Comparison to CAVRZnrc shows gains in efficiency of up to a factor of 64 for a variety of test geometries when computing the ratio of doses to the cavity for two geometries. CSnrc is well suited to in-phantom calculations and is used to calculate the central electrode correction factor P{sub cel} in high-energy photon and electron beams. Current dosimetry protocols base the value of P{sub cel} on earlier Monte Carlo calculations. The current CSnrc calculations achieve 0.02% statistical uncertainties on P{sub cel}, much lower than those previously published. The current values of P{sub cel} compare well with the values used in dosimetry protocols for photon beams. For electrons beams, CSnrc calculations are reported at the reference depth used in recent protocols and show up to a 0.2% correction for a graphite electrode, a correction currently ignored by dosimetry protocols. The calculations show that for a 1 mm diameter aluminum central electrode, the correction factor differs somewhat from the values used in both the IAEA TRS-398 code of practice and the AAPM's TG-51 protocol.
PREFACE: First European Workshop on Monte Carlo Treatment Planning
NASA Astrophysics Data System (ADS)
Reynaert, Nick
2007-07-01
The "First European Workshop on Monte Carlo treatment planning", was an initiative of the European working group on Monte Carlo treatment planning (EWG-MCTP). It was organised at Ghent University (Belgium) on 22-25October 2006. The meeting was very successful and was attended by 150 participants. The impressive list of invited speakers and the scientific contributions (posters and oral presentations) have led to a very interesting program, that was well appreciated by all attendants. In addition, the presence of seven vendors of commercial MCTP software systems provided serious added value to the workshop. For each vendor, a representative has given a presentation in a dedicated session, explaining the current status of their system. It is clear that, for "traditional" radiotherapy applications (using photon or electron beams), Monte Carlo dose calculations have become the state of the art, and are being introduced into almost all commercial treatment planning systems. Invited lectures illustrated that scientific challenges are currently associated with 4D applications (e.g. respiratory motion) and the introduction of MC dose calculations in inverse planning. But it was striking that the Monte Carlo technique is also becoming very important in more novel treatment modalities such as BNCT, hadron therapy, stereotactic radiosurgery, Tomotherapy, etc. This emphasizes the continuous growing interest in MCTP. The people who attended the dosimetry session will certainly remember the high level discussion on the determination of correction factors for different ion chambers, used in small fields. The following proceedings will certainly confirm the high scientific level of the meeting. I would like to thank the members of the local organizing committee for all the hard work done before, during and after this meeting. The organisation of such an event is not a trivial task and it would not have been possible without the help of all my colleagues. I would also like to thank the European working group on MCTP (who formed the scientific committee of the workshop) for all their assistance, especially, concerning the evaluation of the abstracts and the reviewing of the current proceedings. I would also like to thank the sponsors, who really made this possible and who also elevated the level of the workshop. Presentations, poster files and photos are available on http://www.EWG-MCTP.ugent.be. Nick Reynaert Editor
A Post-Monte-Carlo Sensitivity Analysis Code
Energy Science and Technology Software Center (ESTSC)
2000-04-04
SATOOL (Sensitivity Analysis TOOL) is a code for sensitivity analysis, following an uncertainity analysis with Monte Carlo simulations. Sensitivity analysis identifies those input variables, whose variance contributes dominatly to the variance in the output. This analysis can be used to reduce the variance in the output variables by redefining the "sensitive" variables with greater precision, i.e. with lower variance. The code identifies a group of sensitive variables, ranks them in the order of importance andmore » also quantifies the relative importance among the sensitive variables.« less
Variance reduction in Monte Carlo analysis of rarefied gas diffusion
NASA Technical Reports Server (NTRS)
Perlmutter, M.
1972-01-01
The present analysis uses the Monte Carlo method to solve the problem of rarefied diffusion between parallel walls. The diffusing molecules are evaporated or emitted from one of two parallel walls and diffused through another molecular species. The analysis treats the diffusing molecule as undergoing a Markov random walk and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs the expected Markov walk payoff is retained but its variance is reduced so that the M. C. result has a much smaller error.
Monte Carlo simulation of the Neutrino-4 experiment
Serebrov, A. P. Fomin, A. K.; Onegin, M. S.; Ivochkin, V. G.; Matrosov, L. N.
2015-12-15
Monte Carlo simulation of the two-section reactor antineutrino detector of the Neutrino-4 experiment is carried out. The scintillation-type detector is based on the inverse beta-decay reaction. The antineutrino is recorded by two successive signals from the positron and the neutron. The simulation of the detector sections and the active shielding is performed. As a result of the simulation, the distributions of photomultiplier signals from the positron and the neutron are obtained. The efficiency of the detector depending on the signal recording thresholds is calculated.
Monte Carlo simulations of charge transport in heterogeneous organic semiconductors
NASA Astrophysics Data System (ADS)
Aung, Pyie Phyo; Khanal, Kiran; Luettmer-Strathmann, Jutta
2015-03-01
The efficiency of organic solar cells depends on the morphology and electronic properties of the active layer. Research teams have been experimenting with different conducting materials to achieve more efficient solar panels. In this work, we perform Monte Carlo simulations to study charge transport in heterogeneous materials. We have developed a coarse-grained lattice model of polymeric photovoltaics and use it to generate active layers with ordered and disordered regions. We determine carrier mobilities for a range of conditions to investigate the effect of the morphology on charge transport.
Active neutron multiplicity analysis and Monte Carlo calculations
Krick, M.S.; Ensslin, N.; Langner, D.G.; Miller, M.C.; Siebelist, R.; Stewart, J.E.; Ceo, R.N.; May, P.K.; Collins, L.L. Jr
1994-08-01
Active neutron multiplicity measurements of high-enrichment uranium metal and oxide samples have been made at Los Alamos and Y-12. The data from the measurements of standards at Los Alamos were analyzed to obtain values for neutron multiplication and source-sample coupling. These results are compared to equivalent results obtained from Monte Carlo calculations. An approximate relationship between coupling and multiplication is derived and used to correct doubles rates for multiplication and coupling. The utility of singles counting for uranium samples is also examined.
Monte Carlo Simulations and Generation of the SPI Response
NASA Technical Reports Server (NTRS)
Sturner, S. J.; Shrader, C. R.; Weidenspointner, G.; Teegarden, B. J.; Attie, D.; Cordier, B.; Diehl, R.; Ferguson, C.; Jean, P.; vonKienlin, A.
2003-01-01
In this paper we discuss the methods developed for the production of the INTEGRAL/SPI instrument response. The response files were produced using a suite of Monte Carlo simulation software developed at NASA/GSFC based on the GEANT-3 package available from CERN. The production of the INTEGRAL/SPI instrument response also required the development of a detailed computer mass model for SPI. We discuss ow extensive investigations into methods to reduce both the computation time and storage requirements for the SPI response. We also discuss corrections to the simulated response based on our comparison of ground and infiight Calibration data with MGEANT simulations.
Monte Carlo Simulations and Generation of the SPI Response
NASA Technical Reports Server (NTRS)
Sturner, S. J.; Shrader, C. R.; Weidenspointner, G.; Teegarden, B. J.; Attie, D.; Diehl, R.; Ferguson, C.; Jean, P.; vonKienlin, A.
2003-01-01
In this paper we discuss the methods developed for the production of the INTEGRAL/SPI instrument response. The response files were produced using a suite of Monte Carlo simulation software developed at NASA/GSFC based on the GEANT-3 package available from CERN. The production of the INTEGRAL/SPI instrument response also required the development of a detailed computer mass model for SPI. We discuss our extensive investigations into methods to reduce both the computation time and storage requirements for the SPI response. We also discuss corrections to the simulated response based on our comparison of ground and inflight calibration data with MGEANT simulation.
Monte Carlo simulation for neutrino detection from Minna Bluff, Antarctica
NASA Astrophysics Data System (ADS)
Barrella, Taylor; Vieregg, Abigail; Saltzberg, David
2012-03-01
We present a simple Monte Carlo simulation for a possible neutrino detection experiment. The detector would be composed of an array of radio antennas on Minna Bluff, Antarctica, designed to detect Cherenkov radiation from ultra-high-energy neutrinos. The simulation generates neutrino interactions in the Ross Ice Shelf below the antennas to determine the expected number of detected events per year. Though the results predict less than one event per year, the detection of tau neutrinos should increase the event rate for detectors embedded in the ice.
Positronic molecule calculations using Monte Carlo configuration interaction
NASA Astrophysics Data System (ADS)
Coe, Jeremy P.; Paterson, Martin J.
2016-02-01
We modify the Monte Carlo configuration interaction procedure to model atoms and molecules combined with a positron. We test this method with standard quantum chemistry basis sets on a number of positronic systems and compare results with the literature and full configuration interaction when appropriate. We consider positronium hydride, positronium hydroxide, lithium positride and a positron interacting with lithium, magnesium or lithium hydride. We demonstrate that we can capture much of the full configuration interaction results, but often require less than 10% of the configurations of these multireference wavefunctions. The effect of the number of frozen orbitals is also discussed.
Element Agglomeration Algebraic Multilevel Monte-Carlo Library
Energy Science and Technology Software Center (ESTSC)
2015-02-19
ElagMC is a parallel C++ library for Multilevel Monte Carlo simulations with algebraically constructed coarse spaces. ElagMC enables Multilevel variance reduction techniques in the context of general unstructured meshes by using the specialized element-based agglomeration techniques implemented in ELAG (the Element-Agglomeration Algebraic Multigrid and Upscaling Library developed by U. Villa and P. Vassilevski and currently under review for public release). The ElabMC library can support different type of deterministic problems, including mixed finite element discretizationsmore » of subsurface flow problems.« less
Novel extrapolation method in the Monte Carlo shell model
Shimizu, Noritaka; Abe, Takashi; Utsuno, Yutaka; Mizusaki, Takahiro; Otsuka, Takaharu; Honma, Michio
2010-12-15
We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater determinants, which enables us to calculate the energy variance efficiently. The feasibility of the method is demonstrated for the full pf-shell calculation of {sup 56}Ni, and the applicability of the method to a system beyond the current limit of exact diagonalization is shown for the pf+g{sub 9/2}-shell calculation of {sup 64}Ge.
Morphological evolution of growing crystals - A Monte Carlo simulation
NASA Technical Reports Server (NTRS)
Xiao, Rong-Fu; Alexander, J. Iwan D.; Rosenberger, Franz
1988-01-01
The combined effects of nutrient diffusion and surface kinetics on the crystal morphology were investigated using a Monte Carlo model to simulate the evolving morphology of a crystal growing from a two-component gaseous nutrient phase. The model combines nutrient diffusion, based on a modified diffusion-limited aggregation process, with anisotropic surface-attachment kinetics and surface diffusion. A variety of conditions, ranging from kinetic-controlled to diffusion-controlled growth, were examined. Successive transitions from compact faceted (dominant surface kinetics) to open dendritic morphologies (dominant volume diffusion) were obtained.
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.
Studying the information content of TMDs using Monte Carlo generators
Avakian, H.; Matevosyan, H.; Pasquini, B.; Schweitzer, P.
2015-02-05
Theoretical advances in studies of the nucleon structure have been spurred by recent measurements of spin and/or azimuthal asymmetries worldwide. One of the main challenges still remaining is the extraction of the parton distribution functions, generalized to describe transverse momentum and spatial distributions of partons from these observables with no or minimal model dependence. In this topical review we present the latest developments in the field with emphasis on requirements for Monte Carlo event generators, indispensable for studies of the complex 3D nucleon structure, and discuss examples of possible applications.
Quasicontinuum Monte Carlo: A method for surface growth simulations
NASA Astrophysics Data System (ADS)
Russo, G.; Sander, L. M.; Smereka, P.
2004-03-01
We introduce an algorithm for treating growth on surfaces which combines important features of continuum methods (such as the level-set method) and kinetic Monte Carlo (KMC) simulations. We treat the motion of adatoms in continuum theory, but attach them to islands one atom at a time. The technique is borrowed from the dielectric breakdown model. Our method allows us to give a realistic account of fluctuations in island shape, which is lacking in deterministic continuum treatments and which is an important physical effect. Our method should be most important for problems close to equilibrium where KMC becomes impractically slow.
Anisotropic flows from colour strings: Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Braun, M. A.; Pajares, C.; Vechernin, V. V.
2013-05-01
By direct Monte Carlo simulations it is shown that the anisotropic flows can be successfully described in the colour string picture with fusion and percolation provided anisotropy of particle emission from the fused string is taken into account. Quenching of produced particles in the strong colour field of the string is the basic mechanism for this anisotropy. The concrete realization of this mechanism is borrowed from the QED. Due to dependence of this mechanism on the external field strength the found flows grow with energy, with values for v2 at LHC energies greater by 15% than at RHIC energies.
Analysis and Monte Carlo simulation of luminescent solar concentrators
Heinaemaeki, A.
1985-01-01
In the study the applicability of inorganic materials for luminescent solar concentrators (LSCs) is investigated. The materials as well as the physical processes related to absorption and fluorescence are expounded and some examples of materials possibly suitable for LSCs are given. The operation of an LSC and the possible loss sources are considered in detail. Several efficiencies are defined and discussed. The Monte Carlo method is used in simulating the LSC performance to compare various LSCs and to study how the plate size, shape, and dye concentration affect the efficiencies.
Evaluation of adsorbed dose in mammography: Monte Carlo simulation studies
Doi, K.; Chan, H.P.
1980-04-01
Computer programs for calculation of the backscatter factor and absorbed dose in breast phantoms are developed based on Monte Carlo simulation. Rad/roentgen conversion factors are calculated for water, fat, a mixture of 50% water and 50% fat, and lucite irradiated with monoenergetic and polyenergetic x rays from a tungsten or molybdenum anode x-ray tube. These factors can be used to estimate skin dose, average depth dose, or average inegral dose in a breast when the beam quality, exposure in air at the skin position, and composition of the breast are known. Calculated backscatter factors are considerably greater than measured values reported previously.
Monte Carlo simulation of a noisy quantum channel with memory
NASA Astrophysics Data System (ADS)
Akhalwaya, Ismail; Moodley, Mervlyn; Petruccione, Francesco
2015-10-01
The classical capacity of quantum channels is well understood for channels with uncorrelated noise. For the case of correlated noise, however, there are still open questions. We calculate the classical capacity of a forgetful channel constructed by Markov switching between two depolarizing channels. Techniques have previously been applied to approximate the output entropy of this channel and thus its capacity. In this paper, we use a Metropolis-Hastings Monte Carlo approach to numerically calculate the entropy. The algorithm is implemented in parallel and its performance is studied and optimized. The effects of memory on the capacity are explored and previous results are confirmed to higher precision.
Communication: Water on hexagonal boron nitride from diffusion Monte Carlo
Al-Hamdani, Yasmine S.; Ma, Ming; Michaelides, Angelos; Alfè, Dario; Lilienfeld, O. Anatole von
2015-05-14
Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of −84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT.
Parallel kinetic Monte Carlo simulation of Coulomb glasses
NASA Astrophysics Data System (ADS)
Ferrero, E. E.; Kolton, A. B.; Palassini, M.
2014-08-01
We develop a parallel rejection algorithm to tackle the problem of low acceptance in Monte Carlo methods, and apply it to the simulation of the hopping conduction in Coulomb glasses using Graphics Processing Units, for which we also parallelize the update of local energies. In two dimensions, our parallel code achieves speedups of up to two orders of magnitude in computing time over an equivalent serial code. We find numerical evidence of a scaling relation for the relaxation of the conductivity at different temperatures.
Neutronic calculations for CANDU thorium systems using Monte Carlo techniques
NASA Astrophysics Data System (ADS)
Saldideh, M.; Shayesteh, M.; Eshghi, M.
2014-08-01
In this paper, we have investigated the prospects of exploiting the rich world thorium reserves using Canada Deuterium Uranium (CANDU) reactors. The analysis is performed using the Monte Carlo MCNP code in order to understand how much time the reactor is in criticality conduction. Four different fuel compositions have been selected for analysis. We have obtained the infinite multiplication factor, k∞, under full power operation of the reactor over 8 years. The neutronic flux distribution in the full core reactor has already been investigated.
Nonlinear panel response by a Monte Carlo approach
NASA Technical Reports Server (NTRS)
Vaicaitis, R.; Dowell, E. H.; Ventres, C. S.
1974-01-01
The vibration of clamped and simply supported elastic panels due to subsonic and supersonic turbulent boundary-layer flows is investigated by a Monte Carlo technique. The resulting generalized random forces are simulated numerically from boundary-layer turbulence spectra, and the response analysis is performed in the time domain. The mutual interaction between panel motion and external and/or internal airflow is included. Response studies are performed with respect to rms response, probability structure, peak distribution, threshold crossing and spectral density. The effect on the response statistics of in-plane loading, static pressure differential, and cavity pressure is investigated.
More about Zener drag studies with Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Di Prinzio, Carlos L.; Druetta, Esteban; Nasello, Olga Beatriz
2013-03-01
Grain growth (GG) processes in the presence of second-phase and stationary particles have been widely studied but the results found are inconsistent. We present new GG simulations in two- and three-dimensional (2D and 3D) polycrystalline samples with second phase stationary particles, using the Monte Carlo technique. Simulations using values of particle concentration greater than 15% and particle radii different from 1 or 3 are performed, thus covering a range of particle radii and concentrations not previously studied. It is shown that only the results for 3D samples follow Zener's law.
Monte Carlo simulation of reentry flows with ionization
NASA Technical Reports Server (NTRS)
Taylor, Jeff C.; Carlson, Ann B.; Hassan, H. A.
1992-01-01
The Direct Simulation Monte Carlo method is applied to a rarefied, weakly ionized, hypersonic flow over a blunt axisymmetric body. An ionization model based on the concept of ambipolar diffusion is used and a model for the sheath is presented. The effects of the new modeling techniques are investigated for flow over the Project Fire II configuration at 11.37 km/s at an altitude of 84.6 km. The calculated results are presented and compared with both experimental data and solutions where ionization effects were not included. In general, the calculated results overpredict the experimental values by about 15-20 percent.
Monte Carlo simulation of nonadiabatic expansion in cometary atmospheres - Halley
Hodges, R.R. Jr. )
1990-02-01
Monte Carlo methods developed for the characterization of velocity-dependent collision processes and ballistic transports in planetary exospheres form the basis of the present computer simulation of icy comet atmospheres, which iteratively undertakes the simultaneous determination of velocity distribution for five neutral species (water, together with suprathermal OH, H2, O, and H) in a flow regime varying from the hydrodynamic to the ballistic. Experimental data from the neutral mass spectrometer carried by Giotto for its March, 1986 encounter with Halley are compared with a model atmosphere. 31 refs.
Communication: Water on hexagonal boron nitride from diffusion Monte Carlo
NASA Astrophysics Data System (ADS)
Al-Hamdani, Yasmine S.; Ma, Ming; Alfè, Dario; von Lilienfeld, O. Anatole; Michaelides, Angelos
2015-05-01
Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here, we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of -84 ± 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT.
Computational radiology and imaging with the MCNP Monte Carlo code
Estes, G.P.; Taylor, W.M.
1995-05-01
MCNP, a 3D coupled neutron/photon/electron Monte Carlo radiation transport code, is currently used in medical applications such as cancer radiation treatment planning, interpretation of diagnostic radiation images, and treatment beam optimization. This paper will discuss MCNP`s current uses and capabilities, as well as envisioned improvements that would further enhance MCNP role in computational medicine. It will be demonstrated that the methodology exists to simulate medical images (e.g. SPECT). Techniques will be discussed that would enable the construction of 3D computational geometry models of individual patients for use in patient-specific studies that would improve the quality of care for patients.
MONTE CARLO ADVANCES FOR THE EOLUS ASCI PROJECT
J. S. HENDRICK; G. W. MCKINNEY; L. J. COX
2000-01-01
The Eolus ASCI project includes parallel, 3-D transport simulation for various nuclear applications. The codes developed within this project provide neutral and charged particle transport, detailed interaction physics, numerous source and tally capabilities, and general geometry packages. One such code is MCNPW which is a general purpose, 3-dimensional, time-dependent, continuous-energy Monte Carlo fully-coupled N-Particle transport code. Significant advances are also being made in the areas of modern software engineering and parallel computing. These advances are described in detail.
Quantum Monte Carlo calculation of reduced density matrices
NASA Astrophysics Data System (ADS)
Wagner, Lucas
2012-02-01
Quantum Monte Carlo(QMC) methods offer an efficient way to approximate the interacting ground state and some excited states of realistic model Hamiltonians based on the fundamental Coulomb interaction between electrons and nuclei. Many highly accurate results have been obtained using this method; however, it is often a challenge to extract the important correlations that the QMC wave function contains. I will describe some new results using the reduced density matrices(RDM's) to understand the electron correlation in the many-body wave function. The RDM's have both informative usage for describing correlation and pragmatic uses in further improving the variational wave function.
Monte Carlo beam capture and charge breeding simulation
Kim, J.S.; Liu, C.; Edgell, D.H.; Pardo, R.
2006-03-15
A full six-dimensional (6D) phase space Monte Carlo beam capture charge-breeding simulation code examines the beam capture processes of singly charged ion beams injected to an electron cyclotron resonance (ECR) charge breeder from entry to exit. The code traces injected beam ions in an ECR ion source (ECRIS) plasma including Coulomb collisions, ionization, and charge exchange. The background ECRIS plasma is modeled within the current frame work of the generalized ECR ion source model. A simple sample case of an oxygen background plasma with an injected Ar +1 ion beam produces lower charge breeding efficiencies than experimentally obtained. Possible reasons for discrepancies are discussed.
Application of Monte Carlo methods in tomotherapy and radiation biophysics
NASA Astrophysics Data System (ADS)
Hsiao, Ya-Yun
Helical tomotherapy is an attractive treatment for cancer therapy because highly conformal dose distributions can be achieved while the on-board megavoltage CT provides simultaneous images for accurate patient positioning. The convolution/superposition (C/S) dose calculation methods typically used for Tomotherapy treatment planning may overestimate skin (superficial) doses by 3-13%. Although more accurate than C/S methods, Monte Carlo (MC) simulations are too slow for routine clinical treatment planning. However, the computational requirements of MC can be reduced by developing a source model for the parts of the accelerator that do not change from patient to patient. This source model then becomes the starting point for additional simulations of the penetration of radiation through patient. In the first section of this dissertation, a source model for a helical tomotherapy is constructed by condensing information from MC simulations into series of analytical formulas. The MC calculated percentage depth dose and beam profiles computed using the source model agree within 2% of measurements for a wide range of field sizes, which suggests that the proposed source model provides an adequate representation of the tomotherapy head for dose calculations. Monte Carlo methods are a versatile technique for simulating many physical, chemical and biological processes. In the second major of this thesis, a new methodology is developed to simulate of the induction of DNA damage by low-energy photons. First, the PENELOPE Monte Carlo radiation transport code is used to estimate the spectrum of initial electrons produced by photons. The initial spectrum of electrons are then combined with DNA damage yields for monoenergetic electrons from the fast Monte Carlo damage simulation (MCDS) developed earlier by Semenenko and Stewart (Purdue University). Single- and double-strand break yields predicted by the proposed methodology are in good agreement (1%) with the results of published experimental and theoretical studies for 60Co gamma-rays and low-energy x-rays. The reported studies provide new information about the potential biological consequences of diagnostic x-rays and selected gamma-emitting radioisotopes used in brachytherapy for the treatment of cancer. The proposed methodology is computationally efficient and may also be useful in proton therapy, space applications or internal dosimetry.
3D Monte Carlo radiation transfer modelling of photodynamic therapy
NASA Astrophysics Data System (ADS)
Campbell, C. Louise; Christison, Craig; Brown, C. Tom A.; Wood, Kenneth; Valentine, Ronan M.; Moseley, Harry
2015-06-01
The effects of ageing and skin type on Photodynamic Therapy (PDT) for different treatment methods have been theoretically investigated. A multilayered Monte Carlo Radiation Transfer model is presented where both daylight activated PDT and conventional PDT are compared. It was found that light penetrates deeper through older skin with a lighter complexion, which translates into a deeper effective treatment depth. The effect of ageing was found to be larger for darker skin types. The investigation further strengthens the usage of daylight as a potential light source for PDT where effective treatment depths of about 2 mm can be achieved.
Monte Carlo simulation of a noisy quantum channel with memory.
Akhalwaya, Ismail; Moodley, Mervlyn; Petruccione, Francesco
2015-10-01
The classical capacity of quantum channels is well understood for channels with uncorrelated noise. For the case of correlated noise, however, there are still open questions. We calculate the classical capacity of a forgetful channel constructed by Markov switching between two depolarizing channels. Techniques have previously been applied to approximate the output entropy of this channel and thus its capacity. In this paper, we use a Metropolis-Hastings Monte Carlo approach to numerically calculate the entropy. The algorithm is implemented in parallel and its performance is studied and optimized. The effects of memory on the capacity are explored and previous results are confirmed to higher precision. PMID:26565361
AVATAR -- Automatic variance reduction in Monte Carlo calculations
Van Riper, K.A.; Urbatsch, T.J.; Soran, P.D.
1997-05-01
AVATAR{trademark} (Automatic Variance And Time of Analysis Reduction), accessed through the graphical user interface application, Justine{trademark}, is a superset of MCNP{trademark} that automatically invokes THREEDANT{trademark} for a three-dimensional deterministic adjoint calculation on a mesh independent of the Monte Carlo geometry, calculates weight windows, and runs MCNP. Computational efficiency increases by a factor of 2 to 5 for a three-detector oil well logging tool model. Human efficiency increases dramatically, since AVATAR eliminates the need for deep intuition and hours of tedious handwork.
Quantum Monte Carlo Simulation of Overpressurized Liquid {sup 4}He
Vranjes, L.; Boronat, J.; Casulleras, J.; Cazorla, C.
2005-09-30
A diffusion Monte Carlo simulation of superfluid {sup 4}He at zero temperature and pressures up to 275 bar is presented. Increasing the pressure beyond freezing ({approx}25 bar), the liquid enters the overpressurized phase in a metastable state. In this regime, we report results of the equation of state and the pressure dependence of the static structure factor, the condensate fraction, and the excited-state energy corresponding to the roton. Along this large pressure range, both the condensate fraction and the roton energy decrease but do not become zero. The roton energies obtained are compared with recent experimental data in the overpressurized regime.
Monte Carlo analysis of an interatomic potential for He
Boronat, J.; Casulleras, J. )
1994-04-01
By means of a quadratic diffusion Monte Carlo method we have performed a comparative analysis between the Aziz potential and a revised version of it. The results demonstrate that the revised version produces a better description of the equation of state for liquid [sup 4]He. In spite of the improvement in the description of derivative magnitudes of the energy, as the pressure or the compressibility, the energy per particle which comes from this revised potential is lower than the experimental one. The inclusion of three-body interactions, which give a repulsive contribution to the potential energy, makes it feasible that the calculated energy comes close to the experimental result.
Monte Carlo simulations of scattered power from irradiated optical elements
NASA Astrophysics Data System (ADS)
Secco, Eleonora; Sánchez del Río, Manuel
2011-09-01
A computer tool for the evaluation of the absorbed and re-scattered power from optical elements in a synchrotron beamline has been written using the Monte Carlo package PENELOPE. A precise estimation of this power is needed to assist in the design of the shielding inside the optical chambers that receive high power, like for the Upgrade Programme at the ESRF. The results for scattered power calculation are presented for three cases i) a Glidcop mirror for the SESAME Synchrotron, ii) a silicon crystal in use at the ESRF beamline ID06, and iii) a Laue crystal for the new monochromator of the ESRF ID17 beamline.
Monte Carlo simulation of vibrational relaxation in nitrogen
NASA Technical Reports Server (NTRS)
Olynick, David P.; Hassan, H. A.; Moss, James N.
1990-01-01
Monte Carlo simulation of nonequilibrium vibrational relaxation of (rotationless) N2 using transition probabilities form an extended SSH theory is presented. For the range of temperatures considered, 4000-8000 K, the vibrational levels were found to be reasonably close to an equilibrium distribution at an average vibrational temperature based on the vibrational energy of the gas. As a result, they do not show any statistically significant evidence of the bottleneck observed in earlier studies of N2. Based on this finding, it appears that, for the temperature range considered, dissociation commences after all vibrational levels equilibrate at the translational temperature.
Monte-Carlo histories of refractory interstellar dust
NASA Technical Reports Server (NTRS)
Clayton, D. D.; Liffman, K.
1988-01-01
Monte-carlo histories of 6 x 10 to the 6th individual dust particles injected uniformly from stars into the interstellar medium during a 6 x 10 to the 9th year history are calculated. The particles are given a two-phase internal structure of successive thermal condensates, and are distributed in initial radius as 1/a-cubed over the value of a between 0.01 and 0.1 micron. The evolution of this system illustrates the distinction between several different lifetimes for interstellar dust. Most are destroyed, but some grow in size. Several important consequences for interstellar dust are described.
Calibration of the Top-Quark Monte Carlo Mass
NASA Astrophysics Data System (ADS)
Kieseler, Jan; Lipka, Katerina; Moch, Sven-Olaf
2016-04-01
We present a method to establish, experimentally, the relation between the top-quark mass mtMC as implemented in Monte Carlo generators and the Lagrangian mass parameter mt in a theoretically well-defined renormalization scheme. We propose a simultaneous fit of mtMC and an observable sensitive to mt, which does not rely on any prior assumptions about the relation between mt and mtMC. The measured observable is independent of mtMC and can be used subsequently for a determination of mt. The analysis strategy is illustrated with examples for the extraction of mt from inclusive and differential cross sections for hadroproduction of top quarks.
Element Agglomeration Algebraic Multilevel Monte-Carlo Library
2015-02-19
ElagMC is a parallel C++ library for Multilevel Monte Carlo simulations with algebraically constructed coarse spaces. ElagMC enables Multilevel variance reduction techniques in the context of general unstructured meshes by using the specialized element-based agglomeration techniques implemented in ELAG (the Element-Agglomeration Algebraic Multigrid and Upscaling Library developed by U. Villa and P. Vassilevski and currently under review for public release). The ElabMC library can support different type of deterministic problems, including mixed finite element discretizations of subsurface flow problems.
Bounded limit for the Monte Carlo point-flux-estimator
Grimesey, R.A.
1981-01-01
In a Monte Carlo random walk the kernel K(R,E) is used as an expected value estimator at every collision for the collided flux phi/sub c/ r vector,E) at the detector point. A limiting value for the kernel is derived from a diffusion approximation for the probability current at a radius R/sub 1/ from the detector point. The variance of the collided flux at the detector point is thus bounded using this asymptotic form for K(R,E). The bounded point flux estimator is derived. (WHK)
A generalized hard-sphere model for Monte Carlo simulation
NASA Technical Reports Server (NTRS)
Hassan, H. A.; Hash, David B.
1993-01-01
A new molecular model, called the generalized hard-sphere, or GHS model, is introduced. This model contains, as a special case, the variable hard-sphere model of Bird (1981) and is capable of reproducing all of the analytic viscosity coefficients available in the literature that are derived for a variety of interaction potentials incorporating attraction and repulsion. In addition, a new procedure for determining interaction potentials in a gas mixture is outlined. Expressions needed for implementing the new model in the direct simulation Monte Carlo methods are derived. This development makes it possible to employ interaction models that have the same level of complexity as used in Navier-Stokes calculations.
Monte Carlo approaches to the few-nucleon continuum
Schiavilla, R. |; Carlson, J.; Wiringa, R.B.
1994-08-01
Variational and Green`s Function Monte Carlo methods are reviewed as applied to the study of the few-nucleon continuum at low- and intermediate-energies. Results recently obtained for the radiative and weak capture reactions n + {sup 3}He {yields} {sup 4}He + {gamma} and p + {sup 3}He {yields} {sup 4}He + e{sup +} + {nu}{sub e}, the {sup 5}He P-wave resonances, and the inclusive and exclusive electron scattering reactions on {sup 3}H and the helium isotopes are summarized.
On the efficiency of algorithms of Monte Carlo methods
NASA Astrophysics Data System (ADS)
Budak, V. P.; Zheltov, V. S.; Lubenchenko, A. V.; Shagalov, O. V.
2015-11-01
A numerical comparison of algorithms for solving the radiative transfer equation by the Monte-Carlo method is performed for the direct simulation and local estimations. The problems of radiative transfer through a turbid medium slab in the scalar and vector case is considered. The case of reflections from the boundaries of the medium is analyzed. The calculations are performed in a wide variation of parameters of the medium. It is shown that the calculation time with the same accuracy for the local estimation method is less than one - two orders of magnitude.
Continuous-Estimator Representation for Monte Carlo Criticality Diagnostics
Kiedrowski, Brian C.; Brown, Forrest B.
2012-06-18
An alternate means of computing diagnostics for Monte Carlo criticality calculations is proposed. Overlapping spherical regions or estimators are placed covering the fissile material with a minimum center-to-center separation of the 'fission distance', which is defined herein, and a radius that is some multiple thereof. Fission neutron production is recorded based upon a weighted average of proximities to centers for all the spherical estimators. These scores are used to compute the Shannon entropy, and shown to reproduce the value, to within an additive constant, determined from a well-placed mesh by a user. The spherical estimators are also used to assess statistical coverage.
Monte Carlo Simulations of Thermal Conductivity in Nanoporous Si Membranes
NASA Astrophysics Data System (ADS)
Wolf, Stefanie; Neophytou, Neophytos; Stanojevic, Zlatan; Kosina, Hans
2014-10-01
We present a Monte Carlo study of heat transport in Si nanomeshes. Phonons are treated semiclassically as particles of specific energy and velocity that undergo phonon-phonon scattering and boundary scattering on the surfaces of the nanomesh pores. We investigate the influence of: (1) geometric parameters such as the pore arrangement/randomness and porosity, and (2) the roughness amplitude of the pore surfaces on the thermal conductivity of the nanomeshes. We show that the nanomesh porosity has a strong detrimental influence on the thermal conductivity. Boundary roughness still degrades the thermal conductivity, but its influence is smaller.
Monte Carlo simulation of cavitation in pores with nonwetting defects.
Rasmussen, Christopher J; Gor, Gennady Yu; Neimark, Alexander V
2012-03-13
We investigate the onset of cavitation in a metastable fluid confined to nanoscale pores with nonwetting defects present. Using grand canonical and gauge cell mesocanonical Monte Carlo simulations, we study the degree of metastability (relative vapor pressure), at which the critical bubble forms in a spherical pore with a circular nonwetting defect. It is shown that an increase of the defect size leads to a transition from homogeneous to heterogeneous nucleation of critical bubbles formed at the defect site. In this case, the desorption process may be initiated at larger relative vapor pressures than those predicted by the theories of homogeneous cavitation. PMID:22329712
Direct simulation Monte Carlo for thin-film bearings
Alexander, F.J.; Garcia, A.L.; Alder, B.J. )
1994-12-01
The direct simulation Monte Carlo (DSMC) scheme is used to study the gas flow under a read/write head positioned nanometers above a moving disk drive platter (the slider bearing problem). In most cases, impressive agreement is found between the particle-based simulation and numerical solutions of the continuum hydrodynamic Reynolds equation which has been corrected for slip. However, at very high platter speeds the gas is far from equilibrium, and the load capacity for the slider bearing cannot be accurately computed from the hydrodynamic pressure.
Markov chain Monte Carlo based Approaches for Inverse Problems
NASA Astrophysics Data System (ADS)
Chen, J.; Hoverten, M.; Vasco, D.; Hou, Z.; Rubin, Y.
2005-12-01
Inverse modeling of heterogeneous subsurface systems is difficult. One of the main challenges is the lack of effective and flexible inversion methods that can handle complex practical situations, which may be characterized by non-Gaussian likelihood functions and prior distributions, multiple local optimal solutions, as well as nonlinearity and non-uniqueness of the relationships between parameters and measurements. This study presents a Markov chain Monte Carlo (MCMC) based approach for inverting complex data sets. This approach includes three major steps: (1) Build a stochastic model within the Bayesian framework; (2) Generate many samples from the joint posterior distribution using MCMC methods; (3) Make inferences about unknown parameters from the generated samples. The use of MCMC methods makes our approach very flexible for solving complex inversion problems. First, we can virtually use any types of likelihood functions and prior distributions in the Bayesian model. This allows us to build inversion models primarily based on complex practical situations. Second, MCMC methods are well suitable for parallel computing. This allows us to incorporate computationally intensive forward simulation models into the inversion procedures and allows us to avoid being trapped in multiple local modes of the joint posterior distribution. Finally, MCMC methods generate many samples of unknown parameters. This allows for quantification of uncertainty in estimation of each unknown parameter. To demonstrate our approach, we applied it on geophysical seismic and electromagnetic (EM) data for estimating porosity and natural gas saturation in deepwater gas reservoir. Conventional techniques (such as seismic methods) for gas exploration often suffer a large degree of uncertainty because seismic properties of a medium are not sensitive to gas saturation in the medium. In contrast, electrical properties of a medium are very sensitive to gas saturation. Therefore, EM techniques have the potential of providing information for reducing the uncertainty. We explore in this study the combined use of seismic and EM data using MCMC methods based on layered reservoir models. We consider gas saturation and porosity in each layer of the reservoir, seismic velocities and density in the layers below and above the reservoir, and electrical conductivity in the overburden as random variables. We consider pre-stack seismic amplitude versus offsets (AVO) measurements in a given time window and the amplitudes and phases of the recorded electrical field as data. Using the Bayes' theorem, we get the joint posterior distribution function of all the unknowns. Using MCMC sampling methods, we obtain many samples for each of the unknowns. We demonstrate the efficiency of the developed model for joint inversion of seismic AVO and EM data, and the benefits of incorporating EM data into gas saturation estimation, using two case studies, one is a synthetic case study, and the other is a field case study. Results show that the incorporation of EM data reduces the uncertainty within estimation of both gas saturation and porosity.
NASA Astrophysics Data System (ADS)
Tiana, G.; Villa, F.; Zhan, Y.; Capelli, R.; Paissoni, C.; Sormanni, P.; Heard, E.; Giorgetti, L.; Meloni, R.
2015-01-01
Simplified models, including implicit-solvent and coarse-grained models, are useful tools to investigate the physical properties of biological macromolecules of large size, like protein complexes, large DNA/RNA strands and chromatin fibres. While advanced Monte Carlo techniques are quite efficient in sampling the conformational space of such models, the availability of realistic potentials is still a limitation to their general applicability. The recent development of a computational scheme capable of designing potentials to reproduce any kind of experimental data that can be expressed as thermal averages of conformational properties of the system has partially alleviated the problem. Here we present a program that implements the optimization of the potential with respect to the experimental data through an iterative Monte Carlo algorithm and a rescaling of the probability of the sampled conformations. The Monte Carlo sampling includes several types of moves, suitable for different kinds of system, and various sampling schemes, such as fixed-temperature, replica-exchange and adaptive simulated tempering. The conformational properties whose thermal averages are used as inputs currently include contact functions, distances and functions of distances, but can be easily extended to any function of the coordinates of the system.
Automated Monte Carlo biasing for photon-generated electrons near surfaces.
Franke, Brian Claude; Crawford, Martin James; Kensek, Ronald Patrick
2009-09-01
This report describes efforts to automate the biasing of coupled electron-photon Monte Carlo particle transport calculations. The approach was based on weight-windows biasing. Weight-window settings were determined using adjoint-flux Monte Carlo calculations. A variety of algorithms were investigated for adaptivity of the Monte Carlo tallies. Tree data structures were used to investigate spatial partitioning. Functional-expansion tallies were used to investigate higher-order spatial representations.
Monte Carlo simulations will change the way we treat patients with proton beams today
2014-01-01
Within the past two decades, the evolution of Monte Carlo simulation tools, coupled with our better understanding of physics processes and computer technology has enabled accurate and efficient prediction of particle interactions with tissue. Monte Carlo simulations have now been applied for routine clinical applications. This commentary outlines how simulations have the potential to change clinical practice particularly in proton therapy. Specifically, Monte Carlo simulations will impact treatment outcome analysis, reduce treatment volumes and help understand proton-induced radiation biology. PMID:24896200
Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms
Arampatzis, Giorgos; Katsoulakis, Markos A.; Plechac, Petr; Taufer, Michela; Xu, Lifan
2012-10-01
We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decomposition corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors. The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.
A Monte Carlo Dispersion Analysis of the X-33 Simulation Software
NASA Technical Reports Server (NTRS)
Williams, Peggy S.
2001-01-01
A Monte Carlo dispersion analysis has been completed on the X-33 software simulation. The simulation is based on a preliminary version of the software and is primarily used in an effort to define and refine how a Monte Carlo dispersion analysis would have been done on the final flight-ready version of the software. This report gives an overview of the processes used in the implementation of the dispersions and describes the methods used to accomplish the Monte Carlo analysis. Selected results from 1000 Monte Carlo runs are presented with suggestions for improvements in future work.
Monte Carlo analysis of energy dependent anisotropy of bremsstrahlung x-ray spectra
Kakonyi, Robert; Erdelyi, Miklos; Szabo, Gabor
2009-09-15
The energy resolved emission angle dependence of x-ray spectra was analyzed by MCNPX (Monte Carlo N particle Monte Carlo) simulator. It was shown that the spectral photon flux had a maximum at a well-defined emission angle due to the anisotropy of the bremsstrahlung process. The higher the relative photon energy, the smaller the emission angle belonging to the maximum was. The trends predicted by the Monte Carlo simulations were experimentally verified. The Monte Carlo results were compared to both the Institute of Physics and Engineering in Medicine spectra table and the SPEKCALCV1.0 code.
McGill, Jacob A.; Ogunnaike, Babatunde A.; Vlachos, Dionisios G.
2012-08-30
While many optimization and control methods for stochastic processes require gradient information from the process of interest, obtaining gradient information from experiments is prohibitively expensive and time-consuming. As a result, such information is often obtained from stochastic process simulations. Computing gradients efficiently and accurately from stochastic simulations is challenging, especially for simulations involving computationally expensive models with significant inherent noise. In this work, we analyze and characterize the applicability of two gradient estimation methods for kinetic Monte Carlo simulations: finite differencing and likelihood ratio. We developed a systematic method for choosing an optimal perturbation size for finite differencing and discuss, for both methods, important implementation issues such as scaling with respect to the number of elements in the gradient vector. Through a series of numerical experiments, the methods were compared across different time and size regimes to characterize the precision and accuracy associated with each method. We determined that the likelihood ratio method is appropriate for estimating gradients at short (transient) times or for systems with small population sizes, whereas finite differencing is better-suited for gradient estimation at long times (steady state) or for systems with large population sizes.
Improved criticality convergence via a modified Monte Carlo iteration method
Booth, Thomas E; Gubernatis, James E
2009-01-01
Nuclear criticality calculations with Monte Carlo codes are normally done using a power iteration method to obtain the dominant eigenfunction and eigenvalue. In the last few years it has been shown that the power iteration method can be modified to obtain the first two eigenfunctions. This modified power iteration method directly subtracts out the second eigenfunction and thus only powers out the third and higher eigenfunctions. The result is a convergence rate to the dominant eigenfunction being |k{sub 3}|/k{sub 1} instead of |k{sub 2}|/k{sub 1}. One difficulty is that the second eigenfunction contains particles of both positive and negative weights that must sum somehow to maintain the second eigenfunction. Summing negative and positive weights can be done using point detector mechanics, but this sometimes can be quite slow. We show that an approximate cancellation scheme is sufficient to accelerate the convergence to the dominant eigenfunction. A second difficulty is that for some problems the Monte Carlo implementation of the modified power method has some stability problems. We also show that a simple method deals with this in an effective, but ad hoc manner.
Monte Carlo validation of EYEPLAN proton therapy treatment planning
NASA Astrophysics Data System (ADS)
Cirrone, G. A. P.; Cuttone, G.; Di Rosa, F.; Russo, G.; Salamone, V.
2007-10-01
Protons, thanks to their physical features, offer the dosimetric advantage of an highly conformal dose region and the possibility of covering the tumor volume with an elevated accuracy. On the other hand, their precision has to match with the accuracy in the patient positioning and in the dose distributions calculated by the Treatment Planning Systems (TPSs). One of the major application of proton therapy is the treatment of ocular melanoma. In this case the software EYEPLAN is commonly adopted as TPS. In this work we verified the EYEPLAN dose calculations via the GEANT4 Monte Carlo toolkit quantitatively evaluating the agreement between dose distribution curves. The generally accepted parameters, as Distance to Agreement (DTA) and Dose Difference (DD), were adopted for the comparisons. The maximum differences between profiles were 5% for the Dose Difference and 1.2 mm for the Distance To Agreement. These results eventually demonstrated that a Monte Carlo approach can be considered the most accurate method to verify the dose distribution planned by a TPS.
Fourier Monte Carlo renormalization-group approach to crystalline membranes
NASA Astrophysics Data System (ADS)
Tröster, A.
2015-02-01
The computation of the critical exponent η characterizing the universal elastic behavior of crystalline membranes in the flat phase continues to represent challenges to theorists as well as computer simulators that manifest themselves in a considerable spread of numerical results for η published in the literature. We present additional insight into this problem that results from combining Wilson's momentum shell renormalization-group method with the power of modern computer simulations based on the Fourier Monte Carlo algorithm. After discussing the ideas and difficulties underlying this combined scheme, we present a calculation of the renormalization-group flow of the effective two-dimensional Young modulus for momentum shells of different thickness. Extrapolation to infinite shell thickness allows us to produce results in reasonable agreement with those obtained by functional renormalization group or by Fourier Monte Carlo simulations in combination with finite-size scaling. Moreover, our method allows us to obtain a decent estimate for the value of the Wegner exponent ω that determines the leading correction to scaling, which in turn allows us to refine our numerical estimate for η previously obtained from precise finite-size scaling data.
Monte Carlo track structure for radiation biology and space applications
NASA Technical Reports Server (NTRS)
Nikjoo, H.; Uehara, S.; Khvostunov, I. G.; Cucinotta, F. A.; Wilson, W. E.; Goodhead, D. T.
2001-01-01
Over the past two decades event by event Monte Carlo track structure codes have increasingly been used for biophysical modelling and radiotherapy. Advent of these codes has helped to shed light on many aspects of microdosimetry and mechanism of damage by ionising radiation in the cell. These codes have continuously been modified to include new improved cross sections and computational techniques. This paper provides a summary of input data for ionizations, excitations and elastic scattering cross sections for event by event Monte Carlo track structure simulations for electrons and ions in the form of parametric equations, which makes it easy to reproduce the data. Stopping power and radial distribution of dose are presented for ions and compared with experimental data. A model is described for simulation of full slowing down of proton tracks in water in the range 1 keV to 1 MeV. Modelling and calculations are presented for the response of a TEPC proportional counter irradiated with 5 MeV alpha-particles. Distributions are presented for the wall and wall-less counters. Data shows contribution of indirect effects to the lineal energy distribution for the wall counters responses even at such a low ion energy.
Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
NASA Astrophysics Data System (ADS)
Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo
2016-01-01
A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with nonzero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this approach for a simple fermionic model. We introduce an easy to implement Monte Carlo algorithm to sample the dominant thimble. Our algorithm relies only on the integration of the gradient flow in the numerically stable direction, which gives it a distinct advantage over the other proposed algorithms. We demonstrate the stability and efficiency of the algorithm by applying it to an exactly solvable fermionic model and compare our results with the analytical ones. We report a very good agreement for a certain region in the parameter space where the dominant contribution comes from a single thimble, including a region where standard methods suffer from a severe sign problem. However, we find that there are also regions in the parameter space where the contribution from multiple thimbles is important, even in the continuum limit.
Monte Carlo simulation of zinc protoporphyrin fluorescence in the retina
NASA Astrophysics Data System (ADS)
Chen, Xiaoyan; Lane, Stephen
2010-02-01
We have used Monte Carlo simulation of autofluorescence in the retina to determine that noninvasive detection of nutritional iron deficiency is possible. Nutritional iron deficiency (which leads to iron deficiency anemia) affects more than 2 billion people worldwide, and there is an urgent need for a simple, noninvasive diagnostic test. Zinc protoporphyrin (ZPP) is a fluorescent compound that accumulates in red blood cells and is used as a biomarker for nutritional iron deficiency. We developed a computational model of the eye, using parameters that were identified either by literature search, or by direct experimental measurement to test the possibility of detecting ZPP non-invasively in retina. By incorporating fluorescence into Steven Jacques' original code for multi-layered tissue, we performed Monte Carlo simulation of fluorescence in the retina and determined that if the beam is not focused on a blood vessel in a neural retina layer or if part of light is hitting the vessel, ZPP fluorescence will be 10-200 times higher than background lipofuscin fluorescence coming from the retinal pigment epithelium (RPE) layer directly below. In addition we found that if the light can be focused entirely onto a blood vessel in the neural retina layer, the fluorescence signal comes only from ZPP. The fluorescence from layers below in this second situation does not contribute to the signal. Therefore, the possibility that a device could potentially be built and detect ZPP fluorescence in retina looks very promising.
A pure-sampling quantum Monte Carlo algorithm
NASA Astrophysics Data System (ADS)
Ospadov, Egor; Rothstein, Stuart M.
2015-01-01
The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we report a pure-sampling algorithm that combines features of forward walking methods of pure-sampling and reptation quantum Monte Carlo (RQMC). The new algorithm accurately samples properties from the mixed and pure distributions simultaneously in runs performed at a single set of time-steps, over which extrapolation to zero time-step is performed. In a detailed comparison, we found RQMC to be less efficient. It requires different sets of time-steps to accurately determine the energy and other properties, such as the dipole moment. We implement our algorithm by systematically increasing an algorithmic parameter until the properties converge to statistically equivalent values. As a proof in principle, we calculated the fixed-node energy, static α polarizability, and other one-electron expectation values for the ground-states of LiH and water molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We found excellent agreement with the accepted values for the energy and a variety of other properties for those systems.
The ATLAS Fast Monte Carlo Production Chain Project
NASA Astrophysics Data System (ADS)
Jansky, Roland
2015-12-01
During the last years ATLAS has successfully deployed a new integrated simulation framework (ISF) which allows a flexible mixture of full and fast detector simulation techniques within the processing of one event. The thereby achieved possible speed-up in detector simulation of up to a factor 100 makes subsequent digitization and reconstruction the dominant contributions to the Monte Carlo (MC) production CPU cost. The slowest components of both digitization and reconstruction are inside the Inner Detector due to the complex signal modeling needed in the emulation of the detector readout and in reconstruction due to the combinatorial nature of the problem to solve, respectively. Alternative fast approaches have been developed for these components: for the silicon based detectors a simpler geometrical clustering approach has been deployed replacing the charge drift emulation in the standard digitization modules, which achieves a very high accuracy in describing the standard output. For the Inner Detector track reconstruction, a Monte Carlo generator information based trajectory building has been deployed with the aim of bypassing the CPU intensive pattern recognition. Together with the ISF all components have been integrated into a new fast MC production chain, aiming to produce fast MC simulated data with sufficient agreement with fully simulated and reconstructed data at a processing time of seconds per event, compared to several minutes for full simulation.
Monte Carlo Simulation of Sudden Death Bearing Testing
NASA Technical Reports Server (NTRS)
Vlcek, Brian L.; Hendricks, Robert C.; Zaretsky, Erwin V.
2003-01-01
Monte Carlo simulations combined with sudden death testing were used to compare resultant bearing lives to the calculated hearing life and the cumulative test time and calendar time relative to sequential and censored sequential testing. A total of 30 960 virtual 50-mm bore deep-groove ball bearings were evaluated in 33 different sudden death test configurations comprising 36, 72, and 144 bearings each. Variations in both life and Weibull slope were a function of the number of bearings failed independent of the test method used and not the total number of bearings tested. Variation in L10 life as a function of number of bearings failed were similar to variations in lift obtained from sequentially failed real bearings and from Monte Carlo (virtual) testing of entire populations. Reductions up to 40 percent in bearing test time and calendar time can be achieved by testing to failure or the L(sub 50) life and terminating all testing when the last of the predetermined bearing failures has occurred. Sudden death testing is not a more efficient method to reduce bearing test time or calendar time when compared to censored sequential testing.
Treatment planning for a small animal using Monte Carlo simulation
Chow, James C. L.; Leung, Michael K. K.
2007-12-15
The development of a small animal model for radiotherapy research requires a complete setup of customized imaging equipment, irradiators, and planning software that matches the sizes of the subjects. The purpose of this study is to develop and demonstrate the use of a flexible in-house research environment for treatment planning on small animals. The software package, called DOSCTP, provides a user-friendly platform for DICOM computed tomography-based Monte Carlo dose calculation using the EGSnrcMP-based DOSXYZnrc code. Validation of the treatment planning was performed by comparing the dose distributions for simple photon beam geometries calculated through the Pinnacle3 treatment planning system and measurements. A treatment plan for a mouse based on a CT image set by a 360-deg photon arc is demonstrated. It is shown that it is possible to create 3D conformal treatment plans for small animals with consideration of inhomogeneities using small photon beam field sizes in the diameter range of 0.5-5 cm, with conformal dose covering the target volume while sparing the surrounding critical tissue. It is also found that Monte Carlo simulation is suitable to carry out treatment planning dose calculation for small animal anatomy with voxel size about one order of magnitude smaller than that of the human.
High-Fidelity Coupled Monte-Carlo/Thermal-Hydraulics Calculations
NASA Astrophysics Data System (ADS)
Ivanov, Aleksandar; Sanchez, Victor; Ivanov, Kostadin
2014-06-01
Monte Carlo methods have been used as reference reactor physics calculation tools worldwide. The advance in computer technology allows the calculation of detailed flux distributions in both space and energy. In most of the cases however, those calculations are done under the assumption of homogeneous material density and temperature distributions. The aim of this work is to develop a consistent methodology for providing realistic three-dimensional thermal-hydraulic distributions by coupling the in-house developed sub-channel code SUBCHANFLOW with the standard Monte-Carlo transport code MCNP. In addition to the innovative technique of on-the fly material definition, a flux-based weight-window technique has been introduced to improve both the magnitude and the distribution of the relative errors. Finally, a coupled code system for the simulation of steady-state reactor physics problems has been developed. Besides the problem of effective feedback data interchange between the codes, the treatment of temperature dependence of the continuous energy nuclear data has been investigated.
Ultracold atoms at unitarity within quantum Monte Carlo methods
Morris, Andrew J.; Lopez Rios, P.; Needs, R. J.
2010-03-15
Variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the properties of the zero-temperature fermionic gas at unitarity are reported. Our study differs from earlier ones mainly in that we have constructed more accurate trial wave functions and used a larger system size, we have studied the dependence of the energy on the particle density and well width, and we have achieved much smaller statistical error bars. The correct value of the universal ratio of the energy of the interacting to that of the noninteracting gas, {xi}, is still a matter of debate. We find DMC values of {xi} of 0.4244(1) with 66 particles and 0.4339(1) with 128 particles. The spherically averaged pair-correlation functions, momentum densities, and one-body density matrices are very similar in VMC and DMC, which suggests that our results for these quantities are very accurate. We find, however, some differences between the VMC and DMC results for the two-body density matrices and condensate fractions, which indicates that these quantities are more sensitive to the quality of the trial wave function. Our best estimate of the condensate fraction of 0.51 is smaller than the values from earlier quantum Monte Carlo calculations.
Infinite variance in fermion quantum Monte Carlo calculations
NASA Astrophysics Data System (ADS)
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
Variational Monte Carlo investigation of SU (N ) Heisenberg chains
NASA Astrophysics Data System (ADS)
Dufour, Jérôme; Nataf, Pierre; Mila, Frédéric
2015-05-01
Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have investigated the properties of the SU (N) Heisenberg chain with totally antisymmetric irreducible representations, the effective model of Mott phases with m
Monte Carlo modeling of human tooth optical coherence tomography imaging
NASA Astrophysics Data System (ADS)
Shi, Boya; Meng, Zhuo; Wang, Longzhi; Liu, Tiegen
2013-07-01
We present a Monte Carlo model for optical coherence tomography (OCT) imaging of human tooth. The model is implemented by combining the simulation of a Gaussian beam with simulation for photon propagation in a two-layer human tooth model with non-parallel surfaces through a Monte Carlo method. The geometry and the optical parameters of the human tooth model are chosen on the basis of the experimental OCT images. The results show that the simulated OCT images are qualitatively consistent with the experimental ones. Using the model, we demonstrate the following: firstly, two types of photons contribute to the information of morphological features and noise in the OCT image of a human tooth, respectively. Secondly, the critical imaging depth of the tooth model is obtained, and it is found to decrease significantly with increasing mineral loss, simulated as different enamel scattering coefficients. Finally, the best focus position is located below and close to the dental surface by analysis of the effect of focus positions on the OCT signal and critical imaging depth. We anticipate that this modeling will become a powerful and accurate tool for a preliminary numerical study of the OCT technique on diseases of dental hard tissue in human teeth.
Russian roulette efficiency in Monte Carlo resonant absorption calculations
Ghassoun; Jehouani
2000-10-01
The resonant absorption calculation in media containing heavy resonant nuclei is one of the most difficult problems treated in reactor physics. Deterministic techniques need many approximations to solve this kind of problem. On the other hand, the Monte Carlo method is a reliable mathematical tool for evaluating the neutron resonance escape probability. But it suffers from large statistical deviations of results and long computation times. In order to overcome this problem, we have used the Splitting and Russian Roulette technique coupled separately to the survival biasing and to the importance sampling for the energy parameter. These techniques have been used to calculate the neutron resonance absorption in infinite homogenous media containing hydrogen and uranium characterized by the dilution (ratio of the concentrations of hydrogen to uranium). The punctual neutron source energy is taken at Es = 2 MeV and Es = 676.45 eV, whereas the energy cut-off is fixed at Ec = 2.768 eV. The results show a large reduction of computation time and statistical deviation, without altering the mean resonance escape probability compared to the usual analog simulation. The Splitting and Russian Roulette coupled to the survival biasing method is found to be the best methods for studying the neutron resonant absorption, particularly for high energies. A comparison is done between the Monte Carlo and deterministic methods based on the numerical solution of the neutron slowing down equations by the iterative method results for several dilutions. PMID:11003535
Variational Monte Carlo method for electron-phonon coupled systems
NASA Astrophysics Data System (ADS)
Ohgoe, Takahiro; Imada, Masatoshi
2014-05-01
We develop a variational Monte Carlo (VMC) method for electron-phonon coupled systems. The VMC method has been extensively used for investigating strongly correlated electrons over the last decades. However, its applications to electron-phonon coupled systems have been severely restricted because of its large Hilbert space. Here, we propose a variational wave function with a large number of variational parameters, which is suitable and tractable for systems with electron-phonon coupling. In the proposed wave function, we implement an unexplored electron-phonon correlation factor, which takes into account the effect of the entanglement between electrons and phonons. The method is applied to systems with diagonal electron-phonon interactions, i.e., interactions between charge densities and lattice displacements (phonons). As benchmarks, we compare VMC results with previous results obtained by the exact diagonalization, the Green function Monte Carlo method and the density matrix renormalization group for the Holstein and Holstein-Hubbard model. From these benchmarks, we show that the present method offers an efficient way to treat strongly coupled electron-phonon systems.
A pure-sampling quantum Monte Carlo algorithm
Ospadov, Egor; Rothstein, Stuart M.
2015-01-14
The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we report a pure-sampling algorithm that combines features of forward walking methods of pure-sampling and reptation quantum Monte Carlo (RQMC). The new algorithm accurately samples properties from the mixed and pure distributions simultaneously in runs performed at a single set of time-steps, over which extrapolation to zero time-step is performed. In a detailed comparison, we found RQMC to be less efficient. It requires different sets of time-steps to accurately determine the energy and other properties, such as the dipole moment. We implement our algorithm by systematically increasing an algorithmic parameter until the properties converge to statistically equivalent values. As a proof in principle, we calculated the fixed-node energy, static α polarizability, and other one-electron expectation values for the ground-states of LiH and water molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We found excellent agreement with the accepted values for the energy and a variety of other properties for those systems.
James Webb Space Telescope (JWST) Stationkeeping Monte Carlo Simulations
NASA Technical Reports Server (NTRS)
Dichmann, Donald J.; Alberding, Cassandra; Yu, Wayne
2014-01-01
The James Webb Space Telescope (JWST) will launch in 2018 into a Libration Point Orbit (LPO) around the Sun-EarthMoon (SEM) L2 point, with a planned mission lifetime of 11 years. This paper discusses our approach to Stationkeeping (SK) maneuver planning to determine an adequate SK delta-V budget. The SK maneuver planning for JWST is made challenging by two factors: JWST has a large Sunshield, and JWST will be repointed regularly producing significant changes in Solar Radiation Pressure (SRP). To accurately model SRP we employ the Solar Pressure and Drag (SPAD) tool, which uses ray tracing to accurately compute SRP force as a function of attitude. As an additional challenge, the future JWST observation schedule will not be known at the time of SK maneuver planning. Thus there will be significant variation in SRP between SK maneuvers, and the future variation in SRP is unknown. We have enhanced an earlier SK simulation to create a Monte Carlo simulation that incorporates random draws for uncertainties that affect the budget, including random draws of the observation schedule. Each SK maneuver is planned to optimize delta-V magnitude, subject to constraints on spacecraft pointing. We report the results of the Monte Carlo simulations and discuss possible improvements during flight operations to reduce the SK delta-V budget.
A Monte Carlo simulation of ion transport at finite temperatures
NASA Astrophysics Data System (ADS)
Ristivojevic, Zoran; Petrović, Zoran Lj
2012-06-01
We have developed a Monte Carlo simulation for ion transport in hot background gases, which is an alternative way of solving the corresponding Boltzmann equation that determines the distribution function of ions. We consider the limit of low ion densities when the distribution function of the background gas remains unchanged due to collision with ions. Special attention has been paid to properly treating the thermal motion of the host gas particles and their influence on ions, which is very important at low electric fields, when the mean ion energy is comparable to the thermal energy of the host gas. We found the conditional probability distribution of gas velocities that correspond to an ion of specific velocity which collides with a gas particle. Also, we have derived exact analytical formulae for piecewise calculation of the collision frequency integrals. We address the cases when the background gas is monocomponent and when it is a mixture of different gases. The techniques described here are required for Monte Carlo simulations of ion transport and for hybrid models of non-equilibrium plasmas. The range of energies where it is necessary to apply the technique has been defined. The results we obtained are in excellent agreement with the existing ones obtained by complementary methods. Having verified our algorithm, we were able to produce calculations for Ar+ ions in Ar and propose them as a new benchmark for thermal effects. The developed method is widely applicable for solving the Boltzmann equation that appears in many different contexts in physics.
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 BURNUP CALCULATION UNCERTAINTY QUANTIFICATION AND PROPAGATION DETERMINATION
Sternat, M.; Nichols, T.
2011-06-09
Reactor burnup or depletion codes are used thoroughly in the fields of nuclear forensics and nuclear safeguards. Two common codes include MONTEBURNS and MCNPX/CINDER. These are Monte-Carlo depletion routines utilizing MCNP for neutron transport calculations and either ORIGEN or CINDER for burnup calculations. Uncertainties exist in the MCNP steps, but this information is not passed to the depletion calculations or saved. To quantify this transport uncertainty and determine how it propagates between burnup steps, a statistical analysis of multiple repeated depletion runs is performed. The reactor model chosen is the Oak Ridge Research Reactor (ORR) in a single assembly, infinite lattice configuration. This model was burned for a 150 day cycle broken down into three steps. The output isotopics as well as effective multiplication factor (k-effective) were tabulated and histograms were created at each burnup step using the Scott Method to determine the bin width. The distributions for each code are a statistical benchmark and comparisons made. It was expected that the gram quantities and k-effective histograms would produce normally distributed results since they were produced from a Monte-Carlo routine, but some of the results appear to not. Statistical analyses are performed using the {chi}{sup 2} test against a normal distribution for the k-effective results and several isotopes including {sup 134}Cs, {sup 137}Cs, {sup 235}U, {sup 238}U, {sup 237}Np, {sup 238}Pu, {sup 239}Pu, and {sup 240}Pu.
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.
CMS Monte Carlo production in the WLCG computing grid
NASA Astrophysics Data System (ADS)
Hernández, J. M.; Kreuzer, P.; Mohapatra, A.; Filippis, N. D.; Weirdt, S. D.; Hof, C.; Wakefield, S.; Guan, W.; Khomitch, A.; Fanfani, A.; Evans, D.; Flossdorf, A.; Maes, J.; Mulders, P. v.; Villella, I.; Pompili, A.; My, S.; Abbrescia, M.; Maggi, G.; Donvito, G.; Caballero, J.; Sanches, J. A.; Kavka, C.; Lingen, F. v.; Bacchi, W.; Codispoti, G.; Elmer, P.; Eulisse, G.; Lazaridis, C.; Kalini, S.; Sarkar, S.; Hammad, G.
2008-07-01
Monte Carlo production in CMS has received a major boost in performance and scale since the past CHEP06 conference. The production system has been re-engineered in order to incorporate the experience gained in running the previous system and to integrate production with the new CMS event data model, data management system and data processing framework. The system is interfaced to the two major computing Grids used by CMS, the LHC Computing Grid (LCG) and the Open Science Grid (OSG). Operational experience and integration aspects of the new CMS Monte Carlo production system is presented together with an analysis of production statistics. The new system automatically handles job submission, resource monitoring, job queuing, job distribution according to the available resources, data merging, registration of data into the data bookkeeping, data location, data transfer and placement systems. Compared to the previous production system automation, reliability and performance have been considerably improved. A more efficient use of computing resources and a better handling of the inherent Grid unreliability have resulted in an increase of production scale by about an order of magnitude, capable of running in parallel at the order of ten thousand jobs and yielding more than two million events per day.
Energy Modulated Photon Radiotherapy: A Monte Carlo Feasibility Study
Zhang, Ying; Feng, Yuanming; Ming, Xin
2016-01-01
A novel treatment modality termed energy modulated photon radiotherapy (EMXRT) was investigated. The first step of EMXRT was to determine beam energy for each gantry angle/anatomy configuration from a pool of photon energy beams (2 to 10 MV) with a newly developed energy selector. An inverse planning system using gradient search algorithm was then employed to optimize photon beam intensity of various beam energies based on presimulated Monte Carlo pencil beam dose distributions in patient anatomy. Finally, 3D dose distributions in six patients of different tumor sites were simulated with Monte Carlo method and compared between EMXRT plans and clinical IMRT plans. Compared to current IMRT technique, the proposed EMXRT method could offer a better paradigm for the radiotherapy of lung cancers and pediatric brain tumors in terms of normal tissue sparing and integral dose. For prostate, head and neck, spine, and thyroid lesions, the EMXRT plans were generally comparable to the IMRT plans. Our feasibility study indicated that lower energy (<6 MV) photon beams could be considered in modern radiotherapy treatment planning to achieve a more personalized care for individual patient with dosimetric gains. PMID:26977413
Monte Carlo Criticality Methods and Analysis Capabilities in SCALE
Goluoglu, Sedat; Petrie Jr, Lester M; Dunn, Michael E; Hollenbach, Daniel F; Rearden, Bradley T
2011-01-01
This paper describes the Monte Carlo codes KENO V.a and KENO-VI in SCALE that are primarily used to calculate multiplication factors and flux distributions of fissile systems. Both codes allow explicit geometric representation of the target systems and are used internationally for safety analyses involving fissile materials. KENO V.a has limiting geometric rules such as no intersections and no rotations. These limitations make KENO V.a execute very efficiently and run very fast. On the other hand, KENO-VI allows very complex geometric modeling. Both KENO codes can utilize either continuous-energy or multigroup cross-section data and have been thoroughly verified and validated with ENDF libraries through ENDF/B-VII.0, which has been first distributed with SCALE 6. Development of the Monte Carlo solution technique and solution methodology as applied in both KENO codes is explained in this paper. Available options and proper application of the options and techniques are also discussed. Finally, performance of the codes is demonstrated using published benchmark problems.
Monte Carlo field-theoretic simulations of a homopolymer blend
NASA Astrophysics Data System (ADS)
Spencer, Russell; Matsen, Mark
Fluctuation corrections to the macrophase segregation transition (MST) in a symmetric homopolymer blend are examined using Monte Carlo field-theoretic simulations (MC-FTS). This technique involves treating interactions between unlike monomers using standard Monte-Carlo techniques, while enforcing incompressibility as is done in mean-field theory. When using MC-FTS, we need to account for a UV divergence. This is done by renormalizing the Flory-Huggins interaction parameter to incorporate the divergent part of the Hamiltonian. We compare different ways of calculating this effective interaction parameter. Near the MST, the length scale of compositional fluctuations becomes large, however, the high computational requirements of MC-FTS restrict us to small system sizes. We account for these finite size effects using the method of Binder cumulants, allowing us to locate the MST with high precision. We examine fluctuation corrections to the mean field MST, χN = 2 , as they vary with the invariant degree of polymerization, N =ρ2a6 N . These results are compared with particle-based simulations as well as analytical calculations using the renormalized one loop theory. This research was funded by the Center for Sustainable Polymers.
A Quantum Monte Carlo Study of Molecular Titanium Systems
NASA Astrophysics Data System (ADS)
Beaudet, Todd D.; Kim, Jeongnim; Esler, Kenneth; Martin, Richard M.
2010-03-01
We present a quantum Monte Carlo study of molecular TiH2 and Ti-ethylene-hydrogen complexes which have been of recent interest for their relation to systems that can reversibly adsorb hydrogen.footnotetextE. Durgun et al., Phys. Rev. Lett. 97, 226102 (2006).^,footnotetextJ. A. Platts, J. Mol. Struct. 545, 111 (2001).^,footnotetextB. Ma, C. L. Collins, H. F. Schaefer, J. Am. Chem. Soc. 118, 870 (1996). We study these systems using diffusion Monte Carlo with the fixed-node approximation and pseudopotentials. The symmetry and nodal structure used are determined by trial wave functions constructed of molecular orbitals from DFT. In the TiH2 system, the four lowest states have different symmetries and are very close in energy due to the fact that the d-states are almost decoupled from the bonding. We show that partially occupying the relevant d-states at the DFT level allows for the construction of symmetry classified trial functions that are more directly comparable at the DMC level. This procedure has potential to be useful in analogous systems where d-state occupation results in nearly degenerate states of different symmetry.
Utilizing Monte Carlo Simulations to Optimize Institutional Empiric Antipseudomonal Therapy
Tennant, Sarah J.; Burgess, Donna R.; Rybak, Jeffrey M.; Martin, Craig A.; Burgess, David S.
2015-01-01
Pseudomonas aeruginosa is a common pathogen implicated in nosocomial infections with increasing resistance to a limited arsenal of antibiotics. Monte Carlo simulation provides antimicrobial stewardship teams with an additional tool to guide empiric therapy. We modeled empiric therapies with antipseudomonal β-lactam antibiotic regimens to determine which were most likely to achieve probability of target attainment (PTA) of ≥90%. Microbiological data for P. aeruginosa was reviewed for 2012. Antibiotics modeled for intermittent and prolonged infusion were aztreonam, cefepime, meropenem, and piperacillin/tazobactam. Using minimum inhibitory concentrations (MICs) from institution-specific isolates, and pharmacokinetic and pharmacodynamic parameters from previously published studies, a 10,000-subject Monte Carlo simulation was performed for each regimen to determine PTA. MICs from 272 isolates were included in this analysis. No intermittent infusion regimens achieved PTA ≥90%. Prolonged infusions of cefepime 2000 mg Q8 h, meropenem 1000 mg Q8 h, and meropenem 2000 mg Q8 h demonstrated PTA of 93%, 92%, and 100%, respectively. Prolonged infusions of piperacillin/tazobactam 4.5 g Q6 h and aztreonam 2 g Q8 h failed to achieved PTA ≥90% but demonstrated PTA of 81% and 73%, respectively. Standard doses of β-lactam antibiotics as intermittent infusion did not achieve 90% PTA against P. aeruginosa isolated at our institution; however, some prolonged infusions were able to achieve these targets. PMID:27025644
Stationkeeping Monte Carlo Simulation for the James Webb Space Telescope
NASA Technical Reports Server (NTRS)
Dichmann, Donald J.; Alberding, Cassandra M.; Yu, Wayne H.
2014-01-01
The James Webb Space Telescope (JWST) is scheduled to launch in 2018 into a Libration Point Orbit (LPO) around the Sun-Earth/Moon (SEM) L2 point, with a planned mission lifetime of 10.5 years after a six-month transfer to the mission orbit. This paper discusses our approach to Stationkeeping (SK) maneuver planning to determine an adequate SK delta-V budget. The SK maneuver planning for JWST is made challenging by two factors: JWST has a large Sunshield, and JWST will be repointed regularly producing significant changes in Solar Radiation Pressure (SRP). To accurately model SRP we employ the Solar Pressure and Drag (SPAD) tool, which uses ray tracing to accurately compute SRP force as a function of attitude. As an additional challenge, the future JWST observation schedule will not be known at the time of SK maneuver planning. Thus there will be significant variation in SRP between SK maneuvers, and the future variation in SRP is unknown. We have enhanced an earlier SK simulation to create a Monte Carlo simulation that incorporates random draws for uncertainties that affect the budget, including random draws of the observation schedule. Each SK maneuver is planned to optimize delta-V magnitude, subject to constraints on spacecraft pointing. We report the results of the Monte Carlo simulations and discuss possible improvements during flight operations to reduce the SK delta-V budget.
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.
Development of a radiative flux evaluation program with a 3-D Monte Carlo radiative transfer code
NASA Astrophysics Data System (ADS)
Okata, Megumi; Nakajima, Teruyuki; Barker, Howard W.; Donovan, David P.
2013-05-01
In this paper, we have developed a three-dimensional (3D) Monte Carlo radiative transfer code that can treat a broadband solar flux calculation implemented with k-distribution parameters [1]. We used this code for generating the radiative flux profile and heating rate profile in the atmosphere including broken clouds. In order to construct 3-D extinction coefficient fields, we tried following three methods: 1) Minimum cloud Information Deviation Profiling Method (MIDPM), 2) numerical simulations by a non-hydrostatic model with bin cloud microphysics model and 3) idealized stochastic clouds generated by randomized extinction coefficient distribution and regularly-distributed tiled clouds. Using these constructed 3-D cloud systems, we calculated the radiation field by our Monte Carlo radiative transfer code at wavelengths of 0.5, 1.6 and 2.1 microns. We then compared the results with Plane Parallel Approximation (PPA) and a reflectivity of 3-D with Independent Pixel Approximation (IPA). In the case of wavelength 0.5 microns, as expected, all the discrepancies between 3-D clouds and equivalent IPA clouds are smaller than the discrepancies between 3-D clouds and equivalent PPA clouds. At maximum the reflectivity difference for the PPA and IPA is about equal to fluxes of 30 Wm-2 and 10 Wm-2, respectively.
Quantum Monte Carlo algorithms for electronic structure at the petascale; the endstation project.
Kim, J; Ceperley, D M; Purwanto, W; Walter, E J; Krakauer, H; Zhang, S W; Kent, P.R. C; Hennig, R G; Umrigar, C; Bajdich, M; Kolorenc, J; Mitas, L; Srinivasan, A
2008-10-01
Over the past two decades, continuum quantum Monte Carlo (QMC) has proved to be an invaluable tool for predicting of the properties of matter from fundamental principles. By solving the Schrodinger equation through a stochastic projection, it achieves the greatest accuracy and reliability of methods available for physical systems containing more than a few quantum particles. QMC enjoys scaling favorable to quantum chemical methods, with a computational effort which grows with the second or third power of system size. This accuracy and scalability has enabled scientific discovery across a broad spectrum of disciplines. The current methods perform very efficiently at the terascale. The quantum Monte Carlo Endstation project is a collaborative effort among researchers in the field to develop a new generation of algorithms, and their efficient implementations, which will take advantage of the upcoming petaflop architectures. Some aspects of these developments are discussed here. These tools will expand the accuracy, efficiency and range of QMC applicability and enable us to tackle challenges which are currently out of reach. The methods will be applied to several important problems including electronic and structural properties of water, transition metal oxides, nanosystems and ultracold atoms.
Accelerating Monte Carlo simulations with an NVIDIA ® graphics processor
NASA Astrophysics Data System (ADS)
Martinsen, Paul; Blaschke, Johannes; Künnemeyer, Rainer; Jordan, Robert
2009-10-01
Modern graphics cards, commonly used in desktop computers, have evolved beyond a simple interface between processor and display to incorporate sophisticated calculation engines that can be applied to general purpose computing. The Monte Carlo algorithm for modelling photon transport in turbid media has been implemented on an NVIDIA ® 8800 GT graphics card using the CUDA toolkit. The Monte Carlo method relies on following the trajectory of millions of photons through the sample, often taking hours or days to complete. The graphics-processor implementation, processing roughly 110 million scattering events per second, was found to run more than 70 times faster than a similar, single-threaded implementation on a 2.67 GHz desktop computer. Program summaryProgram title: Phoogle-C/Phoogle-G Catalogue identifier: AEEB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEB_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.: 51 264 No. of bytes in distributed program, including test data, etc.: 2 238 805 Distribution format: tar.gz Programming language: C++ Computer: Designed for Intel PCs. Phoogle-G requires a NVIDIA graphics card with support for CUDA 1.1 Operating system: Windows XP Has the code been vectorised or parallelized?: Phoogle-G is written for SIMD architectures RAM: 1 GB Classification: 21.1 External routines: Charles Karney Random number library. Microsoft Foundation Class library. NVIDA CUDA library [1]. Nature of problem: The Monte Carlo technique is an effective algorithm for exploring the propagation of light in turbid media. However, accurate results require tracing the path of many photons within the media. The independence of photons naturally lends the Monte Carlo technique to implementation on parallel architectures. Generally, parallel computing can be expensive, but recent advances in consumer grade graphics cards have opened the possibility of high-performance desktop parallel-computing. Solution method: In this pair of programmes we have implemented the Monte Carlo algorithm described by Prahl et al. [2] for photon transport in infinite scattering media to compare the performance of two readily accessible architectures: a standard desktop PC and a consumer grade graphics card from NVIDIA. Restrictions: The graphics card implementation uses single precision floating point numbers for all calculations. Only photon transport from an isotropic point-source is supported. The graphics-card version has no user interface. The simulation parameters must be set in the source code. The desktop version has a simple user interface; however some properties can only be accessed through an ActiveX client (such as Matlab). Additional comments: The random number library used has a LGPL ( http://www.gnu.org/copyleft/lesser.html) licence. Running time: Runtime can range from minutes to months depending on the number of photons simulated and the optical properties of the medium. References:http://www.nvidia.com/object/cuda_home.html. S. Prahl, M. Keijzer, Sl. Jacques, A. Welch, SPIE Institute Series 5 (1989) 102.
Giorgio, Laura Di; Flaxman, Abraham D.; Moses, Mark W.; Fullman, Nancy; Hanlon, Michael; Conner, Ruben O.; Wollum, Alexandra; Murray, Christopher J. L.
2016-01-01
Low-resource countries can greatly benefit from even small increases in efficiency of health service provision, supporting a strong case to measure and pursue efficiency improvement in low- and middle-income countries (LMICs). However, the knowledge base concerning efficiency measurement remains scarce for these contexts. This study shows that current estimation approaches may not be well suited to measure technical efficiency in LMICs and offers an alternative approach for efficiency measurement in these settings. We developed a simulation environment which reproduces the characteristics of health service production in LMICs, and evaluated the performance of Data Envelopment Analysis (DEA) and Stochastic Distance Function (SDF) for assessing efficiency. We found that an ensemble approach (ENS) combining efficiency estimates from a restricted version of DEA (rDEA) and restricted SDF (rSDF) is the preferable method across a range of scenarios. This is the first study to analyze efficiency measurement in a simulation setting for LMICs. Our findings aim to heighten the validity and reliability of efficiency analyses in LMICs, and thus inform policy dialogues about improving the efficiency of health service production in these settings. PMID:26812685
Giorgio, Laura Di; Flaxman, Abraham D; Moses, Mark W; Fullman, Nancy; Hanlon, Michael; Conner, Ruben O; Wollum, Alexandra; Murray, Christopher J L
2016-01-01
Low-resource countries can greatly benefit from even small increases in efficiency of health service provision, supporting a strong case to measure and pursue efficiency improvement in low- and middle-income countries (LMICs). However, the knowledge base concerning efficiency measurement remains scarce for these contexts. This study shows that current estimation approaches may not be well suited to measure technical efficiency in LMICs and offers an alternative approach for efficiency measurement in these settings. We developed a simulation environment which reproduces the characteristics of health service production in LMICs, and evaluated the performance of Data Envelopment Analysis (DEA) and Stochastic Distance Function (SDF) for assessing efficiency. We found that an ensemble approach (ENS) combining efficiency estimates from a restricted version of DEA (rDEA) and restricted SDF (rSDF) is the preferable method across a range of scenarios. This is the first study to analyze efficiency measurement in a simulation setting for LMICs. Our findings aim to heighten the validity and reliability of efficiency analyses in LMICs, and thus inform policy dialogues about improving the efficiency of health service production in these settings. PMID:26812685