Optimal time step length and statistics in Monte Carlo burnup simulations

2020 ◽  
Vol 139 ◽  
pp. 107244
Author(s):  
Jan Dufek ◽  
Ignas Mickus
Keyword(s):  
Monte Carlo ◽  
Step Length ◽  
Optimal Time ◽  
Time Step

Optimal Time Step Length for Lagrangian Interacting-Particle Simulations of Diffusive Mixing

2022 ◽  
Author(s):  
Michael J. Schmidt ◽  
Nicholas B. Engdahl ◽  
David A. Benson ◽  
Diogo Bolster
Keyword(s):  
Step Length ◽  
Optimal Time ◽  
Time Step ◽  
Interacting Particle ◽  
Particle Simulations ◽  
Diffusive Mixing

Time step length versus efficiency of Monte Carlo burnup calculations

2014 ◽  
Vol 72 ◽  
pp. 409-412 ◽  
Author(s):  
Jan Dufek ◽  
Ville Valtavirta
Keyword(s):  
Monte Carlo ◽  
Step Length ◽  
Time Step

scholarly journals Nonlocal pseudopotentials and time-step errors in diffusion Monte Carlo

2021 ◽  
Vol 154 (21) ◽  
pp. 214110
Author(s):  
Tyler A. Anderson ◽  
C. J. Umrigar
Keyword(s):  
Monte Carlo ◽  
Diffusion Monte Carlo ◽  
Time Step

scholarly journals Regional Associations of Cortical Thickness With Gait Variability: The Tasmanian Study of Cognition and Gait

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 232-233
Author(s):  
Oshadi Jayakody ◽  
Monique Breslin ◽  
Richard Beare ◽  
Velandai Srikanth ◽  
Helena Blumen ◽  
...  
Keyword(s):  
Cortical Thickness ◽  
Step Length ◽  
Gait Variability ◽  
Thickness Ratio ◽  
Sensory Function ◽  
Time Variability ◽  
Step Width ◽  
Time Step ◽  
Cortical Regions ◽  
Regional Associations

Abstract Gait variability is a marker of cognitive decline. However, there is limited understanding of the cortical regions associated with gait variability. We examined associations between regional cortical thickness and gait variability in a population-based sample of older people without dementia. Participants (n=350, mean age 71.9±7.1) were randomly selected from the electoral roll. Variability in step time, step length, step width and double support time (DST) were calculated as the standard deviation of each measure, obtained from the GAITRite walkway. MRI scans were processed through FreeSurfer to obtain cortical thickness of 68 regions. Bayesian regression was used to determine regional associations of mean cortical thickness and thickness ratio (regional thickness/overall mean thickness) with gait variability. Smaller overall cortical thickness was only associated with greater step width and step time variability. Smaller mean thickness in widespread regions important for sensory, cognitive and motor functions were associated with greater step width and step time variability. In contrast, smaller thickness in a few frontal and temporal regions were associated with DST variability and the right cuneus was associated with step length variability. Smaller thickness ratio in frontal and temporal regions important for motor planning, execution and sensory function and, greater thickness ratio in the anterior cingulate was associated with greater variability in all measures. Examining individual cortical regions is important in understanding the relationship between gray matter and gait variability. Cortical thickness ratio highlights that smaller regional thickness relative to global thickness may be important for the consistency of gait.

scholarly journals Monte Carlo Simulation with Time Step Quantification in Terms of Langevin Dynamics

2000 ◽  
Vol 84 (1) ◽  
pp. 163-166 ◽  
Author(s):  
U. Nowak ◽  
R. W. Chantrell ◽  
E. C. Kennedy
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Langevin Dynamics ◽  
Time Step

Monte Carlo Simulation of Precipitate Nucleation and Growth: Time Dependent Results

1988 ◽  
Vol 141 ◽  
Author(s):  
James P. Lavine ◽  
Gilbert A. Hawkins
Keyword(s):  
Monte Carlo ◽  
Crystalline Silicon ◽  
Three Dimensional ◽  
Nucleation Site ◽  
Nucleation And Growth ◽  
Lattice Points ◽  
Growth Time ◽  
Decay Kinetics ◽  
Time Step ◽  
Oxygen Atoms

AbstractA three-dimensional Monte Carlo computer program has been developed to study the heterogeneous nucleation and growth of oxide precipitates during the thermal treatment of crystalline silicon. In the simulations, oxygen atoms move on a lattice with randomly selected lattice points serving as nucleation sites. The change in free energy that the oxygen cluster would experience in gaining or losing one oxygen atom is used to govern growth or dissolution of the cluster. All the oxygen atoms undergo a jump or a growth decision during each time step of the anneal. The growth and decay kinetics of each nucleation site display interesting fluctuation phenomena. The time dependence of the cluster size generally differs from the expected 3/2 power law due to the fluctuations in oxygen arrival at and incorporation in a precipitate. Competition between growing sites and coarsening are observed.

BIASED RANDOM WALKS, PARTIAL DIFFERENTIAL EQUATIONS AND UPDATE SCHEMES

2013 ◽  
Vol 55 (2) ◽  
pp. 93-108 ◽  
Author(s):  
JACK D. HYWOOD ◽  
KERRY A. LANDMAN
Keyword(s):  
Statistical Physics ◽  
Planck Equation ◽  
Step Length ◽  
Physical Object ◽  
Cell Diameter ◽  
Agent Based Models ◽  
Time Step ◽  
Partial Differential ◽  
Agent Based ◽  
Random Walkers

AbstractThere is much interest within the mathematical biology and statistical physics community in converting stochastic agent-based models for random walkers into a partial differential equation description for the average agent density. Here a collection of noninteracting biased random walkers on a one-dimensional lattice is considered. The usual master equation approach requires that two continuum limits, involving three parameters, namely step length, time step and the random walk bias, approach zero in a specific way. We are interested in the case where the two limits are not consistent. New results are obtained using a Fokker–Planck equation and the results are highly dependent on the simulation update schemes. The theoretical results are confirmed with examples. These findings provide insight into the importance of updating schemes to an accurate macroscopic description of stochastic local movement rules in agent-based models when the lattice spacing represents a physical object such as cell diameter.

scholarly journals Estimation of Optimal Time Step and Compare with of ODE Solver of MATLAB Package of RLC Circuit using Numerical Methods

1970 ◽  
Vol 7 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Sheikh Md Rabiul Islam
Keyword(s):  
Mesh Size ◽  
Paper Analysis ◽  
Optimal Time ◽  
Time Step ◽  
Minimum Error ◽  
Optimal Output ◽  
Runge Kutta Method ◽  
Rlc Circuit ◽  
Matlab Package ◽  
Theoretical Results

In this paper analysis of a RLC circuit model that has been described optimal time step and minimize of error using numerical method. The goal is to reach the optimal time response due to the input for which optimal output response reaches a minimum error and also compared with ODE solver of MATLAB packages for the different cell (mesh) size of the RLC model. Table is constructed of the model to evaluate optimal time step and also CPU time into the simulation using MATLAB 7.6.0(R2008a).The values of register, capacitor and inductor as well as electromagnetic force are obtained through the mathematical relations of the model. The general analysis of the RLC circuit due to the optimal time step and minimum error is developed after several analysis and operations. The theoretical results show effectiveness of optimized of the model. Keywords: Optimal time step; MATLAB; Trapezoidal; Implicit Euler; Runge-Kutta method; RLC circuit. DOI: http://dx.doi.org/10.3329/diujst.v7i1.9650   Daffodil International University Journal of Science and Technology Vol.7(1) 2012 67-73

scholarly journals Algorithms for Solving Darcian Flow in Structured Porous Media

10.14311/1829 ◽  
2013 ◽  
Vol 53 (4) ◽  
Author(s):  
Michal Kuráž ◽  
Petr Mayer
Keyword(s):  
Proper Time ◽  
Time Integration ◽  
Mass Term ◽  
Step Length ◽  
Richards Equation ◽  
Parabolic Problems ◽  
Computational Domain ◽  
Wetting Front ◽  
Time Step ◽  
The Matrix

This paper presents several algorithms that were implemented in DRUtES [1], a new open source project. DRUtES is a finite element solver for coupled nonlinear parabolic problems, namely the Richards equation with the dual porosity approach (modeling the flow of liquids in a porous medium). Mass balance consistency is crucial in any hydrological balance and contaminant transportation evaluations. An incorrect approximation of the mass term greatly depreciates the results that are obtained. An algorithm for automatic time step selection is presented, as the proper time step length is crucial for achieving accuracy of the Euler time integration method. Various problems arise with poor conditioning of the Richards equation: the computational domain is clustered into subregions separated by a wetting front, and the nonlinear constitutive functions cover a high range of values, while a very simple diagonal preconditioning method greatly improves the matrix properties. The results are presented here, together with an analysis.

Intelligent Time-Stepping for Practical Numerical Simulation

2021 ◽  
Author(s):  
Soham Sheth ◽  
Francois McKee ◽  
Kieran Neylon ◽  
Ghazala Fazil
Keyword(s):  
Heuristic Method ◽  
Simulation Models ◽  
Model Complexity ◽  
Large Field ◽  
Optimal Time ◽  
Time Step ◽  
Non Linear ◽  
Set Up ◽  
Reservoir Simulator ◽  
Step Selection

Abstract We present a novel reservoir simulator time-step selection approach which uses machine-learning (ML) techniques to analyze the mathematical and physical state of the system and predict time-step sizes which are large while still being efficient to solve, thus making the simulation faster. An optimal time-step choice avoids wasted non-linear and linear equation set-up work when the time-step is too small and avoids highly non-linear systems that take many iterations to solve. Typical time-step selectors use a limited set of features to heuristically predict the size of the next time-step. While they have been effective for simple simulation models, as model complexity increases, there is an increasing need for robust data-driven time-step selection algorithms. We propose two workflows – static and dynamic – that use a diverse set of physical (e.g., well data) and mathematical (e.g., CFL) features to build a predictive ML model. This can be pre-trained or dynamically trained to generate an inference model. The trained model can also be reinforced as new data becomes available and efficiently used for transfer learning. We present the application of these workflows in a commercial reservoir simulator using distinct types of simulation model including black oil, compositional and thermal steam-assisted gravity drainage (SAGD). We have found that history-match and uncertainty/optimization studies benefit most from the static approach while the dynamic approach produces optimum step-sizes for prediction studies. We use a confidence monitor to manage the ML time-step selector at runtime. If the confidence level falls below a threshold, we switch to traditional heuristic method for that time-step. This avoids any degradation in the performance when the model features are outside the training space. Application to several complex cases, including a large field study, shows a significant speedup for single simulations and even better results for multiple simulations. We demonstrate that any simulation can take advantage of the stored state of the trained model and even augment it when new situations are encountered, so the system becomes more effective as it is exposed to more data.

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