Hypothesis testing of scientific Monte Carlo calculations.

PubMed

Wallerberger, Markus; Gull, Emanuel

2017-11-01

The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and programming bugs. However, the testing paradigms developed for deterministic algorithms have proven to be ill suited for stochastic algorithms. In this paper we demonstrate explicitly how the technique of statistical hypothesis testing, which is in wide use in other fields of science, can be used to devise automatic and reliable tests for Monte Carlo methods, and we show that these tests are able to detect some of the common problems encountered in stochastic scientific simulations. We argue that hypothesis testing should become part of the standard testing toolkit for scientific simulations.

Hypothesis testing of scientific Monte Carlo calculations

NASA Astrophysics Data System (ADS)

Wallerberger, Markus; Gull, Emanuel

2017-11-01

The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and programming bugs. However, the testing paradigms developed for deterministic algorithms have proven to be ill suited for stochastic algorithms. In this paper we demonstrate explicitly how the technique of statistical hypothesis testing, which is in wide use in other fields of science, can be used to devise automatic and reliable tests for Monte Carlo methods, and we show that these tests are able to detect some of the common problems encountered in stochastic scientific simulations. We argue that hypothesis testing should become part of the standard testing toolkit for scientific simulations.

Stochastic-field cavitation model

NASA Astrophysics Data System (ADS)

Dumond, J.; Magagnato, F.; Class, A.

2013-07-01

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

Effects of fuel cetane number on the structure of diesel spray combustion: An accelerated Eulerian stochastic fields method

NASA Astrophysics Data System (ADS)

Jangi, Mehdi; Lucchini, Tommaso; Gong, Cheng; Bai, Xue-Song

2015-09-01

An Eulerian stochastic fields (ESF) method accelerated with the chemistry coordinate mapping (CCM) approach for modelling spray combustion is formulated, and applied to model diesel combustion in a constant volume vessel. In ESF-CCM, the thermodynamic states of the discretised stochastic fields are mapped into a low-dimensional phase space. Integration of the chemical stiff ODEs is performed in the phase space and the results are mapped back to the physical domain. After validating the ESF-CCM, the method is used to investigate the effects of fuel cetane number on the structure of diesel spray combustion. It is shown that, depending of the fuel cetane number, liftoff length is varied, which can lead to a change in combustion mode from classical diesel spray combustion to fuel-lean premixed burned combustion. Spray combustion with a shorter liftoff length exhibits the characteristics of the classical conceptual diesel combustion model proposed by Dec in 1997 (http://dx.doi.org/10.4271/970873), whereas in a case with a lower cetane number the liftoff length is much larger and the spray combustion probably occurs in a fuel-lean-premixed mode of combustion. Nevertheless, the transport budget at the liftoff location shows that stabilisation at all cetane numbers is governed primarily by the auto-ignition process.

Advanced Stochastic Collocation Methods for Polynomial Chaos in RAVEN

NASA Astrophysics Data System (ADS)

Talbot, Paul W.

As experiment complexity in fields such as nuclear engineering continually increases, so does the demand for robust computational methods to simulate them. In many simulations, input design parameters and intrinsic experiment properties are sources of uncertainty. Often small perturbations in uncertain parameters have significant impact on the experiment outcome. For instance, in nuclear fuel performance, small changes in fuel thermal conductivity can greatly affect maximum stress on the surrounding cladding. The difficulty quantifying input uncertainty impact in such systems has grown with the complexity of numerical models. Traditionally, uncertainty quantification has been approached using random sampling methods like Monte Carlo. For some models, the input parametric space and corresponding response output space is sufficiently explored with few low-cost calculations. For other models, it is computationally costly to obtain good understanding of the output space. To combat the expense of random sampling, this research explores the possibilities of using advanced methods in Stochastic Collocation for generalized Polynomial Chaos (SCgPC) as an alternative to traditional uncertainty quantification techniques such as Monte Carlo (MC) and Latin Hypercube Sampling (LHS) methods for applications in nuclear engineering. We consider traditional SCgPC construction strategies as well as truncated polynomial spaces using Total Degree and Hyperbolic Cross constructions. We also consider applying anisotropy (unequal treatment of different dimensions) to the polynomial space, and offer methods whereby optimal levels of anisotropy can be approximated. We contribute development to existing adaptive polynomial construction strategies. Finally, we consider High-Dimensional Model Reduction (HDMR) expansions, using SCgPC representations for the subspace terms, and contribute new adaptive methods to construct them. We apply these methods on a series of models of increasing

Monte Carlo Shielding Comparative Analysis Applied to TRIGA HEU and LEU Spent Fuel Transport

NASA Astrophysics Data System (ADS)

Margeanu, C. A.; Margeanu, S.; Barbos, D.; Iorgulis, C.

2010-12-01

The paper is a comparative study of LEU and HEU fuel utilization effects for the shielding analysis during spent fuel transport. A comparison against the measured data for HEU spent fuel, available from the last stage of spent fuel repatriation fulfilled in the summer of 2008, is also presented. All geometrical and material data for the shipping cask were considered according to NAC-LWT Cask approved model. The shielding analysis estimates radiation doses to shipping cask wall surface, and in air at 1 m and 2 m, respectively, from the cask, by means of 3D Monte Carlo MORSE-SGC code. Before loading into the shipping cask, TRIGA spent fuel source terms and spent fuel parameters have been obtained by means of ORIGEN-S code. Both codes are included in ORNL's SCALE 5 programs package. The actinides contribution to total fuel radioactivity is very low in HEU spent fuel case, becoming 10 times greater in LEU spent fuel case. Dose rates for both HEU and LEU fuel contents are below regulatory limits, LEU spent fuel photon dose rates being greater than HEU ones. Comparison between HEU spent fuel theoretical and measured dose rates in selected measuring points shows a good agreement, calculated values being greater than the measured ones both to cask wall surface (about 34% relative difference) and in air at 1 m distance from cask surface (about 15% relative difference).

Stochastic-field cavitation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumond, J., E-mail: julien.dumond@areva.com; AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen; Magagnato, F.

2013-07-15

Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-fieldmore » cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.« less

The costs of production of alternative jet fuel: A harmonized stochastic assessment.

PubMed

Bann, Seamus J; Malina, Robert; Staples, Mark D; Suresh, Pooja; Pearlson, Matthew; Tyner, Wallace E; Hileman, James I; Barrett, Steven

2017-03-01

This study quantifies and compares the costs of production for six alternative jet fuel pathways using consistent financial and technical assumptions. Uncertainty was propagated through the analysis using Monte Carlo simulations. The six processes assessed were HEFA, advanced fermentation, Fischer-Tropsch, aqueous phase processing, hydrothermal liquefaction, and fast pyrolysis. The results indicate that none of the six processes would be profitable in the absence of government incentives, with HEFA using yellow grease, HEFA using tallow, and FT revealing the lowest mean jet fuel prices at $0.91/liter ($0.66/liter-$1.24/liter), $1.06/liter ($0.79/liter-$1.42/liter), and $1.15/liter ($0.95/liter-$1.39/liter), respectively. This study also quantifies plant performance in the United States with a Renewable Fuel Standard policy analysis. Results indicate that some pathways could achieve positive NPV with relatively high likelihood under existing policy supports, with HEFA and FPH revealing the highest probability of positive NPV at 94.9% and 99.7%, respectively, in the best-case scenario. Copyright © 2016 Elsevier Ltd. All rights reserved.

A non-stochastic iterative computational method to model light propagation in turbid media

NASA Astrophysics Data System (ADS)

McIntyre, Thomas J.; Zemp, Roger J.

2015-03-01

Monte Carlo models are widely used to model light transport in turbid media, however their results implicitly contain stochastic variations. These fluctuations are not ideal, especially for inverse problems where Jacobian matrix errors can lead to large uncertainties upon matrix inversion. Yet Monte Carlo approaches are more computationally favorable than solving the full Radiative Transport Equation. Here, a non-stochastic computational method of estimating fluence distributions in turbid media is proposed, which is called the Non-Stochastic Propagation by Iterative Radiance Evaluation method (NSPIRE). Rather than using stochastic means to determine a random walk for each photon packet, the propagation of light from any element to all other elements in a grid is modelled simultaneously. For locally homogeneous anisotropic turbid media, the matrices used to represent scattering and projection are shown to be block Toeplitz, which leads to computational simplifications via convolution operators. To evaluate the accuracy of the algorithm, 2D simulations were done and compared against Monte Carlo models for the cases of an isotropic point source and a pencil beam incident on a semi-infinite turbid medium. The model was shown to have a mean percent error less than 2%. The algorithm represents a new paradigm in radiative transport modelling and may offer a non-stochastic alternative to modeling light transport in anisotropic scattering media for applications where the diffusion approximation is insufficient.

Improvements of MCOR: A Monte Carlo depletion code system for fuel assembly reference calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tippayakul, C.; Ivanov, K.; Misu, S.

2006-07-01

This paper presents the improvements of MCOR, a Monte Carlo depletion code system for fuel assembly reference calculations. The improvements of MCOR were initiated by the cooperation between the Penn State Univ. and AREVA NP to enhance the original Penn State Univ. MCOR version in order to be used as a new Monte Carlo depletion analysis tool. Essentially, a new depletion module using KORIGEN is utilized to replace the existing ORIGEN-S depletion module in MCOR. Furthermore, the online burnup cross section generation by the Monte Carlo calculation is implemented in the improved version instead of using the burnup cross sectionmore » library pre-generated by a transport code. Other code features have also been added to make the new MCOR version easier to use. This paper, in addition, presents the result comparisons of the original and the improved MCOR versions against CASMO-4 and OCTOPUS. It was observed in the comparisons that there were quite significant improvements of the results in terms of k{sub inf}, fission rate distributions and isotopic contents. (authors)« less

A stochastic hybrid systems based framework for modeling dependent failure processes

PubMed Central

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods. PMID:28231313

A stochastic hybrid systems based framework for modeling dependent failure processes.

PubMed

Fan, Mengfei; Zeng, Zhiguo; Zio, Enrico; Kang, Rui; Chen, Ying

2017-01-01

In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.

An improved multilevel Monte Carlo method for estimating probability distribution functions in stochastic oil reservoir simulations

DOE PAGES

Lu, Dan; Zhang, Guannan; Webster, Clayton G.; ...

2016-12-30

In this paper, we develop an improved multilevel Monte Carlo (MLMC) method for estimating cumulative distribution functions (CDFs) of a quantity of interest, coming from numerical approximation of large-scale stochastic subsurface simulations. Compared with Monte Carlo (MC) methods, that require a significantly large number of high-fidelity model executions to achieve a prescribed accuracy when computing statistical expectations, MLMC methods were originally proposed to significantly reduce the computational cost with the use of multifidelity approximations. The improved performance of the MLMC methods depends strongly on the decay of the variance of the integrand as the level increases. However, the main challengemore » in estimating CDFs is that the integrand is a discontinuous indicator function whose variance decays slowly. To address this difficult task, we approximate the integrand using a smoothing function that accelerates the decay of the variance. In addition, we design a novel a posteriori optimization strategy to calibrate the smoothing function, so as to balance the computational gain and the approximation error. The combined proposed techniques are integrated into a very general and practical algorithm that can be applied to a wide range of subsurface problems for high-dimensional uncertainty quantification, such as a fine-grid oil reservoir model considered in this effort. The numerical results reveal that with the use of the calibrated smoothing function, the improved MLMC technique significantly reduces the computational complexity compared to the standard MC approach. Finally, we discuss several factors that affect the performance of the MLMC method and provide guidance for effective and efficient usage in practice.« less

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models

PubMed Central

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful. PMID:28626348

GPU-powered Shotgun Stochastic Search for Dirichlet process mixtures of Gaussian Graphical Models.

PubMed

Mukherjee, Chiranjit; Rodriguez, Abel

2016-01-01

Gaussian graphical models are popular for modeling high-dimensional multivariate data with sparse conditional dependencies. A mixture of Gaussian graphical models extends this model to the more realistic scenario where observations come from a heterogenous population composed of a small number of homogeneous sub-groups. In this paper we present a novel stochastic search algorithm for finding the posterior mode of high-dimensional Dirichlet process mixtures of decomposable Gaussian graphical models. Further, we investigate how to harness the massive thread-parallelization capabilities of graphical processing units to accelerate computation. The computational advantages of our algorithms are demonstrated with various simulated data examples in which we compare our stochastic search with a Markov chain Monte Carlo algorithm in moderate dimensional data examples. These experiments show that our stochastic search largely outperforms the Markov chain Monte Carlo algorithm in terms of computing-times and in terms of the quality of the posterior mode discovered. Finally, we analyze a gene expression dataset in which Markov chain Monte Carlo algorithms are too slow to be practically useful.

Computing Optimal Stochastic Portfolio Execution Strategies: A Parametric Approach Using Simulations

NASA Astrophysics Data System (ADS)

Moazeni, Somayeh; Coleman, Thomas F.; Li, Yuying

2010-09-01

Computing optimal stochastic portfolio execution strategies under appropriate risk consideration presents great computational challenge. We investigate a parametric approach for computing optimal stochastic strategies using Monte Carlo simulations. This approach allows reduction in computational complexity by computing coefficients for a parametric representation of a stochastic dynamic strategy based on static optimization. Using this technique, constraints can be similarly handled using appropriate penalty functions. We illustrate the proposed approach to minimize the expected execution cost and Conditional Value-at-Risk (CVaR).

Inverse Modeling Using Markov Chain Monte Carlo Aided by Adaptive Stochastic Collocation Method with Transformation

NASA Astrophysics Data System (ADS)

Zhang, D.; Liao, Q.

2016-12-01

The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of

Selected-node stochastic simulation algorithm

NASA Astrophysics Data System (ADS)

Duso, Lorenzo; Zechner, Christoph

2018-04-01

Stochastic simulations of biochemical networks are of vital importance for understanding complex dynamics in cells and tissues. However, existing methods to perform such simulations are associated with computational difficulties and addressing those remains a daunting challenge to the present. Here we introduce the selected-node stochastic simulation algorithm (snSSA), which allows us to exclusively simulate an arbitrary, selected subset of molecular species of a possibly large and complex reaction network. The algorithm is based on an analytical elimination of chemical species, thereby avoiding explicit simulation of the associated chemical events. These species are instead described continuously in terms of statistical moments derived from a stochastic filtering equation, resulting in a substantial speedup when compared to Gillespie's stochastic simulation algorithm (SSA). Moreover, we show that statistics obtained via snSSA profit from a variance reduction, which can significantly lower the number of Monte Carlo samples needed to achieve a certain performance. We demonstrate the algorithm using several biological case studies for which the simulation time could be reduced by orders of magnitude.

Analytic continuation of quantum Monte Carlo data by stochastic analytical inference.

PubMed

Fuchs, Sebastian; Pruschke, Thomas; Jarrell, Mark

2010-05-01

We present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad hoc assumptions introduced in similar algorithms to fix the regularization parameter. We apply the algorithm to imaginary-time quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum-entropy calculation.

Stochastic techno-economic analysis of alcohol-to-jet fuel production.

PubMed

Yao, Guolin; Staples, Mark D; Malina, Robert; Tyner, Wallace E

2017-01-01

Alcohol-to-jet (ATJ) is one of the technical feasible biofuel technologies. It produces jet fuel from sugary, starchy, and lignocellulosic biomass, such as sugarcane, corn grain, and switchgrass, via fermentation of sugars to ethanol or other alcohols. This study assesses the ATJ biofuel production pathway for these three biomass feedstocks, and advances existing techno-economic analyses of biofuels in three ways. First, we incorporate technical uncertainty for all by-products and co-products though statistical linkages between conversion efficiencies and input and output levels. Second, future price uncertainty is based on case-by-case time-series estimation, and a local sensitivity analysis is conducted with respect to each uncertain variable. Third, breakeven price distributions are developed to communicate the inherent uncertainty in breakeven price. This research also considers uncertainties in utility input requirements, fuel and by-product outputs, as well as price uncertainties for all major inputs, products, and co-products. All analyses are done from the perspective of a private firm. The stochastic dominance results of net present values (NPV) and breakeven price distributions show that sugarcane is the lowest cost feedstock over the entire range of uncertainty with the least risks, followed by corn grain and switchgrass, with the mean breakeven jet fuel prices being $0.96/L ($3.65/gal), $1.01/L ($3.84/gal), and $1.38/L ($5.21/gal), respectively. The variation of revenues from by-products in corn grain pathway can significantly impact its profitability. Sensitivity analyses show that technical uncertainty significantly impacts breakeven price and NPV distributions. Technical uncertainty is critical in determining the economic performance of the ATJ fuel pathway. Technical uncertainty needs to be considered in future economic analyses. The variation of revenues from by-products plays a significant role in profitability. With the distribution of breakeven

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.

Technical notes and correspondence: Stochastic robustness of linear time-invariant control systems

NASA Technical Reports Server (NTRS)

Stengel, Robert F.; Ray, Laura R.

1991-01-01

A simple numerical procedure for estimating the stochastic robustness of a linear time-invariant system is described. Monte Carlo evaluations of the system's eigenvalues allows the probability of instability and the related stochastic root locus to be estimated. This analysis approach treats not only Gaussian parameter uncertainties but non-Gaussian cases, including uncertain-but-bounded variation. Confidence intervals for the scalar probability of instability address computational issues inherent in Monte Carlo simulation. Trivial extensions of the procedure admit consideration of alternate discriminants; thus, the probabilities that stipulated degrees of instability will be exceeded or that closed-loop roots will leave desirable regions can also be estimated. Results are particularly amenable to graphical presentation.

Stochastic hybrid systems for studying biochemical processes.

PubMed

Singh, Abhyudai; Hespanha, João P

2010-11-13

Many protein and mRNA species occur at low molecular counts within cells, and hence are subject to large stochastic fluctuations in copy numbers over time. Development of computationally tractable frameworks for modelling stochastic fluctuations in population counts is essential to understand how noise at the cellular level affects biological function and phenotype. We show that stochastic hybrid systems (SHSs) provide a convenient framework for modelling the time evolution of population counts of different chemical species involved in a set of biochemical reactions. We illustrate recently developed techniques that allow fast computations of the statistical moments of the population count, without having to run computationally expensive Monte Carlo simulations of the biochemical reactions. Finally, we review different examples from the literature that illustrate the benefits of using SHSs for modelling biochemical processes.

Analytical Assessment for Transient Stability Under Stochastic Continuous Disturbances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ju, Ping; Li, Hongyu; Gan, Chun

Here, with the growing integration of renewable power generation, plug-in electric vehicles, and other sources of uncertainty, increasing stochastic continuous disturbances are brought to power systems. The impact of stochastic continuous disturbances on power system transient stability attracts significant attention. To address this problem, this paper proposes an analytical assessment method for transient stability of multi-machine power systems under stochastic continuous disturbances. In the proposed method, a probability measure of transient stability is presented and analytically solved by stochastic averaging. Compared with the conventional method (Monte Carlo simulation), the proposed method is many orders of magnitude faster, which makes itmore » very attractive in practice when many plans for transient stability must be compared or when transient stability must be analyzed quickly. Also, it is found that the evolution of system energy over time is almost a simple diffusion process by the proposed method, which explains the impact mechanism of stochastic continuous disturbances on transient stability in theory.« less

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

DTIC Science & Technology

2016-10-17

finite volume schemes, discontinuous Galerkin finite element method, and related methods, for solving computational fluid dynamics (CFD) problems and...approximation for finite element methods. (3) The development of methods of simulation and analysis for the study of large scale stochastic systems of...laws, finite element method, Bernstein-Bezier finite elements , weakly interacting particle systems, accelerated Monte Carlo, stochastic networks 16

Stochastic Feedforward Control Technique

NASA Technical Reports Server (NTRS)

Halyo, Nesim

1990-01-01

Class of commanded trajectories modeled as stochastic process. Advanced Transport Operating Systems (ATOPS) research and development program conducted by NASA Langley Research Center aimed at developing capabilities for increases in capacities of airports, safe and accurate flight in adverse weather conditions including shear, winds, avoidance of wake vortexes, and reduced consumption of fuel. Advances in techniques for design of modern controls and increased capabilities of digital flight computers coupled with accurate guidance information from Microwave Landing System (MLS). Stochastic feedforward control technique developed within context of ATOPS program.

Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liang, Faming; Cheng, Yichen; Lin, Guang

2014-06-13

Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to have such a long CPU time. This paper proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation Markov chain Monte Carlo, it is shown that themore » new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, e.g., a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors.« less

A cavitation model based on Eulerian stochastic fields

NASA Astrophysics Data System (ADS)

Magagnato, F.; Dumond, J.

2013-12-01

Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

A Stochastic Diffusion Process for the Dirichlet Distribution

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2013-03-01

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability ofNcoupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded sample space, a coupled nonlinear diffusion process is required: the Wiener processes in the equivalent system of stochastic differential equations are multiplicative with coefficients dependent on all the stochastic variables. Individual samples of a discrete ensemble, obtained from the stochastic process, satisfy a unit-sum constraint at all times. The process may be used to represent realizations of a fluctuating ensemble ofNvariables subject to a conservation principle.more » Similar to the multivariate Wright-Fisher process, whose invariant is also Dirichlet, the univariate case yields a process whose invariant is the beta distribution. As a test of the results, Monte Carlo simulations are used to evolve numerical ensembles toward the invariant Dirichlet distribution.« less

Algebraic, geometric, and stochastic aspects of genetic operators

NASA Technical Reports Server (NTRS)

Foo, N. Y.; Bosworth, J. L.

1972-01-01

Genetic algorithms for function optimization employ genetic operators patterned after those observed in search strategies employed in natural adaptation. Two of these operators, crossover and inversion, are interpreted in terms of their algebraic and geometric properties. Stochastic models of the operators are developed which are employed in Monte Carlo simulations of their behavior.

Stochastic kinetic mean field model

NASA Astrophysics Data System (ADS)

Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, Volodymyr; Tomán, János J.; Gajdics, Bence; Gusak, Andriy M.

2016-07-01

This paper introduces a new model for calculating the change in time of three-dimensional atomic configurations. The model is based on the kinetic mean field (KMF) approach, however we have transformed that model into a stochastic approach by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which produces results similar to the lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to implement the algorithm (open source program code is provided on http://skmf.eu website). We will show that the result of one SKMF run may correspond to the average of several KMC runs. The number of KMC runs is inversely proportional to the amplitude square of the noise in SKMF. This makes SKMF an ideal tool also for statistical purposes.

Compressible cavitation with stochastic field method

NASA Astrophysics Data System (ADS)

Class, Andreas; Dumond, Julien

2012-11-01

Non-linear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrange particles or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic field method solving pdf transport based on Euler fields has been proposed which eliminates the necessity to mix Euler and Lagrange techniques or prescribed pdf assumptions. In the present work, part of the PhD Design and analysis of a Passive Outflow Reducer relying on cavitation, a first application of the stochastic field method to multi-phase flow and in particular to cavitating flow is presented. The application considered is a nozzle subjected to high velocity flow so that sheet cavitation is observed near the nozzle surface in the divergent section. It is demonstrated that the stochastic field formulation captures the wide range of pdf shapes present at different locations. The method is compatible with finite-volume codes where all existing physical models available for Lagrange techniques, presumed pdf or binning methods can be easily extended to the stochastic field formulation.

Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques.

PubMed

Kilinc, Deniz; Demir, Alper

2017-08-01

The brain is extremely energy efficient and remarkably robust in what it does despite the considerable variability and noise caused by the stochastic mechanisms in neurons and synapses. Computational modeling is a powerful tool that can help us gain insight into this important aspect of brain mechanism. A deep understanding and computational design tools can help develop robust neuromorphic electronic circuits and hybrid neuroelectronic systems. In this paper, we present a general modeling framework for biological neuronal circuits that systematically captures the nonstationary stochastic behavior of ion channels and synaptic processes. In this framework, fine-grained, discrete-state, continuous-time Markov chain models of both ion channels and synaptic processes are treated in a unified manner. Our modeling framework features a mechanism for the automatic generation of the corresponding coarse-grained, continuous-state, continuous-time stochastic differential equation models for neuronal variability and noise. Furthermore, we repurpose non-Monte Carlo noise analysis techniques, which were previously developed for analog electronic circuits, for the stochastic characterization of neuronal circuits both in time and frequency domain. We verify that the fast non-Monte Carlo analysis methods produce results with the same accuracy as computationally expensive Monte Carlo simulations. We have implemented the proposed techniques in a prototype simulator, where both biological neuronal and analog electronic circuits can be simulated together in a coupled manner.

Off-diagonal expansion quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

Off-diagonal expansion quantum Monte Carlo.

PubMed

Albash, Tameem; Wagenbreth, Gene; Hen, Itay

2017-12-01

We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.

Distributed parallel computing in stochastic modeling of groundwater systems.

PubMed

Dong, Yanhui; Li, Guomin; Xu, Haizhen

2013-03-01

Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

Stochastic volatility of the futures prices of emission allowances: A Bayesian approach

NASA Astrophysics Data System (ADS)

Kim, Jungmu; Park, Yuen Jung; Ryu, Doojin

2017-01-01

Understanding the stochastic nature of the spot volatility of emission allowances is crucial for risk management in emissions markets. In this study, by adopting a stochastic volatility model with or without jumps to represent the dynamics of European Union Allowances (EUA) futures prices, we estimate the daily volatilities and model parameters by using the Markov Chain Monte Carlo method for stochastic volatility (SV), stochastic volatility with return jumps (SVJ) and stochastic volatility with correlated jumps (SVCJ) models. Our empirical results reveal three important features of emissions markets. First, the data presented herein suggest that EUA futures prices exhibit significant stochastic volatility. Second, the leverage effect is noticeable regardless of whether or not jumps are included. Third, the inclusion of jumps has a significant impact on the estimation of the volatility dynamics. Finally, the market becomes very volatile and large jumps occur at the beginning of a new phase. These findings are important for policy makers and regulators.

Application of stochastic approach based on Monte Carlo (MC) simulation for life cycle inventory (LCI) to the steel process chain: case study.

PubMed

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. Copyright © 2013 Elsevier B.V. All rights reserved.

Stochastic volatility models and Kelvin waves

NASA Astrophysics Data System (ADS)

Lipton, Alex; Sepp, Artur

2008-08-01

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

A Stochastic-Variational Model for Soft Mumford-Shah Segmentation

PubMed Central

2006-01-01

In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model for soft (or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classical hard Mumford-Shah segmentation, the new model allows each pixel to belong to each image pattern with some probability. Soft segmentation could lead to hard segmentation, and hence is more general. The modeling procedure, mathematical analysis on the existence of optimal solutions, and computational implementation of the new model are explored in detail, and numerical examples of both synthetic and natural images are presented. PMID:23165059

Multiple-time-stepping generalized hybrid Monte Carlo methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Escribano, Bruno, E-mail: bescribano@bcamath.org; Akhmatskaya, Elena; IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao

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).more » 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.« less

Discrepancy-based error estimates for Quasi-Monte Carlo III. Error distributions and central limits

NASA Astrophysics Data System (ADS)

Hoogland, Jiri; Kleiss, Ronald

1997-04-01

In Quasi-Monte Carlo integration, the integration error is believed to be generally smaller than in classical Monte Carlo with the same number of integration points. Using an appropriate definition of an ensemble of quasi-random point sets, we derive various results on the probability distribution of the integration error, which can be compared to the standard Central Limit Theorem for normal stochastic sampling. In many cases, a Gaussian error distribution is obtained.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

PubMed

Kalantzis, Georgios

2009-06-01

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Some variance reduction methods for numerical stochastic homogenization

PubMed Central

Blanc, X.; Le Bris, C.; Legoll, F.

2016-01-01

We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. PMID:27002065

Characterizing model uncertainties in the life cycle of lignocellulose-based ethanol fuels.

PubMed

Spatari, Sabrina; MacLean, Heather L

2010-11-15

Renewable and low carbon fuel standards being developed at federal and state levels require an estimation of the life cycle carbon intensity (LCCI) of candidate fuels that can substitute for gasoline, such as second generation bioethanol. Estimating the LCCI of such fuels with a high degree of confidence requires the use of probabilistic methods to account for known sources of uncertainty. We construct life cycle models for the bioconversion of agricultural residue (corn stover) and energy crops (switchgrass) and explicitly examine uncertainty using Monte Carlo simulation. Using statistical methods to identify significant model variables from public data sets and Aspen Plus chemical process models,we estimate stochastic life cycle greenhouse gas (GHG) emissions for the two feedstocks combined with two promising fuel conversion technologies. The approach can be generalized to other biofuel systems. Our results show potentially high and uncertain GHG emissions for switchgrass-ethanol due to uncertain CO₂ flux from land use change and N₂O flux from N fertilizer. However, corn stover-ethanol,with its low-in-magnitude, tight-in-spread LCCI distribution, shows considerable promise for reducing life cycle GHG emissions relative to gasoline and corn-ethanol. Coproducts are important for reducing the LCCI of all ethanol fuels we examine.

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines.

PubMed

Neftci, Emre O; Pedroni, Bruno U; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware.

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

PubMed Central

Neftci, Emre O.; Pedroni, Bruno U.; Joshi, Siddharth; Al-Shedivat, Maruan; Cauwenberghs, Gert

2016-01-01

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines (S2Ms), a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based S2Ms outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware. PMID:27445650

Stochastic simulation and analysis of biomolecular reaction networks

PubMed Central

Frazier, John M; Chushak, Yaroslav; Foy, Brent

2009-01-01

Background In recent years, several stochastic simulation algorithms have been developed to generate Monte Carlo trajectories that describe the time evolution of the behavior of biomolecular reaction networks. However, the effects of various stochastic simulation and data analysis conditions on the observed dynamics of complex biomolecular reaction networks have not recieved much attention. In order to investigate these issues, we employed a a software package developed in out group, called Biomolecular Network Simulator (BNS), to simulate and analyze the behavior of such systems. The behavior of a hypothetical two gene in vitro transcription-translation reaction network is investigated using the Gillespie exact stochastic algorithm to illustrate some of the factors that influence the analysis and interpretation of these data. Results Specific issues affecting the analysis and interpretation of simulation data are investigated, including: (1) the effect of time interval on data presentation and time-weighted averaging of molecule numbers, (2) effect of time averaging interval on reaction rate analysis, (3) effect of number of simulations on precision of model predictions, and (4) implications of stochastic simulations on optimization procedures. Conclusion The two main factors affecting the analysis of stochastic simulations are: (1) the selection of time intervals to compute or average state variables and (2) the number of simulations generated to evaluate the system behavior. PMID:19534796

Acting Irrationally to Improve Performance in Stochastic Worlds

NASA Astrophysics Data System (ADS)

Belavkin, Roman V.

Despite many theories and algorithms for decision-making, after estimating the utility function the choice is usually made by maximising its expected value (the max EU principle). This traditional and 'rational' conclusion of the decision-making process is compared in this paper with several 'irrational' techniques that make choice in Monte-Carlo fashion. The comparison is made by evaluating the performance of simple decision-theoretic agents in stochastic environments. It is shown that not only the random choice strategies can achieve performance comparable to the max EU method, but under certain conditions the Monte-Carlo choice methods perform almost two times better than the max EU. The paper concludes by quoting evidence from recent cognitive modelling works as well as the famous decision-making paradoxes.

PRELIMINARY COUPLING OF THE MONTE CARLO CODE OPENMC AND THE MULTIPHYSICS OBJECT-ORIENTED SIMULATION ENVIRONMENT (MOOSE) FOR ANALYZING DOPPLER FEEDBACK IN MONTE CARLO SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matthew Ellis; Derek Gaston; Benoit Forget

In recent years the use of Monte Carlo methods for modeling reactors has become feasible due to the increasing availability of massively parallel computer systems. One of the primary challenges yet to be fully resolved, however, is the efficient and accurate inclusion of multiphysics feedback in Monte Carlo simulations. The research in this paper presents a preliminary coupling of the open source Monte Carlo code OpenMC with the open source Multiphysics Object-Oriented Simulation Environment (MOOSE). The coupling of OpenMC and MOOSE will be used to investigate efficient and accurate numerical methods needed to include multiphysics feedback in Monte Carlo codes.more » An investigation into the sensitivity of Doppler feedback to fuel temperature approximations using a two dimensional 17x17 PWR fuel assembly is presented in this paper. The results show a functioning multiphysics coupling between OpenMC and MOOSE. The coupling utilizes Functional Expansion Tallies to accurately and efficiently transfer pin power distributions tallied in OpenMC to unstructured finite element meshes used in MOOSE. The two dimensional PWR fuel assembly case also demonstrates that for a simplified model the pin-by-pin doppler feedback can be adequately replicated by scaling a representative pin based on pin relative powers.« less

Stochastic dynamic analysis of marine risers considering Gaussian system uncertainties

NASA Astrophysics Data System (ADS)

Ni, Pinghe; Li, Jun; Hao, Hong; Xia, Yong

2018-03-01

This paper performs the stochastic dynamic response analysis of marine risers with material uncertainties, i.e. in the mass density and elastic modulus, by using Stochastic Finite Element Method (SFEM) and model reduction technique. These uncertainties are assumed having Gaussian distributions. The random mass density and elastic modulus are represented by using the Karhunen-Loève (KL) expansion. The Polynomial Chaos (PC) expansion is adopted to represent the vibration response because the covariance of the output is unknown. Model reduction based on the Iterated Improved Reduced System (IIRS) technique is applied to eliminate the PC coefficients of the slave degrees of freedom to reduce the dimension of the stochastic system. Monte Carlo Simulation (MCS) is conducted to obtain the reference response statistics. Two numerical examples are studied in this paper. The response statistics from the proposed approach are compared with those from MCS. It is noted that the computational time is significantly reduced while the accuracy is kept. The results demonstrate the efficiency of the proposed approach for stochastic dynamic response analysis of marine risers.

Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling

NASA Astrophysics Data System (ADS)

Katsiolides, Grigoris; Müller, Eike H.; Scheichl, Robert; Shardlow, Tony; Giles, Michael B.; Thomson, David J.

2018-02-01

A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations (SDEs). The computational bottleneck is the Monte Carlo algorithm, which simulates the motion of a large number of model particles in a turbulent velocity field; for each particle, a trajectory is calculated with a numerical timestepping method. Choosing an efficient numerical method is particularly important in operational emergency-response applications, such as tracking radioactive clouds from nuclear accidents or predicting the impact of volcanic ash clouds on international aviation, where accurate and timely predictions are essential. In this paper, we investigate the application of the Multilevel Monte Carlo (MLMC) method to simulate the propagation of particles in a representative one-dimensional dispersion scenario in the atmospheric boundary layer. MLMC can be shown to result in asymptotically superior computational complexity and reduced computational cost when compared to the Standard Monte Carlo (StMC) method, which is currently used in atmospheric dispersion modelling. To reduce the absolute cost of the method also in the non-asymptotic regime, it is equally important to choose the best possible numerical timestepping method on each level. To investigate this, we also compare the standard symplectic Euler method, which is used in many operational models, with two improved timestepping algorithms based on SDE splitting methods.

Stochastic solution to quantum dynamics

NASA Technical Reports Server (NTRS)

John, Sarah; Wilson, John W.

1994-01-01

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

Monte Carlo-based Reconstruction in Water Cherenkov Detectors using Chroma

NASA Astrophysics Data System (ADS)

Seibert, Stanley; Latorre, Anthony

2012-03-01

We demonstrate the feasibility of event reconstruction---including position, direction, energy and particle identification---in water Cherenkov detectors with a purely Monte Carlo-based method. Using a fast optical Monte Carlo package we have written, called Chroma, in combination with several variance reduction techniques, we can estimate the value of a likelihood function for an arbitrary event hypothesis. The likelihood can then be maximized over the parameter space of interest using a form of gradient descent designed for stochastic functions. Although slower than more traditional reconstruction algorithms, this completely Monte Carlo-based technique is universal and can be applied to a detector of any size or shape, which is a major advantage during the design phase of an experiment. As a specific example, we focus on reconstruction results from a simulation of the 200 kiloton water Cherenkov far detector option for LBNE.

Learning Weight Uncertainty with Stochastic Gradient MCMC for Shape Classification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Chunyuan; Stevens, Andrew J.; Chen, Changyou

2016-08-10

Learning the representation of shape cues in 2D & 3D objects for recognition is a fundamental task in computer vision. Deep neural networks (DNNs) have shown promising performance on this task. Due to the large variability of shapes, accurate recognition relies on good estimates of model uncertainty, ignored in traditional training of DNNs, typically learned via stochastic optimization. This paper leverages recent advances in stochastic gradient Markov Chain Monte Carlo (SG-MCMC) to learn weight uncertainty in DNNs. It yields principled Bayesian interpretations for the commonly used Dropout/DropConnect techniques and incorporates them into the SG-MCMC framework. Extensive experiments on 2D &more » 3D shape datasets and various DNN models demonstrate the superiority of the proposed approach over stochastic optimization. Our approach yields higher recognition accuracy when used in conjunction with Dropout and Batch-Normalization.« less

Stochastic lattice model of synaptic membrane protein domains.

PubMed

Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A

2017-05-01

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

Mixing Single Scattering Properties in Vector Radiative Transfer for Deterministic and Stochastic Solutions

NASA Astrophysics Data System (ADS)

Mukherjee, L.; Zhai, P.; Hu, Y.; Winker, D. M.

2016-12-01

Among the primary factors, which determine the polarized radiation, field of a turbid medium are the single scattering properties of the medium. When multiple types of scatterers are present, the single scattering properties of the scatterers need to be properly mixed in order to find the solutions to the vector radiative transfer theory (VRT). The VRT solvers can be divided into two types: deterministic and stochastic. The deterministic solver can only accept one set of single scattering property in its smallest discretized spatial volume. When the medium contains more than one kind of scatterer, their single scattering properties are averaged, and then used as input for the deterministic solver. The stochastic solver, can work with different kinds of scatterers explicitly. In this work, two different mixing schemes are studied using the Successive Order of Scattering (SOS) method and Monte Carlo (MC) methods. One scheme is used for deterministic and the other is used for the stochastic Monte Carlo method. It is found that the solutions from the two VRT solvers using two different mixing schemes agree with each other extremely well. This confirms the equivalence to the two mixing schemes and also provides a benchmark for the VRT solution for the medium studied.

Some variance reduction methods for numerical stochastic homogenization.

PubMed

Blanc, X; Le Bris, C; Legoll, F

2016-04-28

We give an overview of a series of recent studies devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires that a set of problems is solved at the microscale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behaviour. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts in the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here. © 2016 The Author(s).

Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arampatzis, Georgios, E-mail: garab@math.uoc.gr; Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003; Katsoulakis, Markos A., E-mail: markos@math.umass.edu

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 themore » 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

Stochastic inversion of cross-borehole radar data from metalliferous vein detection

NASA Astrophysics Data System (ADS)

Zeng, Zhaofa; Huai, Nan; Li, Jing; Zhao, Xueyu; Liu, Cai; Hu, Yingsa; Zhang, Ling; Hu, Zuzhi; Yang, Hui

2017-12-01

In the exploration and evaluation of the metalliferous veins with a cross-borehole radar system, traditional linear inversion methods (least squares inversion, LSQR) only get indirect parameters (permittivity, resistivity, or velocity) to estimate the target structure. They cannot accurately reflect the geological parameters of the metalliferous veins’ media properties. In order to get the intrinsic geological parameters and internal distribution, in this paper, we build a metalliferous veins model based on the stochastic effective medium theory, and carry out stochastic inversion and parameter estimation based on the Monte Carlo sampling algorithm. Compared with conventional LSQR, the stochastic inversion can get higher resolution inversion permittivity and velocity of the target body. We can estimate more accurately the distribution characteristics of abnormality and target internal parameters. It provides a new research idea to evaluate the properties of complex target media.

Fast and Efficient Stochastic Optimization for Analytic Continuation

DOE PAGES

Bao, Feng; Zhang, Guannan; Webster, Clayton G; ...

2016-09-28

In this analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM) as a more accessible variant of the stochastic optimization method introduced by Mishchenko et al. [Phys. Rev. B 62, 6317 (2000)], and we benchmark the resulting spectra with those obtained by the standard maximum entropy method for three representative test cases, including data taken from studies of the two-dimensional Hubbard model. Genearally, we find that our FESOM approach yields spectra similar to the maximum entropy results.more » In particular, while the maximum entropy method yields superior results when the quality of the data is strong, we find that FESOM is able to resolve fine structure with more detail when the quality of the data is poor. In addition, because of its stochastic nature, the method provides detailed information on the frequency-dependent uncertainty of the resulting spectra, while the maximum entropy method does so only for the spectral weight integrated over a finite frequency region. Therefore, we believe that this variant of the stochastic optimization approach provides a viable alternative to the routinely used maximum entropy method, especially for data of poor quality.« less

Heat Source Characterization In A TREAT Fuel Particle Using Coupled Neutronics Binary Collision Monte-Carlo Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Schwen, Daniel; Ghassemi, Pedram

This work presents a multi-physics, multi-scale approach to modeling the Transient Test Reactor (TREAT) currently prepared for restart at the Idaho National Laboratory. TREAT fuel is made up of microscopic fuel grains (r ˜ 20µm) dispersed in a graphite matrix. The novelty of this work is in coupling a binary collision Monte-Carlo (BCMC) model to the Finite Element based code Moose for solving a microsopic heat-conduction problem whose driving source is provided by the BCMC model tracking fission fragment energy deposition. This microscopic model is driven by a transient, engineering scale neutronics model coupled to an adiabatic heating model. Themore » macroscopic model provides local power densities and neutron energy spectra to the microscpic model. Currently, no feedback from the microscopic to the macroscopic model is considered. TREAT transient 15 is used to exemplify the capabilities of the multi-physics, multi-scale model, and it is found that the average fuel grain temperature differs from the average graphite temperature by 80 K despite the low-power transient. The large temperature difference has strong implications on the Doppler feedback a potential LEU TREAT core would see, and it underpins the need for multi-physics, multi-scale modeling of a TREAT LEU core.« less

Studies of concentration and temperature dependences of precipitation kinetics in iron-copper alloys using kinetic Monte Carlo and stochastic statistical simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khromov, K. Yu.; Vaks, V. G., E-mail: vaks@mbslab.kiae.ru; 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 withmore » 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.« less

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

NASA Astrophysics Data System (ADS)

Deng, Zhaojie; Arsenault, Sam; Caranica, Cristian; Griffith, James; Zhu, Taotao; Al-Omari, Ahmad; Schüttler, Heinz-Bernd; Arnold, Jonathan; Mao, Leidong

2016-10-01

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype.

Synchronizing stochastic circadian oscillators in single cells of Neurospora crassa

PubMed Central

Deng, Zhaojie; Arsenault, Sam; Caranica, Cristian; Griffith, James; Zhu, Taotao; Al-Omari, Ahmad; Schüttler, Heinz-Bernd; Arnold, Jonathan; Mao, Leidong

2016-01-01

The synchronization of stochastic coupled oscillators is a central problem in physics and an emerging problem in biology, particularly in the context of circadian rhythms. Most measurements on the biological clock are made at the macroscopic level of millions of cells. Here measurements are made on the oscillators in single cells of the model fungal system, Neurospora crassa, with droplet microfluidics and the use of a fluorescent recorder hooked up to a promoter on a clock controlled gene-2 (ccg-2). The oscillators of individual cells are stochastic with a period near 21 hours (h), and using a stochastic clock network ensemble fitted by Markov Chain Monte Carlo implemented on general-purpose graphical processing units (or GPGPUs) we estimated that >94% of the variation in ccg-2 expression was stochastic (as opposed to experimental error). To overcome this stochasticity at the macroscopic level, cells must synchronize their oscillators. Using a classic measure of similarity in cell trajectories within droplets, the intraclass correlation (ICC), the synchronization surface ICC is measured on >25,000 cells as a function of the number of neighboring cells within a droplet and of time. The synchronization surface provides evidence that cells communicate, and synchronization varies with genotype. PMID:27786253

The influence of Stochastic perturbation of Geotechnical media On Electromagnetic tomography

NASA Astrophysics Data System (ADS)

Song, Lei; Yang, Weihao; Huangsonglei, Jiahui; Li, HaiPeng

2015-04-01

Electromagnetic tomography (CT) are commonly utilized in Civil engineering to detect the structure defects or geological anomalies. CT are generally recognized as a high precision geophysical method and the accuracy of CT are expected to be several centimeters and even to be several millimeters. Then, high frequency antenna with short wavelength are utilized commonly in Civil Engineering. As to the geotechnical media, stochastic perturbation of the EM parameters are inevitably exist in geological scales, in structure scales and in local scales, et al. In those cases, the geometric dimensionings of the target body, the EM wavelength and the accuracy expected might be of the same order. When the high frequency EM wave propagated in the stochastic geotechnical media, the GPR signal would be reflected not only from the target bodies but also from the stochastic perturbation of the background media. To detect the karst caves in dissolution fracture rock, one need to assess the influence of the stochastic distributed dissolution holes and fractures; to detect the void in a concrete structure, one should master the influence of the stochastic distributed stones, et al. In this paper, on the base of stochastic media discrete realizations, the authors try to evaluate quantificationally the influence of the stochastic perturbation of Geotechnical media by Radon/Iradon Transfer through full-combined Monte Carlo numerical simulation. It is found the stochastic noise is related with transfer angle, perturbing strength, angle interval, autocorrelation length, et al. And the quantitative formula of the accuracy of the electromagnetic tomography is also established, which could help on the precision estimation of GPR tomography in stochastic perturbation Geotechnical media. Key words: Stochastic Geotechnical Media; Electromagnetic Tomography; Radon/Iradon Transfer.

Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Müller, Florian, E-mail: florian.mueller@sam.math.ethz.ch; Jenny, Patrick, E-mail: jenny@ifd.mavt.ethz.ch; Meyer, Daniel W., E-mail: meyerda@ethz.ch

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 tomore » 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.« less

Relative frequencies of constrained events in stochastic processes: An analytical approach.

PubMed

Rusconi, S; Akhmatskaya, E; Sokolovski, D; Ballard, N; de la Cal, J C

2015-10-01

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least ≈10(4)). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications.

Comparison of holstein and jersey milk production with a new stochastic animal reproduction model

USDA-ARS?s Scientific Manuscript database

Holsteins and Jerseys are the most popular breeds in the US dairy industry. We built a stochastic, Monte Carlo life events simulation model in Python to test if Jersey cattle’s higher conception rate offsets their lower milk production. The model simulates individual cows and their life events such ...

Stochastic Simulation Tool for Aerospace Structural Analysis

NASA Technical Reports Server (NTRS)

Knight, Norman F.; Moore, David F.

2006-01-01

Stochastic simulation refers to incorporating the effects of design tolerances and uncertainties into the design analysis model and then determining their influence on the design. A high-level evaluation of one such stochastic simulation tool, the MSC.Robust Design tool by MSC.Software Corporation, has been conducted. This stochastic simulation tool provides structural analysts with a tool to interrogate their structural design based on their mathematical description of the design problem using finite element analysis methods. This tool leverages the analyst's prior investment in finite element model development of a particular design. The original finite element model is treated as the baseline structural analysis model for the stochastic simulations that are to be performed. A Monte Carlo approach is used by MSC.Robust Design to determine the effects of scatter in design input variables on response output parameters. The tool was not designed to provide a probabilistic assessment, but to assist engineers in understanding cause and effect. It is driven by a graphical-user interface and retains the engineer-in-the-loop strategy for design evaluation and improvement. The application problem for the evaluation is chosen to be a two-dimensional shell finite element model of a Space Shuttle wing leading-edge panel under re-entry aerodynamic loading. MSC.Robust Design adds value to the analysis effort by rapidly being able to identify design input variables whose variability causes the most influence in response output parameters.

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution - Part 1: theoretical development

NASA Astrophysics Data System (ADS)

Dib, Alain; Kavvas, M. Levent

2018-03-01

The Saint-Venant equations are commonly used as the governing equations to solve for modeling the spatially varied unsteady flow in open channels. The presence of uncertainties in the channel or flow parameters renders these equations stochastic, thus requiring their solution in a stochastic framework in order to quantify the ensemble behavior and the variability of the process. While the Monte Carlo approach can be used for such a solution, its computational expense and its large number of simulations act to its disadvantage. This study proposes, explains, and derives a new methodology for solving the stochastic Saint-Venant equations in only one shot, without the need for a large number of simulations. The proposed methodology is derived by developing the nonlocal Lagrangian-Eulerian Fokker-Planck equation of the characteristic form of the stochastic Saint-Venant equations for an open-channel flow process, with an uncertain roughness coefficient. A numerical method for its solution is subsequently devised. The application and validation of this methodology are provided in a companion paper, in which the statistical results computed by the proposed methodology are compared against the results obtained by the Monte Carlo approach.

Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong

2014-05-30

The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closedmore » solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.« less

Parallelized Stochastic Cutoff Method for Long-Range Interacting Systems

NASA Astrophysics Data System (ADS)

Endo, Eishin; Toga, Yuta; Sasaki, Munetaka

2015-07-01

We present a method of parallelizing the stochastic cutoff (SCO) method, which is a Monte-Carlo method for long-range interacting systems. After interactions are eliminated by the SCO method, we subdivide a lattice into noninteracting interpenetrating sublattices. This subdivision enables us to parallelize the Monte-Carlo calculation in the SCO method. Such subdivision is found by numerically solving the vertex coloring of a graph created by the SCO method. We use an algorithm proposed by Kuhn and Wattenhofer to solve the vertex coloring by parallel computation. This method was applied to a two-dimensional magnetic dipolar system on an L × L square lattice to examine its parallelization efficiency. The result showed that, in the case of L = 2304, the speed of computation increased about 102 times by parallel computation with 288 processors.

Variance reduction for Fokker–Planck based particle Monte Carlo schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorji, M. Hossein, E-mail: gorjih@ifd.mavt.ethz.ch; Andric, Nemanja; Jenny, Patrick

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.more » 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.« less

Online sequential Monte Carlo smoother for partially observed diffusion processes

NASA Astrophysics Data System (ADS)

Gloaguen, Pierre; Étienne, Marie-Pierre; Le Corff, Sylvain

2018-12-01

This paper introduces a new algorithm to approximate smoothed additive functionals of partially observed diffusion processes. This method relies on a new sequential Monte Carlo method which allows to compute such approximations online, i.e., as the observations are received, and with a computational complexity growing linearly with the number of Monte Carlo samples. The original algorithm cannot be used in the case of partially observed stochastic differential equations since the transition density of the latent data is usually unknown. We prove that it may be extended to partially observed continuous processes by replacing this unknown quantity by an unbiased estimator obtained for instance using general Poisson estimators. This estimator is proved to be consistent and its performance are illustrated using data from two models.

A Stochastic Multi-Attribute Assessment of Energy Options for Fairbanks, Alaska

NASA Astrophysics Data System (ADS)

Read, L.; Madani, K.; Mokhtari, S.; Hanks, C. L.; Sheets, B.

2012-12-01

Many competing projects have been proposed to address Interior Alaska's high cost of energy—both for electricity production and for heating. Public and private stakeholders are considering the costs associated with these competing projects which vary in fuel source, subsidy requirements, proximity, and other factors. As a result, the current projects under consideration involve a complex cost structure of potential subsidies and reliance on present and future market prices, introducing a significant amount of uncertainty associated with each selection. Multi-criteria multi-decision making (MCMDM) problems of this nature can benefit from game theory and systems engineering methods, which account for behavior and preferences of stakeholders in the analysis to produce feasible and relevant solutions. This work uses a stochastic MCMDM framework to evaluate the trade-offs of each proposed project based on a complete cost analysis, environmental impact, and long-term sustainability. Uncertainty in the model is quantified via a Monte Carlo analysis, which helps characterize the sensitivity and risk associated with each project. Based on performance measures and criteria outlined by the stakeholders, a decision matrix will inform policy on selecting a project that is both efficient and preferred by the constituents.

The response analysis of fractional-order stochastic system via generalized cell mapping method.

PubMed

Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei

2018-01-01

This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.

Stochastic capture zone analysis of an arsenic-contaminated well using the generalized likelihood uncertainty estimator (GLUE) methodology

NASA Astrophysics Data System (ADS)

Morse, Brad S.; Pohll, Greg; Huntington, Justin; Rodriguez Castillo, Ramiro

2003-06-01

In 1992, Mexican researchers discovered concentrations of arsenic in excess of World Heath Organization (WHO) standards in several municipal wells in the Zimapan Valley of Mexico. This study describes a method to delineate a capture zone for one of the most highly contaminated wells to aid in future well siting. A stochastic approach was used to model the capture zone because of the high level of uncertainty in several input parameters. Two stochastic techniques were performed and compared: "standard" Monte Carlo analysis and the generalized likelihood uncertainty estimator (GLUE) methodology. The GLUE procedure differs from standard Monte Carlo analysis in that it incorporates a goodness of fit (termed a likelihood measure) in evaluating the model. This allows for more information (in this case, head data) to be used in the uncertainty analysis, resulting in smaller prediction uncertainty. Two likelihood measures are tested in this study to determine which are in better agreement with the observed heads. While the standard Monte Carlo approach does not aid in parameter estimation, the GLUE methodology indicates best fit models when hydraulic conductivity is approximately 10-6.5 m/s, with vertically isotropic conditions and large quantities of interbasin flow entering the basin. Probabilistic isochrones (capture zone boundaries) are then presented, and as predicted, the GLUE-derived capture zones are significantly smaller in area than those from the standard Monte Carlo approach.

Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen-Loeve expansion.

PubMed

Barber, Jared; Tanase, Roxana; Yotov, Ivan

2016-06-01

Several Kalman filter algorithms are presented for data assimilation and parameter estimation for a nonlinear diffusion model of epithelial cell migration. These include the ensemble Kalman filter with Monte Carlo sampling and a stochastic collocation (SC) Kalman filter with structured sampling. Further, two types of noise are considered -uncorrelated noise resulting in one stochastic dimension for each element of the spatial grid and correlated noise parameterized by the Karhunen-Loeve (KL) expansion resulting in one stochastic dimension for each KL term. The efficiency and accuracy of the four methods are investigated for two cases with synthetic data with and without noise, as well as data from a laboratory experiment. While it is observed that all algorithms perform reasonably well in matching the target solution and estimating the diffusion coefficient and the growth rate, it is illustrated that the algorithms that employ SC and KL expansion are computationally more efficient, as they require fewer ensemble members for comparable accuracy. In the case of SC methods, this is due to improved approximation in stochastic space compared to Monte Carlo sampling. In the case of KL methods, the parameterization of the noise results in a stochastic space of smaller dimension. The most efficient method is the one combining SC and KL expansion. Copyright © 2016 Elsevier Inc. All rights reserved.

Computer simulation of stochastic processes through model-sampling (Monte Carlo) techniques.

PubMed

Sheppard, C W.

1969-03-01

A simple Monte Carlo simulation program is outlined which can be used for the investigation of random-walk problems, for example in diffusion, or the movement of tracers in the blood circulation. The results given by the simulation are compared with those predicted by well-established theory, and it is shown how the model can be expanded to deal with drift, and with reflexion from or adsorption at a boundary.

The concerted calculation of the BN-600 reactor for the deterministic and stochastic codes

NASA Astrophysics Data System (ADS)

Bogdanova, E. V.; Kuznetsov, A. N.

2017-01-01

The solution of the problem of increasing the safety of nuclear power plants implies the existence of complete and reliable information about the processes occurring in the core of a working reactor. Nowadays the Monte-Carlo method is the most general-purpose method used to calculate the neutron-physical characteristic of the reactor. But it is characterized by large time of calculation. Therefore, it may be useful to carry out coupled calculations with stochastic and deterministic codes. This article presents the results of research for possibility of combining stochastic and deterministic algorithms in calculation the reactor BN-600. This is only one part of the work, which was carried out in the framework of the graduation project at the NRC “Kurchatov Institute” in cooperation with S. S. Gorodkov and M. A. Kalugin. It is considering the 2-D layer of the BN-600 reactor core from the international benchmark test, published in the report IAEA-TECDOC-1623. Calculations of the reactor were performed with MCU code and then with a standard operative diffusion algorithm with constants taken from the Monte - Carlo computation. Macro cross-section, diffusion coefficients, the effective multiplication factor and the distribution of neutron flux and power were obtained in 15 energy groups. The reasonable agreement between stochastic and deterministic calculations of the BN-600 is observed.

Monte Carlo algorithms for Brownian phylogenetic models.

PubMed

Horvilleur, Benjamin; Lartillot, Nicolas

2014-11-01

Brownian models have been introduced in phylogenetics for describing variation in substitution rates through time, with applications to molecular dating or to the comparative analysis of variation in substitution patterns among lineages. Thus far, however, the Monte Carlo implementations of these models have relied on crude approximations, in which the Brownian process is sampled only at the internal nodes of the phylogeny or at the midpoints along each branch, and the unknown trajectory between these sampled points is summarized by simple branchwise average substitution rates. A more accurate Monte Carlo approach is introduced, explicitly sampling a fine-grained discretization of the trajectory of the (potentially multivariate) Brownian process along the phylogeny. Generic Monte Carlo resampling algorithms are proposed for updating the Brownian paths along and across branches. Specific computational strategies are developed for efficient integration of the finite-time substitution probabilities across branches induced by the Brownian trajectory. The mixing properties and the computational complexity of the resulting Markov chain Monte Carlo sampler scale reasonably with the discretization level, allowing practical applications with up to a few hundred discretization points along the entire depth of the tree. The method can be generalized to other Markovian stochastic processes, making it possible to implement a wide range of time-dependent substitution models with well-controlled computational precision. The program is freely available at www.phylobayes.org. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Stochastic effects in a thermochemical system with Newtonian heat exchange.

PubMed

Nowakowski, B; Lemarchand, A

2001-12-01

We develop a mesoscopic description of stochastic effects in the Newtonian heat exchange between a diluted gas system and a thermostat. We explicitly study the homogeneous Semenov model involving a thermochemical reaction and neglecting consumption of reactants. The master equation includes a transition rate for the thermal transfer process, which is derived on the basis of the statistics for inelastic collisions between gas particles and walls of the thermostat. The main assumption is that the perturbation of the Maxwellian particle velocity distribution can be neglected. The transition function for the thermal process admits a continuous spectrum of temperature changes, and consequently, the master equation has a complicated integro-differential form. We perform Monte Carlo simulations based on this equation to study the stochastic effects in the Semenov system in the explosive regime. The dispersion of ignition times is calculated as a function of system size. For sufficiently small systems, the probability distribution of temperature displays transient bimodality during the ignition period. The results of the stochastic description are successfully compared with those of direct simulations of microscopic particle dynamics.

Path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models

NASA Astrophysics Data System (ADS)

Lemmens, D.; Wouters, M.; Tempere, J.; Foulon, S.

2008-07-01

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.

The isolation limits of stochastic vibration

NASA Technical Reports Server (NTRS)

Knopse, C. R.; Allaire, P. E.

1993-01-01

The vibration isolation problem is formulated as a 1D kinematic problem. The geometry of the stochastic wall trajectories arising from the stroke constraint is defined in terms of their significant extrema. An optimal control solution for the minimum acceleration return path determines a lower bound on platform mean square acceleration. This bound is expressed in terms of the probability density function on the significant maxima and the conditional fourth moment of the first passage time inverse. The first of these is found analytically while the second is found using a Monte Carlo simulation. The rms acceleration lower bound as a function of available space is then determined through numerical quadrature.

Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

NASA Astrophysics Data System (ADS)

Lipan, Ovidiu; Ferwerda, Cameron

2018-02-01

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

Monte Carlo Techniques for Nuclear Systems - Theory Lectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Forrest B.

These are lecture notes for a Monte Carlo class given at the University of New Mexico. The following topics are covered: course information; nuclear eng. review & MC; random numbers and sampling; computational geometry; collision physics; tallies and statistics; eigenvalue calculations I; eigenvalue calculations II; eigenvalue calculations III; variance reduction; parallel Monte Carlo; parameter studies; fission matrix and higher eigenmodes; doppler broadening; Monte Carlo depletion; HTGR modeling; coupled MC and T/H calculations; fission energy deposition. Solving particle transport problems with the Monte Carlo method is simple - just simulate the particle behavior. The devil is in the details, however. Thesemore » lectures provide a balanced approach to the theory and practice of Monte Carlo simulation codes. The first lectures provide an overview of Monte Carlo simulation methods, covering the transport equation, random sampling, computational geometry, collision physics, and statistics. The next lectures focus on the state-of-the-art in Monte Carlo criticality simulations, covering the theory of eigenvalue calculations, convergence analysis, dominance ratio calculations, bias in Keff and tallies, bias in uncertainties, a case study of a realistic calculation, and Wielandt acceleration techniques. The remaining lectures cover advanced topics, including HTGR modeling and stochastic geometry, temperature dependence, fission energy deposition, depletion calculations, parallel calculations, and parameter studies. This portion of the class focuses on using MCNP to perform criticality calculations for reactor physics and criticality safety applications. It is an intermediate level class, intended for those with at least some familiarity with MCNP. Class examples provide hands-on experience at running the code, plotting both geometry and results, and understanding the code output. The class includes lectures & hands-on computer use for a variety of Monte Carlo

Calculating the Malliavin derivative of some stochastic mechanics problems

PubMed Central

Hauseux, Paul; Hale, Jack S.

2017-01-01

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. PMID:29261776

Probability density function evolution of power systems subject to stochastic variation of renewable energy

NASA Astrophysics Data System (ADS)

Wei, J. Q.; Cong, Y. C.; Xiao, M. Q.

2018-05-01

As renewable energies are increasingly integrated into power systems, there is increasing interest in stochastic analysis of power systems.Better techniques should be developed to account for the uncertainty caused by penetration of renewables and consequently analyse its impacts on stochastic stability of power systems. In this paper, the Stochastic Differential Equations (SDEs) are used to represent the evolutionary behaviour of the power systems. The stationary Probability Density Function (PDF) solution to SDEs modelling power systems excited by Gaussian white noise is analysed. Subjected to such random excitation, the Joint Probability Density Function (JPDF) solution to the phase angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the numerical method is adopted. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. Both weak and strong intensities of the stochastic excitations are considered in a single machine infinite bus power system. The numerical analysis has the same result as the one given by the Monte Carlo simulation. Potential studies on stochastic behaviour of multi-machine power systems with random excitations are discussed at the end.

Efficient Geometry and Data Handling for Large-Scale Monte Carlo - Thermal-Hydraulics Coupling

NASA Astrophysics Data System (ADS)

Hoogenboom, J. Eduard

2014-06-01

Detailed coupling of thermal-hydraulics calculations to Monte Carlo reactor criticality calculations requires each axial layer of each fuel pin to be defined separately in the input to the Monte Carlo code in order to assign to each volume the temperature according to the result of the TH calculation, and if the volume contains coolant, also the density of the coolant. This leads to huge input files for even small systems. In this paper a methodology for dynamical assignment of temperatures with respect to cross section data is demonstrated to overcome this problem. The method is implemented in MCNP5. The method is verified for an infinite lattice with 3x3 BWR-type fuel pins with fuel, cladding and moderator/coolant explicitly modeled. For each pin 60 axial zones are considered with different temperatures and coolant densities. The results of the axial power distribution per fuel pin are compared to a standard MCNP5 run in which all 9x60 cells for fuel, cladding and coolant are explicitly defined and their respective temperatures determined from the TH calculation. Full agreement is obtained. For large-scale application the method is demonstrated for an infinite lattice with 17x17 PWR-type fuel assemblies with 25 rods replaced by guide tubes. Again all geometrical detailed is retained. The method was used in a procedure for coupled Monte Carlo and thermal-hydraulics iterations. Using an optimised iteration technique, convergence was obtained in 11 iteration steps.

Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations.

PubMed

Bell, John B; Garcia, Alejandro L; Williams, Sarah A

2007-07-01

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

Energy-optimal path planning by stochastic dynamically orthogonal level-set optimization

NASA Astrophysics Data System (ADS)

Subramani, Deepak N.; Lermusiaux, Pierre F. J.

2016-04-01

A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. Based on partial differential equations, the methodology rigorously leverages the level-set equation that governs time-optimal reachability fronts for a given relative vehicle-speed function. To set up the energy optimization, the relative vehicle-speed and headings are considered to be stochastic and new stochastic Dynamically Orthogonal (DO) level-set equations are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle's energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. Numerical schemes to solve the reduced stochastic DO level-set equations are obtained, and accuracy and efficiency considerations are discussed. These reduced equations are first shown to be efficient at solving the governing stochastic level-sets, in part by comparisons with direct Monte Carlo simulations. To validate the methodology and illustrate its accuracy, comparisons with semi-analytical energy-optimal path solutions are then completed. In particular, we consider the energy-optimal crossing of a canonical steady front and set up its semi-analytical solution using a energy-time nested nonlinear double-optimization scheme. We then showcase the inner workings and nuances of the energy-optimal path planning, considering different mission scenarios. Finally, we study and discuss results of energy-optimal missions in a wind-driven barotropic quasi-geostrophic double-gyre ocean circulation.

Adaptive control of stochastic linear systems with unknown parameters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ku, R. T.

1972-01-01

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Stochastic study of solute transport in a nonstationary medium.

PubMed

Hu, Bill X

2006-01-01

A Lagrangian stochastic approach is applied to develop a method of moment for solute transport in a physically and chemically nonstationary medium. Stochastic governing equations for mean solute flux and solute covariance are analytically obtained in the first-order accuracy of log conductivity and/or chemical sorption variances and solved numerically using the finite-difference method. The developed method, the numerical method of moments (NMM), is used to predict radionuclide solute transport processes in the saturated zone below the Yucca Mountain project area. The mean, variance, and upper bound of the radionuclide mass flux through a control plane 5 km downstream of the footprint of the repository are calculated. According to their chemical sorption capacities, the various radionuclear chemicals are grouped as nonreactive, weakly sorbing, and strongly sorbing chemicals. The NMM method is used to study their transport processes and influence factors. To verify the method of moments, a Monte Carlo simulation is conducted for nonreactive chemical transport. Results indicate the results from the two methods are consistent, but the NMM method is computationally more efficient than the Monte Carlo method. This study adds to the ongoing debate in the literature on the effect of heterogeneity on solute transport prediction, especially on prediction uncertainty, by showing that the standard derivation of solute flux is larger than the mean solute flux even when the hydraulic conductivity within each geological layer is mild. This study provides a method that may become an efficient calculation tool for many environmental projects.

Stochastic modelling of turbulent combustion for design optimization of gas turbine combustors

NASA Astrophysics Data System (ADS)

Mehanna Ismail, Mohammed Ali

The present work covers the development and the implementation of an efficient algorithm for the design optimization of gas turbine combustors. The purpose is to explore the possibilities and indicate constructive suggestions for optimization techniques as alternative methods for designing gas turbine combustors. The algorithm is general to the extent that no constraints are imposed on the combustion phenomena or on the combustor configuration. The optimization problem is broken down into two elementary problems: the first is the optimum search algorithm, and the second is the turbulent combustion model used to determine the combustor performance parameters. These performance parameters constitute the objective and physical constraints in the optimization problem formulation. The examination of both turbulent combustion phenomena and the gas turbine design process suggests that the turbulent combustion model represents a crucial part of the optimization algorithm. The basic requirements needed for a turbulent combustion model to be successfully used in a practical optimization algorithm are discussed. In principle, the combustion model should comply with the conflicting requirements of high fidelity, robustness and computational efficiency. To that end, the problem of turbulent combustion is discussed and the current state of the art of turbulent combustion modelling is reviewed. According to this review, turbulent combustion models based on the composition PDF transport equation are found to be good candidates for application in the present context. However, these models are computationally expensive. To overcome this difficulty, two different models based on the composition PDF transport equation were developed: an improved Lagrangian Monte Carlo composition PDF algorithm and the generalized stochastic reactor model. Improvements in the Lagrangian Monte Carlo composition PDF model performance and its computational efficiency were achieved through the

Adaptive hybrid simulations for multiscale stochastic reaction networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such amore » partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.« less

Adaptive hybrid simulations for multiscale stochastic reaction networks.

PubMed

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

2015-01-21

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

A Simple "Boxed Molecular Kinetics" Approach To Accelerate Rare Events in the Stochastic Kinetic Master Equation.

PubMed

Shannon, Robin; Glowacki, David R

2018-02-15

The chemical master equation is a powerful theoretical tool for analyzing the kinetics of complex multiwell potential energy surfaces in a wide range of different domains of chemical kinetics spanning combustion, atmospheric chemistry, gas-surface chemistry, solution phase chemistry, and biochemistry. There are two well-established methodologies for solving the chemical master equation: a stochastic "kinetic Monte Carlo" approach and a matrix-based approach. In principle, the results yielded by both approaches are identical; the decision of which approach is better suited to a particular study depends on the details of the specific system under investigation. In this Article, we present a rigorous method for accelerating stochastic approaches by several orders of magnitude, along with a method for unbiasing the accelerated results to recover the "true" value. The approach we take in this paper is inspired by the so-called "boxed molecular dynamics" (BXD) method, which has previously only been applied to accelerate rare events in molecular dynamics simulations. Here we extend BXD to design a simple algorithmic strategy for accelerating rare events in stochastic kinetic simulations. Tests on a number of systems show that the results obtained using the BXD rare event strategy are in good agreement with unbiased results. To carry out these tests, we have implemented a kinetic Monte Carlo approach in MESMER, which is a cross-platform, open-source, and freely available master equation solver.

An efficient distribution method for nonlinear transport problems in stochastic porous media

NASA Astrophysics Data System (ADS)

Ibrahima, F.; Tchelepi, H.; Meyer, D. W.

2015-12-01

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are convenient to explore possible scenarios and assess risks in subsurface problems. In particular, understanding how uncertainties propagate in porous media with nonlinear two-phase flow is essential, yet challenging, in reservoir simulation and hydrology. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the water saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. The method draws inspiration from the streamline approach and expresses the distributions of interest essentially in terms of an analytically derived mapping and the distribution of the time of flight. In a large class of applications the latter can be estimated at low computational costs (even via conventional Monte Carlo). Once the water saturation distribution is determined, any one-point statistics thereof can be obtained, especially its average and standard deviation. Moreover, rarely available in other approaches, yet crucial information such as the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be derived from the method. We provide various examples and comparisons with Monte Carlo simulations to illustrate the performance of the method.

Comparison of effects of copropagated and precomputed atmosphere profiles on Monte Carlo trajectory simulation

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.

Estimation of parameters and basic reproduction ratio for Japanese encephalitis transmission in the Philippines using sequential Monte Carlo filter

USDA-ARS?s Scientific Manuscript database

We developed a sequential Monte Carlo filter to estimate the states and the parameters in a stochastic model of Japanese Encephalitis (JE) spread in the Philippines. This method is particularly important for its adaptability to the availability of new incidence data. This method can also capture the...

A coupled stochastic inverse-management framework for dealing with nonpoint agriculture pollution under groundwater parameter uncertainty

NASA Astrophysics Data System (ADS)

Llopis-Albert, Carlos; Palacios-Marqués, Daniel; Merigó, José M.

2014-04-01

In this paper a methodology for the stochastic management of groundwater quality problems is presented, which can be used to provide agricultural advisory services. A stochastic algorithm to solve the coupled flow and mass transport inverse problem is combined with a stochastic management approach to develop methods for integrating uncertainty; thus obtaining more reliable policies on groundwater nitrate pollution control from agriculture. The stochastic inverse model allows identifying non-Gaussian parameters and reducing uncertainty in heterogeneous aquifers by constraining stochastic simulations to data. The management model determines the spatial and temporal distribution of fertilizer application rates that maximizes net benefits in agriculture constrained by quality requirements in groundwater at various control sites. The quality constraints can be taken, for instance, by those given by water laws such as the EU Water Framework Directive (WFD). Furthermore, the methodology allows providing the trade-off between higher economic returns and reliability in meeting the environmental standards. Therefore, this new technology can help stakeholders in the decision-making process under an uncertainty environment. The methodology has been successfully applied to a 2D synthetic aquifer, where an uncertainty assessment has been carried out by means of Monte Carlo simulation techniques.

Stochastic multi-reference perturbation theory with application to the linearized coupled cluster method

NASA Astrophysics Data System (ADS)

Jeanmairet, Guillaume; Sharma, Sandeep; Alavi, Ali

2017-01-01

In this article we report a stochastic evaluation of the recently proposed multireference linearized coupled cluster theory [S. Sharma and A. Alavi, J. Chem. Phys. 143, 102815 (2015)]. In this method, both the zeroth-order and first-order wavefunctions are sampled stochastically by propagating simultaneously two populations of signed walkers. The sampling of the zeroth-order wavefunction follows a set of stochastic processes identical to the one used in the full configuration interaction quantum Monte Carlo (FCIQMC) method. To sample the first-order wavefunction, the usual FCIQMC algorithm is augmented with a source term that spawns walkers in the sampled first-order wavefunction from the zeroth-order wavefunction. The second-order energy is also computed stochastically but requires no additional overhead outside of the added cost of sampling the first-order wavefunction. This fully stochastic method opens up the possibility of simultaneously treating large active spaces to account for static correlation and recovering the dynamical correlation using perturbation theory. The method is used to study a few benchmark systems including the carbon dimer and aromatic molecules. We have computed the singlet-triplet gaps of benzene and m-xylylene. For m-xylylene, which has proved difficult for standard complete active space self consistent field theory with perturbative correction, we find the singlet-triplet gap to be in good agreement with the experimental values.

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

A Hybrid Monte Carlo importance sampling of rare events in Turbulence and in Turbulent Models

NASA Astrophysics Data System (ADS)

Margazoglou, Georgios; Biferale, Luca; Grauer, Rainer; Jansen, Karl; Mesterhazy, David; Rosenow, Tillmann; Tripiccione, Raffaele

2017-11-01

Extreme and rare events is a challenging topic in the field of turbulence. Trying to investigate those instances through the use of traditional numerical tools turns to be a notorious task, as they fail to systematically sample the fluctuations around them. On the other hand, we propose that an importance sampling Monte Carlo method can selectively highlight extreme events in remote areas of the phase space and induce their occurrence. We present a brand new computational approach, based on the path integral formulation of stochastic dynamics, and employ an accelerated Hybrid Monte Carlo (HMC) algorithm for this purpose. Through the paradigm of stochastic one-dimensional Burgers' equation, subjected to a random noise that is white-in-time and power-law correlated in Fourier space, we will prove our concept and benchmark our results with standard CFD methods. Furthermore, we will present our first results of constrained sampling around saddle-point instanton configurations (optimal fluctuations). The research leading to these results has received funding from the EU Horizon 2020 research and innovation programme under Grant Agreement No. 642069, and from the EU Seventh Framework Programme (FP7/2007-2013) under ERC Grant Agreement No. 339032.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems

DOE PAGES

Richard V. Field, Jr.; Emery, John M.; Grigoriu, Mircea Dan

2015-05-19

The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems. A recently developed method based on stochastic reduced order models (SROMs) can also be used. Herein we provide a comparison of the three methods for some numerical examples; our evaluation only holds for the examples considered in the paper. The purpose of the comparisons is not to criticize the SC or SG methods, which have proven very useful for a broad range of applications, nor is it to provide overall ratings of these methods as compared to the SROM method.more » Furthermore, our objectives are to present the SROM method as an alternative approach to solving stochastic problems and provide information on the computational effort required by the implementation of each method, while simultaneously assessing their performance for a collection of specific problems.« less

Stochastic series expansion simulation of the t -V model

NASA Astrophysics Data System (ADS)

Wang, Lei; Liu, Ye-Hua; Troyer, Matthias

2016-04-01

We present an algorithm for the efficient simulation of the half-filled spinless t -V model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size, and is free from the time-discretization error. We use it to map out the finite-temperature phase diagram of the spinless t -V model on the honeycomb lattice and observe a suppression of the critical temperature of the charge-density-wave phase in the vicinity of a fermionic quantum critical point.

Monte Carlo simulation of air sampling methods for the measurement of radon decay products.

PubMed

Sima, Octavian; Luca, Aurelian; Sahagia, Maria

2017-08-01

A stochastic model of the processes involved in the measurement of the activity of the 222 Rn decay products was developed. The distributions of the relevant factors, including air sampling and radionuclide collection, are propagated using Monte Carlo simulation to the final distribution of the measurement results. The uncertainties of the 222 Rn decay products concentrations in the air are realistically evaluated. Copyright © 2017 Elsevier Ltd. All rights reserved.

STOCHASTIC DUELS OF LIMITED TIME-DURATION,

DTIC Science & Technology

This paper continues the development of the theory of stochastic duels to include the case where there is a time limitation on the duration of the... duel . An example of this situation is fighter-bomber combat in which the fighter has a very limited fuel supply. In this duel , two contestants (with...variable or (2) constant. The duel proceeds until one or both of the contestants are killed or until the time limit is exceeded. The time limit is either

Kinetic Monte Carlo modeling of chemical reactions coupled with heat transfer.

PubMed

Castonguay, Thomas C; Wang, Feng

2008-03-28

In this paper, we describe two types of effective events for describing heat transfer in a kinetic Monte Carlo (KMC) simulation that may involve stochastic chemical reactions. Simulations employing these events are referred to as KMC-TBT and KMC-PHE. In KMC-TBT, heat transfer is modeled as the stochastic transfer of "thermal bits" between adjacent grid points. In KMC-PHE, heat transfer is modeled by integrating the Poisson heat equation for a short time. Either approach is capable of capturing the time dependent system behavior exactly. Both KMC-PHE and KMC-TBT are validated by simulating pure heat transfer in a rod and a square and modeling a heated desorption problem where exact numerical results are available. KMC-PHE is much faster than KMC-TBT and is used to study the endothermic desorption of a lattice gas. Interesting findings from this study are reported.

Kinetic Monte Carlo modeling of chemical reactions coupled with heat transfer

NASA Astrophysics Data System (ADS)

Castonguay, Thomas C.; Wang, Feng

2008-03-01

In this paper, we describe two types of effective events for describing heat transfer in a kinetic Monte Carlo (KMC) simulation that may involve stochastic chemical reactions. Simulations employing these events are referred to as KMC-TBT and KMC-PHE. In KMC-TBT, heat transfer is modeled as the stochastic transfer of "thermal bits" between adjacent grid points. In KMC-PHE, heat transfer is modeled by integrating the Poisson heat equation for a short time. Either approach is capable of capturing the time dependent system behavior exactly. Both KMC-PHE and KMC-TBT are validated by simulating pure heat transfer in a rod and a square and modeling a heated desorption problem where exact numerical results are available. KMC-PHE is much faster than KMC-TBT and is used to study the endothermic desorption of a lattice gas. Interesting findings from this study are reported.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

A stochastic multi-scale method for turbulent premixed combustion

NASA Astrophysics Data System (ADS)

Cha, Chong M.

2002-11-01

The stochastic chemistry algorithm of Bunker et al. and Gillespie is used to perform the chemical reactions in a transported probability density function (PDF) modeling approach of turbulent combustion. Recently, Kraft & Wagner have demonstrated a 100-fold gain in computational speed (for a 100 species mechanism) using the stochastic approach over the conventional, direct integration method of solving for the chemistry. Here, the stochastic chemistry algorithm is applied to develop a new transported PDF model of turbulent premixed combustion. The methodology relies on representing the relevant spatially dependent physical processes as queuing events. The canonical problem of a one-dimensional premixed flame is used for validation. For the laminar case, molecular diffusion is described by a random walk. For the turbulent case, one of two different material transport submodels can provide the necessary closure: Taylor dispersion or Kerstein's one-dimensional turbulence approach. The former exploits ``eddy diffusivity'' and hence would be much more computationally tractable for practical applications. Various validation studies are performed. Results from the Monte Carlo simulations compare well to asymptotic solutions of laminar premixed flames, both with and without high activation temperatures. The correct scaling of the turbulent burning velocity is predicted in both Damköhler's small- and large-scale turbulence limits. The effect of applying the eddy diffusivity concept in the various regimes is discussed.

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less

Low Variance Couplings for Stochastic Models of Intracellular Processes with Time-Dependent Rate Functions.

PubMed

Anderson, David F; Yuan, Chaojie

2018-04-18

A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an exceptionally low variance between the generated paths. This coupling will be useful in the numerical computation of parametric sensitivities and the fast estimation of expectations via multilevel Monte Carlo methods. We provide the requisite estimators in both cases.

Edgeworth expansions of stochastic trading time

NASA Astrophysics Data System (ADS)

Decamps, Marc; De Schepper, Ann

2010-08-01

Under most local and stochastic volatility models the underlying forward is assumed to be a positive function of a time-changed Brownian motion. It relates nicely the implied volatility smile to the so-called activity rate in the market. Following Young and DeWitt-Morette (1986) [8], we propose to apply the Duru-Kleinert process-cum-time transformation in path integral to formulate the transition density of the forward. The method leads to asymptotic expansions of the transition density around a Gaussian kernel corresponding to the average activity in the market conditional on the forward value. The approximation is numerically illustrated for pricing vanilla options under the CEV model and the popular normal SABR model. The asymptotics can also be used for Monte Carlo simulations or backward integration schemes.

Stochastic simulation of radium-223 dichloride therapy at the sub-cellular level

NASA Astrophysics Data System (ADS)

Gholami, Y.; Zhu, X.; Fulton, R.; Meikle, S.; El-Fakhri, G.; Kuncic, Z.

2015-08-01

Radium-223 dichloride (223Ra) is an alpha particle emitter and a natural bone-seeking radionuclide that is currently used for treating osteoblastic bone metastases associated with prostate cancer. The stochastic nature of alpha emission, hits and energy deposition poses some challenges for estimating radiation damage. In this paper we investigate the distribution of hits to cells by multiple alpha particles corresponding to a typical clinically delivered dose using a Monte Carlo model to simulate the stochastic effects. The number of hits and dose deposition were recorded in the cytoplasm and nucleus of each cell. Alpha particle tracks were also visualized. We found that the stochastic variation in dose deposited in cell nuclei (≃ 40%) can be attributed in part to the variation in LET with pathlength. We also found that ≃ 18% of cell nuclei receive less than one sigma below the average dose per cell (≃ 15.4 Gy). One possible implication of this is that the efficacy of cell kill in alpha particle therapy need not rely solely on ionization clustering on DNA but possibly also on indirect DNA damage through the production of free radicals and ensuing intracellular signaling.

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

NASA Technical Reports Server (NTRS)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

Approximation methods of European option pricing in multiscale stochastic volatility model

NASA Astrophysics Data System (ADS)

Ni, Ying; Canhanga, Betuel; Malyarenko, Anatoliy; Silvestrov, Sergei

2017-01-01

In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown in Christoffersen, Heston and Jacobs [12]. We consider one modified form of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this paper is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. [5, 6]. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi [11] using method of characteristics, Fourier and bivariate Laplace transforms.

Coupled stochastic soil moisture simulation-optimization model of deficit irrigation

NASA Astrophysics Data System (ADS)

Alizadeh, Hosein; Mousavi, S. Jamshid

2013-07-01

This study presents an explicit stochastic optimization-simulation model of short-term deficit irrigation management for large-scale irrigation districts. The model which is a nonlinear nonconvex program with an economic objective function is built on an agrohydrological simulation component. The simulation component integrates (1) an explicit stochastic model of soil moisture dynamics of the crop-root zone considering interaction of stochastic rainfall and irrigation with shallow water table effects, (2) a conceptual root zone salt balance model, and 3) the FAO crop yield model. Particle Swarm Optimization algorithm, linked to the simulation component, solves the resulting nonconvex program with a significantly better computational performance compared to a Monte Carlo-based implicit stochastic optimization model. The model has been tested first by applying it in single-crop irrigation problems through which the effects of the severity of water deficit on the objective function (net benefit), root-zone water balance, and irrigation water needs have been assessed. Then, the model has been applied in Dasht-e-Abbas and Ein-khosh Fakkeh Irrigation Districts (DAID and EFID) of the Karkheh Basin in southwest of Iran. While the maximum net benefit has been obtained for a stress-avoidance (SA) irrigation policy, the highest water profitability has been resulted when only about 60% of the water used in the SA policy is applied. The DAID with respectively 33% of total cultivated area and 37% of total applied water has produced only 14% of the total net benefit due to low-valued crops and adverse soil and shallow water table conditions.

Driven-dissipative quantum Monte Carlo method for open quantum systems

NASA Astrophysics Data System (ADS)

Nagy, Alexandra; Savona, Vincenzo

2018-05-01

We develop a real-time full configuration-interaction quantum Monte Carlo approach to model driven-dissipative open quantum systems with Markovian system-bath coupling. The method enables stochastic sampling of the Liouville-von Neumann time evolution of the density matrix thanks to a massively parallel algorithm, thus providing estimates of observables on the nonequilibrium steady state. We present the underlying theory and introduce an initiator technique and importance sampling to reduce the statistical error. Finally, we demonstrate the efficiency of our approach by applying it to the driven-dissipative two-dimensional X Y Z spin-1/2 model on a lattice.

Stochastic output error vibration-based damage detection and assessment in structures under earthquake excitation

NASA Astrophysics Data System (ADS)

Sakellariou, J. S.; Fassois, S. D.

2006-11-01

A stochastic output error (OE) vibration-based methodology for damage detection and assessment (localization and quantification) in structures under earthquake excitation is introduced. The methodology is intended for assessing the state of a structure following potential damage occurrence by exploiting vibration signal measurements produced by low-level earthquake excitations. It is based upon (a) stochastic OE model identification, (b) statistical hypothesis testing procedures for damage detection, and (c) a geometric method (GM) for damage assessment. The methodology's advantages include the effective use of the non-stationary and limited duration earthquake excitation, the handling of stochastic uncertainties, the tackling of the damage localization and quantification subproblems, the use of "small" size, simple and partial (in both the spatial and frequency bandwidth senses) identified OE-type models, and the use of a minimal number of measured vibration signals. Its feasibility and effectiveness are assessed via Monte Carlo experiments employing a simple simulation model of a 6 storey building. It is demonstrated that damage levels of 5% and 20% reduction in a storey's stiffness characteristics may be properly detected and assessed using noise-corrupted vibration signals.

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.

Simulation of multivariate stationary stochastic processes using dimension-reduction representation methods

NASA Astrophysics Data System (ADS)

Liu, Zhangjun; Liu, Zenghui; Peng, Yongbo

2018-03-01

In view of the Fourier-Stieltjes integral formula of multivariate stationary stochastic processes, a unified formulation accommodating spectral representation method (SRM) and proper orthogonal decomposition (POD) is deduced. By introducing random functions as constraints correlating the orthogonal random variables involved in the unified formulation, the dimension-reduction spectral representation method (DR-SRM) and the dimension-reduction proper orthogonal decomposition (DR-POD) are addressed. The proposed schemes are capable of representing the multivariate stationary stochastic process with a few elementary random variables, bypassing the challenges of high-dimensional random variables inherent in the conventional Monte Carlo methods. In order to accelerate the numerical simulation, the technique of Fast Fourier Transform (FFT) is integrated with the proposed schemes. For illustrative purposes, the simulation of horizontal wind velocity field along the deck of a large-span bridge is proceeded using the proposed methods containing 2 and 3 elementary random variables. Numerical simulation reveals the usefulness of the dimension-reduction representation methods.

Application of stochastic approach based on Monte Carlo (MC) simulation for life cycle inventory (LCI) of the rare earth elements (REEs) in beneficiation rare earth waste from the gold processing: case study

NASA Astrophysics Data System (ADS)

Bieda, Bogusław; Grzesik, Katarzyna

2017-11-01

The study proposes an stochastic approach based on Monte Carlo (MC) simulation for life cycle assessment (LCA) method limited to life cycle inventory (LCI) study for rare earth elements (REEs) recovery from the secondary materials processes production applied to the New Krankberg Mine in Sweden. The MC method is recognizes as an important tool in science and can be considered the most effective quantification approach for uncertainties. The use of stochastic approach helps to characterize the uncertainties better than deterministic method. Uncertainty of data can be expressed through a definition of probability distribution of that data (e.g. through standard deviation or variance). The data used in this study are obtained from: (i) site-specific measured or calculated data, (ii) values based on literature, (iii) the ecoinvent process "rare earth concentrate, 70% REO, from bastnäsite, at beneficiation". Environmental emissions (e.g, particulates, uranium-238, thorium-232), energy and REE (La, Ce, Nd, Pr, Sm, Dy, Eu, Tb, Y, Sc, Yb, Lu, Tm, Y, Gd) have been inventoried. The study is based on a reference case for the year 2016. The combination of MC analysis with sensitivity analysis is the best solution for quantified the uncertainty in the LCI/LCA. The reliability of LCA results may be uncertain, to a certain degree, but this uncertainty can be noticed with the help of MC method.

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.

Stochastic generation of hourly rainstorm events in Johor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nojumuddin, Nur Syereena; Yusof, Fadhilah; Yusop, Zulkifli

2015-02-03

Engineers and researchers in water-related studies are often faced with the problem of having insufficient and long rainfall record. Practical and effective methods must be developed to generate unavailable data from limited available data. Therefore, this paper presents a Monte-Carlo based stochastic hourly rainfall generation model to complement the unavailable data. The Monte Carlo simulation used in this study is based on the best fit of storm characteristics. Hence, by using the Maximum Likelihood Estimation (MLE) and Anderson Darling goodness-of-fit test, lognormal appeared to be the best rainfall distribution. Therefore, the Monte Carlo simulation based on lognormal distribution was usedmore » in the study. The proposed model was verified by comparing the statistical moments of rainstorm characteristics from the combination of the observed rainstorm events under 10 years and simulated rainstorm events under 30 years of rainfall records with those under the entire 40 years of observed rainfall data based on the hourly rainfall data at the station J1 in Johor over the period of 1972–2011. The absolute percentage error of the duration-depth, duration-inter-event time and depth-inter-event time will be used as the accuracy test. The results showed the first four product-moments of the observed rainstorm characteristics were close with the simulated rainstorm characteristics. The proposed model can be used as a basis to derive rainfall intensity-duration frequency in Johor.« less

Patchwork sampling of stochastic differential equations

NASA Astrophysics Data System (ADS)

Kürsten, Rüdiger; Behn, Ulrich

2016-03-01

We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The method is based on a complete, nonoverlapping partition of the state space into patches on which the stochastic process is ergodic. On each of these patches we run simulations of the process strictly truncated to the corresponding patch, which allows effective simulations also in rarely visited regions. The correct weight for each patch is obtained by counting the attempted transitions between all different patches. The results are patchworked to cover the whole state space. We extend the concept of truncated Markov chains which is originally formulated for processes which obey detailed balance to processes not fulfilling detailed balance. The method is illustrated by three examples, describing the one-dimensional diffusion of an overdamped particle in a double-well potential, a system of many globally coupled overdamped particles in double-well potentials subject to additive Gaussian white noise, and the overdamped motion of a particle on the circle in a periodic potential subject to a deterministic drift and additive noise. In an appendix we explain how other well-known Markov chain Monte Carlo algorithms can be related to truncated Markov chains.

Stochastic unilateral free vibration of an in-plane cable network

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice; Barbiellini, Bernardo; Caracoglia, Luca

2015-03-01

Cross-ties are often used on cable-stayed bridges for mitigating wind-induced stay vibration since they can be easily installed on existing systems. The system obtained by connecting two (or more) stays with a transverse restrainer is designated as an "in-plane cable-network". Failures in the restrainers of an existing network have been observed. In a previous study [1] a model was proposed to explain the failures in the cross-ties as being related to a loss in the initial pre-tensioning force imparted to the connector. This effect leads to the "unilateral" free vibration of the network. Deterministic free vibrations of a three-cable network were investigated by using the "equivalent linearization method". Since the value of the initial vibration amplitude is often not well known due to the complex aeroelastic vibration regimes, which can be experienced by the stays, the stochastic nature of the problem must be considered. This issue is investigated in the present paper. Free-vibration dynamics of the cable network, driven by an initial stochastic disturbance associated with uncertain vibration amplitudes, is examined. The corresponding random eigen-value problem for the vibration frequencies is solved through an implementation of Stochastic Approximation, (SA) based on the Robbins-Monro Theorem. Monte-Carlo methods are also used for validating the SA results.

Stochastic stability

NASA Technical Reports Server (NTRS)

Kushner, H. J.

1972-01-01

The field of stochastic stability is surveyed, with emphasis on the invariance theorems and their potential application to systems with randomly varying coefficients. Some of the basic ideas are reviewed, which underlie the stochastic Liapunov function approach to stochastic stability. The invariance theorems are discussed in detail.

Electron transport in the stochastic fields of the reversed-field pinch

NASA Astrophysics Data System (ADS)

Kim, Myung-Hee; Punjabi, Alkesh

1996-08-01

We employ the Monte Carlo method for the calculation of anomalous transport developed by Punjabi and Boozer to calculate the particle diffusion coefficient for electrons in the stochastic magnetic fields of the reversed-field pinch (RFP). in the Monte Carlo calculations represented here, the transport mechanism is the loss of magnetic surfaces due to resistive perturbations. The equilibrium magnetic fields are represented by the Bessel function model for the RFP. The diffusion coefficient D is calculated as a function of a, the amplitude of the perturbation. We see three regimes as the amplitude of the tearing modes is increased: the Rechester—Rosenbluth regime where D scales as a2 the anomalous regime where D scales more rapidly than a2 and the Mynick—Krornmes regime where D scales more slowly than a2. Inclusion of the effects of loop voltage on the particle drift orbits in the RFP does not affect the intervals in the amplitude a where these regimes operate.

Stochastic sampling of quadrature grids for the evaluation of vibrational expectation values

NASA Astrophysics Data System (ADS)

López Ríos, Pablo; Monserrat, Bartomeu; Needs, Richard J.

2018-02-01

The thermal lines method for the evaluation of vibrational expectation values of electronic observables [B. Monserrat, Phys. Rev. B 93, 014302 (2016), 10.1103/PhysRevB.93.014302] was recently proposed as a physically motivated approximation offering balance between the accuracy of direct Monte Carlo integration and the low computational cost of using local quadratic approximations. In this paper we reformulate thermal lines as a stochastic implementation of quadrature-grid integration, analyze the analytical form of its bias, and extend the method to multiple-point quadrature grids applicable to any factorizable harmonic or anharmonic nuclear wave function. The bias incurred by thermal lines is found to depend on the local form of the expectation value, and we demonstrate that the use of finer quadrature grids along selected modes can eliminate this bias, while still offering an ˜30 % lower computational cost than direct Monte Carlo integration in our tests.

Control of Networked Traffic Flow Distribution - A Stochastic Distribution System Perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Hong; Aziz, H M Abdul; Young, Stan

Networked traffic flow is a common scenario for urban transportation, where the distribution of vehicle queues either at controlled intersections or highway segments reflect the smoothness of the traffic flow in the network. At signalized intersections, the traffic queues are controlled by traffic signal control settings and effective traffic lights control would realize both smooth traffic flow and minimize fuel consumption. Funded by the Energy Efficient Mobility Systems (EEMS) program of the Vehicle Technologies Office of the US Department of Energy, we performed a preliminary investigation on the modelling and control framework in context of urban network of signalized intersections.more » In specific, we developed a recursive input-output traffic queueing models. The queue formation can be modeled as a stochastic process where the number of vehicles entering each intersection is a random number. Further, we proposed a preliminary B-Spline stochastic model for a one-way single-lane corridor traffic system based on theory of stochastic distribution control.. It has been shown that the developed stochastic model would provide the optimal probability density function (PDF) of the traffic queueing length as a dynamic function of the traffic signal setting parameters. Based upon such a stochastic distribution model, we have proposed a preliminary closed loop framework on stochastic distribution control for the traffic queueing system to make the traffic queueing length PDF follow a target PDF that potentially realizes the smooth traffic flow distribution in a concerned corridor.« less

Effect of nonlinearity in hybrid kinetic Monte Carlo-continuum models.

PubMed

Balter, Ariel; Lin, Guang; Tartakovsky, Alexandre M

2012-01-01

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a kinetic Monte Carlo (KMC) model for a surface to a finite-difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition-dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition-dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that in this case the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.

A stochastic hybrid model for pricing forward-start variance swaps

NASA Astrophysics Data System (ADS)

Roslan, Teh Raihana Nazirah

2017-11-01

Recently, market players have been exposed to the astounding increase in the trading volume of variance swaps. In this paper, the forward-start nature of a variance swap is being inspected, where hybridizations of equity and interest rate models are used to evaluate the price of discretely-sampled forward-start variance swaps. The Heston stochastic volatility model is being extended to incorporate the dynamics of the Cox-Ingersoll-Ross (CIR) stochastic interest rate model. This is essential since previous studies on variance swaps were mainly focusing on instantaneous-start variance swaps without considering the interest rate effects. This hybrid model produces an efficient semi-closed form pricing formula through the development of forward characteristic functions. The performance of this formula is investigated via simulations to demonstrate how the formula performs for different sampling times and against the real market scenario. Comparison done with the Monte Carlo simulation which was set as our main reference point reveals that our pricing formula gains almost the same precision in a shorter execution time.

Paracousti-UQ: A Stochastic 3-D Acoustic Wave Propagation Algorithm.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Preston, Leiph

Acoustic full waveform algorithms, such as Paracousti, provide deterministic solutions in complex, 3-D variable environments. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected sound levels within an environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. Performing Monte Carlo (MC) simulations is one method of assessing this uncertainty, but it can quickly become computationally intractable for realistic problems. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a fractionmore » of the computational cost of MC. Paracousti-UQ solves the SPDE system of 3-D acoustic wave propagation equations and provides estimates of the uncertainty of the output simulated wave field (e.g., amplitudes, waveforms) based on estimated probability distributions of the input medium and source parameters. This report describes the derivation of the stochastic partial differential equations, their implementation, and comparison of Paracousti-UQ results with MC simulations using simple models.« less

Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches.

PubMed

Li, Michael; Dushoff, Jonathan; Bolker, Benjamin M

2018-07-01

Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Armas-Perez, Julio C.; Londono-Hurtado, Alejandro; Guzman, Orlando

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 crystalmore » 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.« less

Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Armas-Pérez, Julio C.; Londono-Hurtado, Alejandro; Guzmán, Orlando

2015-07-28

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 crystalmore » 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.« less

Deterministic alternatives to the full configuration interaction quantum Monte Carlo method for strongly correlated systems

NASA Astrophysics Data System (ADS)

Tubman, Norm; Whaley, Birgitta

The development of exponential scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, allows exact diagonalization through stochastically sampling of determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, together with a stochastic projected wave function, which are used to explore the important parts of Hilbert space. However, a stochastic representation of the wave function is not required to search Hilbert space efficiently and new deterministic approaches have recently been shown to efficiently find the important parts of determinant space. We shall discuss the technique of Adaptive Sampling Configuration Interaction (ASCI) and the related heat-bath Configuration Interaction approach for ground state and excited state simulations. We will present several applications for strongly correlated Hamiltonians. This work was supported through the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences.

Incorporating Wind Power Forecast Uncertainties Into Stochastic Unit Commitment Using Neural Network-Based Prediction Intervals.

PubMed

Quan, Hao; Srinivasan, Dipti; Khosravi, Abbas

2015-09-01

Penetration of renewable energy resources, such as wind and solar power, into power systems significantly increases the uncertainties on system operation, stability, and reliability in smart grids. In this paper, the nonparametric neural network-based prediction intervals (PIs) are implemented for forecast uncertainty quantification. Instead of a single level PI, wind power forecast uncertainties are represented in a list of PIs. These PIs are then decomposed into quantiles of wind power. A new scenario generation method is proposed to handle wind power forecast uncertainties. For each hour, an empirical cumulative distribution function (ECDF) is fitted to these quantile points. The Monte Carlo simulation method is used to generate scenarios from the ECDF. Then the wind power scenarios are incorporated into a stochastic security-constrained unit commitment (SCUC) model. The heuristic genetic algorithm is utilized to solve the stochastic SCUC problem. Five deterministic and four stochastic case studies incorporated with interval forecasts of wind power are implemented. The results of these cases are presented and discussed together. Generation costs, and the scheduled and real-time economic dispatch reserves of different unit commitment strategies are compared. The experimental results show that the stochastic model is more robust than deterministic ones and, thus, decreases the risk in system operations of smart grids.

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

NASA Astrophysics Data System (ADS)

Hâkansson, P.; Mella, M.; Bressanini, Dario; Morosi, Gabriele; Patrone, Marta

2006-11-01

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with Itô calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Itô calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vidal-Codina, F., E-mail: fvidal@mit.edu; Nguyen, N.C., E-mail: cuongng@mit.edu; Giles, M.B., E-mail: mike.giles@maths.ox.ac.uk

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basismore » approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.« less

Stochastic many-body perturbation theory for anharmonic molecular vibrations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hermes, Matthew R.; Hirata, So, E-mail: sohirata@illinois.edu; CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012

2014-08-28

A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value ofmore » a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.« less

Combinatoric analysis of heterogeneous stochastic self-assembly.

PubMed

D'Orsogna, Maria R; Zhao, Bingyu; Berenji, Bijan; Chou, Tom

2013-09-28

We analyze a fully stochastic model of heterogeneous nucleation and self-assembly in a closed system with a fixed total particle number M, and a fixed number of seeds Ns. Each seed can bind a maximum of N particles. A discrete master equation for the probability distribution of the cluster sizes is derived and the corresponding cluster concentrations are found using kinetic Monte-Carlo simulations in terms of the density of seeds, the total mass, and the maximum cluster size. In the limit of slow detachment, we also find new analytic expressions and recursion relations for the cluster densities at intermediate times and at equilibrium. Our analytic and numerical findings are compared with those obtained from classical mass-action equations and the discrepancies between the two approaches analyzed.

Improved Convergence Rate of Multi-Group Scattering Moment Tallies for Monte Carlo Neutron Transport Codes

NASA Astrophysics Data System (ADS)

Nelson, Adam

Multi-group scattering moment matrices are critical to the solution of the multi-group form of the neutron transport equation, as they are responsible for describing the change in direction and energy of neutrons. These matrices, however, are difficult to correctly calculate from the measured nuclear data with both deterministic and stochastic methods. Calculating these parameters when using deterministic methods requires a set of assumptions which do not hold true in all conditions. These quantities can be calculated accurately with stochastic methods, however doing so is computationally expensive due to the poor efficiency of tallying scattering moment matrices. This work presents an improved method of obtaining multi-group scattering moment matrices from a Monte Carlo neutron transport code. This improved method of tallying the scattering moment matrices is based on recognizing that all of the outgoing particle information is known a priori and can be taken advantage of to increase the tallying efficiency (therefore reducing the uncertainty) of the stochastically integrated tallies. In this scheme, the complete outgoing probability distribution is tallied, supplying every one of the scattering moment matrices elements with its share of data. In addition to reducing the uncertainty, this method allows for the use of a track-length estimation process potentially offering even further improvement to the tallying efficiency. Unfortunately, to produce the needed distributions, the probability functions themselves must undergo an integration over the outgoing energy and scattering angle dimensions. This integration is too costly to perform during the Monte Carlo simulation itself and therefore must be performed in advance by way of a pre-processing code. The new method increases the information obtained from tally events and therefore has a significantly higher efficiency than the currently used techniques. The improved method has been implemented in a code system

MOLNs: A CLOUD PLATFORM FOR INTERACTIVE, REPRODUCIBLE, AND SCALABLE SPATIAL STOCHASTIC COMPUTATIONAL EXPERIMENTS IN SYSTEMS BIOLOGY USING PyURDME

PubMed Central

Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas

2017-01-01

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments. PMID:28190948

MOLNs: A CLOUD PLATFORM FOR INTERACTIVE, REPRODUCIBLE, AND SCALABLE SPATIAL STOCHASTIC COMPUTATIONAL EXPERIMENTS IN SYSTEMS BIOLOGY USING PyURDME.

PubMed

Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas

2016-01-01

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments.

Stochastic Threshold Microdose Model for Cell Killing by Insoluble Metallic Nanomaterial Particles

PubMed Central

Scott, Bobby R.

2010-01-01

This paper introduces a novel microdosimetric model for metallic nanomaterial-particles (MENAP)-induced cytotoxicity. The focus is on the engineered insoluble MENAP which represent a significant breakthrough in the design and development of new products for consumers, industry, and medicine. Increased production is rapidly occurring and may cause currently unrecognized health effects (e.g., nervous system dysfunction, heart disease, cancer); thus, dose-response models for MENAP-induced biological effects are needed to facilitate health risk assessment. The stochastic threshold microdose (STM) model presented introduces novel stochastic microdose metrics for use in constructing dose-response relationships for the frequency of specific cellular (e.g., cell killing, mutations, neoplastic transformation) or subcellular (e.g., mitochondria dysfunction) effects. A key metric is the exposure-time-dependent, specific burden (MENAP count) for a given critical target (e.g., mitochondria, nucleus). Exceeding a stochastic threshold specific burden triggers cell death. For critical targets in the cytoplasm, the autophagic mode of death is triggered. For the nuclear target, the apoptotic mode of death is triggered. Overall cell survival is evaluated for the indicated competing modes of death when both apply. The STM model can be applied to cytotoxicity data using Bayesian methods implemented via Markov chain Monte Carlo. PMID:21191483

On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods

PubMed Central

Lee, Anthony; Yau, Christopher; Giles, Michael B.; Doucet, Arnaud; Holmes, Christopher C.

2011-01-01

We present a case-study on the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods. Graphics cards, containing multiple Graphics Processing Units (GPUs), are self-contained parallel computational devices that can be housed in conventional desktop and laptop computers and can be thought of as prototypes of the next generation of many-core processors. For certain classes of population-based Monte Carlo algorithms they offer massively parallel simulation, with the added advantage over conventional distributed multi-core processors that they are cheap, easily accessible, easy to maintain, easy to code, dedicated local devices with low power consumption. On a canonical set of stochastic simulation examples including population-based Markov chain Monte Carlo methods and Sequential Monte Carlo methods, we nd speedups from 35 to 500 fold over conventional single-threaded computer code. Our findings suggest that GPUs have the potential to facilitate the growth of statistical modelling into complex data rich domains through the availability of cheap and accessible many-core computation. We believe the speedup we observe should motivate wider use of parallelizable simulation methods and greater methodological attention to their design. PMID:22003276

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.

Kinetic Monte Carlo simulations of travelling pulses and spiral waves in the lattice Lotka-Volterra model.

PubMed

Makeev, Alexei G; Kurkina, Elena S; Kevrekidis, Ioannis G

2012-06-01

Kinetic Monte Carlo simulations are used to study the stochastic two-species Lotka-Volterra model on a square lattice. For certain values of the model parameters, the system constitutes an excitable medium: travelling pulses and rotating spiral waves can be excited. Stable solitary pulses travel with constant (modulo stochastic fluctuations) shape and speed along a periodic lattice. The spiral waves observed persist sometimes for hundreds of rotations, but they are ultimately unstable and break-up (because of fluctuations and interactions between neighboring fronts) giving rise to complex dynamic behavior in which numerous small spiral waves rotate and interact with each other. It is interesting that travelling pulses and spiral waves can be exhibited by the model even for completely immobile species, due to the non-local reaction kinetics.

Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

NASA Astrophysics Data System (ADS)

Gelß, Patrick; Matera, Sebastian; Schütte, Christof

2016-06-01

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

Using Equation-Free Computation to Accelerate Network-Free Stochastic Simulation of Chemical Kinetics.

PubMed

Lin, Yen Ting; Chylek, Lily A; Lemons, Nathan W; Hlavacek, William S

2018-06-21

The chemical kinetics of many complex systems can be concisely represented by reaction rules, which can be used to generate reaction events via a kinetic Monte Carlo method that has been termed network-free simulation. Here, we demonstrate accelerated network-free simulation through a novel approach to equation-free computation. In this process, variables are introduced that approximately capture system state. Derivatives of these variables are estimated using short bursts of exact stochastic simulation and finite differencing. The variables are then projected forward in time via a numerical integration scheme, after which a new exact stochastic simulation is initialized and the whole process repeats. The projection step increases efficiency by bypassing the firing of numerous individual reaction events. As we show, the projected variables may be defined as populations of building blocks of chemical species. The maximal number of connected molecules included in these building blocks determines the degree of approximation. Equation-free acceleration of network-free simulation is found to be both accurate and efficient.

Green's Function and Stress Fields in Stochastic Heterogeneous Continua

NASA Astrophysics Data System (ADS)

Negi, Vineet

Many engineering materials used today are heterogenous in composition e.g. Composites - Polymer Matrix Composites, Metal Matrix Composites. Even, conventional engineering materials - metals, plastics, alloys etc. - may develop heterogeneities, like inclusions and residual stresses, during the manufacturing process. Moreover, these materials may also have intrinsic heterogeneities at a nanoscale in the form of grain boundaries in metals, crystallinity in amorphous polymers etc. While, the homogenized constitutive models for these materials may be satisfactory at a macroscale, recent studies of phenomena like fatigue failure, void nucleation, size-dependent brittle-ductile transition in polymeric nanofibers reveal a major play of micro/nanoscale physics in these phenomena. At this scale, heterogeneities in a material may no longer be ignored. Thus, this demands a study into the effects of various material heterogeneities. In this work, spatial heterogeneities in two material properties - elastic modulus and yield stress - have been investigated separately. The heterogeneity in the elastic modulus is studied in the context of Green's function. The Stochastic Finite Element method is adopted to get the mean statistics of the Green's function defined on a stochastic heterogeneous 2D infinite space. A study of the elastic-plastic transition in a domain having stochastic heterogenous yield stress was done using Mont-Carlo methods. The statistics for various stress and strain fields during the transition were obtained. Further, the effects of size of the domain and the strain-hardening rate on the stress fields during the heterogeneous elastic-plastic transition were investigated. Finally, a case is made for the role of the heterogenous elastic-plastic transition in damage nucleation and growth.

Stochastic differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sobczyk, K.

1990-01-01

This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshoremore » structures.« less

An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks.

PubMed

Salis, Howard; Kaznessis, Yiannis N

2005-12-01

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.

Stochastic Inversion of 2D Magnetotelluric Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jinsong

2010-07-01

The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, itmore » provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows« less

A split-step method to include electron–electron collisions via Monte Carlo in multiple rate equation simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huthmacher, Klaus; Molberg, Andreas K.; Rethfeld, Bärbel

2016-10-01

A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron–phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron–electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate howmore » electron–electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.« less

SCOUT: A Fast Monte-Carlo Modeling Tool of Scintillation Camera Output

PubMed Central

Hunter, William C. J.; Barrett, Harrison H.; Lewellen, Thomas K.; Miyaoka, Robert S.; Muzi, John P.; Li, Xiaoli; McDougald, Wendy; MacDonald, Lawrence R.

2011-01-01

We have developed a Monte-Carlo photon-tracking and readout simulator called SCOUT to study the stochastic behavior of signals output from a simplified rectangular scintillation-camera design. SCOUT models the salient processes affecting signal generation, transport, and readout. Presently, we compare output signal statistics from SCOUT to experimental results for both a discrete and a monolithic camera. We also benchmark the speed of this simulation tool and compare it to existing simulation tools. We find this modeling tool to be relatively fast and predictive of experimental results. Depending on the modeled camera geometry, we found SCOUT to be 4 to 140 times faster than other modeling tools. PMID:22072297

A Fast Monte Carlo Simulation for the International Linear Collider Detector

DOE Office of Scientific and Technical Information (OSTI.GOV)

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, descriptionsmore » 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.« less

Stochastic modeling of macrodispersion in unsaturated heterogeneous porous media. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yeh, T.C.J.

1995-02-01

Spatial heterogeneity of geologic media leads to uncertainty in predicting both flow and transport in the vadose zone. In this work an efficient and flexible, combined analytical-numerical Monte Carlo approach is developed for the analysis of steady-state flow and transient transport processes in highly heterogeneous, variably saturated porous media. The approach is also used for the investigation of the validity of linear, first order analytical stochastic models. With the Monte Carlo analysis accurate estimates of the ensemble conductivity, head, velocity, and concentration mean and covariance are obtained; the statistical moments describing displacement of solute plumes, solute breakthrough at a compliancemore » surface, and time of first exceedance of a given solute flux level are analyzed; and the cumulative probability density functions for solute flux across a compliance surface are investigated. The results of the Monte Carlo analysis show that for very heterogeneous flow fields, and particularly in anisotropic soils, the linearized, analytical predictions of soil water tension and soil moisture flux become erroneous. Analytical, linearized Lagrangian transport models also overestimate both the longitudinal and the transverse spreading of the mean solute plume in very heterogeneous soils and in dry soils. A combined analytical-numerical conditional simulation algorithm is also developed to estimate the impact of in-situ soil hydraulic measurements on reducing the uncertainty of concentration and solute flux predictions.« less

Reactive Monte Carlo sampling with an ab initio potential

DOE PAGES

Leiding, Jeff; Coe, Joshua D.

2016-05-04

Here, we present the first application of reactive Monte Carlo in a first-principles context. The algorithm samples in a modified NVT ensemble in which the volume, temperature, and total number of atoms of a given type are held fixed, but molecular composition is allowed to evolve through stochastic variation of chemical connectivity. We also discuss general features of the method, as well as techniques needed to enhance the efficiency of Boltzmann sampling. Finally, we compare the results of simulation of NH 3 to those of ab initio molecular dynamics (AIMD). Furthermore, we find that there are regions of state spacemore » for which RxMC sampling is much more efficient than AIMD due to the “rare-event” character of chemical reactions.« less

Evolution with Stochastic Fitness and Stochastic Migration

PubMed Central

Rice, Sean H.; Papadopoulos, Anthony

2009-01-01

Background Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration. Methodology/Principal Findings We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter. Conclusions/Significance As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory

A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks.

PubMed

Samant, Asawari; Ogunnaike, Babatunde A; Vlachos, Dionisios G

2007-05-24

The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void. The proposed HyMSMC method blends stochastic singular perturbation concepts, to deal with potential stiffness, with a hybrid of exact and coarse-grained stochastic algorithms, to cope with separation in population sizes. In addition, we introduce the computational singular perturbation (CSP) method as a means of systematically partitioning fast and slow networks and computing relaxation times for convergence. We also propose a new criteria of convergence of fast networks to stochastic low-dimensional manifolds, which further accelerates the algorithm. We use several prototype and biological examples, including a gene expression model displaying bistability, to demonstrate the efficiency, accuracy and applicability of the HyMSMC method. Bistable models serve as stringent tests for the success of multiscale MC methods and illustrate limitations of some literature methods.

Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gelß, Patrick, E-mail: p.gelss@fu-berlin.de; Matera, Sebastian, E-mail: matera@math.fu-berlin.de; Schütte, Christof, E-mail: schuette@mi.fu-berlin.de

2016-06-01

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO{sub 2}(110) surface.more » We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.« less

Simulation on reactor TRIGA Puspati core kinetics fueled with thorium (Th) based fuel element

NASA Astrophysics Data System (ADS)

Mohammed, Abdul Aziz; Pauzi, Anas Muhamad; Rahman, Shaik Mohmmed Haikhal Abdul; Zin, Muhamad Rawi Muhammad; Jamro, Rafhayudi; Idris, Faridah Mohamad

2016-01-01

In confronting global energy requirement and the search for better technologies, there is a real case for widening the range of potential variations in the design of nuclear power plants. Smaller and simpler reactors are attractive, provided they can meet safety and security standards and non-proliferation issues. On fuel cycle aspect, thorium fuel cycles produce much less plutonium and other radioactive transuranic elements than uranium fuel cycles. Although not fissile itself, Th-232 will absorb slow neutrons to produce uranium-233 (233U), which is fissile. By introducing Thorium, the numbers of highly enriched uranium fuel element can be reduced while maintaining the core neutronic performance. This paper describes the core kinetic of a small research reactor core like TRIGA fueled with a Th filled fuel element matrix using a general purpose Monte Carlo N-Particle (MCNP) code.

A polynomial-chaos-expansion-based building block approach for stochastic analysis of photonic circuits

NASA Astrophysics Data System (ADS)

Waqas, Abi; Melati, Daniele; Manfredi, Paolo; Grassi, Flavia; Melloni, Andrea

2018-02-01

The Building Block (BB) approach has recently emerged in photonic as a suitable strategy for the analysis and design of complex circuits. Each BB can be foundry related and contains a mathematical macro-model of its functionality. As well known, statistical variations in fabrication processes can have a strong effect on their functionality and ultimately affect the yield. In order to predict the statistical behavior of the circuit, proper analysis of the uncertainties effects is crucial. This paper presents a method to build a novel class of Stochastic Process Design Kits for the analysis of photonic circuits. The proposed design kits directly store the information on the stochastic behavior of each building block in the form of a generalized-polynomial-chaos-based augmented macro-model obtained by properly exploiting stochastic collocation and Galerkin methods. Using this approach, we demonstrate that the augmented macro-models of the BBs can be calculated once and stored in a BB (foundry dependent) library and then used for the analysis of any desired circuit. The main advantage of this approach, shown here for the first time in photonics, is that the stochastic moments of an arbitrary photonic circuit can be evaluated by a single simulation only, without the need for repeated simulations. The accuracy and the significant speed-up with respect to the classical Monte Carlo analysis are verified by means of classical photonic circuit example with multiple uncertain variables.

Stochastic analysis of uncertain thermal parameters for random thermal regime of frozen soil around a single freezing pipe

NASA Astrophysics Data System (ADS)

Wang, Tao; Zhou, Guoqing; Wang, Jianzhou; Zhou, Lei

2018-03-01

The artificial ground freezing method (AGF) is widely used in civil and mining engineering, and the thermal regime of frozen soil around the freezing pipe affects the safety of design and construction. The thermal parameters can be truly random due to heterogeneity of the soil properties, which lead to the randomness of thermal regime of frozen soil around the freezing pipe. The purpose of this paper is to study the one-dimensional (1D) random thermal regime problem on the basis of a stochastic analysis model and the Monte Carlo (MC) method. Considering the uncertain thermal parameters of frozen soil as random variables, stochastic processes and random fields, the corresponding stochastic thermal regime of frozen soil around a single freezing pipe are obtained and analyzed. Taking the variability of each stochastic parameter into account individually, the influences of each stochastic thermal parameter on stochastic thermal regime are investigated. The results show that the mean temperatures of frozen soil around the single freezing pipe with three analogy method are the same while the standard deviations are different. The distributions of standard deviation have a great difference at different radial coordinate location and the larger standard deviations are mainly at the phase change area. The computed data with random variable method and stochastic process method have a great difference from the measured data while the computed data with random field method well agree with the measured data. Each uncertain thermal parameter has a different effect on the standard deviation of frozen soil temperature around the single freezing pipe. These results can provide a theoretical basis for the design and construction of AGF.

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches.

PubMed

Pahle, Jürgen

2009-01-01

Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem.

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches

PubMed Central

2009-01-01

Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem. PMID:19151097

Aerosol properties from spectral extinction and backscatter estimated by an inverse Monte Carlo method.

PubMed

Ligon, D A; Gillespie, J B; Pellegrino, P

2000-08-20

The feasibility of using a generalized stochastic inversion methodology to estimate aerosol size distributions accurately by use of spectral extinction, backscatter data, or both is examined. The stochastic method used, inverse Monte Carlo (IMC), is verified with both simulated and experimental data from aerosols composed of spherical dielectrics with a known refractive index. Various levels of noise are superimposed on the data such that the effect of noise on the stability and results of inversion can be determined. Computational results show that the application of the IMC technique to inversion of spectral extinction or backscatter data or both can produce good estimates of aerosol size distributions. Specifically, for inversions for which both spectral extinction and backscatter data are used, the IMC technique was extremely accurate in determining particle size distributions well outside the wavelength range. Also, the IMC inversion results proved to be stable and accurate even when the data had significant noise, with a signal-to-noise ratio of 3.

A self-adaptive memeplexes robust search scheme for solving stochastic demands vehicle routing problem

NASA Astrophysics Data System (ADS)

Chen, Xianshun; Feng, Liang; Ong, Yew Soon

2012-07-01

In this article, we proposed a self-adaptive memeplex robust search (SAMRS) for finding robust and reliable solutions that are less sensitive to stochastic behaviours of customer demands and have low probability of route failures, respectively, in vehicle routing problem with stochastic demands (VRPSD). In particular, the contribution of this article is three-fold. First, the proposed SAMRS employs the robust solution search scheme (RS 3) as an approximation of the computationally intensive Monte Carlo simulation, thus reducing the computation cost of fitness evaluation in VRPSD, while directing the search towards robust and reliable solutions. Furthermore, a self-adaptive individual learning based on the conceptual modelling of memeplex is introduced in the SAMRS. Finally, SAMRS incorporates a gene-meme co-evolution model with genetic and memetic representation to effectively manage the search for solutions in VRPSD. Extensive experimental results are then presented for benchmark problems to demonstrate that the proposed SAMRS serves as an efficable means of generating high-quality robust and reliable solutions in VRPSD.

Extinction time of a stochastic predator-prey model by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Hu, Bing; Huang, Dongmei; Sun, Jian-Qiao

2018-03-01

The stochastic response and extinction time of a predator-prey model with Gaussian white noise excitations are studied by the generalized cell mapping (GCM) method based on the short-time Gaussian approximation (STGA). The methods for stochastic response probability density functions (PDFs) and extinction time statistics are developed. The Taylor expansion is used to deal with non-polynomial nonlinear terms of the model for deriving the moment equations with Gaussian closure, which are needed for the STGA in order to compute the one-step transition probabilities. The work is validated with direct Monte Carlo simulations. We have presented the transient responses showing the evolution from a Gaussian initial distribution to a non-Gaussian steady-state one. The effects of the model parameter and noise intensities on the steady-state PDFs are discussed. It is also found that the effects of noise intensities on the extinction time statistics are opposite to the effects on the limit probability distributions of the survival species.

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

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.

Moment Lyapunov Exponent and Stochastic Stability of Binary Airfoil under Combined Harmonic and Non-Gaussian Colored Noise Excitations

NASA Astrophysics Data System (ADS)

Hu, D. L.; Liu, X. B.

Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non-Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.

Application of stochastic methods for wind speed forecasting and wind turbines design at the area of Thessaly, Greece

NASA Astrophysics Data System (ADS)

Dimitriadis, Panayiotis; Lazaros, Lappas; Daskalou, Olympia; Filippidou, Ariadni; Giannakou, Marianna; Gkova, Eleni; Ioannidis, Romanos; Polydera, Angeliki; Polymerou, Eleni; Psarrou, Eleftheria; Vyrini, Alexandra; Papalexiou, Simon; Koutsoyiannis, Demetris

2015-04-01

Several methods exist for estimating the statistical properties of wind speed, most of them being deterministic or probabilistic, disregarding though its long-term behaviour. Here, we focus on the stochastic nature of wind. After analyzing several historical timeseries at the area of interest (AoI) in Thessaly (Greece), we show that a Hurst-Kolmogorov (HK) behaviour is apparent. Thus, disregarding the latter could lead to unrealistic predictions and wind load situations, causing some impact on the energy production and management. Moreover, we construct a stochastic model capable of preserving the HK behaviour and we produce synthetic timeseries using a Monte-Carlo approach to estimate the future wind loads in the AoI. Finally, we identify the appropriate types of wind turbines for the AoI (based on the IEC 61400 standards) and propose several industrial solutions. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.

Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids.

PubMed

Ali, S M; Mehmood, C A; Khan, B; Jawad, M; Farid, U; Jadoon, J K; Ali, M; Tareen, N K; Usman, S; Majid, M; Anwar, S M

2016-01-01

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion.

Stochastic and Statistical Analysis of Utility Revenues and Weather Data Analysis for Consumer Demand Estimation in Smart Grids

PubMed Central

Ali, S. M.; Mehmood, C. A; Khan, B.; Jawad, M.; Farid, U; Jadoon, J. K.; Ali, M.; Tareen, N. K.; Usman, S.; Majid, M.; Anwar, S. M.

2016-01-01

In smart grid paradigm, the consumer demands are random and time-dependent, owning towards stochastic probabilities. The stochastically varying consumer demands have put the policy makers and supplying agencies in a demanding position for optimal generation management. The utility revenue functions are highly dependent on the consumer deterministic stochastic demand models. The sudden drifts in weather parameters effects the living standards of the consumers that in turn influence the power demands. Considering above, we analyzed stochastically and statistically the effect of random consumer demands on the fixed and variable revenues of the electrical utilities. Our work presented the Multi-Variate Gaussian Distribution Function (MVGDF) probabilistic model of the utility revenues with time-dependent consumer random demands. Moreover, the Gaussian probabilities outcome of the utility revenues is based on the varying consumer n demands data-pattern. Furthermore, Standard Monte Carlo (SMC) simulations are performed that validated the factor of accuracy in the aforesaid probabilistic demand-revenue model. We critically analyzed the effect of weather data parameters on consumer demands using correlation and multi-linear regression schemes. The statistical analysis of consumer demands provided a relationship between dependent (demand) and independent variables (weather data) for utility load management, generation control, and network expansion. PMID:27314229

Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

NASA Astrophysics Data System (ADS)

Park, Brian T.; Petrosian, Vahe

1996-03-01

Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

Simulation on reactor TRIGA Puspati core kinetics fueled with thorium (Th) based fuel element

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohammed, Abdul Aziz, E-mail: azizM@uniten.edu.my; Rahman, Shaik Mohmmed Haikhal Abdul; Pauzi, Anas Muhamad, E-mail: anas@uniten.edu.my

2016-01-22

In confronting global energy requirement and the search for better technologies, there is a real case for widening the range of potential variations in the design of nuclear power plants. Smaller and simpler reactors are attractive, provided they can meet safety and security standards and non-proliferation issues. On fuel cycle aspect, thorium fuel cycles produce much less plutonium and other radioactive transuranic elements than uranium fuel cycles. Although not fissile itself, Th-232 will absorb slow neutrons to produce uranium-233 ({sup 233}U), which is fissile. By introducing Thorium, the numbers of highly enriched uranium fuel element can be reduced while maintainingmore » the core neutronic performance. This paper describes the core kinetic of a small research reactor core like TRIGA fueled with a Th filled fuel element matrix using a general purpose Monte Carlo N-Particle (MCNP) code.« less

Diagnosing Undersampling Biases in Monte Carlo Eigenvalue and Flux Tally Estimates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perfetti, Christopher M.; Rearden, Bradley T.; Marshall, William J.

2017-02-08

Here, this study focuses on understanding the phenomena in Monte Carlo simulations known as undersampling, in which Monte Carlo tally estimates may not encounter a sufficient number of particles during each generation to obtain unbiased tally estimates. Steady-state Monte Carlo simulations were performed using the KENO Monte Carlo tools within the SCALE code system for models of several burnup credit applications with varying degrees of spatial and isotopic complexities, and the incidence and impact of undersampling on eigenvalue and flux estimates were examined. Using an inadequate number of particle histories in each generation was found to produce a maximum bias of ~100 pcm in eigenvalue estimates and biases that exceeded 10% in fuel pin flux tally estimates. Having quantified the potential magnitude of undersampling biases in eigenvalue and flux tally estimates in these systems, this study then investigated whether Markov Chain Monte Carlo convergence metrics could be integrated into Monte Carlo simulations to predict the onset and magnitude of undersampling biases. Five potential metrics for identifying undersampling biases were implemented in the SCALE code system and evaluated for their ability to predict undersampling biases by comparing the test metric scores with the observed undersampling biases. Finally, of the five convergence metrics that were investigated, three (the Heidelberger-Welch relative half-width, the Gelman-Rubin more » $$\\hat{R}_c$$ diagnostic, and tally entropy) showed the potential to accurately predict the behavior of undersampling biases in the responses examined.« less

Single realization stochastic FDTD for weak scattering waves in biological random media.

PubMed

Tan, Tengmeng; Taflove, Allen; Backman, Vadim

2013-02-01

This paper introduces an iterative scheme to overcome the unresolved issues presented in S-FDTD (stochastic finite-difference time-domain) for obtaining ensemble average field values recently reported by Smith and Furse in an attempt to replace the brute force multiple-realization also known as Monte-Carlo approach with a single-realization scheme. Our formulation is particularly useful for studying light interactions with biological cells and tissues having sub-wavelength scale features. Numerical results demonstrate that such a small scale variation can be effectively modeled with a random medium problem which when simulated with the proposed S-FDTD indeed produces a very accurate result.

Single realization stochastic FDTD for weak scattering waves in biological random media

PubMed Central

Tan, Tengmeng; Taflove, Allen; Backman, Vadim

2015-01-01

This paper introduces an iterative scheme to overcome the unresolved issues presented in S-FDTD (stochastic finite-difference time-domain) for obtaining ensemble average field values recently reported by Smith and Furse in an attempt to replace the brute force multiple-realization also known as Monte-Carlo approach with a single-realization scheme. Our formulation is particularly useful for studying light interactions with biological cells and tissues having sub-wavelength scale features. Numerical results demonstrate that such a small scale variation can be effectively modeled with a random medium problem which when simulated with the proposed S-FDTD indeed produces a very accurate result. PMID:27158153

Ensemble methods for stochastic networks with special reference to the biological clock of Neurospora crassa.

PubMed

Caranica, C; Al-Omari, A; Deng, Z; Griffith, J; Nilsen, R; Mao, L; Arnold, J; Schüttler, H-B

2018-01-01

A major challenge in systems biology is to infer the parameters of regulatory networks that operate in a noisy environment, such as in a single cell. In a stochastic regime it is hard to distinguish noise from the real signal and to infer the noise contribution to the dynamical behavior. When the genetic network displays oscillatory dynamics, it is even harder to infer the parameters that produce the oscillations. To address this issue we introduce a new estimation method built on a combination of stochastic simulations, mass action kinetics and ensemble network simulations in which we match the average periodogram and phase of the model to that of the data. The method is relatively fast (compared to Metropolis-Hastings Monte Carlo Methods), easy to parallelize, applicable to large oscillatory networks and large (~2000 cells) single cell expression data sets, and it quantifies the noise impact on the observed dynamics. Standard errors of estimated rate coefficients are typically two orders of magnitude smaller than the mean from single cell experiments with on the order of ~1000 cells. We also provide a method to assess the goodness of fit of the stochastic network using the Hilbert phase of single cells. An analysis of phase departures from the null model with no communication between cells is consistent with a hypothesis of Stochastic Resonance describing single cell oscillators. Stochastic Resonance provides a physical mechanism whereby intracellular noise plays a positive role in establishing oscillatory behavior, but may require model parameters, such as rate coefficients, that differ substantially from those extracted at the macroscopic level from measurements on populations of millions of communicating, synchronized cells.

Noise stochastic corrected maximum a posteriori estimator for birefringence imaging using polarization-sensitive optical coherence tomography

PubMed Central

Kasaragod, Deepa; Makita, Shuichi; Hong, Young-Joo; Yasuno, Yoshiaki

2017-01-01

This paper presents a noise-stochastic corrected maximum a posteriori estimator for birefringence imaging using Jones matrix optical coherence tomography. The estimator described in this paper is based on the relationship between probability distribution functions of the measured birefringence and the effective signal to noise ratio (ESNR) as well as the true birefringence and the true ESNR. The Monte Carlo method is used to numerically describe this relationship and adaptive 2D kernel density estimation provides the likelihood for a posteriori estimation of the true birefringence. Improved estimation is shown for the new estimator with stochastic model of ESNR in comparison to the old estimator, both based on the Jones matrix noise model. A comparison with the mean estimator is also done. Numerical simulation validates the superiority of the new estimator. The superior performance of the new estimator was also shown by in vivo measurement of optic nerve head. PMID:28270974

SCOUT: a fast Monte-Carlo modeling tool of scintillation camera output†

PubMed Central

Hunter, William C J; Barrett, Harrison H.; Muzi, John P.; McDougald, Wendy; MacDonald, Lawrence R.; Miyaoka, Robert S.; Lewellen, Thomas K.

2013-01-01

We have developed a Monte-Carlo photon-tracking and readout simulator called SCOUT to study the stochastic behavior of signals output from a simplified rectangular scintillation-camera design. SCOUT models the salient processes affecting signal generation, transport, and readout of a scintillation camera. Presently, we compare output signal statistics from SCOUT to experimental results for both a discrete and a monolithic camera. We also benchmark the speed of this simulation tool and compare it to existing simulation tools. We find this modeling tool to be relatively fast and predictive of experimental results. Depending on the modeled camera geometry, we found SCOUT to be 4 to 140 times faster than other modeling tools. PMID:23640136

Algorithms for adaptive stochastic control for a class of linear systems

NASA Technical Reports Server (NTRS)

Toda, M.; Patel, R. V.

1977-01-01

Control of linear, discrete time, stochastic systems with unknown control gain parameters is discussed. Two suboptimal adaptive control schemes are derived: one is based on underestimating future control and the other is based on overestimating future control. Both schemes require little on-line computation and incorporate in their control laws some information on estimation errors. The performance of these laws is studied by Monte Carlo simulations on a computer. Two single input, third order systems are considered, one stable and the other unstable, and the performance of the two adaptive control schemes is compared with that of the scheme based on enforced certainty equivalence and the scheme where the control gain parameters are known.

Stochastic thermodynamics

NASA Astrophysics Data System (ADS)

Eichhorn, Ralf; Aurell, Erik

2014-04-01

'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response

Portfolio Optimization with Stochastic Dividends and Stochastic Volatility

ERIC Educational Resources Information Center

Varga, Katherine Yvonne

2015-01-01

We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…

GPU Computing in Bayesian Inference of Realized Stochastic Volatility Model

NASA Astrophysics Data System (ADS)

Takaishi, Tetsuya

2015-01-01

The realized stochastic volatility (RSV) model that utilizes the realized volatility as additional information has been proposed to infer volatility of financial time series. We consider the Bayesian inference of the RSV model by the Hybrid Monte Carlo (HMC) algorithm. The HMC algorithm can be parallelized and thus performed on the GPU for speedup. The GPU code is developed with CUDA Fortran. We compare the computational time in performing the HMC algorithm on GPU (GTX 760) and CPU (Intel i7-4770 3.4GHz) and find that the GPU can be up to 17 times faster than the CPU. We also code the program with OpenACC and find that appropriate coding can achieve the similar speedup with CUDA Fortran.

Applying stochastic small-scale damage functions to German winter storms

NASA Astrophysics Data System (ADS)

Prahl, B. F.; Rybski, D.; Kropp, J. P.; Burghoff, O.; Held, H.

2012-03-01

Analyzing insurance-loss data we derive stochastic storm-damage functions for residential buildings. On district level we fit power-law relations between daily loss and maximum wind speed, typically spanning more than 4 orders of magnitude. The estimated exponents for 439 German districts roughly range from 8 to 12. In addition, we find correlations among the parameters and socio-demographic data, which we employ in a simplified parametrization of the damage function with just 3 independent parameters for each district. A Monte Carlo method is used to generate loss estimates and confidence bounds of daily and annual storm damages in Germany. Our approach reproduces the annual progression of winter storm losses and enables to estimate daily losses over a wide range of magnitudes.

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

Stochastic associative memory

NASA Astrophysics Data System (ADS)

Baumann, Erwin W.; Williams, David L.

1993-08-01

Artificial neural networks capable of learning and recalling stochastic associations between non-deterministic quantities have received relatively little attention to date. One potential application of such stochastic associative networks is the generation of sensory 'expectations' based on arbitrary subsets of sensor inputs to support anticipatory and investigate behavior in sensor-based robots. Another application of this type of associative memory is the prediction of how a scene will look in one spectral band, including noise, based upon its appearance in several other wavebands. This paper describes a semi-supervised neural network architecture composed of self-organizing maps associated through stochastic inter-layer connections. This 'Stochastic Associative Memory' (SAM) can learn and recall non-deterministic associations between multi-dimensional probability density functions. The stochastic nature of the network also enables it to represent noise distributions that are inherent in any true sensing process. The SAM architecture, training process, and initial application to sensor image prediction are described. Relationships to Fuzzy Associative Memory (FAM) are discussed.

Confinement and diffusion modulate bistability and stochastic switching in a reaction network with positive feedback

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mlynarczyk, Paul J.; Pullen, Robert H.; Abel, Steven M., E-mail: abel@utk.edu

2016-01-07

Positive feedback is a common feature in signal transduction networks and can lead to phenomena such as bistability and signal propagation by domain growth. Physical features of the cellular environment, such as spatial confinement and the mobility of proteins, play important but inadequately understood roles in shaping the behavior of signaling networks. Here, we use stochastic, spatially resolved kinetic Monte Carlo simulations to explore a positive feedback network as a function of system size, system shape, and mobility of molecules. We show that these physical properties can markedly alter characteristics of bistability and stochastic switching when compared with well-mixed simulations.more » Notably, systems of equal volume but different shapes can exhibit qualitatively different behaviors under otherwise identical conditions. We show that stochastic switching to a state maintained by positive feedback occurs by cluster formation and growth. Additionally, the frequency at which switching occurs depends nontrivially on the diffusion coefficient, which can promote or suppress switching relative to the well-mixed limit. Taken together, the results provide a framework for understanding how confinement and protein mobility influence emergent features of the positive feedback network by modulating molecular concentrations, diffusion-influenced rate parameters, and spatiotemporal correlations between molecules.« less

A statistical approach to nuclear fuel design and performance

NASA Astrophysics Data System (ADS)

Cunning, Travis Andrew

As CANDU fuel failures can have significant economic and operational consequences on the Canadian nuclear power industry, it is essential that factors impacting fuel performance are adequately understood. Current industrial practice relies on deterministic safety analysis and the highly conservative "limit of operating envelope" approach, where all parameters are assumed to be at their limits simultaneously. This results in a conservative prediction of event consequences with little consideration given to the high quality and precision of current manufacturing processes. This study employs a novel approach to the prediction of CANDU fuel reliability. Probability distributions are fitted to actual fuel manufacturing datasets provided by Cameco Fuel Manufacturing, Inc. They are used to form input for two industry-standard fuel performance codes: ELESTRES for the steady-state case and ELOCA for the transient case---a hypothesized 80% reactor outlet header break loss of coolant accident. Using a Monte Carlo technique for input generation, 105 independent trials are conducted and probability distributions are fitted to key model output quantities. Comparing model output against recognized industrial acceptance criteria, no fuel failures are predicted for either case. Output distributions are well removed from failure limit values, implying that margin exists in current fuel manufacturing and design. To validate the results and attempt to reduce the simulation burden of the methodology, two dimensional reduction methods are assessed. Using just 36 trials, both methods are able to produce output distributions that agree strongly with those obtained via the brute-force Monte Carlo method, often to a relative discrepancy of less than 0.3% when predicting the first statistical moment, and a relative discrepancy of less than 5% when predicting the second statistical moment. In terms of global sensitivity, pellet density proves to have the greatest impact on fuel performance

Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Peng; Barajas-Solano, David A.; Constantinescu, Emil

Wind and solar power generators are commonly described by a system of stochastic ordinary differential equations (SODEs) where random input parameters represent uncertainty in wind and solar energy. The existing methods for SODEs are mostly limited to delta-correlated random parameters (white noise). Here we use the Probability Density Function (PDF) method for deriving a closed-form deterministic partial differential equation (PDE) for the joint probability density function of the SODEs describing a power generator with time-correlated power input. The resulting PDE is solved numerically. A good agreement with Monte Carlo Simulations shows accuracy of the PDF method.

Evaluation of Electric Power Procurement Strategies by Stochastic Dynamic Programming

NASA Astrophysics Data System (ADS)

Saisho, Yuichi; Hayashi, Taketo; Fujii, Yasumasa; Yamaji, Kenji

In deregulated electricity markets, the role of a distribution company is to purchase electricity from the wholesale electricity market at randomly fluctuating prices and to provide it to its customers at a given fixed price. Therefore the company has to take risk stemming from the uncertainties of electricity prices and/or demand fluctuation instead of the customers. The way to avoid the risk is to make a bilateral contact with generating companies or install its own power generation facility. This entails the necessity to develop a certain method to make an optimal strategy for electric power procurement. In such a circumstance, this research has the purpose for proposing a mathematical method based on stochastic dynamic programming and additionally considering the characteristics of the start-up cost of electric power generation facility to evaluate strategies of combination of the bilateral contract and power auto-generation with its own facility for procuring electric power in deregulated electricity market. In the beginning we proposed two approaches to solve the stochastic dynamic programming, and they are a Monte Carlo simulation method and a finite difference method to derive the solution of a partial differential equation of the total procurement cost of electric power. Finally we discussed the influences of the price uncertainty on optimal strategies of power procurement.

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering

NASA Technical Reports Server (NTRS)

Deepak, A.; Fluellen, A.

1978-01-01

An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.

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.

A theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall

NASA Astrophysics Data System (ADS)

Lombardo, F.; Volpi, E.; Koutsoyiannis, D.; Serinaldi, F.

2017-06-01

Generating fine-scale time series of intermittent rainfall that are fully consistent with any given coarse-scale totals is a key and open issue in many hydrological problems. We propose a stationary disaggregation method that simulates rainfall time series with given dependence structure, wet/dry probability, and marginal distribution at a target finer (lower-level) time scale, preserving full consistency with variables at a parent coarser (higher-level) time scale. We account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths. This approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean, variance, and autocorrelation function (ACF) for a mixed-type stochastic process in terms of mean, variance, and ACFs of both continuous and discrete components, respectively. To achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse-scale totals, the generated lower-level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model. To assess model performance, we study rainfall process as intermittent with both independent and dependent occurrences, where dependence is quantified by the probability that two consecutive time intervals are dry. In either case, we provide analytical formulations of main statistics of our mixed-type disaggregation model and show their clear accordance with Monte Carlo simulations. An application to rainfall time series from real world is shown as a proof of concept.

Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system

NASA Astrophysics Data System (ADS)

Yang, J. H.; Sanjuán, Miguel A. F.; Liu, H. G.; Litak, G.; Li, X.

2016-12-01

We investigate the stochastic response of a noisy bistable fractional-order system when the fractional-order lies in the interval (0, 2]. We focus mainly on the stochastic P-bifurcation and the phenomenon of the stochastic resonance. We compare the generalized Euler algorithm and the predictor-corrector approach which are commonly used for numerical calculations of fractional-order nonlinear equations. Based on the predictor-corrector approach, the stochastic P-bifurcation and the stochastic resonance are investigated. Both the fractional-order value and the noise intensity can induce an stochastic P-bifurcation. The fractional-order may lead the stationary probability density function to turn from a single-peak mode to a double-peak mode. However, the noise intensity may transform the stationary probability density function from a double-peak mode to a single-peak mode. The stochastic resonance is investigated thoroughly, according to the linear and the nonlinear response theory. In the linear response theory, the optimal stochastic resonance may occur when the value of the fractional-order is larger than one. In previous works, the fractional-order is usually limited to the interval (0, 1]. Moreover, the stochastic resonance at the subharmonic frequency and the superharmonic frequency are investigated respectively, by using the nonlinear response theory. When it occurs at the subharmonic frequency, the resonance may be strong and cannot be ignored. When it occurs at the superharmonic frequency, the resonance is weak. We believe that the results in this paper might be useful for the signal processing of nonlinear systems.

Determining Reduced Order Models for Optimal Stochastic Reduced Order Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonney, Matthew S.; Brake, Matthew R.W.

2015-08-01

The use of parameterized reduced order models(PROMs) within the stochastic reduced order model (SROM) framework is a logical progression for both methods. In this report, five different parameterized reduced order models are selected and critiqued against the other models along with truth model for the example of the Brake-Reuss beam. The models are: a Taylor series using finite difference, a proper orthogonal decomposition of the the output, a Craig-Bampton representation of the model, a method that uses Hyper-Dual numbers to determine the sensitivities, and a Meta-Model method that uses the Hyper-Dual results and constructs a polynomial curve to better representmore » the output data. The methods are compared against a parameter sweep and a distribution propagation where the first four statistical moments are used as a comparison. Each method produces very accurate results with the Craig-Bampton reduction having the least accurate results. The models are also compared based on time requirements for the evaluation of each model where the Meta- Model requires the least amount of time for computation by a significant amount. Each of the five models provided accurate results in a reasonable time frame. The determination of which model to use is dependent on the availability of the high-fidelity model and how many evaluations can be performed. Analysis of the output distribution is examined by using a large Monte-Carlo simulation along with a reduced simulation using Latin Hypercube and the stochastic reduced order model sampling technique. Both techniques produced accurate results. The stochastic reduced order modeling technique produced less error when compared to an exhaustive sampling for the majority of methods.« less

Isolating intrinsic noise sources in a stochastic genetic switch.

PubMed

Newby, Jay M

2012-01-01

The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produced. Either one of the promotors can be repressed at any given time or both can be unrepressed, leaving three possible promotor states. This model is analysed in its bistable regime in which the deterministic limit exhibits two stable fixed points and an unstable saddle, and the case of small noise is considered. On small timescales, the stochastic process fluctuates near one of the stable fixed points, and on large timescales, a metastable transition can occur, where fluctuations drive the system past the unstable saddle to the other stable fixed point. To explore how different intrinsic noise sources affect these transitions, fluctuations in protein production and degradation are eliminated, leaving fluctuations in the promotor state as the only source of noise in the system. The process without protein noise is then compared to the process with weak protein noise using perturbation methods and Monte Carlo simulations. It is found that some significant differences in the random process emerge when the intrinsic noise source is removed.

Stochastic approach to the derivation of emission limits for wastewater treatment plants.

PubMed

Stransky, D; Kabelkova, I; Bares, V

2009-01-01

Stochastic approach to the derivation of WWTP emission limits meeting probabilistically defined environmental quality standards (EQS) is presented. The stochastic model is based on the mixing equation with input data defined by probability density distributions and solved by Monte Carlo simulations. The approach was tested on a study catchment for total phosphorus (P(tot)). The model assumes input variables independency which was proved for the dry-weather situation. Discharges and P(tot) concentrations both in the study creek and WWTP effluent follow log-normal probability distribution. Variation coefficients of P(tot) concentrations differ considerably along the stream (c(v)=0.415-0.884). The selected value of the variation coefficient (c(v)=0.420) affects the derived mean value (C(mean)=0.13 mg/l) of the P(tot) EQS (C(90)=0.2 mg/l). Even after supposed improvement of water quality upstream of the WWTP to the level of the P(tot) EQS, the WWTP emission limits calculated would be lower than the values of the best available technology (BAT). Thus, minimum dilution ratios for the meaningful application of the combined approach to the derivation of P(tot) emission limits for Czech streams are discussed.

Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons

PubMed Central

Buesing, Lars; Bill, Johannes; Nessler, Bernhard; Maass, Wolfgang

2011-01-01

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons. PMID:22096452

Probabilistic homogenization of random composite with ellipsoidal particle reinforcement by the iterative stochastic finite element method

NASA Astrophysics Data System (ADS)

Sokołowski, Damian; Kamiński, Marcin

2018-01-01

This study proposes a framework for determination of basic probabilistic characteristics of the orthotropic homogenized elastic properties of the periodic composite reinforced with ellipsoidal particles and a high stiffness contrast between the reinforcement and the matrix. Homogenization problem, solved by the Iterative Stochastic Finite Element Method (ISFEM) is implemented according to the stochastic perturbation, Monte Carlo simulation and semi-analytical techniques with the use of cubic Representative Volume Element (RVE) of this composite containing single particle. The given input Gaussian random variable is Young modulus of the matrix, while 3D homogenization scheme is based on numerical determination of the strain energy of the RVE under uniform unit stretches carried out in the FEM system ABAQUS. The entire series of several deterministic solutions with varying Young modulus of the matrix serves for the Weighted Least Squares Method (WLSM) recovery of polynomial response functions finally used in stochastic Taylor expansions inherent for the ISFEM. A numerical example consists of the High Density Polyurethane (HDPU) reinforced with the Carbon Black particle. It is numerically investigated (1) if the resulting homogenized characteristics are also Gaussian and (2) how the uncertainty in matrix Young modulus affects the effective stiffness tensor components and their PDF (Probability Density Function).

Markov Chain Monte Carlo Bayesian Learning for Neural Networks

NASA Technical Reports Server (NTRS)

Goodrich, Michael S.

2011-01-01

Conventional training methods for neural networks involve starting al a random location in the solution space of the network weights, navigating an error hyper surface to reach a minimum, and sometime stochastic based techniques (e.g., genetic algorithms) to avoid entrapment in a local minimum. It is further typically necessary to preprocess the data (e.g., normalization) to keep the training algorithm on course. Conversely, Bayesian based learning is an epistemological approach concerned with formally updating the plausibility of competing candidate hypotheses thereby obtaining a posterior distribution for the network weights conditioned on the available data and a prior distribution. In this paper, we developed a powerful methodology for estimating the full residual uncertainty in network weights and therefore network predictions by using a modified Jeffery's prior combined with a Metropolis Markov Chain Monte Carlo method.

Towards sub-optimal stochastic control of partially observable stochastic systems

NASA Technical Reports Server (NTRS)

Ruzicka, G. J.

1980-01-01

A class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design is examined. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in dimensions is proven.

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.

Progressive Stochastic Reconstruction Technique (PSRT) for cryo electron tomography.

PubMed

Turoňová, Beata; Marsalek, Lukas; Davidovič, Tomáš; Slusallek, Philipp

2015-03-01

Cryo Electron Tomography (cryoET) plays an essential role in Structural Biology, as it is the only technique that allows to study the structure of large macromolecular complexes in their close to native environment in situ. The reconstruction methods currently in use, such as Weighted Back Projection (WBP) or Simultaneous Iterative Reconstruction Technique (SIRT), deliver noisy and low-contrast reconstructions, which complicates the application of high-resolution protocols, such as Subtomogram Averaging (SA). We propose a Progressive Stochastic Reconstruction Technique (PSRT) - a novel iterative approach to tomographic reconstruction in cryoET based on Monte Carlo random walks guided by Metropolis-Hastings sampling strategy. We design a progressive reconstruction scheme to suit the conditions present in cryoET and apply it successfully to reconstructions of macromolecular complexes from both synthetic and experimental datasets. We show how to integrate PSRT into SA, where it provides an elegant solution to the region-of-interest problem and delivers high-contrast reconstructions that significantly improve template-based localization without any loss of high-resolution structural information. Furthermore, the locality of SA is exploited to design an importance sampling scheme which significantly speeds up the otherwise slow Monte Carlo approach. Finally, we design a new memory efficient solution for the specimen-level interior problem of cryoET, removing all associated artifacts. Copyright © 2015 Elsevier Inc. All rights reserved.

On the comparison of stochastic model predictive control strategies applied to a hydrogen-based microgrid

NASA Astrophysics Data System (ADS)

Velarde, P.; Valverde, L.; Maestre, J. M.; Ocampo-Martinez, C.; Bordons, C.

2017-03-01

In this paper, a performance comparison among three well-known stochastic model predictive control approaches, namely, multi-scenario, tree-based, and chance-constrained model predictive control is presented. To this end, three predictive controllers have been designed and implemented in a real renewable-hydrogen-based microgrid. The experimental set-up includes a PEM electrolyzer, lead-acid batteries, and a PEM fuel cell as main equipment. The real experimental results show significant differences from the plant components, mainly in terms of use of energy, for each implemented technique. Effectiveness, performance, advantages, and disadvantages of these techniques are extensively discussed and analyzed to give some valid criteria when selecting an appropriate stochastic predictive controller.

Concurrent Monte Carlo transport and fluence optimization with fluence adjusting scalable transport Monte Carlo

PubMed Central

Svatos, M.; Zankowski, C.; Bednarz, B.

2016-01-01

Purpose: The future of radiation therapy will require advanced inverse planning solutions to support single-arc, multiple-arc, and “4π” delivery modes, which present unique challenges in finding an optimal treatment plan over a vast search space, while still preserving dosimetric accuracy. The successful clinical implementation of such methods would benefit from Monte Carlo (MC) based dose calculation methods, which can offer improvements in dosimetric accuracy when compared to deterministic methods. The standard method for MC based treatment planning optimization leverages the accuracy of the MC dose calculation and efficiency of well-developed optimization methods, by precalculating the fluence to dose relationship within a patient with MC methods and subsequently optimizing the fluence weights. However, the sequential nature of this implementation is computationally time consuming and memory intensive. Methods to reduce the overhead of the MC precalculation have been explored in the past, demonstrating promising reductions of computational time overhead, but with limited impact on the memory overhead due to the sequential nature of the dose calculation and fluence optimization. The authors propose an entirely new form of “concurrent” Monte Carlo treat plan optimization: a platform which optimizes the fluence during the dose calculation, reduces wasted computation time being spent on beamlets that weakly contribute to the final dose distribution, and requires only a low memory footprint to function. In this initial investigation, the authors explore the key theoretical and practical considerations of optimizing fluence in such a manner. Methods: The authors present a novel derivation and implementation of a gradient descent algorithm that allows for optimization during MC particle transport, based on highly stochastic information generated through particle transport of very few histories. A gradient rescaling and renormalization algorithm, and the

Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited.

PubMed

Vellela, Melissa; Qian, Hong

2009-10-06

Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.

Extensions of the MCNP5 and TRIPOLI4 Monte Carlo Codes for Transient Reactor Analysis

NASA Astrophysics Data System (ADS)

Hoogenboom, J. Eduard; Sjenitzer, Bart L.

2014-06-01

To simulate reactor transients for safety analysis with the Monte Carlo method the generation and decay of delayed neutron precursors is implemented in the MCNP5 and TRIPOLI4 general purpose Monte Carlo codes. Important new variance reduction techniques like forced decay of precursors in each time interval and the branchless collision method are included to obtain reasonable statistics for the power production per time interval. For simulation of practical reactor transients also the feedback effect from the thermal-hydraulics must be included. This requires coupling of the Monte Carlo code with a thermal-hydraulics (TH) code, providing the temperature distribution in the reactor, which affects the neutron transport via the cross section data. The TH code also provides the coolant density distribution in the reactor, directly influencing the neutron transport. Different techniques for this coupling are discussed. As a demonstration a 3x3 mini fuel assembly with a moving control rod is considered for MCNP5 and a mini core existing of 3x3 PWR fuel assemblies with control rods and burnable poisons for TRIPOLI4. Results are shown for reactor transients due to control rod movement or withdrawal. The TRIPOLI4 transient calculation is started at low power and includes thermal-hydraulic feedback. The power rises about 10 decades and finally stabilises the reactor power at a much higher level than initial. The examples demonstrate that the modified Monte Carlo codes are capable of performing correct transient calculations, taking into account all geometrical and cross section detail.

Ultimate open pit stochastic optimization

NASA Astrophysics Data System (ADS)

Marcotte, Denis; Caron, Josiane

2013-02-01

Classical open pit optimization (maximum closure problem) is made on block estimates, without directly considering the block grades uncertainty. We propose an alternative approach of stochastic optimization. The stochastic optimization is taken as the optimal pit computed on the block expected profits, rather than expected grades, computed from a series of conditional simulations. The stochastic optimization generates, by construction, larger ore and waste tonnages than the classical optimization. Contrary to the classical approach, the stochastic optimization is conditionally unbiased for the realized profit given the predicted profit. A series of simulated deposits with different variograms are used to compare the stochastic approach, the classical approach and the simulated approach that maximizes expected profit among simulated designs. Profits obtained with the stochastic optimization are generally larger than the classical or simulated pit. The main factor controlling the relative gain of stochastic optimization compared to classical approach and simulated pit is shown to be the information level as measured by the boreholes spacing/range ratio. The relative gains of the stochastic approach over the classical approach increase with the treatment costs but decrease with mining costs. The relative gains of the stochastic approach over the simulated pit approach increase both with the treatment and mining costs. At early stages of an open pit project, when uncertainty is large, the stochastic optimization approach appears preferable to the classical approach or the simulated pit approach for fair comparison of the values of alternative projects and for the initial design and planning of the open pit.

Stochastic Modeling of Direct Radiation Transmission in Particle-Laden Turbulent Flows

NASA Astrophysics Data System (ADS)

Banko, Andrew; Villafane, Laura; Kim, Ji Hoon; Esmaily Moghadam, Mahdi; Eaton, John K.

2017-11-01

Direct radiation transmission in turbulent flows laden with heavy particles plays a fundamental role in systems such as clouds, spray combustors, and particle-solar-receivers. Owing to their inertia, the particles preferentially concentrate and the resulting voids and clusters lead to deviations in mean transmission from the classical Beer-Lambert law for exponential extinction. Additionally, the transmission fluctuations can exceed those of Poissonian media by an order of magnitude, which implies a gross misprediction in transmission statistics if the correlations in particle positions are neglected. On the other hand, tracking millions of particles in a turbulence simulation can be prohibitively expensive. This work presents stochastic processes as computationally cheap reduced order models for the instantaneous particle number density field and radiation transmission therein. Results from the stochastic processes are compared to Monte Carlo Ray Tracing (MCRT) simulations using the particle positions obtained from the point-particle DNS of isotropic turbulence at a Taylor Reynolds number of 150. Accurate transmission statistics are predicted with respect to MCRT by matching the mean, variance, and correlation length of DNS number density fields. Funded by the U.S. Department of Energy under Grant No. DE-NA0002373-1 and the National Science Foundation under Grant No. DGE-114747.

One-dimensional model of interacting-step fluctuations on vicinal surfaces: Analytical formulas and kinetic Monte-Carlo simulations

NASA Astrophysics Data System (ADS)

Patrone, Paul; Einstein, T. L.; Margetis, Dionisios

2011-03-01

We study a 1+1D, stochastic, Burton-Cabrera-Frank (BCF) model of interacting steps fluctuating on a vicinal crystal. The step energy accounts for entropic and nearest-neighbor elastic-dipole interactions. Our goal is to formulate and validate a self-consistent mean-field (MF) formalism to approximately solve the system of coupled, nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. We derive formulas for the time-dependent terrace width distribution (TWD) and its steady-state limit. By comparison with kinetic Monte-Carlo simulations, we show that our MF formalism improves upon models in which step interactions are linearized. We also indicate how fitting parameters of our steady state MF TWD may be used to determine the mass transport regime and step interaction energy of certain experimental systems. PP and TLE supported by NSF MRSEC under Grant DMR 05-20471 at U. of Maryland; DM supported by NSF under Grant DMS 08-47587.

A dual theory of price and value in a meso-scale economic model with stochastic profit rate

NASA Astrophysics Data System (ADS)

Greenblatt, R. E.

2014-12-01

The problem of commodity price determination in a market-based, capitalist economy has a long and contentious history. Neoclassical microeconomic theories are based typically on marginal utility assumptions, while classical macroeconomic theories tend to be value-based. In the current work, I study a simplified meso-scale model of a commodity capitalist economy. The production/exchange model is represented by a network whose nodes are firms, workers, capitalists, and markets, and whose directed edges represent physical or monetary flows. A pair of multivariate linear equations with stochastic input parameters represent physical (supply/demand) and monetary (income/expense) balance. The input parameters yield a non-degenerate profit rate distribution across firms. Labor time and price are found to be eigenvector solutions to the respective balance equations. A simple relation is derived relating the expected value of commodity price to commodity labor content. Results of Monte Carlo simulations are consistent with the stochastic price/labor content relation.

Mass fluctuation kinetics: Capturing stochastic effects in systems of chemical reactions through coupled mean-variance computations

NASA Astrophysics Data System (ADS)

Gómez-Uribe, Carlos A.; Verghese, George C.

2007-01-01

The intrinsic stochastic effects in chemical reactions, and particularly in biochemical networks, may result in behaviors significantly different from those predicted by deterministic mass action kinetics (MAK). Analyzing stochastic effects, however, is often computationally taxing and complex. The authors describe here the derivation and application of what they term the mass fluctuation kinetics (MFK), a set of deterministic equations to track the means, variances, and covariances of the concentrations of the chemical species in the system. These equations are obtained by approximating the dynamics of the first and second moments of the chemical master equation. Apart from needing knowledge of the system volume, the MFK description requires only the same information used to specify the MAK model, and is not significantly harder to write down or apply. When the effects of fluctuations are negligible, the MFK description typically reduces to MAK. The MFK equations are capable of describing the average behavior of the network substantially better than MAK, because they incorporate the effects of fluctuations on the evolution of the means. They also account for the effects of the means on the evolution of the variances and covariances, to produce quite accurate uncertainty bands around the average behavior. The MFK computations, although approximate, are significantly faster than Monte Carlo methods for computing first and second moments in systems of chemical reactions. They may therefore be used, perhaps along with a few Monte Carlo simulations of sample state trajectories, to efficiently provide a detailed picture of the behavior of a chemical system.

Spent nuclear fuel/water interface behavior: Alpha dose rate profile determination for model surfaces and microcracks by using Monte-Carlo methods

NASA Astrophysics Data System (ADS)

Tribet, M.; Mougnaud, S.; Jégou, C.

2017-05-01

This work aims to better understand the nature and evolution of energy deposits at the UO2/water reactional interface subjected to alpha irradiation, through an original approach based on Monte-Carlo-type simulations, using the MCNPX code. Such an approach has the advantage of describing the energy deposit profiles on both sides of the interface (UO2 and water). The calculations have been performed on simple geometries, with data from an irradiated UOX fuel (burnup of 47 GWd.tHM-1 and 15 years of alpha decay). The influence of geometric parameters such as the diameter and the calculation steps at the reactional interface are discussed, and the exponential laws to be used in practice are suggested. The case of cracks with various different apertures (from 5 to 35 μm) has also been examined and these calculations have also enabled new information on the mean range of radiolytic species in cracks, and thus on the local chemistry.

Accelerated rescaling of single Monte Carlo simulation runs with the Graphics Processing Unit (GPU).

PubMed

Yang, Owen; Choi, Bernard

2013-01-01

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.

Simulation studies of phase inversion in agitated vessels using a Monte Carlo technique.

PubMed

Yeo, Leslie Y; Matar, Omar K; Perez de Ortiz, E Susana; Hewitt, Geoffrey F

2002-04-15

A speculative study on the conditions under which phase inversion occurs in agitated liquid-liquid dispersions is conducted using a Monte Carlo technique. The simulation is based on a stochastic model, which accounts for fundamental physical processes such as drop deformation, breakup, and coalescence, and utilizes the minimization of interfacial energy as a criterion for phase inversion. Profiles of the interfacial energy indicate that a steady-state equilibrium is reached after a sufficiently large number of random moves and that predictions are insensitive to initial drop conditions. The calculated phase inversion holdup is observed to increase with increasing density and viscosity ratio, and to decrease with increasing agitation speed for a fixed viscosity ratio. It is also observed that, for a fixed viscosity ratio, the phase inversion holdup remains constant for large enough agitation speeds. The proposed model is therefore capable of achieving reasonable qualitative agreement with general experimental trends and of reproducing key features observed experimentally. The results of this investigation indicate that this simple stochastic method could be the basis upon which more advanced models for predicting phase inversion behavior can be developed.

Stochastic computing with biomolecular automata

PubMed Central

Adar, Rivka; Benenson, Yaakov; Linshiz, Gregory; Rosner, Amit; Tishby, Naftali; Shapiro, Ehud

2004-01-01

Stochastic computing has a broad range of applications, yet electronic computers realize its basic step, stochastic choice between alternative computation paths, in a cumbersome way. Biomolecular computers use a different computational paradigm and hence afford novel designs. We constructed a stochastic molecular automaton in which stochastic choice is realized by means of competition between alternative biochemical pathways, and choice probabilities are programmed by the relative molar concentrations of the software molecules coding for the alternatives. Programmable and autonomous stochastic molecular automata have been shown to perform direct analysis of disease-related molecular indicators in vitro and may have the potential to provide in situ medical diagnosis and cure. PMID:15215499

Application of tabu search to deterministic and stochastic optimization problems

NASA Astrophysics Data System (ADS)

Gurtuna, Ozgur

During the past two decades, advances in computer science and operations research have resulted in many new optimization methods for tackling complex decision-making problems. One such method, tabu search, forms the basis of this thesis. Tabu search is a very versatile optimization heuristic that can be used for solving many different types of optimization problems. Another research area, real options, has also gained considerable momentum during the last two decades. Real options analysis is emerging as a robust and powerful method for tackling decision-making problems under uncertainty. Although the theoretical foundations of real options are well-established and significant progress has been made in the theory side, applications are lagging behind. A strong emphasis on practical applications and a multidisciplinary approach form the basic rationale of this thesis. The fundamental concepts and ideas behind tabu search and real options are investigated in order to provide a concise overview of the theory supporting both of these two fields. This theoretical overview feeds into the design and development of algorithms that are used to solve three different problems. The first problem examined is a deterministic one: finding the optimal servicing tours that minimize energy and/or duration of missions for servicing satellites around Earth's orbit. Due to the nature of the space environment, this problem is modeled as a time-dependent, moving-target optimization problem. Two solution methods are developed: an exhaustive method for smaller problem instances, and a method based on tabu search for larger ones. The second and third problems are related to decision-making under uncertainty. In the second problem, tabu search and real options are investigated together within the context of a stochastic optimization problem: option valuation. By merging tabu search and Monte Carlo simulation, a new method for studying options, Tabu Search Monte Carlo (TSMC) method, is

Intrinsic noise analyzer: a software package for the exploration of stochastic biochemical kinetics using the system size expansion.

PubMed

Thomas, Philipp; Matuschek, Hannes; Grima, Ramon

2012-01-01

The accepted stochastic descriptions of biochemical dynamics under well-mixed conditions are given by the Chemical Master Equation and the Stochastic Simulation Algorithm, which are equivalent. The latter is a Monte-Carlo method, which, despite enjoying broad availability in a large number of existing software packages, is computationally expensive due to the huge amounts of ensemble averaging required for obtaining accurate statistical information. The former is a set of coupled differential-difference equations for the probability of the system being in any one of the possible mesoscopic states; these equations are typically computationally intractable because of the inherently large state space. Here we introduce the software package intrinsic Noise Analyzer (iNA), which allows for systematic analysis of stochastic biochemical kinetics by means of van Kampen's system size expansion of the Chemical Master Equation. iNA is platform independent and supports the popular SBML format natively. The present implementation is the first to adopt a complementary approach that combines state-of-the-art analysis tools using the computer algebra system Ginac with traditional methods of stochastic simulation. iNA integrates two approximation methods based on the system size expansion, the Linear Noise Approximation and effective mesoscopic rate equations, which to-date have not been available to non-expert users, into an easy-to-use graphical user interface. In particular, the present methods allow for quick approximate analysis of time-dependent mean concentrations, variances, covariances and correlations coefficients, which typically outperforms stochastic simulations. These analytical tools are complemented by automated multi-core stochastic simulations with direct statistical evaluation and visualization. We showcase iNA's performance by using it to explore the stochastic properties of cooperative and non-cooperative enzyme kinetics and a gene network associated with

Intrinsic Noise Analyzer: A Software Package for the Exploration of Stochastic Biochemical Kinetics Using the System Size Expansion

PubMed Central

Grima, Ramon

2012-01-01

The accepted stochastic descriptions of biochemical dynamics under well-mixed conditions are given by the Chemical Master Equation and the Stochastic Simulation Algorithm, which are equivalent. The latter is a Monte-Carlo method, which, despite enjoying broad availability in a large number of existing software packages, is computationally expensive due to the huge amounts of ensemble averaging required for obtaining accurate statistical information. The former is a set of coupled differential-difference equations for the probability of the system being in any one of the possible mesoscopic states; these equations are typically computationally intractable because of the inherently large state space. Here we introduce the software package intrinsic Noise Analyzer (iNA), which allows for systematic analysis of stochastic biochemical kinetics by means of van Kampen’s system size expansion of the Chemical Master Equation. iNA is platform independent and supports the popular SBML format natively. The present implementation is the first to adopt a complementary approach that combines state-of-the-art analysis tools using the computer algebra system Ginac with traditional methods of stochastic simulation. iNA integrates two approximation methods based on the system size expansion, the Linear Noise Approximation and effective mesoscopic rate equations, which to-date have not been available to non-expert users, into an easy-to-use graphical user interface. In particular, the present methods allow for quick approximate analysis of time-dependent mean concentrations, variances, covariances and correlations coefficients, which typically outperforms stochastic simulations. These analytical tools are complemented by automated multi-core stochastic simulations with direct statistical evaluation and visualization. We showcase iNA’s performance by using it to explore the stochastic properties of cooperative and non-cooperative enzyme kinetics and a gene network associated with

Exact nonstationary responses of rectangular thin plate on Pasternak foundation excited by stochastic moving loads

NASA Astrophysics Data System (ADS)

Chen, Guohai; Meng, Zeng; Yang, Dixiong

2018-01-01

This paper develops an efficient method termed as PE-PIM to address the exact nonstationary responses of pavement structure, which is modeled as a rectangular thin plate resting on bi-parametric Pasternak elastic foundation subjected to stochastic moving loads with constant acceleration. Firstly, analytical power spectral density (PSD) functions of random responses for thin plate are derived by integrating pseudo excitation method (PEM) with Duhamel's integral. Based on PEM, the new equivalent von Mises stress (NEVMS) is proposed, whose PSD function contains all cross-PSD functions between stress components. Then, the PE-PIM that combines the PEM with precise integration method (PIM) is presented to achieve efficiently stochastic responses of the plate by replacing Duhamel's integral with the PIM. Moreover, the semi-analytical Monte Carlo simulation is employed to verify the computational results of the developed PE-PIM. Finally, numerical examples demonstrate the high accuracy and efficiency of PE-PIM for nonstationary random vibration analysis. The effects of velocity and acceleration of moving load, boundary conditions of the plate and foundation stiffness on the deflection and NEVMS responses are scrutinized.

Groundwater management under uncertainty using a stochastic multi-cell model

NASA Astrophysics Data System (ADS)

Joodavi, Ata; Zare, Mohammad; Ziaei, Ali Naghi; Ferré, Ty P. A.

2017-08-01

The optimization of spatially complex groundwater management models over long time horizons requires the use of computationally efficient groundwater flow models. This paper presents a new stochastic multi-cell lumped-parameter aquifer model that explicitly considers uncertainty in groundwater recharge. To achieve this, the multi-cell model is combined with the constrained-state formulation method. In this method, the lower and upper bounds of groundwater heads are incorporated into the mass balance equation using indicator functions. This provides expressions for the means, variances and covariances of the groundwater heads, which can be included in the constraint set in an optimization model. This method was used to formulate two separate stochastic models: (i) groundwater flow in a two-cell aquifer model with normal and non-normal distributions of groundwater recharge; and (ii) groundwater management in a multiple cell aquifer in which the differences between groundwater abstractions and water demands are minimized. The comparison between the results obtained from the proposed modeling technique with those from Monte Carlo simulation demonstrates the capability of the proposed models to approximate the means, variances and covariances. Significantly, considering covariances between the heads of adjacent cells allows a more accurate estimate of the variances of the groundwater heads. Moreover, this modeling technique requires no discretization of state variables, thus offering an efficient alternative to computationally demanding methods.

A stochastic Iwan-type model for joint behavior variability modeling

NASA Astrophysics Data System (ADS)

Mignolet, Marc P.; Song, Pengchao; Wang, X. Q.

2015-08-01

This paper focuses overall on the development and validation of a stochastic model to describe the dissipation and stiffness properties of a bolted joint for which experimental data is available and exhibits a large scatter. An extension of the deterministic parallel-series Iwan model for the characterization of the force-displacement behavior of joints is first carried out. This new model involves dynamic and static coefficients of friction differing from each other and a broadly defined distribution of Jenkins elements. Its applicability is next investigated using the experimental data, i.e. stiffness and dissipation measurements obtained in harmonic testing of 9 nominally identical bolted joints. The model is found to provide a very good fit of the experimental data for each bolted joint notwithstanding the significant variability of their behavior. This finding suggests that this variability can be simulated through the randomization of only the parameters of the proposed Iwan-type model. The distribution of these parameters is next selected based on maximum entropy concepts and their corresponding parameters, i.e. the hyperparameters of the model, are identified using a maximum likelihood strategy. Proceeding with a Monte Carlo simulation of this stochastic Iwan model demonstrates that the experimental data fits well within the uncertainty band corresponding to the 5th and 95th percentiles of the model predictions which well supports the adequacy of the modeling effort.

Modeling Stochastic Energy and Water Consumption to Manage Residential Water Uses

NASA Astrophysics Data System (ADS)

Abdallah, A. M.; Rosenberg, D. E.; Water; Energy Conservation

2011-12-01

Water energy linkages have received growing attention from the water and energy utilities as utilities recognize that collaborative efforts can implement more effective conservation and efficiency improvement programs at lower cost with less effort. To date, limited energy-water household data has allowed only deterministic analysis for average, representative households and required coarse assumptions - like the water heater (the primary energy use in a home apart from heating and cooling) be a single end use. Here, we use recent available disaggregated hot and cold water household end-use data to estimate water and energy consumption for toilet, shower, faucet, dishwasher, laundry machine, leaks, and other household uses and savings from appliance retrofits. The disaggregated hot water and bulk water end-use data was previously collected by the USEPA for 96 single family households in Seattle WA and Oakland CA, and Tampa FL between the period from 2000 and 2003 for two weeks before and four weeks after each household was retrofitted with water efficient appliances. Using the disaggregated data, we developed a stochastic model that represents factors that influence water use for each appliance: behavioral (use frequency and duration), demographical (household size), and technological (use volume or flowrate). We also include stochastic factors that govern energy to heat hot water: hot water fraction (percentage of hot water volume to total water volume used in a certain end-use event), heater water intake and dispense temperatures, and energy source for the heater (gas, electric, etc). From the empirical household end-use data, we derive stochastic probability distributions for each water and energy factor where each distribution represents the range and likelihood of values that the factor may take. The uncertainty of the stochastic water and energy factors is propagated using Monte Carlo simulations to calculate the composite probability distribution for water

A fixed-memory moving, expanding window for obtaining scatter corrections in X-ray CT and other stochastic averages

NASA Astrophysics Data System (ADS)

Levine, Zachary H.; Pintar, Adam L.

2015-11-01

A simple algorithm for averaging a stochastic sequence of 1D arrays in a moving, expanding window is provided. The samples are grouped in bins which increase exponentially in size so that a constant fraction of the samples is retained at any point in the sequence. The algorithm is shown to have particular relevance for a class of Monte Carlo sampling problems which includes one characteristic of iterative reconstruction in computed tomography. The code is available in the CPC program library in both Fortran 95 and C and is also available in R through CRAN.

2–stage stochastic Runge–Kutta for stochastic delay differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosli, Norhayati; Jusoh Awang, Rahimah; Bahar, Arifah

2015-05-15

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

Low-complexity stochastic modeling of wall-bounded shear flows

NASA Astrophysics Data System (ADS)

Zare, Armin

Turbulent flows are ubiquitous in nature and they appear in many engineering applications. Transition to turbulence, in general, increases skin-friction drag in air/water vehicles compromising their fuel-efficiency and reduces the efficiency and longevity of wind turbines. While traditional flow control techniques combine physical intuition with costly experiments, their effectiveness can be significantly enhanced by control design based on low-complexity models and optimization. In this dissertation, we develop a theoretical and computational framework for the low-complexity stochastic modeling of wall-bounded shear flows. Part I of the dissertation is devoted to the development of a modeling framework which incorporates data-driven techniques to refine physics-based models. We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate optimization problems to identify the dynamics and directionality of input excitation in order to explain and complete available covariance data. For problem sizes that general-purpose solvers cannot handle, we develop customized optimization algorithms based on alternating direction methods. The solution to the optimization problem provides information about critical directions that have maximal effect in bringing model and statistics in agreement. In Part II, we employ our modeling framework to account for statistical signatures of turbulent channel flow using low-complexity stochastic dynamical models. We demonstrate that white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics and develop models for colored-in-time forcing of the linearized Navier-Stokes equations. We also examine the efficacy of stochastically forced linearized NS equations and their

MCNP-REN - A Monte Carlo Tool for Neutron Detector Design Without Using the Point Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abhold, M.E.; Baker, M.C.

1999-07-25

The development of neutron detectors makes extensive use of the predictions of detector response through the use of Monte Carlo techniques in conjunction with the point reactor model. Unfortunately, the point reactor model fails to accurately predict detector response in common applications. For this reason, the general Monte Carlo N-Particle code (MCNP) was modified to simulate the pulse streams that would be generated by a neutron detector and normally analyzed by a shift register. This modified code, MCNP - Random Exponentially Distributed Neutron Source (MCNP-REN), along with the Time Analysis Program (TAP) predict neutron detector response without using the pointmore » reactor model, making it unnecessary for the user to decide whether or not the assumptions of the point model are met for their application. MCNP-REN is capable of simulating standard neutron coincidence counting as well as neutron multiplicity counting. Measurements of MOX fresh fuel made using the Underwater Coincidence Counter (UWCC) as well as measurements of HEU reactor fuel using the active neutron Research Reactor Fuel Counter (RRFC) are compared with calculations. The method used in MCNP-REN is demonstrated to be fundamentally sound and shown to eliminate the need to use the point model for detector performance predictions.« less

Economic-Oriented Stochastic Optimization in Advanced Process Control of Chemical Processes

PubMed Central

Dobos, László; Király, András; Abonyi, János

2012-01-01

Finding the optimal operating region of chemical processes is an inevitable step toward improving economic performance. Usually the optimal operating region is situated close to process constraints related to product quality or process safety requirements. Higher profit can be realized only by assuring a relatively low frequency of violation of these constraints. A multilevel stochastic optimization framework is proposed to determine the optimal setpoint values of control loops with respect to predetermined risk levels, uncertainties, and costs of violation of process constraints. The proposed framework is realized as direct search-type optimization of Monte-Carlo simulation of the controlled process. The concept is illustrated throughout by a well-known benchmark problem related to the control of a linear dynamical system and the model predictive control of a more complex nonlinear polymerization process. PMID:23213298

RES: Regularized Stochastic BFGS Algorithm

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Ribeiro, Alejandro

2014-12-01

RES, a regularized stochastic version of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve convex optimization problems with stochastic objectives. The use of stochastic gradient descent algorithms is widespread, but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional problems. Application of second order methods, on the other hand, is impracticable because computation of objective function Hessian inverses incurs excessive computational cost. BFGS modifies gradient descent by introducing a Hessian approximation matrix computed from finite gradient differences. RES utilizes stochastic gradients in lieu of deterministic gradients for both, the determination of descent directions and the approximation of the objective function's curvature. Since stochastic gradients can be computed at manageable computational cost RES is realizable and retains the convergence rate advantages of its deterministic counterparts. Convergence results show that lower and upper bounds on the Hessian egeinvalues of the sample functions are sufficient to guarantee convergence to optimal arguments. Numerical experiments showcase reductions in convergence time relative to stochastic gradient descent algorithms and non-regularized stochastic versions of BFGS. An application of RES to the implementation of support vector machines is developed.

Space-time-modulated stochastic processes

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

Starting from the physical problem associated with the Lorentzian transformation of a Poisson-Kac process in inertial frames, the concept of space-time-modulated stochastic processes is introduced for processes possessing finite propagation velocity. This class of stochastic processes provides a two-way coupling between the stochastic perturbation acting on a physical observable and the evolution of the physical observable itself, which in turn influences the statistical properties of the stochastic perturbation during its evolution. The definition of space-time-modulated processes requires the introduction of two functions: a nonlinear amplitude modulation, controlling the intensity of the stochastic perturbation, and a time-horizon function, which modulates its statistical properties, providing irreducible feedback between the stochastic perturbation and the physical observable influenced by it. The latter property is the peculiar fingerprint of this class of models that makes them suitable for extension to generic curved-space times. Considering Poisson-Kac processes as prototypical examples of stochastic processes possessing finite propagation velocity, the balance equations for the probability density functions associated with their space-time modulations are derived. Several examples highlighting the peculiarities of space-time-modulated processes are thoroughly analyzed.

A Stochastic Seismic Model for the European Arctic

NASA Astrophysics Data System (ADS)

Hauser, J.; Dyer, K.; Pasyanos, M. E.; Bungum, H.; Faleide, J. I.; Clark, S. A.

2009-12-01

The development of three-dimensional seismic models for the crust and upper mantle has traditionally focused on finding one model that provides the best fit to the data, while observing some regularization constraints. Such deterministic models however ignore a fundamental property of many inverse problems in geophysics, non-uniqueness, that is, if a model can be found to satisfy given datasets an infinite number of alternative models will exist that satisfy the datasets equally well. The solution to the inverse problem presented here is therefore a stochastic model, an ensemble of models that satisfy all available data to the same degree, the posterior distribution. It is based on two sources of information, (1) the data, in this work surface-wave group velocities, regional body-wave travel times, gravity data, compiled 1D velocity models, and thickness relationships between sedimentary rocks and underlying crystalline rocks, and (2) prior information, which is independent from the data. A Monte Carlo Markov Chain (MCMC) algorithm allows us to sample models from the prior distribution and test them against the data to generate the posterior distribution. While being computationally much more expensive, such a stochastic inversion provides a more complete picture of solution space and allows to seamlessly combine various datasets. The resulting stochastic model gives an overview of the different structures that can explain the observed datasets while taking the uncertainties in the data into account. Stochastic models are important for improving seismic monitoring capabilities as they allow to not only predict new observables but also their uncertainties. The model introduced here for the crust and upper mantle structure of the European Arctic is parametrized by a series of 8 layers in an equidistant mesh. Within each layer the seismic parameters (Vp, Vs and density) can vary linearly with depth. This allows to model changes of seismic parameters within the

On Stochastic Dependence

ERIC Educational Resources Information Center

Meyer, Joerg M.

2018-01-01

The contrary of stochastic independence splits up into two cases: pairs of events being favourable or being unfavourable. Examples show that both notions have quite unexpected properties, some of them being opposite to intuition. For example, transitivity does not hold. Stochastic dependence is also useful to explain cases of Simpson's paradox.

Detecting seasonal variations of soil parameters via field measurements and stochastic simulations in the hillslope

NASA Astrophysics Data System (ADS)

Noh, Seong Jin; An, Hyunuk; Kim, Sanghyun

2015-04-01

Soil moisture, a critical factor in hydrologic systems, plays a key role in synthesizing interactions among soil, climate, hydrological response, solute transport and ecosystem dynamics. The spatial and temporal distribution of soil moisture at a hillslope scale is essential for understanding hillslope runoff generation processes. In this study, we implement Monte Carlo simulations in the hillslope scale using a three-dimensional surface-subsurface integrated model (3D model). Numerical simulations are compared with multiple soil moistures which had been measured using TDR(Mini_TRASE) for 22 locations in 2 or 3 depths during a whole year at a hillslope (area: 2100 square meters) located in Bongsunsa Watershed, South Korea. In stochastic simulations via Monte Carlo, uncertainty of the soil parameters and input forcing are considered and model ensembles showing good performance are selected separately for several seasonal periods. The presentation will be focused on the characterization of seasonal variations of model parameters based on simulations with field measurements. In addition, structural limitations of the contemporary modeling method will be discussed.

Synchronous parallel spatially resolved stochastic cluster dynamics

DOE PAGES

Dunn, Aaron; Dingreville, Rémi; Martínez, Enrique; ...

2016-04-23

In this work, a spatially resolved stochastic cluster dynamics (SRSCD) model for radiation damage accumulation in metals is implemented using a synchronous parallel kinetic Monte Carlo algorithm. The parallel algorithm is shown to significantly increase the size of representative volumes achievable in SRSCD simulations of radiation damage accumulation. Additionally, weak scaling performance of the method is tested in two cases: (1) an idealized case of Frenkel pair diffusion and annihilation, and (2) a characteristic example problem including defect cluster formation and growth in α-Fe. For the latter case, weak scaling is tested using both Frenkel pair and displacement cascade damage.more » To improve scaling of simulations with cascade damage, an explicit cascade implantation scheme is developed for cases in which fast-moving defects are created in displacement cascades. For the first time, simulation of radiation damage accumulation in nanopolycrystals can be achieved with a three dimensional rendition of the microstructure, allowing demonstration of the effect of grain size on defect accumulation in Frenkel pair-irradiated α-Fe.« less

Metrics for Diagnosing Undersampling in Monte Carlo Tally Estimates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perfetti, Christopher M.; Rearden, Bradley T.

This study explored the potential of using Markov chain convergence diagnostics to predict the prevalence and magnitude of biases due to undersampling in Monte Carlo eigenvalue and flux tally estimates. Five metrics were applied to two models of pressurized water reactor fuel assemblies and their potential for identifying undersampling biases was evaluated by comparing the calculated test metrics with known biases in the tallies. Three of the five undersampling metrics showed the potential to accurately predict the behavior of undersampling biases in the responses examined in this study.

Output Feedback Stabilization for a Class of Multi-Variable Bilinear Stochastic Systems with Stochastic Coupling Attenuation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Qichun; Zhou, Jinglin; Wang, Hong

In this paper, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.

Variational principles for stochastic fluid dynamics

PubMed Central

Holm, Darryl D.

2015-01-01

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083

Effluent trading in river systems through stochastic decision-making process: a case study.

PubMed

Zolfagharipoor, Mohammad Amin; Ahmadi, Azadeh

2017-09-01

The objective of this paper is to provide an efficient framework for effluent trading in river systems. The proposed framework consists of two pessimistic and optimistic decision-making models to increase the executability of river water quality trading programs. The models used for this purpose are (1) stochastic fallback bargaining (SFB) to reach an agreement among wastewater dischargers and (2) stochastic multi-criteria decision-making (SMCDM) to determine the optimal treatment strategy. The Monte-Carlo simulation method is used to incorporate the uncertainty into analysis. This uncertainty arises from stochastic nature and the errors in the calculation of wastewater treatment costs. The results of river water quality simulation model are used as the inputs of models. The proposed models are used in a case study on the Zarjoub River in northern Iran to determine the best solution for the pollution load allocation. The best treatment alternatives selected by each model are imported, as the initial pollution discharge permits, into an optimization model developed for trading of pollution discharge permits among pollutant sources. The results show that the SFB-based water pollution trading approach reduces the costs by US$ 14,834 while providing a relative consensus among pollutant sources. Meanwhile, the SMCDM-based water pollution trading approach reduces the costs by US$ 218,852, but it is less acceptable by pollutant sources. Therefore, it appears that giving due attention to stability, or in other words acceptability of pollution trading programs for all pollutant sources, is an essential element of their success.

Monte Carlo Simulations for VLBI2010

NASA Astrophysics Data System (ADS)

Wresnik, J.; Böhm, J.; Schuh, H.

2007-07-01

Monte Carlo simulations are carried out at the Institute of Geodesy and Geophysics (IGG), Vienna, and at Goddard Space Flight Center (GSFC), Greenbelt (USA), with the goal to design a new geodetic Very Long Baseline Interferometry (VLBI) system. Influences of the schedule, the network geometry and the main stochastic processes on the geodetic results are investigated. Therefore schedules are prepared with the software package SKED (Vandenberg 1999), and different strategies are applied to produce temporally very dense schedules which are compared in terms of baseline length repeatabilities. For the simulation of VLBI observations a Monte Carlo Simulator was set up which creates artificial observations by randomly simulating wet zenith delay and clock values as well as additive white noise representing the antenna errors. For the simulation at IGG the VLBI analysis software OCCAM (Titov et al. 2004) was adapted. Random walk processes with power spectrum densities of 0.7 and 0.1 psec2/sec are used for the simulation of wet zenith delays. The clocks are simulated with Allan Standard Deviations of 1*10^-14 @ 50 min and 2*10^-15 @ 15 min and three levels of white noise, 4 psec, 8 psec and, 16 psec, are added to the artificial observations. The variations of the power spectrum densities of the clocks and wet zenith delays, and the application of different white noise levels show clearly that the wet delay is the critical factor for the improvement of the geodetic VLBI system. At GSFC the software CalcSolve is used for the VLBI analysis, therefore a comparison between the software packages OCCAM and CalcSolve was done with simulated data. For further simulations the wet zenith delay was modeled by a turbulence model. This data was provided by Nilsson T. and was added to the simulation work. Different schedules have been run.

Adaptive time-stepping Monte Carlo integration of Coulomb collisions

NASA Astrophysics Data System (ADS)

Särkimäki, K.; Hirvijoki, E.; Terävä, J.

2018-01-01

We report an accessible and robust tool for evaluating the effects of Coulomb collisions on a test particle in a plasma that obeys Maxwell-Jüttner statistics. The implementation is based on the Beliaev-Budker collision integral which allows both the test particle and the background plasma to be relativistic. The integration method supports adaptive time stepping, which is shown to greatly improve the computational efficiency. The Monte Carlo method is implemented for both the three-dimensional particle momentum space and the five-dimensional guiding center phase space. Detailed description is provided for both the physics and implementation of the operator. The focus is in adaptive integration of stochastic differential equations, which is an overlooked aspect among existing Monte Carlo implementations of Coulomb collision operators. We verify that our operator converges to known analytical results and demonstrate that careless implementation of the adaptive time step can lead to severely erroneous results. The operator is provided as a self-contained Fortran 95 module and can be included into existing orbit-following tools that trace either the full Larmor motion or the guiding center dynamics. The adaptive time-stepping algorithm is expected to be useful in situations where the collision frequencies vary greatly over the course of a simulation. Examples include the slowing-down of fusion products or other fast ions, and the Dreicer generation of runaway electrons as well as the generation of fast ions or electrons with ion or electron cyclotron resonance heating.

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arampatzis, Giorgos, E-mail: garab@math.uoc.gr; Katsoulakis, Markos A., E-mail: markos@math.umass.edu; Plechac, Petr, E-mail: plechac@math.udel.edu

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 decompositionmore » 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

Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student's t-distribution.

PubMed

Leão, William L; Abanto-Valle, Carlos A; Chen, Ming-Hui

2017-01-01

A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor's 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model.

Stochastic Estimation via Polynomial Chaos

DTIC Science & Technology

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks.

PubMed

Rathinam, Muruhan; Sheppard, Patrick W; Khammash, Mustafa

2010-01-21

Parametric sensitivity of biochemical networks is an indispensable tool for studying system robustness properties, estimating network parameters, and identifying targets for drug therapy. For discrete stochastic representations of biochemical networks where Monte Carlo methods are commonly used, sensitivity analysis can be particularly challenging, as accurate finite difference computations of sensitivity require a large number of simulations for both nominal and perturbed values of the parameters. In this paper we introduce the common random number (CRN) method in conjunction with Gillespie's stochastic simulation algorithm, which exploits positive correlations obtained by using CRNs for nominal and perturbed parameters. We also propose a new method called the common reaction path (CRP) method, which uses CRNs together with the random time change representation of discrete state Markov processes due to Kurtz to estimate the sensitivity via a finite difference approximation applied to coupled reaction paths that emerge naturally in this representation. While both methods reduce the variance of the estimator significantly compared to independent random number finite difference implementations, numerical evidence suggests that the CRP method achieves a greater variance reduction. We also provide some theoretical basis for the superior performance of CRP. The improved accuracy of these methods allows for much more efficient sensitivity estimation. In two example systems reported in this work, speedup factors greater than 300 and 10,000 are demonstrated.

Assessment of a stochastic downscaling methodology in generating an ensemble of hourly future climate time series

NASA Astrophysics Data System (ADS)

Fatichi, S.; Ivanov, V. Y.; Caporali, E.

2013-04-01

This study extends a stochastic downscaling methodology to generation of an ensemble of hourly time series of meteorological variables that express possible future climate conditions at a point-scale. The stochastic downscaling uses general circulation model (GCM) realizations and an hourly weather generator, the Advanced WEather GENerator (AWE-GEN). Marginal distributions of factors of change are computed for several climate statistics using a Bayesian methodology that can weight GCM realizations based on the model relative performance with respect to a historical climate and a degree of disagreement in projecting future conditions. A Monte Carlo technique is used to sample the factors of change from their respective marginal distributions. As a comparison with traditional approaches, factors of change are also estimated by averaging GCM realizations. With either approach, the derived factors of change are applied to the climate statistics inferred from historical observations to re-evaluate parameters of the weather generator. The re-parameterized generator yields hourly time series of meteorological variables that can be considered to be representative of future climate conditions. In this study, the time series are generated in an ensemble mode to fully reflect the uncertainty of GCM projections, climate stochasticity, as well as uncertainties of the downscaling procedure. Applications of the methodology in reproducing future climate conditions for the periods of 2000-2009, 2046-2065 and 2081-2100, using the period of 1962-1992 as the historical baseline are discussed for the location of Firenze (Italy). The inferences of the methodology for the period of 2000-2009 are tested against observations to assess reliability of the stochastic downscaling procedure in reproducing statistics of meteorological variables at different time scales.

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

NASA Astrophysics Data System (ADS)

Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido

2016-06-01

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

Phenomenology of stochastic exponential growth

NASA Astrophysics Data System (ADS)

Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya

2017-06-01

Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.

Stochastic resonance in the majority vote model on regular and small-world lattices

NASA Astrophysics Data System (ADS)

Krawiecki, A.

2017-11-01

The majority vote model with two states on regular and small-world networks is considered under the influence of periodic driving. Monte Carlo simulations show that the time-dependent magnetization, playing the role of the output signal, exhibits maximum periodicity at nonzero values of the internal noise parameter q, which is manifested as the occurrence of the maximum of the spectral power amplification; the location of the maximum depends in a nontrivial way on the amplitude and frequency of the periodic driving as well as on the network topology. This indicates the appearance of stochastic resonance in the system as a function of the intensity of the internal noise. Besides, for low frequencies and for certain narrow ranges of the amplitudes of the periodic driving double maxima of the spectral power amplification as a function of q occur, i.e., stochastic multiresonance appears. The above-mentioned results quantitatively agree with those obtained from numerical simulations of the mean-field equations for the time-dependent magnetization. In contrast, analytic solutions for the spectral power amplification obtained from the latter equations using the linear response approximation deviate significanlty from the numerical results since the effect of the periodic driving on the system is not small even for vanishing amplitude.

Stochastic dynamics for reinfection by transmitted diseases

NASA Astrophysics Data System (ADS)

Barros, Alessandro S.; Pinho, Suani T. R.

2017-06-01

The use of stochastic models to study the dynamics of infectious diseases is an important tool to understand the epidemiological process. For several directly transmitted diseases, reinfection is a relevant process, which can be expressed by endogenous reactivation of the pathogen or by exogenous reinfection due to direct contact with an infected individual (with smaller reinfection rate σ β than infection rate β ). In this paper, we examine the stochastic susceptible, infected, recovered, infected (SIRI) model simulating the endogenous reactivation by a spontaneous reaction, while exogenous reinfection by a catalytic reaction. Analyzing the mean-field approximations of a site and pairs of sites, and Monte Carlo (MC) simulations for the particular case of exogenous reinfection, we obtained continuous phase transitions involving endemic, epidemic, and no transmission phases for the simple approach; the approach of pairs is better to describe the phase transition from endemic phase (susceptible, infected, susceptible (SIS)-like model) to epidemic phase (susceptible, infected, and removed or recovered (SIR)-like model) considering the comparison with MC results; the reinfection increases the peaks of outbreaks until the system reaches endemic phase. For the particular case of endogenous reactivation, the approach of pairs leads to a continuous phase transition from endemic phase (SIS-like model) to no transmission phase. Finally, there is no phase transition when both effects are taken into account. We hope the results of this study can be generalized for the susceptible, exposed, infected, and removed or recovered (SEIRIE) model, for which the state exposed (infected but not infectious), describing more realistically transmitted diseases such as tuberculosis. In future work, we also intend to investigate the effect of network topology on phase transitions when the SIRI model describes both transmitted diseases (σ <1 ) and social contagions (σ >1 ).

Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation.

PubMed

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student’s t-distribution*

PubMed Central

Leão, William L.; Chen, Ming-Hui

2017-01-01

A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor’s 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model. PMID:29333210

Optimal Control for Stochastic Delay Evolution Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meng, Qingxin, E-mail: mqx@hutc.zj.cn; Shen, Yang, E-mail: skyshen87@gmail.com

2016-08-15

In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we applymore » stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.« less

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

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.

Rare events in stochastic populations under bursty reproduction

NASA Astrophysics Data System (ADS)

Be'er, Shay; Assaf, Michael

2016-11-01

Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise—uncertainty in the step size of the reaction—on the dynamics of stochastic populations. This was done by investigating the effect of bursty influx on the switching dynamics of stochastic populations. Here we extend this formalism to account for bursty reproduction processes, and improve the accuracy of the formalism to include subleading-order corrections. Bursty reproduction appears in various contexts, where notable examples include bursty viral production from infected cells, and reproduction of mammals involving varying number of offspring. The main question we quantitatively address is how bursty reproduction affects the overall fate of the population. We consider two complementary scenarios: population extinction and population survival; in the former a population gets extinct after maintaining a long-lived metastable state, whereas in the latter a population proliferates despite undergoing a deterministic drift towards extinction. In both models reproduction occurs in bursts, sampled from an arbitrary distribution. Using the WKB approach, we show in the extinction problem that bursty reproduction broadens the quasi-stationary distribution of population sizes in the metastable state, which results in a drastic reduction of the mean time to extinction compared to the non-bursty case. In the survival problem, it is shown that bursty reproduction drastically increases the survival probability of the population. Close to the bifurcation limit our analytical results simplify considerably and are shown to depend solely on the mean and variance of the burst-size distribution. Our formalism is demonstrated on several realistic distributions which all compare well with numerical Monte-Carlo simulations.

Stochastic description of quantum Brownian dynamics

NASA Astrophysics Data System (ADS)

Yan, Yun-An; Shao, Jiushu

2016-08-01

Classical Brownian motion has well been investigated since the pioneering work of Einstein, which inspired mathematicians to lay the theoretical foundation of stochastic processes. A stochastic formulation for quantum dynamics of dissipative systems described by the system-plus-bath model has been developed and found many applications in chemical dynamics, spectroscopy, quantum transport, and other fields. This article provides a tutorial review of the stochastic formulation for quantum dissipative dynamics. The key idea is to decouple the interaction between the system and the bath by virtue of the Hubbard-Stratonovich transformation or Itô calculus so that the system and the bath are not directly entangled during evolution, rather they are correlated due to the complex white noises introduced. The influence of the bath on the system is thereby defined by an induced stochastic field, which leads to the stochastic Liouville equation for the system. The exact reduced density matrix can be calculated as the stochastic average in the presence of bath-induced fields. In general, the plain implementation of the stochastic formulation is only useful for short-time dynamics, but not efficient for long-time dynamics as the statistical errors go very fast. For linear and other specific systems, the stochastic Liouville equation is a good starting point to derive the master equation. For general systems with decomposable bath-induced processes, the hierarchical approach in the form of a set of deterministic equations of motion is derived based on the stochastic formulation and provides an effective means for simulating the dissipative dynamics. A combination of the stochastic simulation and the hierarchical approach is suggested to solve the zero-temperature dynamics of the spin-boson model. This scheme correctly describes the coherent-incoherent transition (Toulouse limit) at moderate dissipation and predicts a rate dynamics in the overdamped regime. Challenging problems

Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations.

PubMed

Inglis, Stephen; Melko, Roger G

2013-01-01

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.

Assessing predictability of a hydrological stochastic-dynamical system

NASA Astrophysics Data System (ADS)

Gelfan, Alexander

2014-05-01

to those of the corresponding series of the actual data measured at the station. Beginning from the initial conditions and being forced by Monte-Carlo generated synthetic meteorological series, the model simulated diverging trajectories of soil moisture characteristics (water content of soil column, moisture of different soil layers, etc.). Limit of predictability of the specific characteristic was determined through time of stabilization of variance of the characteristic between the trajectories, as they move away from the initial state. Numerical experiments were carried out with the stochastic-dynamical model to analyze sensitivity of the soil moisture predictability assessments to uncertainty in the initial conditions, to determine effects of the soil hydraulic properties and processes of soil freezing on the predictability. It was found, particularly, that soil water content predictability is sensitive to errors in the initial conditions and strongly depends on the hydraulic properties of soil under both unfrozen and frozen conditions. Even if the initial conditions are "well-established", the assessed predictability of water content of unfrozen soil does not exceed 30-40 days, while for frozen conditions it may be as long as 3-4 months. The latter creates opportunity for utilizing the autumn water content of soil as the predictor for spring snowmelt runoff in the region under consideration.

Variance decomposition in stochastic simulators.

PubMed

Le Maître, O P; Knio, O M; Moraes, A

2015-06-28

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

Variance decomposition in stochastic simulators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Le Maître, O. P., E-mail: olm@limsi.fr; Knio, O. M., E-mail: knio@duke.edu; Moraes, A., E-mail: alvaro.moraesgutierrez@kaust.edu.sa

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance.more » Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.« less

Variance decomposition in stochastic simulators

NASA Astrophysics Data System (ADS)

Le Maître, O. P.; Knio, O. M.; Moraes, A.

2015-06-01

This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.

Investigation of the SCS-CN initial abstraction ratio using a Monte Carlo simulation for the derived flood frequency curves

NASA Astrophysics Data System (ADS)

Caporali, E.; Chiarello, V.; Galeati, G.

2014-12-01

Peak discharges estimates for a given return period are of primary importance in engineering practice for risk assessment and hydraulic structure design. Different statistical methods are chosen here for the assessment of flood frequency curve: one indirect technique based on the extreme rainfall event analysis, the Peak Over Threshold (POT) model and the Annual Maxima approach as direct techniques using river discharge data. In the framework of the indirect method, a Monte Carlo simulation approach is adopted to determine a derived frequency distribution of peak runoff using a probabilistic formulation of the SCS-CN method as stochastic rainfall-runoff model. A Monte Carlo simulation is used to generate a sample of different runoff events from different stochastic combination of rainfall depth, storm duration, and initial loss inputs. The distribution of the rainfall storm events is assumed to follow the GP law whose parameters are estimated through GEV's parameters of annual maximum data. The evaluation of the initial abstraction ratio is investigated since it is one of the most questionable assumption in the SCS-CN model and plays a key role in river basin characterized by high-permeability soils, mainly governed by infiltration excess mechanism. In order to take into account the uncertainty of the model parameters, this modified approach, that is able to revise and re-evaluate the original value of the initial abstraction ratio, is implemented. In the POT model the choice of the threshold has been an essential issue, mainly based on a compromise between bias and variance. The Generalized Extreme Value (GEV) distribution fitted to the annual maxima discharges is therefore compared with the Pareto distributed peaks to check the suitability of the frequency of occurrence representation. The methodology is applied to a large dam in the Serchio river basin, located in the Tuscany Region. The application has shown as Monte Carlo simulation technique can be a useful

Stochastic Nature in Cellular Processes

NASA Astrophysics Data System (ADS)

Liu, Bo; Liu, Sheng-Jun; Wang, Qi; Yan, Shi-Wei; Geng, Yi-Zhao; Sakata, Fumihiko; Gao, Xing-Fa

2011-11-01

The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.

Finite element modelling of woven composite failure modes at the mesoscopic scale: deterministic versus stochastic approaches

NASA Astrophysics Data System (ADS)

Roirand, Q.; Missoum-Benziane, D.; Thionnet, A.; Laiarinandrasana, L.

2017-09-01

Textile composites are composed of 3D complex architecture. To assess the durability of such engineering structures, the failure mechanisms must be highlighted. Examinations of the degradation have been carried out thanks to tomography. The present work addresses a numerical damage model dedicated to the simulation of the crack initiation and propagation at the scale of the warp yarns. For the 3D woven composites under study, loadings in tension and combined tension and bending were considered. Based on an erosion procedure of broken elements, the failure mechanisms have been modelled on 3D periodic cells by finite element calculations. The breakage of one element was determined using a failure criterion at the mesoscopic scale based on the yarn stress at failure. The results were found to be in good agreement with the experimental data for the two kinds of macroscopic loadings. The deterministic approach assumed a homogeneously distributed stress at failure all over the integration points in the meshes of woven composites. A stochastic approach was applied to a simple representative elementary periodic cell. The distribution of the Weibull stress at failure was assigned to the integration points using a Monte Carlo simulation. It was shown that this stochastic approach allowed more realistic failure simulations avoiding the idealised symmetry due to the deterministic modelling. In particular, the stochastic simulations performed have shown several variations of the stress as well as strain at failure and the failure modes of the yarn.

An offline approach for output-only Bayesian identification of stochastic nonlinear systems using unscented Kalman filtering

NASA Astrophysics Data System (ADS)

Erazo, Kalil; Nagarajaiah, Satish

2017-06-01

In this paper an offline approach for output-only Bayesian identification of stochastic nonlinear systems is presented. The approach is based on a re-parameterization of the joint posterior distribution of the parameters that define a postulated state-space stochastic model class. In the re-parameterization the state predictive distribution is included, marginalized, and estimated recursively in a state estimation step using an unscented Kalman filter, bypassing state augmentation as required by existing online methods. In applications expectations of functions of the parameters are of interest, which requires the evaluation of potentially high-dimensional integrals; Markov chain Monte Carlo is adopted to sample the posterior distribution and estimate the expectations. The proposed approach is suitable for nonlinear systems subjected to non-stationary inputs whose realization is unknown, and that are modeled as stochastic processes. Numerical verification and experimental validation examples illustrate the effectiveness and advantages of the approach, including: (i) an increased numerical stability with respect to augmented-state unscented Kalman filtering, avoiding divergence of the estimates when the forcing input is unmeasured; (ii) the ability to handle arbitrary prior and posterior distributions. The experimental validation of the approach is conducted using data from a large-scale structure tested on a shake table. It is shown that the approach is robust to inherent modeling errors in the description of the system and forcing input, providing accurate prediction of the dynamic response when the excitation history is unknown.

The stochastic runoff-runon process: Extending its analysis to a finite hillslope

NASA Astrophysics Data System (ADS)

Jones, O. D.; Lane, P. N. J.; Sheridan, G. J.

2016-10-01

The stochastic runoff-runon process models the volume of infiltration excess runoff from a hillslope via the overland flow path. Spatial variability is represented in the model by the spatial distribution of rainfall and infiltration, and their ;correlation scale;, that is, the scale at which the spatial correlation of rainfall and infiltration become negligible. Notably, the process can produce runoff even when the mean rainfall rate is less than the mean infiltration rate, and it displays a gradual increase in net runoff as the rainfall rate increases. In this paper we present a number of contributions to the analysis of the stochastic runoff-runon process. Firstly we illustrate the suitability of the process by fitting it to experimental data. Next we extend previous asymptotic analyses to include the cases where the mean rainfall rate equals or exceeds the mean infiltration rate, and then use Monte Carlo simulation to explore the range of parameters for which the asymptotic limit gives a good approximation on finite hillslopes. Finally we use this to obtain an equation for the mean net runoff, consistent with our asymptotic results but providing an excellent approximation for finite hillslopes. Our function uses a single parameter to capture spatial variability, and varying this parameter gives us a family of curves which interpolate between known upper and lower bounds for the mean net runoff.

The Two-On-One Stochastic Duel

DTIC Science & Technology

1983-12-01

ACN 67500 TRASANA-TR-43-83 (.0 (v THE TWO-ON-ONE STOCHASTIC DUEL I • Prepared By A.V. Gafarian C.J. Ancker, Jr. DECEMBER 19833D I°"’" " TIC ELECTE...83 M A IL / _ _ 4. TITLE (and Subtitle) TYPE OF REPORT & PERIOD CO\\,ERED The Two-On-One Stochastic Duel Final Report 6. PERFORMING ORG. REPORT NUMBER...Stochastic Duels , Stochastic Processed, and Attrition. 5-14cIa~c fal roLCS-e ss 120. ABSTRACT (C’ntfMte am reverse Ed& if necesemay and idemtitf by block

Kinetic Monte Carlo simulation of dopant-defect systems under submicrosecond laser thermal processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fisicaro, G.; Pelaz, Lourdes; Lopez, P.

2012-11-06

An innovative Kinetic Monte Carlo (KMC) code has been developed, which rules the post-implant kinetics of the defects system in the extremely far-from-the equilibrium conditions caused by the laser irradiation close to the liquid-solid interface. It considers defect diffusion, annihilation and clustering. The code properly implements, consistently to the stochastic formalism, the fast varying local event rates related to the thermal field T(r,t) evolution. This feature of our numerical method represents an important advancement with respect to current state of the art KMC codes. The reduction of the implantation damage and its reorganization in defect aggregates are studied as amore » function of the process conditions. Phosphorus activation efficiency, experimentally determined in similar conditions, has been related to the emerging damage scenario.« less

Monte Carlo simulation of edge placement error

NASA Astrophysics Data System (ADS)

Kobayashi, Shinji; Okada, Soichiro; Shimura, Satoru; Nafus, Kathleen; Fonseca, Carlos; Estrella, Joel; Enomoto, Masashi

2018-03-01

In the discussion of edge placement error (EPE), we proposed interactive pattern fidelity error (IPFE) as an indicator to judge pass/fail of integrated patterns. IPFE consists of lower and upper layer EPEs (CD and center of gravity: COG) and overlay, which is decided from the combination of each maximum variation. We succeeded in obtaining the IPFE density function by Monte Carlo simulation. In the results, we also found that the standard deviation (σ) of each indicator should be controlled by 4.0σ, at the semiconductor grade, such as 100 billion patterns per die. Moreover, CD, COG and overlay were analyzed by analysis of variance (ANOVA); we can discuss all variations from wafer to wafer (WTW), pattern to pattern (PTP), line edge roughness (LWR) and stochastic pattern noise (SPN) on an equal footing. From the analysis results, we can determine that these variations belong to which process and tools. Furthermore, measurement length of LWR is also discussed in ANOVA. We propose that the measurement length for IPFE analysis should not be decided to the micro meter order, such as >2 μm length, but for which device is actually desired.

Impacts of renewable fuel regulation and production on agriculture, energy, and welfare

NASA Astrophysics Data System (ADS)

McPhail, Lihong Lu

The purpose of this dissertation is to study the impact of U.S. federal renewable fuel regulations on energy and agriculture commodity markets and welfare. We consider two federal ethanol policies: the Renewable Fuel Standard (RFS) contained in the Energy Security and Independence Act of 2007 and tax credits to ethanol blenders contained in the Food, Conservation, and Energy Act of 2008. My first essay estimates the distribution of short-run impacts of changing federal ethanol policies on U.S. energy prices, agricultural commodity prices, and welfare through a stochastic partial equilibrium model of U.S. corn, ethanol, and gasoline markets. My second essay focuses on studying the price behavior of the renewable fuel credit (RFC) market, which is the mechanism developed by the Environmental Protection Agency (EPA) to meet the RFS. RFCs are a tradable, bankable, and borrowable accounting mechanism to ensure that all obligated parties use a mandated level of renewable fuel. I first develop a conceptual framework to understand how the market works and then apply stochastic dynamic programming to simulate prices for RFCs, examine the sensitivity of prices to relevant shocks, and estimate RFC option premiums. My third essay assesses the impact of policy led U.S. ethanol on the markets of global crude oil and U.S. gasoline using a structural Vector Auto Regression model of global crude oil, U.S. gasoline and ethanol markets.

Validation of MCNP: SPERT-D and BORAX-V fuel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crawford, C.; Palmer, B.

1992-11-01

This report discusses critical experiments involving SPERT-D{sup 1,2} fuel elements and BORAX-V{sup 3-8} fuel which have been modeled and calculations performed with MCNP. MCNP is a Monte Carlo based transport code. For this study continuous-energy nuclear data from the ENDF/B-V cross section library was used. The SPERT-D experiments consisted of various arrays of fuel elements moderated and reflected with either water or a uranyl nitrate solution. Some SPERT-D experiments used cadmium as a fixed neutron poison, while others were poisoned with various concentrations of boron in the moderating/reflecting solution. ne BORAX-V experiments were arrays of either boiling fuel rod assembliesmore » or superheater assemblies, both types of arrays were moderated and reflected with water. In one boiling fuel experiment, two fuel rods were replaced with borated stainless steel poison rods.« less

Validation of MCNP: SPERT-D and BORAX-V fuel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crawford, C.; Palmer, B.

1992-11-01

This report discusses critical experiments involving SPERT-D[sup 1,2] fuel elements and BORAX-V[sup 3-8] fuel which have been modeled and calculations performed with MCNP. MCNP is a Monte Carlo based transport code. For this study continuous-energy nuclear data from the ENDF/B-V cross section library was used. The SPERT-D experiments consisted of various arrays of fuel elements moderated and reflected with either water or a uranyl nitrate solution. Some SPERT-D experiments used cadmium as a fixed neutron poison, while others were poisoned with various concentrations of boron in the moderating/reflecting solution. ne BORAX-V experiments were arrays of either boiling fuel rod assembliesmore » or superheater assemblies, both types of arrays were moderated and reflected with water. In one boiling fuel experiment, two fuel rods were replaced with borated stainless steel poison rods.« less

Neutron monitor generated data distributions in quantum variational Monte Carlo

NASA Astrophysics Data System (ADS)

Kussainov, A. S.; Pya, N.

2016-08-01

We have assessed the potential applications of the neutron monitor hardware as random number generator for normal and uniform distributions. The data tables from the acquisition channels with no extreme changes in the signal level were chosen as the retrospective model. The stochastic component was extracted by fitting the raw data with splines and then subtracting the fit. Scaling the extracted data to zero mean and variance of one is sufficient to obtain a stable standard normal random variate. Distributions under consideration pass all available normality tests. Inverse transform sampling is suggested to use as a source of the uniform random numbers. Variational Monte Carlo method for quantum harmonic oscillator was used to test the quality of our random numbers. If the data delivery rate is of importance and the conventional one minute resolution neutron count is insufficient, we could always settle for an efficient seed generator to feed into the faster algorithmic random number generator or create a buffer.

Momentum Maps and Stochastic Clebsch Action Principles

NASA Astrophysics Data System (ADS)

Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S.

2018-01-01

We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise couples to the phase space variables through a momentum map. This special coupling simplifies the structure of the resulting stochastic Hamilton equations for the momentum map. In particular, these stochastic Hamilton equations collectivize for Hamiltonians that depend only on the momentum map variable. The Stratonovich equations are derived from the Clebsch variational principle and then converted into Itô form. In comparing the Stratonovich and Itô forms of the stochastic dynamical equations governing the components of the momentum map, we find that the Itô contraction term turns out to be a double Poisson bracket. Finally, we present the stochastic Hamiltonian formulation of the collectivized momentum map dynamics and derive the corresponding Kolmogorov forward and backward equations.

Extreme-Scale Stochastic Particle Tracing for Uncertain Unsteady Flow Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Hanqi; He, Wenbin; Seo, Sangmin

2016-11-13

We present an efficient and scalable solution to estimate uncertain transport behaviors using stochastic flow maps (SFM,) for visualizing and analyzing uncertain unsteady flows. SFM computation is extremely expensive because it requires many Monte Carlo runs to trace densely seeded particles in the flow. We alleviate the computational cost by decoupling the time dependencies in SFMs so that we can process adjacent time steps independently and then compose them together for longer time periods. Adaptive refinement is also used to reduce the number of runs for each location. We then parallelize over tasks—packets of particles in our design—to achieve highmore » efficiency in MPI/thread hybrid programming. Such a task model also enables CPU/GPU coprocessing. We show the scalability on two supercomputers, Mira (up to 1M Blue Gene/Q cores) and Titan (up to 128K Opteron cores and 8K GPUs), that can trace billions of particles in seconds.« less

Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

NASA Astrophysics Data System (ADS)

Validi, AbdoulAhad

2014-03-01

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

Separating the optical contributions to line-edge roughness in EUV lithography using stochastic simulations

NASA Astrophysics Data System (ADS)

Chunder, Anindarupa; Latypov, Azat; Chen, Yulu; Biafore, John J.; Levinson, Harry J.; Bailey, Todd

2017-03-01

Minimization and control of line-edge roughness (LER) and contact-edge roughness (CER) is one of the current challenges limiting EUV line-space and contact hole printability. One significant contributor to feature roughness and CD variability in EUV is photon shot noise (PSN); others are the physical and chemical processes in photoresists, known as resist stochastic effect. Different approaches are available to mitigate each of these contributions. In order to facilitate this mitigation, it is important to assess the magnitude of each of these contributions separately from others. In this paper, we present and test a computational approach based on the concept of an `ideal resist'. An ideal resist is assumed to be devoid of all resist stochastic effects. Hence, such an ideal resist can only be simulated as an `ideal resist model' (IRM) through explicit utilization of the Poisson statistics of PSN2 or direct Monte Carlo simulation of photon absorption in resist. LER estimated using IRM, thus quantifies the exclusive contribution of PSN to LER. The result of the simulation study done using IRM indicates higher magnitude of contribution (60%) from PSN to LER with respect to total or final LER for a sufficiently optimized high dose `state of the art' EUV chemically amplified resist (CAR) model.

Quantum stochastic calculus associated with quadratic quantum noises

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in

2016-02-15

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculusmore » extends the Hudson-Parthasarathy quantum stochastic calculus.« less

Itô-SDE MCMC method for Bayesian characterization of errors associated with data limitations in stochastic expansion methods for uncertainty quantification

NASA Astrophysics Data System (ADS)

Arnst, M.; Abello Álvarez, B.; Ponthot, J.-P.; Boman, R.

2017-11-01

This paper is concerned with the characterization and the propagation of errors associated with data limitations in polynomial-chaos-based stochastic methods for uncertainty quantification. Such an issue can arise in uncertainty quantification when only a limited amount of data is available. When the available information does not suffice to accurately determine the probability distributions that must be assigned to the uncertain variables, the Bayesian method for assigning these probability distributions becomes attractive because it allows the stochastic model to account explicitly for insufficiency of the available information. In previous work, such applications of the Bayesian method had already been implemented by using the Metropolis-Hastings and Gibbs Markov Chain Monte Carlo (MCMC) methods. In this paper, we present an alternative implementation, which uses an alternative MCMC method built around an Itô stochastic differential equation (SDE) that is ergodic for the Bayesian posterior. We draw together from the mathematics literature a number of formal properties of this Itô SDE that lend support to its use in the implementation of the Bayesian method, and we describe its discretization, including the choice of the free parameters, by using the implicit Euler method. We demonstrate the proposed methodology on a problem of uncertainty quantification in a complex nonlinear engineering application relevant to metal forming.

Stochastic architecture for Hopfield neural nets

NASA Technical Reports Server (NTRS)

Pavel, Sandy

1992-01-01

An expandable stochastic digital architecture for recurrent (Hopfield like) neural networks is proposed. The main features and basic principles of stochastic processing are presented. The stochastic digital architecture is based on a chip with n full interconnected neurons with a pipeline, bit processing structure. For large applications, a flexible way to interconnect many such chips is provided.

Selection of polynomial chaos bases via Bayesian model uncertainty methods with applications to sparse approximation of PDEs with stochastic inputs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karagiannis, Georgios, E-mail: georgios.karagiannis@pnnl.gov; Lin, Guang, E-mail: guang.lin@pnnl.gov

2014-02-15

Generalized polynomial chaos (gPC) expansions allow us to represent the solution of a stochastic system using a series of polynomial chaos basis functions. The number of gPC terms increases dramatically as the dimension of the random input variables increases. When the number of the gPC terms is larger than that of the available samples, a scenario that often occurs when the corresponding deterministic solver is computationally expensive, evaluation of the gPC expansion can be inaccurate due to over-fitting. We propose a fully Bayesian approach that allows for global recovery of the stochastic solutions, in both spatial and random domains, bymore » coupling Bayesian model uncertainty and regularization regression methods. It allows the evaluation of the PC coefficients on a grid of spatial points, via (1) the Bayesian model average (BMA) or (2) the median probability model, and their construction as spatial functions on the spatial domain via spline interpolation. The former accounts for the model uncertainty and provides Bayes-optimal predictions; while the latter provides a sparse representation of the stochastic solutions by evaluating the expansion on a subset of dominating gPC bases. Moreover, the proposed methods quantify the importance of the gPC bases in the probabilistic sense through inclusion probabilities. We design a Markov chain Monte Carlo (MCMC) sampler that evaluates all the unknown quantities without the need of ad-hoc techniques. The proposed methods are suitable for, but not restricted to, problems whose stochastic solutions are sparse in the stochastic space with respect to the gPC bases while the deterministic solver involved is expensive. We demonstrate the accuracy and performance of the proposed methods and make comparisons with other approaches on solving elliptic SPDEs with 1-, 14- and 40-random dimensions.« less

An efficient distribution method for nonlinear transport problems in highly heterogeneous stochastic porous media

NASA Astrophysics Data System (ADS)

Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi

2016-04-01

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are crucial to explore possible scenarios and assess risks in subsurface problems. In particular, nonlinear two-phase flows in porous media are essential, yet challenging, in reservoir simulation and hydrology. Adding highly heterogeneous and uncertain input, such as the permeability and porosity fields, transforms the estimation of the flow response into a tough stochastic problem for which computationally expensive Monte Carlo (MC) simulations remain the preferred option.We propose an alternative approach to evaluate the probability distribution of the (water) saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the (water) saturation. The distribution method draws inspiration from a Lagrangian approach of the stochastic transport problem and expresses the saturation PDF and CDF essentially in terms of a deterministic mapping and the distribution and statistics of scalar random fields. In a large class of applications these random fields can be estimated at low computational costs (few MC runs), thus making the distribution method attractive. Even though the method relies on a key assumption of fixed streamlines, we show that it performs well for high input variances, which is the case of interest. Once the saturation distribution is determined, any one-point statistics thereof can be obtained, especially the saturation average and standard deviation. Moreover, the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be efficiently derived from the distribution method. These statistics can then be used for risk assessment, as well as data assimilation and uncertainty reduction

A Stochastic Employment Problem

ERIC Educational Resources Information Center

Wu, Teng

2013-01-01

The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…

Application analysis of Monte Carlo to estimate the capacity of geothermal resources in Lawu Mount

DOE Office of Scientific and Technical Information (OSTI.GOV)

Supriyadi, E-mail: supriyadi-uno@yahoo.co.nz; Srigutomo, Wahyu; Munandar, Arif

2014-03-24

Monte Carlo analysis has been applied in calculation of geothermal resource capacity based on volumetric method issued by Standar Nasional Indonesia (SNI). A deterministic formula is converted into a stochastic formula to take into account the nature of uncertainties in input parameters. The method yields a range of potential power probability stored beneath Lawu Mount geothermal area. For 10,000 iterations, the capacity of geothermal resources is in the range of 139.30-218.24 MWe with the most likely value is 177.77 MWe. The risk of resource capacity above 196.19 MWe is less than 10%. The power density of the prospect area coveringmore » 17 km{sup 2} is 9.41 MWe/km{sup 2} with probability 80%.« less

Efficient stochastic approaches for sensitivity studies of an Eulerian large-scale air pollution model

NASA Astrophysics Data System (ADS)

Dimov, I.; Georgieva, R.; Todorov, V.; Ostromsky, Tz.

2017-10-01

Reliability of large-scale mathematical models is an important issue when such models are used to support decision makers. Sensitivity analysis of model outputs to variation or natural uncertainties of model inputs is crucial for improving the reliability of mathematical models. A comprehensive experimental study of Monte Carlo algorithms based on Sobol sequences for multidimensional numerical integration has been done. A comparison with Latin hypercube sampling and a particular quasi-Monte Carlo lattice rule based on generalized Fibonacci numbers has been presented. The algorithms have been successfully applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters (six chemical reactions rates and four different groups of pollutants) on the concentrations of important air pollutants. The concentration values have been generated by the Unified Danish Eulerian Model. The sensitivity study has been done for the areas of several European cities with different geographical locations. The numerical tests show that the stochastic algorithms under consideration are efficient for multidimensional integration and especially for computing small by value sensitivity indices. It is a crucial element since even small indices may be important to be estimated in order to achieve a more accurate distribution of inputs influence and a more reliable interpretation of the mathematical model results.

Stochastic flux freezing and magnetic dynamo.

PubMed

Eyink, Gregory L

2011-05-01

Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr(m)) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr(m)=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered. © 2011 American Physical Society

p-adic stochastic hidden variable model

NASA Astrophysics Data System (ADS)

Khrennikov, Andrew

1998-03-01

We propose stochastic hidden variables model in which hidden variables have a p-adic probability distribution ρ(λ) and at the same time conditional probabilistic distributions P(U,λ), U=A,A',B,B', are ordinary probabilities defined on the basis of the Kolmogorov measure-theoretical axiomatics. A frequency definition of p-adic probability is quite similar to the ordinary frequency definition of probability. p-adic frequency probability is defined as the limit of relative frequencies νn but in the p-adic metric. We study a model with p-adic stochastics on the level of the hidden variables description. But, of course, responses of macroapparatuses have to be described by ordinary stochastics. Thus our model describes a mixture of p-adic stochastics of the microworld and ordinary stochastics of macroapparatuses. In this model probabilities for physical observables are the ordinary probabilities. At the same time Bell's inequality is violated.

Population density approach for discrete mRNA distributions in generalized switching models for stochastic gene expression.

PubMed

Stinchcombe, Adam R; Peskin, Charles S; Tranchina, Daniel

2012-06-01

We present a generalization of a population density approach for modeling and analysis of stochastic gene expression. In the model, the gene of interest fluctuates stochastically between an inactive state, in which transcription cannot occur, and an active state, in which discrete transcription events occur; and the individual mRNA molecules are degraded stochastically in an independent manner. This sort of model in simplest form with exponential dwell times has been used to explain experimental estimates of the discrete distribution of random mRNA copy number. In our generalization, the random dwell times in the inactive and active states, T_{0} and T_{1}, respectively, are independent random variables drawn from any specified distributions. Consequently, the probability per unit time of switching out of a state depends on the time since entering that state. Our method exploits a connection between the fully discrete random process and a related continuous process. We present numerical methods for computing steady-state mRNA distributions and an analytical derivation of the mRNA autocovariance function. We find that empirical estimates of the steady-state mRNA probability mass function from Monte Carlo simulations of laboratory data do not allow one to distinguish between underlying models with exponential and nonexponential dwell times in some relevant parameter regimes. However, in these parameter regimes and where the autocovariance function has negative lobes, the autocovariance function disambiguates the two types of models. Our results strongly suggest that temporal data beyond the autocovariance function is required in general to characterize gene switching.

Global identification of stochastic dynamical systems under different pseudo-static operating conditions: The functionally pooled ARMAX case

NASA Astrophysics Data System (ADS)

Sakellariou, J. S.; Fassois, S. D.

2017-01-01

The identification of a single global model for a stochastic dynamical system operating under various conditions is considered. Each operating condition is assumed to have a pseudo-static effect on the dynamics and be characterized by a single measurable scheduling variable. Identification is accomplished within a recently introduced Functionally Pooled (FP) framework, which offers a number of advantages over Linear Parameter Varying (LPV) identification techniques. The focus of the work is on the extension of the framework to include the important FP-ARMAX model case. Compared to their simpler FP-ARX counterparts, FP-ARMAX models are much more general and offer improved flexibility in describing various types of stochastic noise, but at the same time lead to a more complicated, non-quadratic, estimation problem. Prediction Error (PE), Maximum Likelihood (ML), and multi-stage estimation methods are postulated, and the PE estimator optimality, in terms of consistency and asymptotic efficiency, is analytically established. The postulated estimators are numerically assessed via Monte Carlo experiments, while the effectiveness of the approach and its superiority over its FP-ARX counterpart are demonstrated via an application case study pertaining to simulated railway vehicle suspension dynamics under various mass loading conditions.

A novel algorithm for solving the true coincident counting issues in Monte Carlo simulations for radiation spectroscopy.

PubMed

Guan, Fada; Johns, Jesse M; Vasudevan, Latha; Zhang, Guoqing; Tang, Xiaobin; Poston, John W; Braby, Leslie A

2015-06-01

Coincident counts can be observed in experimental radiation spectroscopy. Accurate quantification of the radiation source requires the detection efficiency of the spectrometer, which is often experimentally determined. However, Monte Carlo analysis can be used to supplement experimental approaches to determine the detection efficiency a priori. The traditional Monte Carlo method overestimates the detection efficiency as a result of omitting coincident counts caused mainly by multiple cascade source particles. In this study, a novel "multi-primary coincident counting" algorithm was developed using the Geant4 Monte Carlo simulation toolkit. A high-purity Germanium detector for ⁶⁰Co gamma-ray spectroscopy problems was accurately modeled to validate the developed algorithm. The simulated pulse height spectrum agreed well qualitatively with the measured spectrum obtained using the high-purity Germanium detector. The developed algorithm can be extended to other applications, with a particular emphasis on challenging radiation fields, such as counting multiple types of coincident radiations released from nuclear fission or used nuclear fuel.

A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S.

2008-05-15

We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive globalmore » information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.« less

Topology optimization under stochastic stiffness

NASA Astrophysics Data System (ADS)

Asadpoure, Alireza

Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations

Stochastic demographic forecasting.

PubMed

Lee, R D

1992-11-01

"This paper describes a particular approach to stochastic population forecasting, which is implemented for the U.S.A. through 2065. Statistical time series methods are combined with demographic models to produce plausible long run forecasts of vital rates, with probability distributions. The resulting mortality forecasts imply gains in future life expectancy that are roughly twice as large as those forecast by the Office of the Social Security Actuary.... Resulting stochastic forecasts of the elderly population, elderly dependency ratios, and payroll tax rates for health, education and pensions are presented." excerpt

Multi-element stochastic spectral projection for high quantile estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ko, Jordan, E-mail: jordan.ko@mac.com; Garnier, Josselin

2013-06-15

We investigate quantile estimation by multi-element generalized Polynomial Chaos (gPC) metamodel where the exact numerical model is approximated by complementary metamodels in overlapping domains that mimic the model’s exact response. The gPC metamodel is constructed by the non-intrusive stochastic spectral projection approach and function evaluation on the gPC metamodel can be considered as essentially free. Thus, large number of Monte Carlo samples from the metamodel can be used to estimate α-quantile, for moderate values of α. As the gPC metamodel is an expansion about the means of the inputs, its accuracy may worsen away from these mean values where themore » extreme events may occur. By increasing the approximation accuracy of the metamodel, we may eventually improve accuracy of quantile estimation but it is very expensive. A multi-element approach is therefore proposed by combining a global metamodel in the standard normal space with supplementary local metamodels constructed in bounded domains about the design points corresponding to the extreme events. To improve the accuracy and to minimize the sampling cost, sparse-tensor and anisotropic-tensor quadratures are tested in addition to the full-tensor Gauss quadrature in the construction of local metamodels; different bounds of the gPC expansion are also examined. The global and local metamodels are combined in the multi-element gPC (MEgPC) approach and it is shown that MEgPC can be more accurate than Monte Carlo or importance sampling methods for high quantile estimations for input dimensions roughly below N=8, a limit that is very much case- and α-dependent.« less

Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Chia -Chen; Rubenstein, Brenda M.; Morales, Miguel A.

2016-12-19

Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wavemore » function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Lastly, our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.« less

Enhanced algorithms for stochastic programming

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishna, Alamuru S.

1993-09-01

In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean ofmore » a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.« less

Dynamics of non-holonomic systems with stochastic transport

NASA Astrophysics Data System (ADS)

Holm, D. D.; Putkaradze, V.

2018-01-01

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.

Numerical methods for stochastic differential equations

NASA Astrophysics Data System (ADS)

Kloeden, Peter; Platen, Eckhard

1991-06-01

The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to the peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, both theory and applications. The main emphasise is placed on the numerical methods needed to solve such equations. It assumes an undergraduate background in mathematical methods typical of engineers and physicists, through many chapters begin with a descriptive summary which may be accessible to others who only require numerical recipes. To help the reader develop an intuitive understanding of the underlying mathematicals and hand-on numerical skills exercises and over 100 PC Exercises (PC-personal computer) are included. The stochastic Taylor expansion provides the key tool for the systematic derivation and investigation of discrete time numerical methods for stochastic differential equations. The book presents many new results on higher order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation and variance-reduction methods. Besides serving as a basic text on such methods. the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable.

Stochastic entrainment of a stochastic oscillator.

PubMed

Wang, Guanyu; Peskin, Charles S

2015-01-01

In this work, we consider a stochastic oscillator described by a discrete-state continuous-time Markov chain, in which the states are arranged in a circle, and there is a constant probability per unit time of jumping from one state to the next in a specified direction around the circle. At each of a sequence of equally spaced times, the oscillator has a specified probability of being reset to a particular state. The focus of this work is the entrainment of the oscillator by this periodic but stochastic stimulus. We consider a distinguished limit, in which (i) the number of states of the oscillator approaches infinity, as does the probability per unit time of jumping from one state to the next, so that the natural mean period of the oscillator remains constant, (ii) the resetting probability approaches zero, and (iii) the period of the resetting signal approaches a multiple, by a ratio of small integers, of the natural mean period of the oscillator. In this distinguished limit, we use analytic and numerical methods to study the extent to which entrainment occurs.

Accelerator-Driven Subcritical System for Disposing of the U.S. Spent Nuclear Fuel Inventory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gohar, Yousry; Cao, Yan; Kraus, Adam R.

The current United States inventory of the spent nuclear fuel (SNF) is ~80,000 metric tons of heavy metal (MTHM), including ~131 tons of minor actinides (MAs) and ~669 tons of plutonium. This study describes a conceptual design of an accelerator-driven subcritical (ADS) system for disposing of this SNF inventory by utilizing the 131 tons of MAs inventory and a fraction of the plutonium inventory for energy production, and transmuting some long-lived fission products. An ADS system with a homogeneous subcritical fission blanket was first examined. A spallation neutron source is used to drive the blanket and it is produced frommore » the interaction of a 1-GeV proton beam with a lead-bismuth eutectic (LBE) target. The blanket has a liquid mobile fuel using LBE as the fuel carrier. The fuel materials are dissolved, mixed, or suspended in the liquid fuel carrier. Monte Carlo analyses were performed to determine the overall parameters of the concept. Steady-state Monte Carlo simulations were performed for three similar fission blankets. Except for, the loaded amount of actinide materials in the LBE is either 5, 7, or 10% of the total volume of the blanket, respectively. The neutron multiplication factors of the three blankets are ~0.98 and the initial MAs blanket inventories are ~10 tons. In addition, Monte Carlo burnup simulations using the MCB5 code were performed to analyze the performance of the three conceptual ADS systems. During operation, fresh fuel was fed into the fission blanket to adjust its reactivity and to control the system power. The burnup analysis shows that the three ADS concepts consume about 1.2 tons of actinides per full power year and produce 3 GW thermal power, with a proton beam power of 25 MW. For the blankets with 5, 7, or 10% actinide fuel particles loaded in the LBE, assuming that the ADS systems can be operated for 35 full-power years, the total MA materials consumed in the three ADS systems are about 30.6, 35.3, and 37.2 tons

Stochastic modelling of intermittency.

PubMed

Stemler, Thomas; Werner, Johannes P; Benner, Hartmut; Just, Wolfram

2010-01-13

Recently, methods have been developed to model low-dimensional chaotic systems in terms of stochastic differential equations. We tested such methods in an electronic circuit experiment. We aimed to obtain reliable drift and diffusion coefficients even without a pronounced time-scale separation of the chaotic dynamics. By comparing the analytical solutions of the corresponding Fokker-Planck equation with experimental data, we show here that crisis-induced intermittency can be described in terms of a stochastic model which is dominated by state-space-dependent diffusion. Further on, we demonstrate and discuss some limits of these modelling approaches using numerical simulations. This enables us to state a criterion that can be used to decide whether a stochastic model will capture the essential features of a given time series. This journal is © 2010 The Royal Society

Stochastic inflation in phase space: is slow roll a stochastic attractor?

NASA Astrophysics Data System (ADS)

Grain, Julien; Vennin, Vincent

2017-05-01

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ``slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue. The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.

Stochastic inflation in phase space: is slow roll a stochastic attractor?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grain, Julien; Vennin, Vincent, E-mail: julien.grain@ias.u-psud.fr, E-mail: vincent.vennin@port.ac.uk

An appealing feature of inflationary cosmology is the presence of a phase-space attractor, ''slow roll'', which washes out the dependence on initial field velocities. We investigate the robustness of this property under backreaction from quantum fluctuations using the stochastic inflation formalism in the phase-space approach. A Hamiltonian formulation of stochastic inflation is presented, where it is shown that the coarse-graining procedure—where wavelengths smaller than the Hubble radius are integrated out—preserves the canonical structure of free fields. This means that different sets of canonical variables give rise to the same probability distribution which clarifies the literature with respect to this issue.more » The role played by the quantum-to-classical transition is also analysed and is shown to constrain the coarse-graining scale. In the case of free fields, we find that quantum diffusion is aligned in phase space with the slow-roll direction. This implies that the classical slow-roll attractor is immune to stochastic effects and thus generalises to a stochastic attractor regardless of initial conditions, with a relaxation time at least as short as in the classical system. For non-test fields or for test fields with non-linear self interactions however, quantum diffusion and the classical slow-roll flow are misaligned. We derive a condition on the coarse-graining scale so that observational corrections from this misalignment are negligible at leading order in slow roll.« less

Partial ASL extensions for stochastic programming.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gay, David

2010-03-31

partially completed extensions for stochastic programming to the AMPL/solver interface library (ASL).modeling and experimenting with stochastic recourse problems. This software is not primarily for military applications

Coupling of kinetic Monte Carlo simulations of surface reactions to transport in a fluid for heterogeneous catalytic reactor modeling.

PubMed

Schaefer, C; Jansen, A P J

2013-02-07

We have developed a method to couple kinetic Monte Carlo simulations of surface reactions at a molecular scale to transport equations at a macroscopic scale. This method is applicable to steady state reactors. We use a finite difference upwinding scheme and a gap-tooth scheme to efficiently use a limited amount of kinetic Monte Carlo simulations. In general the stochastic kinetic Monte Carlo results do not obey mass conservation so that unphysical accumulation of mass could occur in the reactor. We have developed a method to perform mass balance corrections that is based on a stoichiometry matrix and a least-squares problem that is reduced to a non-singular set of linear equations that is applicable to any surface catalyzed reaction. The implementation of these methods is validated by comparing numerical results of a reactor simulation with a unimolecular reaction to an analytical solution. Furthermore, the method is applied to two reaction mechanisms. The first is the ZGB model for CO oxidation in which inevitable poisoning of the catalyst limits the performance of the reactor. The second is a model for the oxidation of NO on a Pt(111) surface, which becomes active due to lateral interaction at high coverages of oxygen. This reaction model is based on ab initio density functional theory calculations from literature.

Constant-pH molecular dynamics using stochastic titration

NASA Astrophysics Data System (ADS)

Baptista, António M.; Teixeira, Vitor H.; Soares, Cláudio M.

2002-09-01

A new method is proposed for performing constant-pH molecular dynamics (MD) simulations, that is, MD simulations where pH is one of the external thermodynamic parameters, like the temperature or the pressure. The protonation state of each titrable site in the solute is allowed to change during a molecular mechanics (MM) MD simulation, the new states being obtained from a combination of continuum electrostatics (CE) calculations and Monte Carlo (MC) simulation of protonation equilibrium. The coupling between the MM/MD and CE/MC algorithms is done in a way that ensures a proper Markov chain, sampling from the intended semigrand canonical distribution. This stochastic titration method is applied to succinic acid, aimed at illustrating the method and examining the choice of its adjustable parameters. The complete titration of succinic acid, using constant-pH MD simulations at different pH values, gives a clear picture of the coupling between the trans/gauche isomerization and the protonation process, making it possible to reconcile some apparently contradictory results of previous studies. The present constant-pH MD method is shown to require a moderate increase of computational cost when compared to the usual MD method.

The Sharma-Parthasarathy stochastic two-body problem

NASA Astrophysics Data System (ADS)

Cresson, J.; Pierret, F.; Puig, B.

2015-03-01

We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in ["Dynamics of a stochastically perturbed two-body problem," Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss's equations in the planar case.

The Effect of Stochastic Perturbation of Fuel Distribution on the Criticality of a One Speed Reactor and the Development of Multi-Material Multinomial Line Statistics

NASA Technical Reports Server (NTRS)

Jahshan, S. N.; Singleterry, R. C.

2001-01-01

The effect of random fuel redistribution on the eigenvalue of a one-speed reactor is investigated. An ensemble of such reactors that are identical to a homogeneous reference critical reactor except for the fissile isotope density distribution is constructed such that it meets a set of well-posed redistribution requirements. The average eigenvalue, , is evaluated when the total fissile loading per ensemble element, or realization, is conserved. The perturbation is proven to increase the reactor criticality on average when it is uniformly distributed. The various causes of the change in reactivity, and their relative effects are identified and ranked. From this, a path towards identifying the causes. and relative effects of reactivity fluctuations for the energy dependent problem is pointed to. The perturbation method of using multinomial distributions for representing the perturbed reactor is developed. This method has some advantages that can be of use in other stochastic problems. Finally, some of the features of this perturbation problem are related to other techniques that have been used for addressing similar problems.

Derivation of flood frequency curves in poorly gauged Mediterranean catchments using a simple stochastic hydrological rainfall-runoff model

NASA Astrophysics Data System (ADS)

Aronica, G. T.; Candela, A.

2007-12-01

SummaryIn this paper a Monte Carlo procedure for deriving frequency distributions of peak flows using a semi-distributed stochastic rainfall-runoff model is presented. The rainfall-runoff model here used is very simple one, with a limited number of parameters and practically does not require any calibration, resulting in a robust tool for those catchments which are partially or poorly gauged. The procedure is based on three modules: a stochastic rainfall generator module, a hydrologic loss module and a flood routing module. In the rainfall generator module the rainfall storm, i.e. the maximum rainfall depth for a fixed duration, is assumed to follow the two components extreme value (TCEV) distribution whose parameters have been estimated at regional scale for Sicily. The catchment response has been modelled by using the Soil Conservation Service-Curve Number (SCS-CN) method, in a semi-distributed form, for the transformation of total rainfall to effective rainfall and simple form of IUH for the flood routing. Here, SCS-CN method is implemented in probabilistic form with respect to prior-to-storm conditions, allowing to relax the classical iso-frequency assumption between rainfall and peak flow. The procedure is tested on six practical case studies where synthetic FFC (flood frequency curve) were obtained starting from model variables distributions by simulating 5000 flood events combining 5000 values of total rainfall depth for the storm duration and AMC (antecedent moisture conditions) conditions. The application of this procedure showed how Monte Carlo simulation technique can reproduce the observed flood frequency curves with reasonable accuracy over a wide range of return periods using a simple and parsimonious approach, limited data input and without any calibration of the rainfall-runoff model.

Fixed-node quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Anderson, James B.

Quantum Monte Carlo methods cannot at present provide exact solutions of the Schrödinger equation for systems with more than a few electrons. But, quantum Monte Carlo calculations can provide very low energy, highly accurate solutions for many systems ranging up to several hundred electrons. These systems include atoms such as Be and Fe, molecules such as H2O, CH4, and HF, and condensed materials such as solid N2 and solid silicon. The quantum Monte Carlo predictions of their energies and structures may not be `exact', but they are the best available. Most of the Monte Carlo calculations for these systems have been carried out using approximately correct fixed nodal hypersurfaces and they have come to be known as `fixed-node quantum Monte Carlo' calculations. In this paper we review these `fixed node' calculations and the accuracies they yield.

Stochastic effects in a seasonally forced epidemic model

NASA Astrophysics Data System (ADS)

Rozhnova, G.; Nunes, A.

2010-10-01

The interplay of seasonality, the system’s nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.

Stochastic approach for radionuclides quantification

NASA Astrophysics Data System (ADS)

Clement, A.; Saurel, N.; Perrin, G.

2018-01-01

Gamma spectrometry is a passive non-destructive assay used to quantify radionuclides present in more or less complex objects. Basic methods using empirical calibration with a standard in order to quantify the activity of nuclear materials by determining the calibration coefficient are useless on non-reproducible, complex and single nuclear objects such as waste packages. Package specifications as composition or geometry change from one package to another and involve a high variability of objects. Current quantification process uses numerical modelling of the measured scene with few available data such as geometry or composition. These data are density, material, screen, geometric shape, matrix composition, matrix and source distribution. Some of them are strongly dependent on package data knowledge and operator backgrounds. The French Commissariat à l'Energie Atomique (CEA) is developing a new methodology to quantify nuclear materials in waste packages and waste drums without operator adjustment and internal package configuration knowledge. This method suggests combining a global stochastic approach which uses, among others, surrogate models available to simulate the gamma attenuation behaviour, a Bayesian approach which considers conditional probability densities of problem inputs, and Markov Chains Monte Carlo algorithms (MCMC) which solve inverse problems, with gamma ray emission radionuclide spectrum, and outside dimensions of interest objects. The methodology is testing to quantify actinide activity in different kind of matrix, composition, and configuration of sources standard in terms of actinide masses, locations and distributions. Activity uncertainties are taken into account by this adjustment methodology.

Discrimination of irradiated MOX fuel from UOX fuel by multivariate statistical analysis of simulated activities of gamma-emitting isotopes

NASA Astrophysics Data System (ADS)

Åberg Lindell, M.; Andersson, P.; Grape, S.; Hellesen, C.; Håkansson, A.; Thulin, M.

2018-03-01

This paper investigates how concentrations of certain fission products and their related gamma-ray emissions can be used to discriminate between uranium oxide (UOX) and mixed oxide (MOX) type fuel. Discrimination of irradiated MOX fuel from irradiated UOX fuel is important in nuclear facilities and for transport of nuclear fuel, for purposes of both criticality safety and nuclear safeguards. Although facility operators keep records on the identity and properties of each fuel, tools for nuclear safeguards inspectors that enable independent verification of the fuel are critical in the recovery of continuity of knowledge, should it be lost. A discrimination methodology for classification of UOX and MOX fuel, based on passive gamma-ray spectroscopy data and multivariate analysis methods, is presented. Nuclear fuels and their gamma-ray emissions were simulated in the Monte Carlo code Serpent, and the resulting data was used as input to train seven different multivariate classification techniques. The trained classifiers were subsequently implemented and evaluated with respect to their capabilities to correctly predict the classes of unknown fuel items. The best results concerning successful discrimination of UOX and MOX-fuel were acquired when using non-linear classification techniques, such as the k nearest neighbors method and the Gaussian kernel support vector machine. For fuel with cooling times up to 20 years, when it is considered that gamma-rays from the isotope 134Cs can still be efficiently measured, success rates of 100% were obtained. A sensitivity analysis indicated that these methods were also robust.

Markov stochasticity coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

Stochastic simulation in systems biology

PubMed Central

Székely, Tamás; Burrage, Kevin

2014-01-01

Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity). In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology. There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest. PMID:25505503

An efficient Bayesian data-worth analysis using a multilevel Monte Carlo method

NASA Astrophysics Data System (ADS)

Lu, Dan; Ricciuto, Daniel; Evans, Katherine

2018-03-01

Improving the understanding of subsurface systems and thus reducing prediction uncertainty requires collection of data. As the collection of subsurface data is costly, it is important that the data collection scheme is cost-effective. Design of a cost-effective data collection scheme, i.e., data-worth analysis, requires quantifying model parameter, prediction, and both current and potential data uncertainties. Assessment of these uncertainties in large-scale stochastic subsurface hydrological model simulations using standard Monte Carlo (MC) sampling or surrogate modeling is extremely computationally intensive, sometimes even infeasible. In this work, we propose an efficient Bayesian data-worth analysis using a multilevel Monte Carlo (MLMC) method. Compared to the standard MC that requires a significantly large number of high-fidelity model executions to achieve a prescribed accuracy in estimating expectations, the MLMC can substantially reduce computational costs using multifidelity approximations. Since the Bayesian data-worth analysis involves a great deal of expectation estimation, the cost saving of the MLMC in the assessment can be outstanding. While the proposed MLMC-based data-worth analysis is broadly applicable, we use it for a highly heterogeneous two-phase subsurface flow simulation to select an optimal candidate data set that gives the largest uncertainty reduction in predicting mass flow rates at four production wells. The choices made by the MLMC estimation are validated by the actual measurements of the potential data, and consistent with the standard MC estimation. But compared to the standard MC, the MLMC greatly reduces the computational costs.

The Sharma-Parthasarathy stochastic two-body problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cresson, J.; SYRTE/Observatoire de Paris, 75014 Paris; Pierret, F.

2015-03-15

We study the Sharma-Parthasarathy stochastic two-body problem introduced by Sharma and Parthasarathy in [“Dynamics of a stochastically perturbed two-body problem,” Proc. R. Soc. A 463, 979-1003 (2007)]. In particular, we focus on the preservation of some fundamental features of the classical two-body problem like the Hamiltonian structure and first integrals in the stochastic case. Numerical simulations are performed which illustrate the dynamical behaviour of the osculating elements as the semi-major axis, the eccentricity, and the pericenter. We also derive a stochastic version of Gauss’s equations in the planar case.

Second Cancers After Fractionated Radiotherapy: Stochastic Population Dynamics Effects

NASA Technical Reports Server (NTRS)

Sachs, Rainer K.; Shuryak, Igor; Brenner, David; Fakir, Hatim; Hahnfeldt, Philip

2007-01-01

When ionizing radiation is used in cancer therapy it can induce second cancers in nearby organs. Mainly due to longer patient survival times, these second cancers have become of increasing concern. Estimating the risk of solid second cancers involves modeling: because of long latency times, available data is usually for older, obsolescent treatment regimens. Moreover, modeling second cancers gives unique insights into human carcinogenesis, since the therapy involves administering well characterized doses of a well studied carcinogen, followed by long-term monitoring. In addition to putative radiation initiation that produces pre-malignant cells, inactivation (i.e. cell killing), and subsequent cell repopulation by proliferation can be important at the doses relevant to second cancer situations. A recent initiation/inactivation/proliferation (IIP) model characterized quantitatively the observed occurrence of second breast and lung cancers, using a deterministic cell population dynamics approach. To analyze ifradiation-initiated pre-malignant clones become extinct before full repopulation can occur, we here give a stochastic version of this I I model. Combining Monte Carlo simulations with standard solutions for time-inhomogeneous birth-death equations, we show that repeated cycles of inactivation and repopulation, as occur during fractionated radiation therapy, can lead to distributions of pre-malignant cells per patient with variance >> mean, even when pre-malignant clones are Poisson-distributed. Thus fewer patients would be affected, but with a higher probability, than a deterministic model, tracking average pre-malignant cell numbers, would predict. Our results are applied to data on breast cancers after radiotherapy for Hodgkin disease. The stochastic IIP analysis, unlike the deterministic one, indicates: a) initiated, pre-malignant cells can have a growth advantage during repopulation, not just during the longer tumor latency period that follows; b) weekend

Optimality, stochasticity, and variability in motor behavior

PubMed Central

Guigon, Emmanuel; Baraduc, Pierre; Desmurget, Michel

2008-01-01

Recent theories of motor control have proposed that the nervous system acts as a stochastically optimal controller, i.e. it plans and executes motor behaviors taking into account the nature and statistics of noise. Detrimental effects of noise are converted into a principled way of controlling movements. Attractive aspects of such theories are their ability to explain not only characteristic features of single motor acts, but also statistical properties of repeated actions. Here, we present a critical analysis of stochastic optimality in motor control which reveals several difficulties with this hypothesis. We show that stochastic control may not be necessary to explain the stochastic nature of motor behavior, and we propose an alternative framework, based on the action of a deterministic controller coupled with an optimal state estimator, which relieves drawbacks of stochastic optimality and appropriately explains movement variability. PMID:18202922

Dynamically orthogonal field equations for stochastic flows and particle dynamics

DTIC Science & Technology

2011-02-01

where uncertainty ‘lives’ as well as a system of Stochastic Di erential Equations that de nes how the uncertainty evolves in the time varying stochastic ... stochastic dynamical component that are both time and space dependent, we derive a system of field equations consisting of a Partial Differential Equation...a system of Stochastic Differential Equations that defines how the stochasticity evolves in the time varying stochastic subspace. These new

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less

A stochastic discrete optimization model for designing container terminal facilities

NASA Astrophysics Data System (ADS)

Zukhruf, Febri; Frazila, Russ Bona; Burhani, Jzolanda Tsavalista

2017-11-01

As uncertainty essentially affect the total transportation cost, it remains important in the container terminal that incorporates several modes and transshipments process. This paper then presents a stochastic discrete optimization model for designing the container terminal, which involves the decision of facilities improvement action. The container terminal operation model is constructed by accounting the variation of demand and facilities performance. In addition, for illustrating the conflicting issue that practically raises in the terminal operation, the model also takes into account the possible increment delay of facilities due to the increasing number of equipment, especially the container truck. Those variations expectantly reflect the uncertainty issue in the container terminal operation. A Monte Carlo simulation is invoked to propagate the variations by following the observed distribution. The problem is constructed within the framework of the combinatorial optimization problem for investigating the optimal decision of facilities improvement. A new variant of glow-worm swarm optimization (GSO) is thus proposed for solving the optimization, which is rarely explored in the transportation field. The model applicability is tested by considering the actual characteristics of the container terminal.

Some Stochastic-Duel Models of Combat.

DTIC Science & Technology

1983-03-01

AD-R127 879 SOME STOCHASTIC- DUEL MODELS OF CONBAT(U) NAVAL - / POSTGRADUATE SCHOOL MONTEREY CA J S CHOE MAR 83 UNCLASSiIED FC1/Ehhh1; F/ 12/ ,iE...SCHOOL Monterey, California DTIC ELECTE :MAY 10 1983 "T !H ES IS SOME STOCHASTIC- DUEL MODELS OF COMBAT by Jum Soo Choe March 1983 Thesis Advisor: J. G...TYPE OF RETORT a PERIOD COVIOCe Master’s Thesis Some Stochastic- Duel Models of Combat March 1983 S. PERFORINGi *no. 44POOi umet 7. AUTHORW.) a

Numerical simulations in stochastic mechanics

NASA Astrophysics Data System (ADS)

McClendon, Marvin; Rabitz, Herschel

1988-05-01

The stochastic differential equation of Nelson's stochastic mechanics is integrated numerically for several simple quantum systems. The calculations are performed with use of Helfand and Greenside's method and pseudorandom numbers. The resulting trajectories are analyzed both individually and collectively to yield insight into momentum, uncertainty principles, interference, tunneling, quantum chaos, and common models of diatomic molecules from the stochastic quantization point of view. In addition to confirming Shucker's momentum theorem, these simulations illustrate, within the context of stochastic mechanics, the position-momentum and time-energy uncertainty relations, the two-slit diffraction pattern, exponential decay of an unstable system, and the greater degree of anticorrelation in a valence-bond model as compared with a molecular-orbital model of H2. The attempt to find exponential divergence of initially nearby trajectories, potentially useful as a criterion for quantum chaos, in a periodically forced oscillator is inconclusive. A way of computing excited energies from the ground-state motion is presented. In all of these studies the use of particle trajectories allows a more insightful interpretation of physical phenomena than is possible within traditional wave mechanics.

Fluctuating chemohydrodynamics and the stochastic motion of self-diffusiophoretic particles

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Kapral, Raymond

2018-04-01

The propulsion of active particles by self-diffusiophoresis is driven by asymmetric catalytic reactions on the particle surface that generate a mechanochemical coupling between the fluid velocity and the concentration fields of fuel and product in the surrounding solution. Because of thermal and molecular fluctuations in the solution, the motion of micrometric or submicrometric active particles is stochastic. Coupled Langevin equations describing the translation, rotation, and reaction of such active particles are deduced from fluctuating chemohydrodynamics and fluctuating boundary conditions at the interface between the fluid and the particle. These equations are consistent with microreversibility and the Onsager-Casimir reciprocal relations between affinities and currents and provide a thermodynamically consistent basis for the investigation of the dynamics of active particles propelled by diffusiophoretic mechanisms.

Scenario generation for stochastic optimization problems via the sparse grid method

DOE PAGES

Chen, Michael; Mehrotra, Sanjay; Papp, David

2015-04-19

We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid methodmore » can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.« less

Automated Flight Routing Using Stochastic Dynamic Programming

NASA Technical Reports Server (NTRS)

Ng, Hok K.; Morando, Alex; Grabbe, Shon

2010-01-01

Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

Determination of the NPP Kr\\vsko spent fuel decay heat

NASA Astrophysics Data System (ADS)

Kromar, Marjan; Kurinčič, Bojan

2017-07-01

Nuclear fuel is designed to support fission process in a reactor core. Some of the isotopes, formed during the fission, decay and produce decay heat and radiation. Accurate knowledge of the nuclide inventory producing decay heat is important after reactor shut down, during the fuel storage and subsequent reprocessing or disposal. In this paper possibility to calculate the fuel isotopic composition and determination of the fuel decay heat with the Serpent code is investigated. Serpent is a well-known Monte Carlo code used primarily for the calculation of the neutron transport in a reactor. It has been validated for the burn-up calculations. In the calculation of the fuel decay heat different set of isotopes is important than in the neutron transport case. Comparison with the Origen code is performed to verify that the Serpent is taking into account all isotopes important to assess the fuel decay heat. After the code validation, a sensitivity study is carried out. Influence of several factors such as enrichment, fuel temperature, moderator temperature (density), soluble boron concentration, average power, burnable absorbers, and burnup is analyzed.

Plasma Equilibria With Stochastic Magnetic Fields

NASA Astrophysics Data System (ADS)

Krommes, J. A.; Reiman, A. H.

2009-05-01

Plasma equilibria that include regions of stochastic magnetic fields are of interest in a variety of applications, including tokamaks with ergodic limiters and high-pressure stellarators. Such equilibria are examined theoretically, and a numerical algorithm for their construction is described.^2,3 % The balance between stochastic diffusion of magnetic lines and small effects^2 omitted from the simplest MHD description can support pressure and current profiles that need not be flattened in stochastic regions. The diffusion can be described analytically by renormalizing stochastic Langevin equations for pressure and parallel current j, with particular attention being paid to the satisfaction of the periodicity constraints in toroidal configurations with sheared magnetic fields. The equilibrium field configuration can then be constructed by coupling the prediction for j to Amp'ere's law, which is solved numerically. A. Reiman et al., Pressure-induced breaking of equilibrium flux surfaces in the W7AS stellarator, Nucl. Fusion 47, 572--8 (2007). J. A. Krommes and A. H. Reiman, Plasma equilibrium in a magnetic field with stochastic regions, submitted to Phys. Plasmas. J. A. Krommes, Fundamental statistical theories of plasma turbulence in magnetic fields, Phys. Reports 360, 1--351.

Stochastic evaluation of annual micropollutant loads and their uncertainties in separate storm sewers.

PubMed

Hannouche, Ali; Chebbo, Ghassan; Joannis, Claude; Gasperi, Johnny; Gromaire, Marie-Christine; Moilleron, Régis; Barraud, Sylvie; Ruban, Véronique

2017-12-01

This article describes a stochastic method to calculate the annual pollutant loads and its application over several years at the outlet of three catchments drained by separate storm sewers. A stochastic methodology using Monte Carlo simulations is proposed for assessing annual pollutant load, as well as the associated uncertainties, from a few event sampling campaigns and/or continuous turbidity measurements (representative of the total suspended solids concentration (TSS)). Indeed, in the latter case, the proposed method takes into account the correlation between pollutants and TSS. The developed method was applied to data acquired within the French research project "INOGEV" (innovations for a sustainable management of urban water) at the outlet of three urban catchments drained by separate storm sewers. Ten or so event sampling campaigns for a large range of pollutants (46 pollutants and 2 conventional water quality parameters: TSS and total organic carbon (TOC)) are combined with hundreds of rainfall events for which, at least one among three continuously monitored parameters (rainfall intensity, flow rate, and turbidity) is available. Results obtained for the three catchments show that the annual pollutant loads can be estimated with uncertainties ranging from 10 to 60%, and the added value of turbidity monitoring for lowering the uncertainty is demonstrated. A low inter-annual and inter-site variability of pollutant loads, for many of studied pollutants, is observed with respect to the estimated uncertainties, and can be explained mainly by annual precipitation.

Spatial vs. individual variability with inheritance in a stochastic Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Dobramysl, Ulrich; Tauber, Uwe C.

2012-02-01

We investigate a stochastic spatial Lotka-Volterra predator-prey model with randomized interaction rates that are either affixed to the lattice sites and quenched, and / or specific to individuals in either population. In the latter situation, we include rate inheritance with mutations from the particles' progenitors. Thus we arrive at a simple model for competitive evolution with environmental variability and selection pressure. We employ Monte Carlo simulations in zero and two dimensions to study the time evolution of both species' densities and their interaction rate distributions. The predator and prey concentrations in the ensuing steady states depend crucially on the environmental variability, whereas the temporal evolution of the individualized rate distributions leads to largely neutral optimization. Contrary to, e.g., linear gene expression models, this system does not experience fixation at extreme values. An approximate description of the resulting data is achieved by means of an effective master equation approach for the interaction rate distribution.

Stochastic gene expression in Arabidopsis thaliana.

PubMed

Araújo, Ilka Schultheiß; Pietsch, Jessica Magdalena; Keizer, Emma Mathilde; Greese, Bettina; Balkunde, Rachappa; Fleck, Christian; Hülskamp, Martin

2017-12-14

Although plant development is highly reproducible, some stochasticity exists. This developmental stochasticity may be caused by noisy gene expression. Here we analyze the fluctuation of protein expression in Arabidopsis thaliana. Using the photoconvertible KikGR marker, we show that the protein expressions of individual cells fluctuate over time. A dual reporter system was used to study extrinsic and intrinsic noise of marker gene expression. We report that extrinsic noise is higher than intrinsic noise and that extrinsic noise in stomata is clearly lower in comparison to several other tissues/cell types. Finally, we show that cells are coupled with respect to stochastic protein expression in young leaves, hypocotyls and roots but not in mature leaves. Our data indicate that stochasticity of gene expression can vary between tissues/cell types and that it can be coupled in a non-cell-autonomous manner.

Decentralized stochastic control

NASA Technical Reports Server (NTRS)

Speyer, J. L.

1980-01-01

Decentralized stochastic control is characterized by being decentralized in that the information to one controller is not the same as information to another controller. The system including the information has a stochastic or uncertain component. This complicates the development of decision rules which one determines under the assumption that the system is deterministic. The system is dynamic which means the present decisions affect future system responses and the information in the system. This circumstance presents a complex problem where tools like dynamic programming are no longer applicable. These difficulties are discussed from an intuitive viewpoint. Particular assumptions are introduced which allow a limited theory which produces mechanizable affine decision rules.

Stochastic modelling of microstructure formation in solidification processes

NASA Astrophysics Data System (ADS)

Nastac, Laurentiu; Stefanescu, Doru M.

1997-07-01

To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

Stochastic Community Assembly: Does It Matter in Microbial Ecology?

PubMed

Zhou, Jizhong; Ning, Daliang

2017-12-01

Understanding the mechanisms controlling community diversity, functions, succession, and biogeography is a central, but poorly understood, topic in ecology, particularly in microbial ecology. Although stochastic processes are believed to play nonnegligible roles in shaping community structure, their importance relative to deterministic processes is hotly debated. The importance of ecological stochasticity in shaping microbial community structure is far less appreciated. Some of the main reasons for such heavy debates are the difficulty in defining stochasticity and the diverse methods used for delineating stochasticity. Here, we provide a critical review and synthesis of data from the most recent studies on stochastic community assembly in microbial ecology. We then describe both stochastic and deterministic components embedded in various ecological processes, including selection, dispersal, diversification, and drift. We also describe different approaches for inferring stochasticity from observational diversity patterns and highlight experimental approaches for delineating ecological stochasticity in microbial communities. In addition, we highlight research challenges, gaps, and future directions for microbial community assembly research. Copyright © 2017 American Society for Microbiology.

A guide to differences between stochastic point-source and stochastic finite-fault simulations

USGS Publications Warehouse

Atkinson, G.M.; Assatourians, K.; Boore, D.M.; Campbell, K.; Motazedian, D.

2009-01-01

Why do stochastic point-source and finite-fault simulation models not agree on the predicted ground motions for moderate earthquakes at large distances? This question was posed by Ken Campbell, who attempted to reproduce the Atkinson and Boore (2006) ground-motion prediction equations for eastern North America using the stochastic point-source program SMSIM (Boore, 2005) in place of the finite-source stochastic program EXSIM (Motazedian and Atkinson, 2005) that was used by Atkinson and Boore (2006) in their model. His comparisons suggested that a higher stress drop is needed in the context of SMSIM to produce an average match, at larger distances, with the model predictions of Atkinson and Boore (2006) based on EXSIM; this is so even for moderate magnitudes, which should be well-represented by a point-source model. Why? The answer to this question is rooted in significant differences between point-source and finite-source stochastic simulation methodologies, specifically as implemented in SMSIM (Boore, 2005) and EXSIM (Motazedian and Atkinson, 2005) to date. Point-source and finite-fault methodologies differ in general in several important ways: (1) the geometry of the source; (2) the definition and application of duration; and (3) the normalization of finite-source subsource summations. Furthermore, the specific implementation of the methods may differ in their details. The purpose of this article is to provide a brief overview of these differences, their origins, and implications. This sets the stage for a more detailed companion article, "Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM," in which Boore (2009) provides modifications and improvements in the implementations of both programs that narrow the gap and result in closer agreement. These issues are important because both SMSIM and EXSIM have been widely used in the development of ground-motion prediction equations and in modeling the parameters that control

Monte Carlo characterization of PWR spent fuel assemblies to determine the detectability of pin diversion

NASA Astrophysics Data System (ADS)

Burdo, James S.

This research is based on the concept that the diversion of nuclear fuel pins from Light Water Reactor (LWR) spent fuel assemblies is feasible by a careful comparison of spontaneous fission neutron and gamma levels in the guide tube locations of the fuel assemblies. The goal is to be able to determine whether some of the assembly fuel pins are either missing or have been replaced with dummy or fresh fuel pins. It is known that for typical commercial power spent fuel assemblies, the dominant spontaneous neutron emissions come from Cm-242 and Cm-244. Because of the shorter half-life of Cm-242 (0.45 yr) relative to that of Cm-244 (18.1 yr), Cm-244 is practically the only neutron source contributing to the neutron source term after the spent fuel assemblies are more than two years old. Initially, this research focused upon developing MCNP5 models of PWR fuel assemblies, modeling their depletion using the MONTEBURNS code, and by carrying out a preliminary depletion of a ¼ model 17x17 assembly from the TAKAHAMA-3 PWR. Later, the depletion and more accurate isotopic distribution in the pins at discharge was modeled using the TRITON depletion module of the SCALE computer code. Benchmarking comparisons were performed with the MONTEBURNS and TRITON results. Subsequently, the neutron flux in each of the guide tubes of the TAKAHAMA-3 PWR assembly at two years after discharge as calculated by the MCNP5 computer code was determined for various scenarios. Cases were considered for all spent fuel pins present and for replacement of a single pin at a position near the center of the assembly (10,9) and at the corner (17,1). Some scenarios were duplicated with a gamma flux calculation for high energies associated with Cm-244. For each case, the difference between the flux (neutron or gamma) for all spent fuel pins and with a pin removed or replaced is calculated for each guide tube. Different detection criteria were established. The first was whether the relative error of the

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

Feynman-Kac formula for stochastic hybrid systems.

PubMed

Bressloff, Paul C

2017-01-01

We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the continuous process. We then analyze the stochastic Liouville equation using methods recently developed for diffusion processes in randomly switching environments. In particular, we obtain dynamical equations for the moment generating function, averaged with respect to realizations of the discrete Markov process. The resulting Feynman-Kac formula takes the form of a differential Chapman-Kolmogorov equation. We illustrate the theory by calculating the occupation time for a one-dimensional velocity jump process on the infinite or semi-infinite real line. Finally, we present an alternative derivation of the Feynman-Kac formula based on a recent path-integral formulation of stochastic hybrid systems.

Stochastic goal-oriented error estimation with memory

NASA Astrophysics Data System (ADS)

Ackmann, Jan; Marotzke, Jochem; Korn, Peter

2017-11-01

We propose a stochastic dual-weighted error estimator for the viscous shallow-water equation with boundaries. For this purpose, previous work on memory-less stochastic dual-weighted error estimation is extended by incorporating memory effects. The memory is introduced by describing the local truncation error as a sum of time-correlated random variables. The random variables itself represent the temporal fluctuations in local truncation errors and are estimated from high-resolution information at near-initial times. The resulting error estimator is evaluated experimentally in two classical ocean-type experiments, the Munk gyre and the flow around an island. In these experiments, the stochastic process is adapted locally to the respective dynamical flow regime. Our stochastic dual-weighted error estimator is shown to provide meaningful error bounds for a range of physically relevant goals. We prove, as well as show numerically, that our approach can be interpreted as a linearized stochastic-physics ensemble.

Stochastic gain in finite populations

NASA Astrophysics Data System (ADS)

Röhl, Torsten; Traulsen, Arne; Claussen, Jens Christian; Schuster, Heinz Georg

2008-08-01

Flexible learning rates can lead to increased payoffs under the influence of noise. In a previous paper [Traulsen , Phys. Rev. Lett. 93, 028701 (2004)], we have demonstrated this effect based on a replicator dynamics model which is subject to external noise. Here, we utilize recent advances on finite population dynamics and their connection to the replicator equation to extend our findings and demonstrate the stochastic gain effect in finite population systems. Finite population dynamics is inherently stochastic, depending on the population size and the intensity of selection, which measures the balance between the deterministic and the stochastic parts of the dynamics. This internal noise can be exploited by a population using an appropriate microscopic update process, even if learning rates are constant.

Stochastic resonance in micro/nano cantilever sensors

NASA Astrophysics Data System (ADS)

Singh, Priyanka; Yadava, R. D. S.

2018-05-01

In this paper we present a comparative study on the stochastic resonance in micro/nano cantilever resonators due to fluctuations in the fundamental frequency or the damping coefficient. Considering DC+AC electrostatic actuation in the presence of zero-mean Gaussian noise with exponential autocorrelation we analyze stochastic resonance behaviors for the frequency and the damping fluctuations separately, and compare the effects of stochastic resonance on Q-factor of the resonators for different levels of damping losses. It is found that even though the stochastic resonance occurs for both types of fluctuations, only the damping fluctuation produces right cooperative influence on the fundamental resonance that improves both the amplitude response and the quality factor of the resonator.

Memristor-based neural networks: Synaptic versus neuronal stochasticity

NASA Astrophysics Data System (ADS)

Naous, Rawan; AlShedivat, Maruan; Neftci, Emre; Cauwenberghs, Gert; Salama, Khaled Nabil

2016-11-01

In neuromorphic circuits, stochasticity in the cortex can be mapped into the synaptic or neuronal components. The hardware emulation of these stochastic neural networks are currently being extensively studied using resistive memories or memristors. The ionic process involved in the underlying switching behavior of the memristive elements is considered as the main source of stochasticity of its operation. Building on its inherent variability, the memristor is incorporated into abstract models of stochastic neurons and synapses. Two approaches of stochastic neural networks are investigated. Aside from the size and area perspective, the impact on the system performance, in terms of accuracy, recognition rates, and learning, among these two approaches and where the memristor would fall into place are the main comparison points to be considered.

Towards Stochastic Optimization-Based Electric Vehicle Penetration in a Novel Archipelago Microgrid.

PubMed

Yang, Qingyu; An, Dou; Yu, Wei; Tan, Zhengan; Yang, Xinyu

2016-06-17

Due to the advantage of avoiding upstream disturbance and voltage fluctuation from a power transmission system, Islanded Micro-Grids (IMG) have attracted much attention. In this paper, we first propose a novel self-sufficient Cyber-Physical System (CPS) supported by Internet of Things (IoT) techniques, namely "archipelago micro-grid (MG)", which integrates the power grid and sensor networks to make the grid operation effective and is comprised of multiple MGs while disconnected with the utility grid. The Electric Vehicles (EVs) are used to replace a portion of Conventional Vehicles (CVs) to reduce CO 2 emission and operation cost. Nonetheless, the intermittent nature and uncertainty of Renewable Energy Sources (RESs) remain a challenging issue in managing energy resources in the system. To address these issues, we formalize the optimal EV penetration problem as a two-stage Stochastic Optimal Penetration (SOP) model, which aims to minimize the emission and operation cost in the system. Uncertainties coming from RESs (e.g., wind, solar, and load demand) are considered in the stochastic model and random parameters to represent those uncertainties are captured by the Monte Carlo-based method. To enable the reasonable deployment of EVs in each MGs, we develop two scheduling schemes, namely Unlimited Coordinated Scheme (UCS) and Limited Coordinated Scheme (LCS), respectively. An extensive simulation study based on a modified 9 bus system with three MGs has been carried out to show the effectiveness of our proposed schemes. The evaluation data indicates that our proposed strategy can reduce both the environmental pollution created by CO 2 emissions and operation costs in UCS and LCS.

Fuel-injector/air-swirl characterization

NASA Technical Reports Server (NTRS)

Mcvey, J. B.; Kennedy, J. B.; Bennett, J. C.

1985-01-01

The objectives of this program are to establish an experimental data base documenting the behavior of gas turbine engine fuel injector sprays as the spray interacts with the swirling gas flow existing in the combustor dome, and to conduct an assessment of the validity of current analytical techniques for predicting fuel spray behavior. Emphasis is placed on the acquisition of data using injector/swirler components which closely resemble components currently in use in advanced aircraft gas turbine engines, conducting tests under conditions that closely simulate or closely approximate those developed in actual combustors, and conducting a well-controlled experimental effort which will comprise using a combination of low-risk experiments and experiments requiring the use of state-of-the-art diagnostic instrumentation. Analysis of the data is to be conducted using an existing, TEACH-type code which employs a stochastic analysis of the motion of the dispersed phase in the turbulent continuum flow field.

Temporal acceleration of spatially distributed kinetic Monte Carlo simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chatterjee, Abhijit; Vlachos, Dionisios G.

The computational intensity of kinetic Monte Carlo (KMC) simulation is a major impediment in simulating large length and time scales. In recent work, an approximate method for KMC simulation of spatially uniform systems, termed the binomial {tau}-leap method, was introduced [A. Chatterjee, D.G. Vlachos, M.A. Katsoulakis, Binomial distribution based {tau}-leap accelerated stochastic simulation, J. Chem. Phys. 122 (2005) 024112], where molecular bundles instead of individual processes are executed over coarse-grained time increments. This temporal coarse-graining can lead to significant computational savings but its generalization to spatially lattice KMC simulation has not been realized yet. Here we extend the binomial {tau}-leapmore » method to lattice KMC simulations by combining it with spatially adaptive coarse-graining. Absolute stability and computational speed-up analyses for spatial systems along with simulations provide insights into the conditions where accuracy and substantial acceleration of the new spatio-temporal coarse-graining method are ensured. Model systems demonstrate that the r-time increment criterion of Chatterjee et al. obeys the absolute stability limit for values of r up to near 1.« less

Time-ordered product expansions for computational stochastic system biology.

PubMed

Mjolsness, Eric

2013-06-01

The time-ordered product framework of quantum field theory can also be used to understand salient phenomena in stochastic biochemical networks. It is used here to derive Gillespie's stochastic simulation algorithm (SSA) for chemical reaction networks; consequently, the SSA can be interpreted in terms of Feynman diagrams. It is also used here to derive other, more general simulation and parameter-learning algorithms including simulation algorithms for networks of stochastic reaction-like processes operating on parameterized objects, and also hybrid stochastic reaction/differential equation models in which systems of ordinary differential equations evolve the parameters of objects that can also undergo stochastic reactions. Thus, the time-ordered product expansion can be used systematically to derive simulation and parameter-fitting algorithms for stochastic systems.

Universality in stochastic exponential growth.

PubMed

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Universality in Stochastic Exponential Growth

NASA Astrophysics Data System (ADS)

Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.

2014-07-01

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Improving the Fitness of High-Dimensional Biomechanical Models via Data-Driven Stochastic Exploration

PubMed Central

Bustamante, Carlos D.; Valero-Cuevas, Francisco J.

2010-01-01

The field of complex biomechanical modeling has begun to rely on Monte Carlo techniques to investigate the effects of parameter variability and measurement uncertainty on model outputs, search for optimal parameter combinations, and define model limitations. However, advanced stochastic methods to perform data-driven explorations, such as Markov chain Monte Carlo (MCMC), become necessary as the number of model parameters increases. Here, we demonstrate the feasibility and, what to our knowledge is, the first use of an MCMC approach to improve the fitness of realistically large biomechanical models. We used a Metropolis–Hastings algorithm to search increasingly complex parameter landscapes (3, 8, 24, and 36 dimensions) to uncover underlying distributions of anatomical parameters of a “truth model” of the human thumb on the basis of simulated kinematic data (thumbnail location, orientation, and linear and angular velocities) polluted by zero-mean, uncorrelated multivariate Gaussian “measurement noise.” Driven by these data, ten Markov chains searched each model parameter space for the subspace that best fit the data (posterior distribution). As expected, the convergence time increased, more local minima were found, and marginal distributions broadened as the parameter space complexity increased. In the 36-D scenario, some chains found local minima but the majority of chains converged to the true posterior distribution (confirmed using a cross-validation dataset), thus demonstrating the feasibility and utility of these methods for realistically large biomechanical problems. PMID:19272906

Stochasticity in materials structure, properties, and processing—A review

NASA Astrophysics Data System (ADS)

Hull, Robert; Keblinski, Pawel; Lewis, Dan; Maniatty, Antoinette; Meunier, Vincent; Oberai, Assad A.; Picu, Catalin R.; Samuel, Johnson; Shephard, Mark S.; Tomozawa, Minoru; Vashishth, Deepak; Zhang, Shengbai

2018-03-01

We review the concept of stochasticity—i.e., unpredictable or uncontrolled fluctuations in structure, chemistry, or kinetic processes—in materials. We first define six broad classes of stochasticity: equilibrium (thermodynamic) fluctuations; structural/compositional fluctuations; kinetic fluctuations; frustration and degeneracy; imprecision in measurements; and stochasticity in modeling and simulation. In this review, we focus on the first four classes that are inherent to materials phenomena. We next develop a mathematical framework for describing materials stochasticity and then show how it can be broadly applied to these four materials-related stochastic classes. In subsequent sections, we describe structural and compositional fluctuations at small length scales that modify material properties and behavior at larger length scales; systems with engineered fluctuations, concentrating primarily on composite materials; systems in which stochasticity is developed through nucleation and kinetic phenomena; and configurations in which constraints in a given system prevent it from attaining its ground state and cause it to attain several, equally likely (degenerate) states. We next describe how stochasticity in these processes results in variations in physical properties and how these variations are then accentuated by—or amplify—stochasticity in processing and manufacturing procedures. In summary, the origins of materials stochasticity, the degree to which it can be predicted and/or controlled, and the possibility of using stochastic descriptions of materials structure, properties, and processing as a new degree of freedom in materials design are described.

Multivariate moment closure techniques for stochastic kinetic models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporallymore » evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.« less

(U) Introduction to Monte Carlo Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hungerford, Aimee L.

2017-03-20

Monte Carlo methods are very valuable for representing solutions to particle transport problems. Here we describe a “cook book” approach to handling the terms in a transport equation using Monte Carlo methods. Focus is on the mechanics of a numerical Monte Carlo code, rather than the mathematical foundations of the method.

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

NASA Astrophysics Data System (ADS)

Urteaga, Iñigo; Bugallo, Mónica F.; Djurić, Petar M.

2017-12-01

We consider the problem of sequential inference of latent time-series with innovations correlated in time and observed via nonlinear functions. We accommodate time-varying phenomena with diverse properties by means of a flexible mathematical representation of the data. We characterize statistically such time-series by a Bayesian analysis of their densities. The density that describes the transition of the state from time t to the next time instant t+1 is used for implementation of novel sequential Monte Carlo (SMC) methods. We present a set of SMC methods for inference of latent ARMA time-series with innovations correlated in time for different assumptions in knowledge of parameters. The methods operate in a unified and consistent manner for data with diverse memory properties. We show the validity of the proposed approach by comprehensive simulations of the challenging stochastic volatility model.

Parallelization of KENO-Va Monte Carlo code

NASA Astrophysics Data System (ADS)

Ramón, Javier; Peña, Jorge

1995-07-01

KENO-Va is a code integrated within the SCALE system developed by Oak Ridge that solves the transport equation through the Monte Carlo Method. It is being used at the Consejo de Seguridad Nuclear (CSN) to perform criticality calculations for fuel storage pools and shipping casks. Two parallel versions of the code: one for shared memory machines and other for distributed memory systems using the message-passing interface PVM have been generated. In both versions the neutrons of each generation are tracked in parallel. In order to preserve the reproducibility of the results in both versions, advanced seeds for random numbers were used. The CONVEX C3440 with four processors and shared memory at CSN was used to implement the shared memory version. A FDDI network of 6 HP9000/735 was employed to implement the message-passing version using proprietary PVM. The speedup obtained was 3.6 in both cases.

A high-fidelity Monte Carlo evaluation of CANDU-6 safety parameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Y.; Hartanto, D.

2012-07-01

Important safety parameters such as the fuel temperature coefficient (FTC) and the power coefficient of reactivity (PCR) of the CANDU-6 (CANada Deuterium Uranium) reactor have been evaluated by using a modified MCNPX code. For accurate analysis of the parameters, the DBRC (Doppler Broadening Rejection Correction) scheme was implemented in MCNPX in order to account for the thermal motion of the heavy uranium nucleus in the neutron-U scattering reactions. In this work, a standard fuel lattice has been modeled and the fuel is depleted by using the MCNPX and the FTC value is evaluated for several burnup points including the mid-burnupmore » representing a near-equilibrium core. The Doppler effect has been evaluated by using several cross section libraries such as ENDF/B-VI, ENDF/B-VII, JEFF, JENDLE. The PCR value is also evaluated at mid-burnup conditions to characterize safety features of equilibrium CANDU-6 reactor. To improve the reliability of the Monte Carlo calculations, huge number of neutron histories are considered in this work and the standard deviation of the k-inf values is only 0.5{approx}1 pcm. It has been found that the FTC is significantly enhanced by accounting for the Doppler broadening of scattering resonance and the PCR are clearly improved. (authors)« less

Quantum Gibbs ensemble Monte Carlo

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fantoni, Riccardo, E-mail: rfantoni@ts.infn.it; Moroni, Saverio, E-mail: moroni@democritos.it

We present a path integral Monte Carlo method which is the full quantum analogue of the Gibbs ensemble Monte Carlo method of Panagiotopoulos to study the gas-liquid coexistence line of a classical fluid. Unlike previous extensions of Gibbs ensemble Monte Carlo to include quantum effects, our scheme is viable even for systems with strong quantum delocalization in the degenerate regime of temperature. This is demonstrated by an illustrative application to the gas-superfluid transition of {sup 4}He in two dimensions.

Comparison of UWCC MOX fuel measurements to MCNP-REN calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abhold, M.; Baker, M.; Jie, R.

1998-12-31

The development of neutron coincidence counting has greatly improved the accuracy and versatility of neutron-based techniques to assay fissile materials. Today, the shift register analyzer connected to either a passive or active neutron detector is widely used by both domestic and international safeguards organizations. The continued development of these techniques and detectors makes extensive use of the predictions of detector response through the use of Monte Carlo techniques in conjunction with the point reactor model. Unfortunately, the point reactor model, as it is currently used, fails to accurately predict detector response in highly multiplying mediums such as mixed-oxide (MOX) lightmore » water reactor fuel assemblies. For this reason, efforts have been made to modify the currently used Monte Carlo codes and to develop new analytical methods so that this model is not required to predict detector response. The authors describe their efforts to modify a widely used Monte Carlo code for this purpose and also compare calculational results with experimental measurements.« less

Monte Carlo wave packet study of negative ion mediated vibrationally inelastic scattering of NO from the metal surface

NASA Astrophysics Data System (ADS)

Li, Shenmin; Guo, Hua

2002-09-01

The scattering dynamics of vibrationally excited NO from a metal surface is investigated theoretically using a dissipative model that includes both the neutral and negative ion states. The Liouville-von Neumann equation is solved numerically by a Monte Carlo wave packet method, in which the wave packet is allowed to "jump" between the neutral and negative ion states in a stochastic fashion. It is shown that the temporary population of the negative ion state results in significant changes in vibrational dynamics, which eventually lead to vibrationally inelastic scattering of NO. Reasonable agreement with experiment is obtained with empirical potential energy surfaces. In particular, the experimentally observed facile multiquantum relaxation of the vibrationally highly excited NO is reproduced. The simulation also provides interesting insight into the scattering dynamics.

Monte-Carlo Orbit/Full Wave Simulation of Fast Alfvén Wave (FW) Damping on Resonant Ions in Tokamaks

NASA Astrophysics Data System (ADS)

Choi, M.; Chan, V. S.; Tang, V.; Bonoli, P.; Pinsker, R. I.; Wright, J.

2005-09-01

To simulate the resonant interaction of fast Alfvén wave (FW) heating and Coulomb collisions on energetic ions, including finite orbit effects, a Monte-Carlo code ORBIT-RF has been coupled with a 2D full wave code TORIC4. ORBIT-RF solves Hamiltonian guiding center drift equations to follow trajectories of test ions in 2D axisymmetric numerical magnetic equilibrium under Coulomb collisions and ion cyclotron radio frequency quasi-linear heating. Monte-Carlo operators for pitch-angle scattering and drag calculate the changes of test ions in velocity and pitch angle due to Coulomb collisions. A rf-induced random walk model describing fast ion stochastic interaction with FW reproduces quasi-linear diffusion in velocity space. FW fields and its wave numbers from TORIC are passed on to ORBIT-RF to calculate perpendicular rf kicks of resonant ions valid for arbitrary cyclotron harmonics. ORBIT-RF coupled with TORIC using a single dominant toroidal and poloidal wave number has demonstrated consistency of simulations with recent DIII-D FW experimental results for interaction between injected neutral-beam ions and FW, including measured neutron enhancement and enhanced high energy tail. Comparison with C-Mod fundamental heating discharges also yielded reasonable agreement.

Monte Carlo simulations for generic granite repository studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chu, Shaoping; Lee, Joon H; Wang, Yifeng

In a collaborative study between Los Alamos National Laboratory (LANL) and Sandia National Laboratories (SNL) for the DOE-NE Office of Fuel Cycle Technologies Used Fuel Disposition (UFD) Campaign project, we have conducted preliminary system-level analyses to support the development of a long-term strategy for geologic disposal of high-level radioactive waste. A general modeling framework consisting of a near- and a far-field submodel for a granite GDSE was developed. A representative far-field transport model for a generic granite repository was merged with an integrated systems (GoldSim) near-field model. Integrated Monte Carlo model runs with the combined near- and farfield transport modelsmore » were performed, and the parameter sensitivities were evaluated for the combined system. In addition, a sub-set of radionuclides that are potentially important to repository performance were identified and evaluated for a series of model runs. The analyses were conducted with different waste inventory scenarios. Analyses were also conducted for different repository radionuelide release scenarios. While the results to date are for a generic granite repository, the work establishes the method to be used in the future to provide guidance on the development of strategy for long-term disposal of high-level radioactive waste in a granite repository.« less

AREVA Developments for an Efficient and Reliable use of Monte Carlo codes for Radiation Transport Applications

NASA Astrophysics Data System (ADS)

Chapoutier, Nicolas; Mollier, François; Nolin, Guillaume; Culioli, Matthieu; Mace, Jean-Reynald

2017-09-01

In the context of the rising of Monte Carlo transport calculations for any kind of application, AREVA recently improved its suite of engineering tools in order to produce efficient Monte Carlo workflow. Monte Carlo codes, such as MCNP or TRIPOLI, are recognized as reference codes to deal with a large range of radiation transport problems. However the inherent drawbacks of theses codes - laboring input file creation and long computation time - contrast with the maturity of the treatment of the physical phenomena. The goals of the recent AREVA developments were to reach similar efficiency as other mature engineering sciences such as finite elements analyses (e.g. structural or fluid dynamics). Among the main objectives, the creation of a graphical user interface offering CAD tools for geometry creation and other graphical features dedicated to the radiation field (source definition, tally definition) has been reached. The computations times are drastically reduced compared to few years ago thanks to the use of massive parallel runs, and above all, the implementation of hybrid variance reduction technics. From now engineering teams are capable to deliver much more prompt support to any nuclear projects dealing with reactors or fuel cycle facilities from conceptual phase to decommissioning.

Stochastic Modeling of Laminar-Turbulent Transition

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Choudhari, Meelan

2002-01-01

Stochastic versions of stability equations are developed in order to develop integrated models of transition and turbulence and to understand the effects of uncertain initial conditions on disturbance growth. Stochastic forms of the resonant triad equations, a high Reynolds number asymptotic theory, and the parabolized stability equations are developed.

Spreaders and Sponges define metastasis in lung cancer: A Markov chain Monte Carlo Mathematical Model

PubMed Central

Newton, Paul K.; Mason, Jeremy; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Norton, Larry; Kuhn, Peter

2013-01-01

The classic view of metastatic cancer progression is that it is a unidirectional process initiated at the primary tumor site, progressing to variably distant metastatic sites in a fairly predictable, though not perfectly understood, fashion. A Markov chain Monte Carlo mathematical approach can determine a pathway diagram that classifies metastatic tumors as ‘spreaders’ or ‘sponges’ and orders the timescales of progression from site to site. In light of recent experimental evidence highlighting the potential significance of self-seeding of primary tumors, we use a Markov chain Monte Carlo (MCMC) approach, based on large autopsy data sets, to quantify the stochastic, systemic, and often multi-directional aspects of cancer progression. We quantify three types of multi-directional mechanisms of progression: (i) self-seeding of the primary tumor; (ii) re-seeding of the primary tumor from a metastatic site (primary re-seeding); and (iii) re-seeding of metastatic tumors (metastasis re-seeding). The model shows that the combined characteristics of the primary and the first metastatic site to which it spreads largely determine the future pathways and timescales of systemic disease. For lung cancer, the main ‘spreaders’ of systemic disease are the adrenal gland and kidney, whereas the main ‘sponges’ are regional lymph nodes, liver, and bone. Lung is a significant self-seeder, although it is a ‘sponge’ site with respect to progression characteristics. PMID:23447576

Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution - Part 2: numerical application

NASA Astrophysics Data System (ADS)

Dib, Alain; Kavvas, M. Levent

2018-03-01

The characteristic form of the Saint-Venant equations is solved in a stochastic setting by using a newly proposed Fokker-Planck Equation (FPE) methodology. This methodology computes the ensemble behavior and variability of the unsteady flow in open channels by directly solving for the flow variables' time-space evolutionary probability distribution. The new methodology is tested on a stochastic unsteady open-channel flow problem, with an uncertainty arising from the channel's roughness coefficient. The computed statistical descriptions of the flow variables are compared to the results obtained through Monte Carlo (MC) simulations in order to evaluate the performance of the FPE methodology. The comparisons show that the proposed methodology can adequately predict the results of the considered stochastic flow problem, including the ensemble averages, variances, and probability density functions in time and space. Unlike the large number of simulations performed by the MC approach, only one simulation is required by the FPE methodology. Moreover, the total computational time of the FPE methodology is smaller than that of the MC approach, which could prove to be a particularly crucial advantage in systems with a large number of uncertain parameters. As such, the results obtained in this study indicate that the proposed FPE methodology is a powerful and time-efficient approach for predicting the ensemble average and variance behavior, in both space and time, for an open-channel flow process under an uncertain roughness coefficient.

A Stochastic Polygons Model for Glandular Structures in Colon Histology Images.

PubMed

Sirinukunwattana, Korsuk; Snead, David R J; Rajpoot, Nasir M

2015-11-01

In this paper, we present a stochastic model for glandular structures in histology images of tissue slides stained with Hematoxylin and Eosin, choosing colon tissue as an example. The proposed Random Polygons Model (RPM) treats each glandular structure in an image as a polygon made of a random number of vertices, where the vertices represent approximate locations of epithelial nuclei. We formulate the RPM as a Bayesian inference problem by defining a prior for spatial connectivity and arrangement of neighboring epithelial nuclei and a likelihood for the presence of a glandular structure. The inference is made via a Reversible-Jump Markov chain Monte Carlo simulation. To the best of our knowledge, all existing published algorithms for gland segmentation are designed to mainly work on healthy samples, adenomas, and low grade adenocarcinomas. One of them has been demonstrated to work on intermediate grade adenocarcinomas at its best. Our experimental results show that the RPM yields favorable results, both quantitatively and qualitatively, for extraction of glandular structures in histology images of normal human colon tissues as well as benign and cancerous tissues, excluding undifferentiated carcinomas.

Quantifying parameter uncertainty in stochastic models using the Box Cox transformation

NASA Astrophysics Data System (ADS)

Thyer, Mark; Kuczera, George; Wang, Q. J.

2002-08-01

The Box-Cox transformation is widely used to transform hydrological data to make it approximately Gaussian. Bayesian evaluation of parameter uncertainty in stochastic models using the Box-Cox transformation is hindered by the fact that there is no analytical solution for the posterior distribution. However, the Markov chain Monte Carlo method known as the Metropolis algorithm can be used to simulate the posterior distribution. This method properly accounts for the nonnegativity constraint implicit in the Box-Cox transformation. Nonetheless, a case study using the AR(1) model uncovered a practical problem with the implementation of the Metropolis algorithm. The use of a multivariate Gaussian jump distribution resulted in unacceptable convergence behaviour. This was rectified by developing suitable parameter transformations for the mean and variance of the AR(1) process to remove the strong nonlinear dependencies with the Box-Cox transformation parameter. Applying this methodology to the Sydney annual rainfall data and the Burdekin River annual runoff data illustrates the efficacy of these parameter transformations and demonstrate the value of quantifying parameter uncertainty.

Self-consistent Monte Carlo study of high-field carrier transport in graded heterostructures

NASA Astrophysics Data System (ADS)

Al-Omar, A.; Krusius, J. P.

1987-11-01

Hot-electron transport over graded heterostructures was investigated. A new formulation of the carrier transport, based on the effective mass theorem, a position-dependent Hamiltonian, scattering rates that included overlap integrals with correct symmetry, and ohmic contact models preserving the stochastic nature of carrier injection, was developed and implemented into the self-consistent ensemble Monte Carlo method. Hot-carrier transport in a graded Al(x)Ga(1-x)As device was explored with the following results: (1) the transport across compositionally graded semiconductor structures cannot be described with drift and diffusion concepts; (2) although heterostructure launchers generate a ballistic electron fraction as high as 15 percent and 40 percent of the total electron population for 300 and 77 K, respectively, they simultaneously reduce macroscopic average currents and carrier velocities; and (3) the width of the ballistic electron distribution and the magnitude of the ballistic fraction are primarily determined by material parameters and operating voltages rather than details of the device structure.

Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks.

PubMed

Adalsteinsson, David; McMillen, David; Elston, Timothy C

2004-03-08

Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA) molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. We have developed the software package Biochemical Network Stochastic Simulator (BioNetS) for efficiently and accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous) for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solves the appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS. We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.

Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

NASA Astrophysics Data System (ADS)

Barthel, Thomas; De Bacco, Caterina; Franz, Silvio

2018-01-01

We introduce and apply an efficient method for the precise simulation of stochastic dynamical processes on locally treelike graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, our approach is based on a matrix product approximation of the so-called edge messages—conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both single instances as well as the thermodynamic limit. We employ it to examine prototypical nonequilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

Stochastic system identification in structural dynamics

USGS Publications Warehouse

Safak, Erdal

1988-01-01

Recently, new identification methods have been developed by using the concept of optimal-recursive filtering and stochastic approximation. These methods, known as stochastic identification, are based on the statistical properties of the signal and noise, and do not require the assumptions of current methods. The criterion for stochastic system identification is that the difference between the recorded output and the output from the identified system (i.e., the residual of the identification) should be equal to white noise. In this paper, first a brief review of the theory is given. Then, an application of the method is presented by using ambient vibration data from a nine-story building.

Coupled Monte Carlo neutronics and thermal hydraulics for power reactors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernnat, W.; Buck, M.; Mattes, M.

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 ormore » 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)« less

A stochastic SIS epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming

2017-11-01

In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s < 1, under some mild extra conditions, there exists a disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.

Perspective: Stochastic magnetic devices for cognitive computing

NASA Astrophysics Data System (ADS)

Roy, Kaushik; Sengupta, Abhronil; Shim, Yong

2018-06-01

Stochastic switching of nanomagnets can potentially enable probabilistic cognitive hardware consisting of noisy neural and synaptic components. Furthermore, computational paradigms inspired from the Ising computing model require stochasticity for achieving near-optimality in solutions to various types of combinatorial optimization problems such as the Graph Coloring Problem or the Travelling Salesman Problem. Achieving optimal solutions in such problems are computationally exhaustive and requires natural annealing to arrive at the near-optimal solutions. Stochastic switching of devices also finds use in applications involving Deep Belief Networks and Bayesian Inference. In this article, we provide a multi-disciplinary perspective across the stack of devices, circuits, and algorithms to illustrate how the stochastic switching dynamics of spintronic devices in the presence of thermal noise can provide a direct mapping to the computational units of such probabilistic intelligent systems.

An improved method to represent DEM uncertainty in glacial lake outburst flood propagation using stochastic simulations

NASA Astrophysics Data System (ADS)

Watson, Cameron S.; Carrivick, Jonathan; Quincey, Duncan

2015-10-01

Modelling glacial lake outburst floods (GLOFs) or 'jökulhlaups', necessarily involves the propagation of large and often stochastic uncertainties throughout the source to impact process chain. Since flood routing is primarily a function of underlying topography, communication of digital elevation model (DEM) uncertainty should accompany such modelling efforts. Here, a new stochastic first-pass assessment technique was evaluated against an existing GIS-based model and an existing 1D hydrodynamic model, using three DEMs with different spatial resolution. The analysis revealed the effect of DEM uncertainty and model choice on several flood parameters and on the prediction of socio-economic impacts. Our new model, which we call MC-LCP (Monte Carlo Least Cost Path) and which is distributed in the supplementary information, demonstrated enhanced 'stability' when compared to the two existing methods, and this 'stability' was independent of DEM choice. The MC-LCP model outputs an uncertainty continuum within its extent, from which relative socio-economic risk can be evaluated. In a comparison of all DEM and model combinations, the Shuttle Radar Topography Mission (SRTM) DEM exhibited fewer artefacts compared to those with the Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM), and were comparable to those with a finer resolution Advanced Land Observing Satellite Panchromatic Remote-sensing Instrument for Stereo Mapping (ALOS PRISM) derived DEM. Overall, we contend that the variability we find between flood routing model results suggests that consideration of DEM uncertainty and pre-processing methods is important when assessing flow routing and when evaluating potential socio-economic implications of a GLOF event. Incorporation of a stochastic variable provides an illustration of uncertainty that is important when modelling and communicating assessments of an inherently complex process.

Sampling errors for satellite-derived tropical rainfall - Monte Carlo study using a space-time stochastic model

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.

Memory effects on stochastic resonance

NASA Astrophysics Data System (ADS)

Neiman, Alexander; Sung, Wokyung

1996-02-01

We study the phenomenon of stochastic resonance (SR) in a bistable system with internal colored noise. In this situation the system possesses time-dependent memory friction connected with noise via the fluctuation-dissipation theorem, so that in the absence of periodic driving the system approaches the thermodynamic equilibrium state. For this non-Markovian case we find that memory usually suppresses stochastic resonance. However, for a large memory time SR can be enhanced by the memory.

Stochastic Processes in Physics: Deterministic Origins and Control

NASA Astrophysics Data System (ADS)

Demers, Jeffery

Stochastic processes are ubiquitous in the physical sciences and engineering. While often used to model imperfections and experimental uncertainties in the macroscopic world, stochastic processes can attain deeper physical significance when used to model the seemingly random and chaotic nature of the underlying microscopic world. Nowhere more prevalent is this notion than in the field of stochastic thermodynamics - a modern systematic framework used describe mesoscale systems in strongly fluctuating thermal environments which has revolutionized our understanding of, for example, molecular motors, DNA replication, far-from equilibrium systems, and the laws of macroscopic thermodynamics as they apply to the mesoscopic world. With progress, however, come further challenges and deeper questions, most notably in the thermodynamics of information processing and feedback control. Here it is becoming increasingly apparent that, due to divergences and subtleties of interpretation, the deterministic foundations of the stochastic processes themselves must be explored and understood. This thesis presents a survey of stochastic processes in physical systems, the deterministic origins of their emergence, and the subtleties associated with controlling them. First, we study time-dependent billiards in the quivering limit - a limit where a billiard system is indistinguishable from a stochastic system, and where the simplified stochastic system allows us to view issues associated with deterministic time-dependent billiards in a new light and address some long-standing problems. Then, we embark on an exploration of the deterministic microscopic Hamiltonian foundations of non-equilibrium thermodynamics, and we find that important results from mesoscopic stochastic thermodynamics have simple microscopic origins which would not be apparent without the benefit of both the micro and meso perspectives. Finally, we study the problem of stabilizing a stochastic Brownian particle with

Hybrid approaches for multiple-species stochastic reaction–diffusion models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spill, Fabian, E-mail: fspill@bu.edu; Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139; Guerrero, Pilar

2015-10-15

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and smallmore » in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.« less

The underwater coincidence counter (UWCC) for plutonium measurements in mixed oxide fuels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eccleston, G.W.; Menlove, H.O.; Abhold, M.

1998-12-31

The use of fresh uranium-plutonium mixed oxide (MOX) fuel in light-water reactors (LWR) is increasing in Europe and Japan and it is necessary to verify the plutonium content in the fuel for international safeguards purposes. The UWCC is a new instrument that has been designed to operate underwater and nondestructively measure the plutonium in unirradiated MOX fuel assemblies. The UWCC can be quickly configured to measure either boiling-water reactor (BWR) or pressurized-water reactor (PWR) fuel assemblies. The plutonium loading per unit length is measured using the UWCC to precisions of less than 1% in a measurement time of 2 tomore » 3 minutes. Initial calibrations of the UWCC were completed on measurements of MOX fuel in Mol, Belgium. The MCNP-REN Monte Carlo simulation code is being benchmarked to the calibration measurements to allow accurate simulations for extended calibrations of the UWCC.« less

Utilization of advanced calibration techniques in stochastic rock fall analysis of quarry slopes

NASA Astrophysics Data System (ADS)

Preh, Alexander; Ahmadabadi, Morteza; Kolenprat, Bernd

2016-04-01

In order to study rock fall dynamics, a research project was conducted by the Vienna University of Technology and the Austrian Central Labour Inspectorate (Federal Ministry of Labour, Social Affairs and Consumer Protection). A part of this project included 277 full-scale drop tests at three different quarries in Austria and recording key parameters of the rock fall trajectories. The tests involved a total of 277 boulders ranging from 0.18 to 1.8 m in diameter and from 0.009 to 8.1 Mg in mass. The geology of these sites included strong rock belonging to igneous, metamorphic and volcanic types. In this paper the results of the tests are used for calibration and validation a new stochastic computer model. It is demonstrated that the error of the model (i.e. the difference between observed and simulated results) has a lognormal distribution. Selecting two parameters, advanced calibration techniques including Markov Chain Monte Carlo Technique, Maximum Likelihood and Root Mean Square Error (RMSE) are utilized to minimize the error. Validation of the model based on the cross validation technique reveals that in general, reasonable stochastic approximations of the rock fall trajectories are obtained in all dimensions, including runout, bounce heights and velocities. The approximations are compared to the measured data in terms of median, 95% and maximum values. The results of the comparisons indicate that approximate first-order predictions, using a single set of input parameters, are possible and can be used to aid practical hazard and risk assessment.

Stochastic Simulation and Forecast of Hydrologic Time Series Based on Probabilistic Chaos Expansion

NASA Astrophysics Data System (ADS)

Li, Z.; Ghaith, M.

2017-12-01

Hydrological processes are characterized by many complex features, such as nonlinearity, dynamics and uncertainty. How to quantify and address such complexities and uncertainties has been a challenging task for water engineers and managers for decades. To support robust uncertainty analysis, an innovative approach for the stochastic simulation and forecast of hydrologic time series is developed is this study. Probabilistic Chaos Expansions (PCEs) are established through probabilistic collocation to tackle uncertainties associated with the parameters of traditional hydrological models. The uncertainties are quantified in model outputs as Hermite polynomials with regard to standard normal random variables. Sequentially, multivariate analysis techniques are used to analyze the complex nonlinear relationships between meteorological inputs (e.g., temperature, precipitation, evapotranspiration, etc.) and the coefficients of the Hermite polynomials. With the established relationships between model inputs and PCE coefficients, forecasts of hydrologic time series can be generated and the uncertainties in the future time series can be further tackled. The proposed approach is demonstrated using a case study in China and is compared to a traditional stochastic simulation technique, the Markov-Chain Monte-Carlo (MCMC) method. Results show that the proposed approach can serve as a reliable proxy to complicated hydrological models. It can provide probabilistic forecasting in a more computationally efficient manner, compared to the traditional MCMC method. This work provides technical support for addressing uncertainties associated with hydrological modeling and for enhancing the reliability of hydrological modeling results. Applications of the developed approach can be extended to many other complicated geophysical and environmental modeling systems to support the associated uncertainty quantification and risk analysis.

Artificial Neural Network Metamodels of Stochastic Computer Simulations

DTIC Science & Technology

1994-08-10

SUBTITLE r 5. FUNDING NUMBERS Artificial Neural Network Metamodels of Stochastic I () Computer Simulations 6. AUTHOR(S) AD- A285 951 Robert Allen...8217!298*1C2 ARTIFICIAL NEURAL NETWORK METAMODELS OF STOCHASTIC COMPUTER SIMULATIONS by Robert Allen Kilmer B.S. in Education Mathematics, Indiana...dedicate this document to the memory of my father, William Ralph Kilmer. mi ABSTRACT Signature ARTIFICIAL NEURAL NETWORK METAMODELS OF STOCHASTIC

Doubly stochastic radial basis function methods

NASA Astrophysics Data System (ADS)

Yang, Fenglian; Yan, Liang; Ling, Leevan

2018-06-01

We propose a doubly stochastic radial basis function (DSRBF) method for function recoveries. Instead of a constant, we treat the RBF shape parameters as stochastic variables whose distribution were determined by a stochastic leave-one-out cross validation (LOOCV) estimation. A careful operation count is provided in order to determine the ranges of all the parameters in our methods. The overhead cost for setting up the proposed DSRBF method is O (n2) for function recovery problems with n basis. Numerical experiments confirm that the proposed method not only outperforms constant shape parameter formulation (in terms of accuracy with comparable computational cost) but also the optimal LOOCV formulation (in terms of both accuracy and computational cost).

Stochastic multi-scale models of competition within heterogeneous cellular populations: Simulation methods and mean-field analysis.

PubMed

Cruz, Roberto de la; Guerrero, Pilar; Spill, Fabian; Alarcón, Tomás

2016-10-21

We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated proliferation rate. Our formulation is based on an age-dependent stochastic process. Cells within the population are characterised by their age (i.e. time elapsed since they were born). The age-dependent (oxygen-regulated) birth rate is given by a stochastic model of oxygen-dependent cell cycle progression. Once the birth rate is determined, we formulate an age-dependent birth-and-death process, which dictates the time evolution of the cell population. The population is under a feedback loop which controls its steady state size (carrying capacity): cells consume oxygen which in turn fuels cell proliferation. We show that our stochastic model of cell cycle progression allows for heterogeneity within the cell population induced by stochastic effects. Such heterogeneous behaviour is reflected in variations in the proliferation rate. Within this set-up, we have established three main results. First, we have shown that the age to the G1/S transition, which essentially determines the birth rate, exhibits a remarkably simple scaling behaviour. Besides the fact that this simple behaviour emerges from a rather complex model, this allows for a huge simplification of our numerical methodology. A further result is the observation that heterogeneous populations undergo an internal process of quasi-neutral competition. Finally, we investigated the effects of cell-cycle-phase dependent therapies (such as radiation therapy) on heterogeneous populations. In particular, we have studied the case in which the population contains a quiescent sub-population. Our mean-field analysis and numerical simulations confirm that, if the survival fraction of the therapy is too high, rescue of the quiescent population occurs. This gives rise to emergence of resistance

Stochasticity and determinism in models of hematopoiesis.

PubMed

Kimmel, Marek

2014-01-01

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

Sensitivity Analysis and Optimization of the Nuclear Fuel Cycle: A Systematic Approach

NASA Astrophysics Data System (ADS)

Passerini, Stefano

the robustness of the conclusions presented in the MIT Fuel Cycle Study. These conclusions are found to still hold, even when considering alternative technologies and different sets of simulation assumptions. Additionally, a first of a kind optimization scheme for the nuclear fuel cycle analysis is proposed and the applications of such an optimization are discussed. Optimization metrics of interest for different stakeholders in the fuel cycle (economics, fuel resource utilization, high level waste, transuranics/proliferation management, and environmental impact) are utilized for two different optimization techniques: a linear one and a stochastic one. Stakeholder elicitation provided sets of relative weights for the identified metrics appropriate to each stakeholder group, which were then successfully used to arrive at optimum fuel cycle configurations for recycling technologies. The stochastic optimization tool, based on a genetic algorithm, was used to identify non-inferior solutions according to Pareto's dominance approach to optimization. The main tradeoff for fuel cycle optimization was found to be between economics and most of the other identified metrics. (Copies available exclusively from MIT Libraries, libraries.mit.edu/docs - docs mit.edu)

Interrupted monitoring of a stochastic process

NASA Technical Reports Server (NTRS)

Palmer, E.

1977-01-01

Normative strategies are developed for tasks where the pilot must interrupt his monitoring of a stochastic process in order to attend to other duties. Results are given as to how characteristics of the stochastic process and the other tasks affect the optimal strategies. The optimum strategy is also compared to the strategies used by subjects in a pilot experiment.

MarkoLAB: A simulator to study ionic channel's stochastic behavior.

PubMed

da Silva, Robson Rodrigues; Goroso, Daniel Gustavo; Bers, Donald M; Puglisi, José Luis

2017-08-01

Mathematical models of the cardiac cell have started to include markovian representations of the ionic channels instead of the traditional Hodgkin & Huxley formulations. There are many reasons for this: Markov models are not restricted to the idea of independent gates defining the channel, they allow more complex description with specific transitions between open, closed or inactivated states, and more importantly those states can be closely related to the underlying channel structure and conformational changes. We used the LabVIEW ® and MATLAB ® programs to implement the simulator MarkoLAB that allow a dynamical 3D representation of the markovian model of the channel. The Monte Carlo simulation was used to implement the stochastic transitions among states. The user can specify the voltage protocol by setting the holding potential, the step-to voltage and the duration of the stimuli. The most studied feature of a channel is the current flowing through it. This happens when the channel stays in the open state, but most of the time, as revealed by the low open probability values, the channel remains on the inactive or closed states. By focusing only when the channel enters or leaves the open state we are missing most of its activity. MarkoLAB proved to be quite useful to visualize the whole behavior of the channel and not only when the channel produces a current. Such dynamic representation provides more complete information about channel kinetics and will be a powerful tool to demonstrate the effect of gene mutations or drugs on the channel function. MarkoLAB provides an original way of visualizing the stochastic behavior of a channel. It clarifies concepts, such as recovery from inactivation, calcium- versus voltage-dependent inactivation, and tail currents. It is not restricted to ionic channels only but it can be extended to other transporters, such as exchangers and pumps. This program is intended as a didactical tool to illustrate the dynamical behavior of a

Stochastic theory of fatigue corrosion

NASA Astrophysics Data System (ADS)

Hu, Haiyun

1999-10-01

A stochastic theory of corrosion has been constructed. The stochastic equations are described giving the transportation corrosion rate and fluctuation corrosion coefficient. In addition the pit diameter distribution function, the average pit diameter and the most probable pit diameter including other related empirical formula have been derived. In order to clarify the effect of stress range on the initiation and growth behaviour of pitting corrosion, round smooth specimen were tested under cyclic loading in 3.5% NaCl solution.

Stochastic Background from Coalescences of Neutron Star-Neutron Star Binaries

NASA Astrophysics Data System (ADS)

Regimbau, T.; de Freitas Pacheco, J. A.

2006-05-01

In this work, numerical simulations were used to investigate the gravitational stochastic background produced by coalescences of double neutron star systems occurring up to z~5. The cosmic coalescence rate was derived from Monte Carlo methods using the probability distributions for massive binaries to form and for a coalescence to occur in a given redshift. A truly continuous background is produced by events located only beyond the critical redshift z*=0.23. Events occurring in the redshift interval 0.027

Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model

NASA Astrophysics Data System (ADS)

Chen, Sheng; Täuber, Uwe C.

2016-04-01

We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population’s proximity to its extinction threshold.

Stochastic Swift-Hohenberg Equation with Degenerate Linear Multiplicative Noise

NASA Astrophysics Data System (ADS)

Hernández, Marco; Ong, Kiah Wah

2018-03-01

We study the dynamic transition of the Swift-Hohenberg equation (SHE) when linear multiplicative noise acting on a finite set of modes of the dominant linear flow is introduced. Existence of a stochastic flow and a local stochastic invariant manifold for this stochastic form of SHE are both addressed in this work. We show that the approximate reduced system corresponding to the invariant manifold undergoes a stochastic pitchfork bifurcation, and obtain numerical evidence suggesting that this picture is a good approximation for the full system as well.

Dynamical Epidemic Suppression Using Stochastic Prediction and Control

DTIC Science & Technology

2004-10-28

initial probability density function (PDF), p: D C R2 -- R, is defined by the stochastic Frobenius - Perron For deterministic systems, normal methods of...induced chaos. To analyze the qualitative change, we apply the technique of the stochastic Frobenius - Perron operator [L. Billings et al., Phys. Rev. Lett...transition matrix describing the probability of transport from one region of phase space to another, which approximates the stochastic Frobenius - Perron

Optimal Stochastic Modeling and Control of Flexible Structures

DTIC Science & Technology

1988-09-01

1.37] and McLane [1.18] considered multivariable systems and derived their optimal control characteristics. Kleinman, Gorman and Zaborsky considered...Leondes [1.72,1.73] studied various aspects of multivariable linear stochastic, discrete-time systems that are partly deterministic, and partly stochastic...June 1966. 1.8. A.V. Balaknishnan, Applied Functional Analaysis , 2nd ed., New York, N.Y.: Springer-Verlag, 1981 1.9. Peter S. Maybeck, Stochastic

Stochastic Analysis of the Efficiency of a Wireless Power Transfer System Subject to Antenna Variability and Position Uncertainties

PubMed Central

Rossi, Marco; Stockman, Gert-Jan; Rogier, Hendrik; Vande Ginste, Dries

2016-01-01

The efficiency of a wireless power transfer (WPT) system in the radiative near-field is inevitably affected by the variability in the design parameters of the deployed antennas and by uncertainties in their mutual position. Therefore, we propose a stochastic analysis that combines the generalized polynomial chaos (gPC) theory with an efficient model for the interaction between devices in the radiative near-field. This framework enables us to investigate the impact of random effects on the power transfer efficiency (PTE) of a WPT system. More specifically, the WPT system under study consists of a transmitting horn antenna and a receiving textile antenna operating in the Industrial, Scientific and Medical (ISM) band at 2.45 GHz. First, we model the impact of the textile antenna’s variability on the WPT system. Next, we include the position uncertainties of the antennas in the analysis in order to quantify the overall variations in the PTE. The analysis is carried out by means of polynomial-chaos-based macromodels, whereas a Monte Carlo simulation validates the complete technique. It is shown that the proposed approach is very accurate, more flexible and more efficient than a straightforward Monte Carlo analysis, with demonstrated speedup factors up to 2500. PMID:27447632

Stochastic Analysis of the Efficiency of a Wireless Power Transfer System Subject to Antenna Variability and Position Uncertainties.

PubMed

Rossi, Marco; Stockman, Gert-Jan; Rogier, Hendrik; Vande Ginste, Dries

2016-07-19

The efficiency of a wireless power transfer (WPT) system in the radiative near-field is inevitably affected by the variability in the design parameters of the deployed antennas and by uncertainties in their mutual position. Therefore, we propose a stochastic analysis that combines the generalized polynomial chaos (gPC) theory with an efficient model for the interaction between devices in the radiative near-field. This framework enables us to investigate the impact of random effects on the power transfer efficiency (PTE) of a WPT system. More specifically, the WPT system under study consists of a transmitting horn antenna and a receiving textile antenna operating in the Industrial, Scientific and Medical (ISM) band at 2.45 GHz. First, we model the impact of the textile antenna's variability on the WPT system. Next, we include the position uncertainties of the antennas in the analysis in order to quantify the overall variations in the PTE. The analysis is carried out by means of polynomial-chaos-based macromodels, whereas a Monte Carlo simulation validates the complete technique. It is shown that the proposed approach is very accurate, more flexible and more efficient than a straightforward Monte Carlo analysis, with demonstrated speedup factors up to 2500.

A Statistical Approach Reveals Designs for the Most Robust Stochastic Gene Oscillators

PubMed Central

2016-01-01

The engineering of transcriptional networks presents many challenges due to the inherent uncertainty in the system structure, changing cellular context, and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we examine the parametric robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. The central questions that we address are: Can we build genetic oscillators that are more robust than those already constructed? Can we make genetic oscillators arbitrarily robust? These questions are technically challenging due to the large model and parameter spaces that must be efficiently explored. Here we use a measure of robustness that coincides with the Bayesian model evidence, combined with an efficient Monte Carlo method to traverse model space and concentrate on regions of high robustness, which enables the accurate evaluation of the relative robustness of gene network models governed by stochastic dynamics. We report the most robust two and three gene oscillator systems, plus examine how the number of interactions, the presence of autoregulation, and degradation of mRNA and protein affects the frequency, amplitude, and robustness of transcriptional oscillators. We also find that there is a limit to parametric robustness, beyond which there is nothing to be gained by adding additional feedback. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modeling approaches to systems and synthetic biology. PMID:26835539

Towards Stochastic Optimization-Based Electric Vehicle Penetration in a Novel Archipelago Microgrid

PubMed Central

Yang, Qingyu; An, Dou; Yu, Wei; Tan, Zhengan; Yang, Xinyu

2016-01-01

Due to the advantage of avoiding upstream disturbance and voltage fluctuation from a power transmission system, Islanded Micro-Grids (IMG) have attracted much attention. In this paper, we first propose a novel self-sufficient Cyber-Physical System (CPS) supported by Internet of Things (IoT) techniques, namely “archipelago micro-grid (MG)”, which integrates the power grid and sensor networks to make the grid operation effective and is comprised of multiple MGs while disconnected with the utility grid. The Electric Vehicles (EVs) are used to replace a portion of Conventional Vehicles (CVs) to reduce CO2 emission and operation cost. Nonetheless, the intermittent nature and uncertainty of Renewable Energy Sources (RESs) remain a challenging issue in managing energy resources in the system. To address these issues, we formalize the optimal EV penetration problem as a two-stage Stochastic Optimal Penetration (SOP) model, which aims to minimize the emission and operation cost in the system. Uncertainties coming from RESs (e.g., wind, solar, and load demand) are considered in the stochastic model and random parameters to represent those uncertainties are captured by the Monte Carlo-based method. To enable the reasonable deployment of EVs in each MGs, we develop two scheduling schemes, namely Unlimited Coordinated Scheme (UCS) and Limited Coordinated Scheme (LCS), respectively. An extensive simulation study based on a modified 9 bus system with three MGs has been carried out to show the effectiveness of our proposed schemes. The evaluation data indicates that our proposed strategy can reduce both the environmental pollution created by CO2 emissions and operation costs in UCS and LCS. PMID:27322281

Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.

PubMed

Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong

2014-12-01

In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.

Stochastic models for inferring genetic regulation from microarray gene expression data.

PubMed

Tian, Tianhai

2010-03-01

Microarray expression profiles are inherently noisy and many different sources of variation exist in microarray experiments. It is still a significant challenge to develop stochastic models to realize noise in microarray expression profiles, which has profound influence on the reverse engineering of genetic regulation. Using the target genes of the tumour suppressor gene p53 as the test problem, we developed stochastic differential equation models and established the relationship between the noise strength of stochastic models and parameters of an error model for describing the distribution of the microarray measurements. Numerical results indicate that the simulated variance from stochastic models with a stochastic degradation process can be represented by a monomial in terms of the hybridization intensity and the order of the monomial depends on the type of stochastic process. The developed stochastic models with multiple stochastic processes generated simulations whose variance is consistent with the prediction of the error model. This work also established a general method to develop stochastic models from experimental information. 2009 Elsevier Ireland Ltd. All rights reserved.

Effect of randomness on multi-frequency aeroelastic responses resolved by Unsteady Adaptive Stochastic Finite Elements

NASA Astrophysics Data System (ADS)

Witteveen, Jeroen A. S.; Bijl, Hester

2009-10-01

The Unsteady Adaptive Stochastic Finite Elements (UASFE) method resolves the effect of randomness in numerical simulations of single-mode aeroelastic responses with a constant accuracy in time for a constant number of samples. In this paper, the UASFE framework is extended to multi-frequency responses and continuous structures by employing a wavelet decomposition pre-processing step to decompose the sampled multi-frequency signals into single-frequency components. The effect of the randomness on the multi-frequency response is then obtained by summing the results of the UASFE interpolation at constant phase for the different frequency components. Results for multi-frequency responses and continuous structures show a three orders of magnitude reduction of computational costs compared to crude Monte Carlo simulations in a harmonically forced oscillator, a flutter panel problem, and the three-dimensional transonic AGARD 445.6 wing aeroelastic benchmark subject to random fields and random parameters with various probability distributions.

Analysis of convergence of an evolutionary algorithm with self-adaptation using a stochastic Lyapunov function.

PubMed

Semenov, Mikhail A; Terkel, Dmitri A

2003-01-01

This paper analyses the convergence of evolutionary algorithms using a technique which is based on a stochastic Lyapunov function and developed within the martingale theory. This technique is used to investigate the convergence of a simple evolutionary algorithm with self-adaptation, which contains two types of parameters: fitness parameters, belonging to the domain of the objective function; and control parameters, responsible for the variation of fitness parameters. Although both parameters mutate randomly and independently, they converge to the "optimum" due to the direct (for fitness parameters) and indirect (for control parameters) selection. We show that the convergence velocity of the evolutionary algorithm with self-adaptation is asymptotically exponential, similar to the velocity of the optimal deterministic algorithm on the class of unimodal functions. Although some martingale inequalities have not be proved analytically, they have been numerically validated with 0.999 confidence using Monte-Carlo simulations.

Simulations of DSB Yields and Radiation-induced Chromosomal Aberrations in Human Cells Based on the Stochastic Track Structure Induced by HZE Particles

NASA Technical Reports Server (NTRS)

Ponomarev, Artem; Plante, Ianik; George, Kerry; Wu, Honglu

2014-01-01

The formation of double-strand breaks (DSBs) and chromosomal aberrations (CAs) is of great importance in radiation research and, specifically, in space applications. We are presenting a new particle track and DNA damage model, in which the particle stochastic track structure is combined with the random walk (RW) structure of chromosomes in a cell nucleus. The motivation for this effort stems from the fact that the model with the RW chromosomes, NASARTI (NASA radiation track image) previously relied on amorphous track structure, while the stochastic track structure model RITRACKS (Relativistic Ion Tracks) was focused on more microscopic targets than the entire genome. We have combined chromosomes simulated by RWs with stochastic track structure, which uses nanoscopic dose calculations performed with the Monte-Carlo simulation by RITRACKS in a voxelized space. The new simulations produce the number of DSBs as function of dose and particle fluence for high-energy particles, including iron, carbon and protons, using voxels of 20 nm dimension. The combined model also calculates yields of radiation-induced CAs and unrejoined chromosome breaks in normal and repair deficient cells. The joined computational model is calibrated using the relative frequencies and distributions of chromosomal aberrations reported in the literature. The model considers fractionated deposition of energy to approximate dose rates of the space flight environment. The joined model also predicts of the yields and sizes of translocations, dicentrics, rings, and more complex-type aberrations formed in the G0/G1 cell cycle phase during the first cell division after irradiation. We found that the main advantage of the joined model is our ability to simulate small doses: 0.05-0.5 Gy. At such low doses, the stochastic track structure proved to be indispensable, as the action of individual delta-rays becomes more important.

MASSCLEANCOLORS-MASS-DEPENDENT INTEGRATED COLORS FOR STELLAR CLUSTERS DERIVED FROM 30 MILLION MONTE CARLO SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Popescu, Bogdan; Hanson, M. M.

2010-04-10

We present Monte Carlo models of open stellar clusters with the purpose of mapping out the behavior of integrated colors with mass and age. Our cluster simulation package allows for stochastic variations in the stellar mass function to evaluate variations in integrated cluster properties. We find that UBVK colors from our simulations are consistent with simple stellar population (SSP) models, provided the cluster mass is large, M {sub cluster} {>=} 10{sup 6} M {sub sun}. Below this mass, our simulations show two significant effects. First, the mean value of the distribution of integrated colors moves away from the SSP predictionsmore » and is less red, in the first 10{sup 7} to 10{sup 8} years in UBV colors, and for all ages in (V - K). Second, the 1{sigma} dispersion of observed colors increases significantly with lower cluster mass. We attribute the former to the reduced number of red luminous stars in most of the lower mass clusters and the latter to the increased stochastic effect of a few of these stars on lower mass clusters. This latter point was always assumed to occur, but we now provide the first public code able to quantify this effect. We are completing a more extensive database of magnitudes and colors as a function of stellar cluster age and mass that will allow the determination of the correlation coefficients among different bands, and improve estimates of cluster age and mass from integrated photometry.« less

Monte Carlo Study Elucidates the Type 1/Type 2 Choice in Apoptotic Death Signaling in Healthy and Cancer Cells

PubMed Central

Raychaudhuri, Subhadip; Raychaudhuri, Somkanya C

2013-01-01

Apoptotic cell death is coordinated through two distinct (type 1 and type 2) intracellular signaling pathways. How the type 1/type 2 choice is made remains a central problem in the biology of apoptosis and has implications for apoptosis related diseases and therapy. We study the problem of type 1/type 2 choice in silico utilizing a kinetic Monte Carlo model of cell death signaling. Our results show that the type 1/type 2 choice is linked to deterministic versus stochastic cell death activation, elucidating a unique regulatory control of the apoptotic pathways. Consistent with previous findings, our results indicate that caspase 8 activation level is a key regulator of the choice between deterministic type 1 and stochastic type 2 pathways, irrespective of cell types. Expression levels of signaling molecules downstream also regulate the type 1/type 2 choice. A simplified model of DISC clustering elucidates the mechanism of increased active caspase 8 generation and type 1 activation in cancer cells having increased sensitivity to death receptor activation. We demonstrate that rapid deterministic activation of the type 1 pathway can selectively target such cancer cells, especially if XIAP is also inhibited; while inherent cell-to-cell variability would allow normal cells stay protected. PMID:24709706

Modeling stochasticity and robustness in gene regulatory networks.

PubMed

Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis

2009-06-15

Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

The relationship between stochastic and deterministic quasi-steady state approximations.

PubMed

Kim, Jae Kyoung; Josić, Krešimir; Bennett, Matthew R

2015-11-23

The quasi steady-state approximation (QSSA) is frequently used to reduce deterministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used to define reaction propensities. Despite their popularity, it remains unclear when such stochastic reductions are valid. It is frequently assumed that the stochastic reduction can be trusted whenever its deterministic counterpart is accurate. However, a number of recent examples show that this is not necessarily the case. Here we explain the origin of these discrepancies, and demonstrate a clear relationship between the accuracy of the deterministic and the stochastic QSSA for examples widely used in biological systems. With an analysis of a two-state promoter model, and numerical simulations for a variety of other models, we find that the stochastic QSSA is accurate whenever its deterministic counterpart provides an accurate approximation over a range of initial conditions which cover the likely fluctuations from the quasi steady-state (QSS). We conjecture that this relationship provides a simple and computationally inexpensive way to test the accuracy of reduced stochastic models using deterministic simulations. The stochastic QSSA is one of the most popular multi-scale stochastic simulation methods. While the use of QSSA, and the resulting non-elementary functions has been justified in the deterministic case, it is not clear when their stochastic counterparts are accurate. In this study, we show how the accuracy of the stochastic QSSA can be tested using their deterministic counterparts providing a concrete method to test when non-elementary rate functions can be used in stochastic simulations.

A Time-Variant Reliability Model for Copper Bending Pipe under Seawater-Active Corrosion Based on the Stochastic Degradation Process

PubMed Central

Li, Mengmeng; Feng, Qiang; Yang, Dezhen

2018-01-01

In the degradation process, the randomness and multiplicity of variables are difficult to describe by mathematical models. However, they are common in engineering and cannot be neglected, so it is necessary to study this issue in depth. In this paper, the copper bending pipe in seawater piping systems is taken as the analysis object, and the time-variant reliability is calculated by solving the interference of limit strength and maximum stress. We did degradation experiments and tensile experiments on copper material, and obtained the limit strength at each time. In addition, degradation experiments on copper bending pipe were done and the thickness at each time has been obtained, then the response of maximum stress was calculated by simulation. Further, with the help of one kind of Monte Carlo method we propose, the time-variant reliability of copper bending pipe was calculated based on the stochastic degradation process and interference theory. Compared with traditional methods and verified by maintenance records, the results show that the time-variant reliability model based on the stochastic degradation process proposed in this paper has better applicability in the reliability analysis, and it can be more convenient and accurate to predict the replacement cycle of copper bending pipe under seawater-active corrosion. PMID:29584695

Many-Versus-Many Stochastic Duels

DTIC Science & Technology

1984-01-14

MANY-VERSUS-MANY STOCHAS!’IC DUELS FINAL REPORT cO C. J, ANCKER, JR. 00 A. V. GAFARIAN JANUARY 14, 1985 U. S, ARMY RESEARCH OFFICE CONTRACT/DAAG29-81...Y) n- N/A 14. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED Final, 21 September 1981 MANY-VERSUS-MANY STOCHASTIC DUELS through 20 September...necessary and Identify by block number) -. Stochastic) Duels ) Many-Versus-Many) Bibliography, 2(L ABSTRACT (Centhoue so reverse sEsfl R necessay and

Girsanov's transformation based variance reduced Monte Carlo simulation schemes for reliability estimation in nonlinear stochastic dynamics

NASA Astrophysics Data System (ADS)

Kanjilal, Oindrila; Manohar, C. S.

2017-07-01

The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.

Efficient 3D kinetic Monte Carlo method for modeling of molecular structure and dynamics.

PubMed

Panshenskov, Mikhail; Solov'yov, Ilia A; Solov'yov, Andrey V

2014-06-30

Self-assembly of molecular systems is an important and general problem that intertwines physics, chemistry, biology, and material sciences. Through understanding of the physical principles of self-organization, it often becomes feasible to control the process and to obtain complex structures with tailored properties, for example, bacteria colonies of cells or nanodevices with desired properties. Theoretical studies and simulations provide an important tool for unraveling the principles of self-organization and, therefore, have recently gained an increasing interest. The present article features an extension of a popular code MBN EXPLORER (MesoBioNano Explorer) aiming to provide a universal approach to study self-assembly phenomena in biology and nanoscience. In particular, this extension involves a highly parallelized module of MBN EXPLORER that allows simulating stochastic processes using the kinetic Monte Carlo approach in a three-dimensional space. We describe the computational side of the developed code, discuss its efficiency, and apply it for studying an exemplary system. Copyright © 2014 Wiley Periodicals, Inc.

Hyperbolic Cross Truncations for Stochastic Fourier Cosine Series

PubMed Central

Zhang, Zhihua

2014-01-01

Based on our decomposition of stochastic processes and our asymptotic representations of Fourier cosine coefficients, we deduce an asymptotic formula of approximation errors of hyperbolic cross truncations for bivariate stochastic Fourier cosine series. Moreover we propose a kind of Fourier cosine expansions with polynomials factors such that the corresponding Fourier cosine coefficients decay very fast. Although our research is in the setting of stochastic processes, our results are also new for deterministic functions. PMID:25147842

The Effect of Stochastically Varying Creep Parameters on Residual Stresses in Ceramic Matrix Composites

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Mital, Subodh K.; Bednarcyk, Brett A.; Arnold, Steven M.

2015-01-01

Constituent properties, along with volume fraction, have a first order effect on the microscale fields within a composite material and influence the macroscopic response. Therefore, there is a need to assess the significance of stochastic variation in the constituent properties of composites at the higher scales. The effect of variability in the parameters controlling the time-dependent behavior, in a unidirectional SCS-6 SiC fiber-reinforced RBSN matrix composite lamina, on the residual stresses induced during processing is investigated numerically. The generalized method of cells micromechanics theory is utilized to model the ceramic matrix composite lamina using a repeating unit cell. The primary creep phases of the constituents are approximated using a Norton-Bailey, steady state, power law creep model. The effect of residual stresses on the proportional limit stress and strain to failure of the composite is demonstrated. Monte Carlo simulations were conducted using a normal distribution for the power law parameters and the resulting residual stress distributions were predicted.

Detection methods for non-Gaussian gravitational wave stochastic backgrounds

NASA Astrophysics Data System (ADS)

Drasco, Steve; Flanagan, Éanna É.

2003-04-01

A gravitational wave stochastic background can be produced by a collection of independent gravitational wave events. There are two classes of such backgrounds, one for which the ratio of the average time between events to the average duration of an event is small (i.e., many events are on at once), and one for which the ratio is large. In the first case the signal is continuous, sounds something like a constant hiss, and has a Gaussian probability distribution. In the second case, the discontinuous or intermittent signal sounds something like popcorn popping, and is described by a non-Gaussian probability distribution. In this paper we address the issue of finding an optimal detection method for such a non-Gaussian background. As a first step, we examine the idealized situation in which the event durations are short compared to the detector sampling time, so that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. For this situation we derive an appropriate version of the maximum likelihood detection statistic. We compare the performance of this statistic to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. In general the maximum likelihood statistic performs better than the cross-correlation statistic when the stochastic background is sufficiently non-Gaussian, resulting in a gain factor in the minimum gravitational-wave energy density necessary for detection. This gain factor ranges roughly between 1 and 3, depending on the duty cycle of the background, for realistic observing times and signal strengths for both ground and space based detectors. The computational cost of the statistic, although significantly greater than that of the cross-correlation statistic, is not unreasonable. Before the statistic can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems.

PubMed

Wolf, Elizabeth Skubak; Anderson, David F

2015-01-21

Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations of model output quantities with respect to model parameters, are useful in this setting for a variety of applications. In this paper, we introduce a class of hybrid pathwise differentiation methods for the numerical estimation of parametric sensitivities. The new hybrid methods combine elements from the three main classes of procedures for sensitivity estimation and have a number of desirable qualities. First, the new methods are unbiased for a broad class of problems. Second, the methods are applicable to nearly any physically relevant biochemical CTMC model. Third, and as we demonstrate on several numerical examples, the new methods are quite efficient, particularly if one wishes to estimate the full gradient of parametric sensitivities. The methods are rather intuitive and utilize the multilevel Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.

Hybrid pathwise sensitivity methods for discrete stochastic models of chemical reaction systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolf, Elizabeth Skubak, E-mail: ewolf@saintmarys.edu; Anderson, David F., E-mail: anderson@math.wisc.edu

2015-01-21

Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations of model output quantities with respect to model parameters, are useful in this setting for a variety of applications. In this paper, we introduce a class of hybrid pathwise differentiation methods for the numerical estimation of parametric sensitivities. The new hybrid methods combine elements from the three main classes of procedures for sensitivity estimation and have a number of desirable qualities. First, the new methods are unbiased formore » a broad class of problems. Second, the methods are applicable to nearly any physically relevant biochemical CTMC model. Third, and as we demonstrate on several numerical examples, the new methods are quite efficient, particularly if one wishes to estimate the full gradient of parametric sensitivities. The methods are rather intuitive and utilize the multilevel Monte Carlo philosophy of splitting an expectation into separate parts and handling each in an efficient manner.« less

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…

Stochastic receding horizon control: application to an octopedal robot

NASA Astrophysics Data System (ADS)

Shah, Shridhar K.; Tanner, Herbert G.

2013-06-01

Miniature autonomous systems are being developed under ARL's Micro Autonomous Systems and Technology (MAST). These systems can only be fitted with a small-size processor, and their motion behavior is inherently uncertain due to manufacturing and platform-ground interactions. One way to capture this uncertainty is through a stochastic model. This paper deals with stochastic motion control design and implementation for MAST- specific eight-legged miniature crawling robots, which have been kinematically modeled as systems exhibiting the behavior of a Dubin's car with stochastic noise. The control design takes the form of stochastic receding horizon control, and is implemented on a Gumstix Overo Fire COM with 720 MHz processor and 512 MB RAM, weighing 5.5 g. The experimental results show the effectiveness of this control law for miniature autonomous systems perturbed by stochastic noise.

Stochastic Stabilityfor Contracting Lorenz Maps and Flows

NASA Astrophysics Data System (ADS)

Metzger, R. J.

In a previous work [M], we proved the existence of absolutely continuous invariant measures for contracting Lorenz-like maps, and constructed Sinai-Ruelle-Bowen measures f or the flows that generate them. Here, we prove stochastic stability for such one-dimensional maps and use this result to prove that the corresponding flows generating these maps are stochastically stable under small diffusion-type perturbations, even though, as shown by Rovella [Ro], they are persistent only in a measure theoretical sense in a parameter space. For the one-dimensional maps we also prove strong stochastic stability in the sense of Baladi and Viana[BV].

Environmental Stochasticity and the Speed of Evolution

NASA Astrophysics Data System (ADS)

Danino, Matan; Kessler, David A.; Shnerb, Nadav M.

2018-03-01

Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. The rate in which the average fitness of a community increases has been considered so far using models with pure demographic stochasticity; here we present some theoretical considerations and numerical results for the general case where environmental variations are taken into account. When the competition is pairwise, fitness fluctuations are shown to reduce the speed of evolution, while under global competition the speed increases due to environmental stochasticity.

Environmental Stochasticity and the Speed of Evolution

NASA Astrophysics Data System (ADS)

Danino, Matan; Kessler, David A.; Shnerb, Nadav M.

2018-07-01

Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. The rate in which the average fitness of a community increases has been considered so far using models with pure demographic stochasticity; here we present some theoretical considerations and numerical results for the general case where environmental variations are taken into account. When the competition is pairwise, fitness fluctuations are shown to reduce the speed of evolution, while under global competition the speed increases due to environmental stochasticity.

Mechanical Autonomous Stochastic Heat Engine

NASA Astrophysics Data System (ADS)

Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara

2016-07-01

Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.

Mechanical Autonomous Stochastic Heat Engine.

PubMed

Serra-Garcia, Marc; Foehr, André; Molerón, Miguel; Lydon, Joseph; Chong, Christopher; Daraio, Chiara

2016-07-01

Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.

Stochastic determination of matrix determinants

NASA Astrophysics Data System (ADS)

Dorn, Sebastian; Enßlin, Torsten A.

2015-07-01

Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations—matrices—acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Intrinsic optimization using stochastic nanomagnets

PubMed Central

Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo

2017-01-01

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets. PMID:28295053

Intrinsic optimization using stochastic nanomagnets

NASA Astrophysics Data System (ADS)

Sutton, Brian; Camsari, Kerem Yunus; Behin-Aein, Behtash; Datta, Supriyo

2017-03-01

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the ±1 Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets.

Stochastic determination of matrix determinants.

PubMed

Dorn, Sebastian; Ensslin, Torsten A

2015-07-01

Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations-matrices-acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.

Directed Abelian algebras and their application to stochastic models.

PubMed

Alcaraz, F C; Rittenberg, V

2008-10-01

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma_(tau)=32 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma_(tau)=1.780+/-0.005 .

Fast stochastic algorithm for simulating evolutionary population dynamics

NASA Astrophysics Data System (ADS)

Tsimring, Lev; Hasty, Jeff; Mather, William

2012-02-01

Evolution and co-evolution of ecological communities are stochastic processes often characterized by vastly different rates of reproduction and mutation and a coexistence of very large and very small sub-populations of co-evolving species. This creates serious difficulties for accurate statistical modeling of evolutionary dynamics. In this talk, we introduce a new exact algorithm for fast fully stochastic simulations of birth/death/mutation processes. It produces a significant speedup compared to the direct stochastic simulation algorithm in a typical case when the total population size is large and the mutation rates are much smaller than birth/death rates. We illustrate the performance of the algorithm on several representative examples: evolution on a smooth fitness landscape, NK model, and stochastic predator-prey system.

Tsunamis: stochastic models of occurrence and generation mechanisms

USGS Publications Warehouse

Geist, Eric L.; Oglesby, David D.

2014-01-01

The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.

Stochastic dynamic modeling of regular and slow earthquakes

NASA Astrophysics Data System (ADS)

Aso, N.; Ando, R.; Ide, S.

2017-12-01

Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal

Stochastic Multi-Timescale Power System Operations With Variable Wind Generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Hongyu; Krad, Ibrahim; Florita, Anthony

This paper describes a novel set of stochastic unit commitment and economic dispatch models that consider stochastic loads and variable generation at multiple operational timescales. The stochastic model includes four distinct stages: stochastic day-ahead security-constrained unit commitment (SCUC), stochastic real-time SCUC, stochastic real-time security-constrained economic dispatch (SCED), and deterministic automatic generation control (AGC). These sub-models are integrated together such that they are continually updated with decisions passed from one to another. The progressive hedging algorithm (PHA) is applied to solve the stochastic models to maintain the computational tractability of the proposed models. Comparative case studies with deterministic approaches are conductedmore » in low wind and high wind penetration scenarios to highlight the advantages of the proposed methodology, one with perfect forecasts and the other with current state-of-the-art but imperfect deterministic forecasts. The effectiveness of the proposed method is evaluated with sensitivity tests using both economic and reliability metrics to provide a broader view of its impact.« less

A stochastic method for computing hadronic matrix elements

DOE PAGES

Alexandrou, Constantia; Constantinou, Martha; Dinter, Simon; ...

2014-01-24

In this study, we present a stochastic method for the calculation of baryon 3-point functions which is an alternative to the typically used sequential method offering more versatility. We analyze the scaling of the error of the stochastically evaluated 3-point function with the lattice volume and find a favorable signal to noise ratio suggesting that the stochastic method can be extended to large volumes providing an efficient approach to compute hadronic matrix elements and form factors.

Evolutionary stability concepts in a stochastic environment

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2017-09-01

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sousedík, Bedřich, E-mail: sousedik@umbc.edu; Elman, Howard C., E-mail: elman@cs.umd.edu

2016-07-01

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Galerkin methods for the steady-state Navier–Stokes equations

DOE PAGES

Sousedík, Bedřich; Elman, Howard C.

2016-04-12

We study the steady-state Navier–Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For the resulting stochastic problem, we formulate the model and linearization schemes using Picard and Newton iterations in the framework of the stochastic Galerkin method, and we explore properties of the resulting stochastic solutions. We also propose a preconditioner for solving the linear systems of equations arising at each step of the stochastic (Galerkin) nonlinear iteration and demonstrate its effectiveness for solving a set of benchmarkmore » problems.« less

Stochastic Cell Fate Progression in Embryonic Stem Cells

NASA Astrophysics Data System (ADS)

Zou, Ling-Nan; Doyle, Adele; Jang, Sumin; Ramanathan, Sharad

2013-03-01

Studies on the directed differentiation of embryonic stem (ES) cells suggest that some early developmental decisions may be stochastic in nature. To identify the sources of this stochasticity, we analyzed the heterogeneous expression of key transcription factors in single ES cells as they adopt distinct germ layer fates. We find that under sufficiently stringent signaling conditions, the choice of lineage is unambiguous. ES cells flow into differentiated fates via diverging paths, defined by sequences of transitional states that exhibit characteristic co-expression of multiple transcription factors. These transitional states have distinct responses to morphogenic stimuli; by sequential exposure to multiple signaling conditions, ES cells are steered towards specific fates. However, the rate at which cells travel down a developmental path is stochastic: cells exposed to the same signaling condition for the same amount of time can populate different states along the same path. The heterogeneity of cell states seen in our experiments therefore does not reflect the stochastic selection of germ layer fates, but the stochastic rate of progression along a chosen developmental path. Supported in part by the Jane Coffin Childs Fund

Doubly stochastic Poisson processes in artificial neural learning.

PubMed

Card, H C

1998-01-01

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Entropic stochastic resonance of a self-propelled Janus particle

NASA Astrophysics Data System (ADS)

Liu, Zhenzhen; Du, Luchun; Guo, Wei; Mei, Dong-Cheng

2016-10-01

Entropic stochastic resonance is investigated when a self-propelled Janus particle moves in a double-cavity container. Numerical simulation results indicate the entropic stochastic resonance can survive even if there is no symmetry breaking in any direction. This is the essential distinction between the property of a self-propelled Janus particle and that of a passive Brownian particle, for the symmetry breaking is necessary for the entropic stochastic resonance of a passive Brownian particle. With the rotational noise intensity growing at small fixed noise intensity of translational motion, the signal power amplification increases monotonically towards saturation which also can be regarded as a kind of stochastic resonance effect. Besides, the increase in the natural frequency of the periodic driving depresses the degree of the stochastic resonance, whereas the rise in its amplitude enhances and then suppresses the behavior.

The effect of stochastic re-acceleration on the energy spectrum of shock-accelerated protons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Afanasiev, Alexandr; Vainio, Rami; Kocharov, Leon

2014-07-20

The energy spectra of particles in gradual solar energetic particle (SEP) events do not always have a power-law form attributed to the diffusive shock acceleration mechanism. In particular, the observed spectra in major SEP events can take the form of a broken (double) power law. In this paper, we study the effect of a process that can modify the power-law spectral form produced by the diffusive shock acceleration: the stochastic re-acceleration of energetic protons by enhanced Alfvénic turbulence in the downstream region of a shock wave. There are arguments suggesting that this process can be important when the shock propagatesmore » in the corona. We consider a coronal magnetic loop traversed by a shock and perform Monte Carlo simulations of interactions of shock-accelerated protons with Alfvén waves in the loop. The wave-particle interactions are treated self-consistently, so the finiteness of the available turbulent energy is taken into account. The initial energy spectrum of particles is taken to be a power law. The simulations reveal that the stochastic re-acceleration leads either to the formation of a spectrum that is described in a wide energy range by a power law (although the resulting power-law index is different from the initial one) or to a broken power-law spectrum. The resulting spectral form is determined by the ratio of the energy density of shock-accelerated protons to the wave energy density in the shock's downstream region.« less

Bidirectional Classical Stochastic Processes with Measurements and Feedback

NASA Technical Reports Server (NTRS)

Hahne, G. E.

2005-01-01

A measurement on a quantum system is said to cause the "collapse" of the quantum state vector or density matrix. An analogous collapse occurs with measurements on a classical stochastic process. This paper addresses the question of describing the response of a classical stochastic process when there is feedback from the output of a measurement to the input, and is intended to give a model for quantum-mechanical processes that occur along a space-like reaction coordinate. The classical system can be thought of in physical terms as two counterflowing probability streams, which stochastically exchange probability currents in a way that the net probability current, and hence the overall probability, suitably interpreted, is conserved. The proposed formalism extends the . mathematics of those stochastic processes describable with linear, single-step, unidirectional transition probabilities, known as Markov chains and stochastic matrices. It is shown that a certain rearrangement and combination of the input and output of two stochastic matrices of the same order yields another matrix of the same type. Each measurement causes the partial collapse of the probability current distribution in the midst of such a process, giving rise to calculable, but non-Markov, values for the ensuing modification of the system's output probability distribution. The paper concludes with an analysis of a classical probabilistic version of the so-called grandfather paradox.

From Complex to Simple: Interdisciplinary Stochastic Models

ERIC Educational Resources Information Center

Mazilu, D. A.; Zamora, G.; Mazilu, I.

2012-01-01

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…

Simulations of DSB Yields and Radiation-induced Chromosomal Aberrations in Human Cells Based on the Stochastic Track Structure iIduced by HZE Particles

NASA Technical Reports Server (NTRS)

Ponomarev, Artem; Plante, Ianik; George, Kerry; Wu, Honglu

2014-01-01

The formation of double-strand breaks (DSBs) and chromosomal aberrations (CAs) is of great importance in radiation research and, specifically, in space applications. We are presenting a new particle track and DNA damage model, in which the particle stochastic track structure is combined with the random walk (RW) structure of chromosomes in a cell nucleus. The motivation for this effort stems from the fact that the model with the RW chromosomes, NASARTI (NASA radiation track image) previously relied on amorphous track structure, while the stochastic track structure model RITRACKS (Relativistic Ion Tracks) was focused on more microscopic targets than the entire genome. We have combined chromosomes simulated by RWs with stochastic track structure, which uses nanoscopic dose calculations performed with the Monte-Carlo simulation by RITRACKS in a voxelized space. The new simulations produce the number of DSBs as function of dose and particle fluence for high-energy particles, including iron, carbon and protons, using voxels of 20 nm dimension. The combined model also calculates yields of radiation-induced CAs and unrejoined chromosome breaks in normal and repair deficient cells. The joined computational model is calibrated using the relative frequencies and distributions of chromosomal aberrations reported in the literature. The model considers fractionated deposition of energy to approximate dose rates of the space flight environment. The joined model also predicts of the yields and sizes of translocations, dicentrics, rings, and more complex-type aberrations formed in the G0/G1 cell cycle phase during the first cell division after irradiation. We found that the main advantage of the joined model is our ability to simulate small doses: 0.05-0.5 Gy. At such low doses, the stochastic track structure proved to be indispensable, as the action of individual delta-rays becomes more important.

Fractional noise destroys or induces a stochastic bifurcation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Qigui, E-mail: qgyang@scut.edu.cn; Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn; School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640

2013-12-15

Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.

3D aquifer characterization using stochastic streamline calibration

NASA Astrophysics Data System (ADS)

Jang, Minchul

2007-03-01

In this study, a new inverse approach, stochastic streamline calibration is proposed. Using both a streamline concept and a stochastic technique, stochastic streamline calibration optimizes an identified field to fit in given observation data in a exceptionally fast and stable fashion. In the stochastic streamline calibration, streamlines are adopted as basic elements not only for describing fluid flow but also for identifying the permeability distribution. Based on the streamline-based inversion by Agarwal et al. [Agarwal B, Blunt MJ. Streamline-based method with full-physics forward simulation for history matching performance data of a North sea field. SPE J 2003;8(2):171-80], Wang and Kovscek [Wang Y, Kovscek AR. Streamline approach for history matching production data. SPE J 2000;5(4):353-62], permeability is modified rather along streamlines than at the individual gridblocks. Permeabilities in the gridblocks which a streamline passes are adjusted by being multiplied by some factor such that we can match flow and transport properties of the streamline. This enables the inverse process to achieve fast convergence. In addition, equipped with a stochastic module, the proposed technique supportively calibrates the identified field in a stochastic manner, while incorporating spatial information into the field. This prevents the inverse process from being stuck in local minima and helps search for a globally optimized solution. Simulation results indicate that stochastic streamline calibration identifies an unknown permeability exceptionally quickly. More notably, the identified permeability distribution reflected realistic geological features, which had not been achieved in the original work by Agarwal et al. with the limitations of the large modifications along streamlines for matching production data only. The constructed model by stochastic streamline calibration forecasted transport of plume which was similar to that of a reference model. By this, we can expect

Stochastic maps, continuous approximation, and stable distribution

NASA Astrophysics Data System (ADS)

Kessler, David A.; Burov, Stanislav

2017-10-01

A continuous approximation framework for general nonlinear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the Itô lemma, we obtain a Langevin type of equation. Specifically, we show how nonlinear maps give rise to a Langevin description that involves multiplicative noise. The multiplicative nature of the noise induces an additional effective force, not present in the absence of noise. We further exploit the continuum description and provide an explicit formula for the stable distribution of the stochastic map and conditions for its existence. Our results are in good agreement with numerical simulations of several maps.

Self-learning Monte Carlo method

DOE PAGES

Liu, Junwei; Qi, Yang; Meng, Zi Yang; ...

2017-01-04

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of a general and efficient update algorithm for large size systems close to the phase transition, for which local updates perform badly. In this Rapid Communication, we propose a general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. Lastly, we demonstrate the efficiency of SLMC in a spin model at the phasemore » transition point, achieving a 10–20 times speedup.« less

Monte Carlo Analysis of the Battery-Type High Temperature Gas Cooled Reactor

NASA Astrophysics Data System (ADS)

Grodzki, Marcin; Darnowski, Piotr; Niewiński, Grzegorz

2017-12-01

The paper presents a neutronic analysis of the battery-type 20 MWth high-temperature gas cooled reactor. The developed reactor model is based on the publicly available data being an `early design' variant of the U-battery. The investigated core is a battery type small modular reactor, graphite moderated, uranium fueled, prismatic, helium cooled high-temperature gas cooled reactor with graphite reflector. The two core alternative designs were investigated. The first has a central reflector and 30×4 prismatic fuel blocks and the second has no central reflector and 37×4 blocks. The SERPENT Monte Carlo reactor physics computer code, with ENDF and JEFF nuclear data libraries, was applied. Several nuclear design static criticality calculations were performed and compared with available reference results. The analysis covered the single assembly models and full core simulations for two geometry models: homogenous and heterogenous (explicit). A sensitivity analysis of the reflector graphite density was performed. An acceptable agreement between calculations and reference design was obtained. All calculations were performed for the fresh core state.

Stochastic uncertainty analysis for unconfined flow systems

USGS Publications Warehouse

Liu, Gaisheng; Zhang, Dongxiao; Lu, Zhiming

2006-01-01

A new stochastic approach proposed by Zhang and Lu (2004), called the Karhunen‐Loeve decomposition‐based moment equation (KLME), has been extended to solving nonlinear, unconfined flow problems in randomly heterogeneous aquifers. This approach is on the basis of an innovative combination of Karhunen‐Loeve decomposition, polynomial expansion, and perturbation methods. The random log‐transformed hydraulic conductivity field (lnKS) is first expanded into a series in terms of orthogonal Gaussian standard random variables with their coefficients obtained as the eigenvalues and eigenfunctions of the covariance function of lnKS. Next, head h is decomposed as a perturbation expansion series Σh(m), where h(m) represents the mth‐order head term with respect to the standard deviation of lnKS. Then h(m) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients hi1,i2,...,im(m) are deterministic and solved sequentially from low to high expansion orders using MODFLOW‐2000. Finally, the statistics of head and flux are computed using simple algebraic operations on hi1,i2,...,im(m). A series of numerical test results in 2‐D and 3‐D unconfined flow systems indicated that the KLME approach is effective in estimating the mean and (co)variance of both heads and fluxes and requires much less computational effort as compared to the traditional Monte Carlo simulation technique.

Stochastic Semidefinite Programming: Applications and Algorithms

DTIC Science & Technology

2012-03-03

doi: 2011/09/07 13:38:21 13 TOTAL: 1 Number of Papers published in non peer-reviewed journals: Baha M. Alzalg and K. A. Ariyawansa, Stochastic...symmetric programming over integers. International Conference on Scientific Computing, Las Vegas, Nevada, July 18--21, 2011. Baha M. Alzalg. On recent...Proceeding publications (other than abstracts): PaperReceived Baha M. Alzalg, K. A. Ariyawansa. Stochastic mixed integer second-order cone programming

A developmental basis for stochasticity in floral organ numbers

PubMed Central

Kitazawa, Miho S.; Fujimoto, Koichi

2014-01-01

Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning. PMID:25404932

Random-order fractional bistable system and its stochastic resonance

NASA Astrophysics Data System (ADS)

Gao, Shilong; Zhang, Li; Liu, Hui; Kan, Bixia

2017-01-01

In this paper, the diffusion motion of Brownian particles in a viscous liquid suffering from stochastic fluctuations of the external environment is modeled as a random-order fractional bistable equation, and as a typical nonlinear dynamic behavior, the stochastic resonance phenomena in this system are investigated. At first, the derivation process of the random-order fractional bistable system is given. In particular, the random-power-law memory is deeply discussed to obtain the physical interpretation of the random-order fractional derivative. Secondly, the stochastic resonance evoked by random-order and external periodic force is mainly studied by numerical simulation. In particular, the frequency shifting phenomena of the periodical output are observed in SR induced by the excitation of the random order. Finally, the stochastic resonance of the system under the double stochastic excitations of the random order and the internal color noise is also investigated.

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

PubMed

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

Maximum principle for a stochastic delayed system involving terminal state constraints.

PubMed

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

Bayesian statistics and Monte Carlo methods

NASA Astrophysics Data System (ADS)

Koch, K. R.

2018-03-01

The Bayesian approach allows an intuitive way to derive the methods of statistics. Probability is defined as a measure of the plausibility of statements or propositions. Three rules are sufficient to obtain the laws of probability. If the statements refer to the numerical values of variables, the so-called random variables, univariate and multivariate distributions follow. They lead to the point estimation by which unknown quantities, i.e. unknown parameters, are computed from measurements. The unknown parameters are random variables, they are fixed quantities in traditional statistics which is not founded on Bayes' theorem. Bayesian statistics therefore recommends itself for Monte Carlo methods, which generate random variates from given distributions. Monte Carlo methods, of course, can also be applied in traditional statistics. The unknown parameters, are introduced as functions of the measurements, and the Monte Carlo methods give the covariance matrix and the expectation of these functions. A confidence region is derived where the unknown parameters are situated with a given probability. Following a method of traditional statistics, hypotheses are tested by determining whether a value for an unknown parameter lies inside or outside the confidence region. The error propagation of a random vector by the Monte Carlo methods is presented as an application. If the random vector results from a nonlinearly transformed vector, its covariance matrix and its expectation follow from the Monte Carlo estimate. This saves a considerable amount of derivatives to be computed, and errors of the linearization are avoided. The Monte Carlo method is therefore efficient. If the functions of the measurements are given by a sum of two or more random vectors with different multivariate distributions, the resulting distribution is generally not known. TheMonte Carlo methods are then needed to obtain the covariance matrix and the expectation of the sum.

One-Week Module on Stochastic Groundwater Modeling

ERIC Educational Resources Information Center

Mays, David C.

2010-01-01

This article describes a one-week introduction to stochastic groundwater modeling, intended for the end of a first course on groundwater hydrology, or the beginning of a second course on stochastic hydrogeology or groundwater modeling. The motivation for this work is to strengthen groundwater education, which has been identified among the factors…

Stochastic Game Analysis and Latency Awareness for Self-Adaptation

DTIC Science & Technology

2014-01-01

this paper, we introduce a formal analysis technique based on model checking of stochastic multiplayer games (SMGs) that enables us to quantify the...Additional Key Words and Phrases: Proactive adaptation, Stochastic multiplayer games , Latency 1. INTRODUCTION When planning how to adapt, self-adaptive...contribution of this paper is twofold: (1) A novel analysis technique based on model checking of stochastic multiplayer games (SMGs) that enables us to

Stochastic Approaches Within a High Resolution Rapid Refresh Ensemble

NASA Astrophysics Data System (ADS)

Jankov, I.

2017-12-01

It is well known that global and regional numerical weather prediction (NWP) ensemble systems are under-dispersive, producing unreliable and overconfident ensemble forecasts. Typical approaches to alleviate this problem include the use of multiple dynamic cores, multiple physics suite configurations, or a combination of the two. While these approaches may produce desirable results, they have practical and theoretical deficiencies and are more difficult and costly to maintain. An active area of research that promotes a more unified and sustainable system is the use of stochastic physics. Stochastic approaches include Stochastic Parameter Perturbations (SPP), Stochastic Kinetic Energy Backscatter (SKEB), and Stochastic Perturbation of Physics Tendencies (SPPT). The focus of this study is to assess model performance within a convection-permitting ensemble at 3-km grid spacing across the Contiguous United States (CONUS) using a variety of stochastic approaches. A single physics suite configuration based on the operational High-Resolution Rapid Refresh (HRRR) model was utilized and ensemble members produced by employing stochastic methods. Parameter perturbations (using SPP) for select fields were employed in the Rapid Update Cycle (RUC) land surface model (LSM) and Mellor-Yamada-Nakanishi-Niino (MYNN) Planetary Boundary Layer (PBL) schemes. Within MYNN, SPP was applied to sub-grid cloud fraction, mixing length, roughness length, mass fluxes and Prandtl number. In the RUC LSM, SPP was applied to hydraulic conductivity and tested perturbing soil moisture at initial time. First iterative testing was conducted to assess the initial performance of several configuration settings (e.g. variety of spatial and temporal de-correlation lengths). Upon selection of the most promising candidate configurations using SPP, a 10-day time period was run and more robust statistics were gathered. SKEB and SPPT were included in additional retrospective tests to assess the impact of using

Sparse Learning with Stochastic Composite Optimization.

PubMed

Zhang, Weizhong; Zhang, Lijun; Jin, Zhongming; Jin, Rong; Cai, Deng; Li, Xuelong; Liang, Ronghua; He, Xiaofei

2017-06-01

In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate O(1/λT), but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain O(√{log(1/δ)/T}) with δ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately O(log(log(T)/δ)/λT).

Quantifying Stochastic Noise in Cultured Circadian Reporter Cells

DOE PAGES

John, Peter C.; Doyle, III, Francis J.

2015-11-20

We report that stochastic noise at the cellular level has been shown to play a fundamental role in circadian oscillations, influencing how groups of cells entrain to external cues and likely serving as the mechanism by which cell-autonomous rhythms are generated. Despite this importance, few studies have investigated how clock perturbations affect stochastic noise—even as increasing numbers of high-throughput screens categorize how gene knockdowns or small molecules can change clock period and amplitude. This absence is likely due to the difficulty associated with measuring cell-autonomous stochastic noise directly, which currently requires the careful collection and processing of single-cell data. Inmore » this study, we show that the damping rate of population-level bioluminescence recordings can serve as an accurate measure of overall stochastic noise, and one that can be applied to future and existing high-throughput circadian screens. Using cell-autonomous fibroblast data, we first show directly that higher noise at the single-cell results in faster damping at the population level. Next, we show that the damping rate of cultured cells can be changed in a dose-dependent fashion by small molecule modulators, and confirm that such a change can be explained by single-cell noise using a mathematical model. We further demonstrate the insights that can be gained by applying our method to a genome-wide siRNA screen, revealing that stochastic noise is altered independently from period, amplitude, and phase. Finally, we hypothesize that the unperturbed clock is highly optimized for robust rhythms, as very few gene perturbations are capable of simultaneously increasing amplitude and lowering stochastic noise. Ultimately, this study demonstrates the importance of considering the effect of circadian perturbations on stochastic noise, particularly with regard to the development of small-molecule circadian therapeutics.« less

The stochastic spectator

NASA Astrophysics Data System (ADS)

Hardwick, Robert J.; Vennin, Vincent; Byrnes, Christian T.; Torrado, Jesús; Wands, David

2017-10-01

We study the stochastic distribution of spectator fields predicted in different slow-roll inflation backgrounds. Spectator fields have a negligible energy density during inflation but may play an important dynamical role later, even giving rise to primordial density perturbations within our observational horizon today. During de-Sitter expansion there is an equilibrium solution for the spectator field which is often used to estimate the stochastic distribution during slow-roll inflation. However slow roll only requires that the Hubble rate varies slowly compared to the Hubble time, while the time taken for the stochastic distribution to evolve to the de-Sitter equilibrium solution can be much longer than a Hubble time. We study both chaotic (monomial) and plateau inflaton potentials, with quadratic, quartic and axionic spectator fields. We give an adiabaticity condition for the spectator field distribution to relax to the de-Sitter equilibrium, and find that the de-Sitter approximation is never a reliable estimate for the typical distribution at the end of inflation for a quadratic spectator during monomial inflation. The existence of an adiabatic regime at early times can erase the dependence on initial conditions of the final distribution of field values. In these cases, spectator fields acquire sub-Planckian expectation values. Otherwise spectator fields may acquire much larger field displacements than suggested by the de-Sitter equilibrium solution. We quantify the information about initial conditions that can be obtained from the final field distribution. Our results may have important consequences for the viability of spectator models for the origin of structure, such as the simplest curvaton models.

Hybrid deterministic-stochastic modeling of x-ray beam bowtie filter scatter on a CT system.

PubMed

Liu, Xin; Hsieh, Jiang

2015-01-01

Knowledge of scatter generated by bowtie filter (i.e. x-ray beam compensator) is crucial for providing artifact free images on the CT scanners. Our approach is to use a hybrid deterministic-stochastic simulation to estimate the scatter level generated by a bowtie filter made of a material with low atomic number. First, major components of CT systems, such as source, flat filter, bowtie filter, body phantom, are built into a 3D model. The scattered photon fluence and the primary transmitted photon fluence are simulated by MCNP - a Monte Carlo simulation toolkit. The rejection of scattered photon by the post patient collimator (anti-scatter grid) is simulated with an analytical formula. The biased sinogram is created by superimposing scatter signal generated by the simulation onto the primary x-ray beam signal. Finally, images with artifacts are reconstructed with the biased signal. The effect of anti-scatter grid height on scatter rejection are also discussed and demonstrated.

Robust Bayesian Analysis of Heavy-tailed Stochastic Volatility Models using Scale Mixtures of Normal Distributions

PubMed Central

Abanto-Valle, C. A.; Bandyopadhyay, D.; Lachos, V. H.; Enriquez, I.

2009-01-01

A Bayesian analysis of stochastic volatility (SV) models using the class of symmetric scale mixtures of normal (SMN) distributions is considered. In the face of non-normality, this provides an appealing robust alternative to the routine use of the normal distribution. Specific distributions examined include the normal, student-t, slash and the variance gamma distributions. Using a Bayesian paradigm, an efficient Markov chain Monte Carlo (MCMC) algorithm is introduced for parameter estimation. Moreover, the mixing parameters obtained as a by-product of the scale mixture representation can be used to identify outliers. The methods developed are applied to analyze daily stock returns data on S&P500 index. Bayesian model selection criteria as well as out-of- sample forecasting results reveal that the SV models based on heavy-tailed SMN distributions provide significant improvement in model fit as well as prediction to the S&P500 index data over the usual normal model. PMID:20730043

Asymptotic problems for stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Salins, Michael

Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

Theory of Stochastic Duels - Miscellaneous Results

DTIC Science & Technology