scholarly journals Monte Carlo implementation of a guiding-center Fokker-Planck kinetic equation

2013 ◽  
Vol 20 (9) ◽  
pp. 092505 ◽  
Author(s):  
E. Hirvijoki ◽  
A. Brizard ◽  
A. Snicker ◽  
T. Kurki-Suonio
Keyword(s):  
Monte Carlo ◽  
Kinetic Equation ◽  
Monte Carlo Implementation ◽  
Fokker Planck

scholarly journals Alignment of Dust Grains by Magnetic Relaxation: A Comparison Between Results Obtained by Two Different Methods

1973 ◽  
Vol 52 ◽  
pp. 187-189
Author(s):  
P. Cugnon
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Magnetic Relaxation ◽  
Planck Equation ◽  
Dust Grains ◽  
Fokker Planck Equation ◽  
The Monte Carlo Method ◽  
Good Agreement ◽  
Fokker Planck

This paper is devoted to a comparison between results obtained by Purcell and Spitzer (1971) using a Monte-Carlo method and by the author (1971) using a Fokker-Planck equation. It is shown that there is a good agreement between the results within the dispersion expected from the Monte-Carlo method.

Geometry entrapment in Walk-on-Subdomains

2019 ◽  
Vol 25 (4) ◽  
pp. 329-340 ◽  
Author(s):  
Preston Hamlin ◽  
W. John Thrasher ◽  
Walid Keyrouz ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Method ◽  
Electrostatic Energy ◽  
Potential Solution ◽  
Long Time ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Monte Carlo Implementation

Abstract One method of computing the electrostatic energy of a biomolecule in a solution uses a continuum representation of the solution via the Poisson–Boltzmann equation. This can be solved in many ways, and we consider a Monte Carlo method of our design that combines the Walk-on-Spheres and Walk-on-Subdomains algorithms. In the course of examining the Monte Carlo implementation of this method, an issue was discovered in the Walk-on-Subdomains portion of the algorithm which caused the algorithm to sometimes take an abnormally long time to complete. As the problem occurs when a walker repeatedly oscillates between two subdomains, it is something that could cause a large increase in runtime for any method that used a similar algorithm. This issue is described in detail and a potential solution is examined.

scholarly journals Accelerated procedure to solve kinetic equation for neutral atoms in a hot plasma

2018 ◽  
Vol 09 (05) ◽  
pp. 1850048 ◽  
Author(s):  
Mikhail Z. Tokar
Keyword(s):  
Monte Carlo ◽  
Kinetic Equation ◽  
Energy Spectrum ◽  
Erosion Rate ◽  
Fusion Reactor ◽  
Two Dimensional ◽  
First Wall ◽  
One Dimensional ◽  
Hot Plasma ◽  
Electrons And Ions

By reaching the first wall of a fusion reactor, charged plasma particles, electrons and ions are recombined into neutral molecules and atoms of hydrogen isotopes. These species recycle back into the plasma volume and participate, in particular, in charge–exchange (cx) collisions with ions. As a result, hot atoms with chaotically directed velocities are generated and some of them hit the wall. Statistical Monte Carlo methods often used to model the behavior of cx atoms are too time-consuming for comprehensive parameter studies. Recently1 an alternative iteration approach to solve one-dimensional kinetic equation2 has been significantly accelerated, by a factor of 30–50, by applying a pass method to evaluate the arising integrals from functions, involving the ion velocity distribution. Here, this approach is used by solving a two-dimensional kinetic equation, describing the transport of cx atoms in the vicinity of an opening in the wall, e.g., the entrance of a duct guiding to a diagnostic installation. To assess the erosion rate and lifetime of the installation, one need to know the energy spectrum of hot cx atoms escaping from the plasma into the duct. Calculations are done for a first mirror of molybdenum under plasma conditions expected in a fusion reactor like DEMO.3,4 The results of kinetic modeling are compared with those found by using a diffusion approximation5 relevant for cx atoms if the time between cx collisions with ions is much smaller than the time till the ionization of atoms by electrons. The present more exact kinetic consideration predicts a mirror erosion rate by a factor of 2 larger than the approximate diffusion approach.

A Monte Carlo Implementation of the James-Ford-Jivkov Microstructurally Informed Local Approach Applied to Predict Fracture Toughness Across Irradiation Conditions

2016 ◽  
Author(s):  
Michael Ford ◽  
Peter James
Keyword(s):  
Fracture Toughness ◽  
Monte Carlo ◽  
Transition Region ◽  
Crack Size ◽  
Model Parameters ◽  
Pressure Vessel Steel ◽  
Local Approach ◽  
Vessel Steel ◽  
Reactor Pressure Vessel Steel ◽  
Monte Carlo Implementation

The need to predict changes in fracture toughness for materials where the tensile properties change through life, such as with irradiation, whilst accounting for geometric constraint effects, such as crack size, are clearly important. Currently one of the most likely approaches by which to develop such ability are through application of local approach models. These approaches appear to be sufficient in predicting lower shelf toughness under high constraint conditions, but may fail when attempting to predict toughness in the transition region, for low constraint geometries or for different irradiation states, when using the same parameters, making reliable predictions impossible. Cleavage toughness predictions in the transition regime are here made with a stochastic, Monte Carlo implementation of the recently proposed James-Ford-Jivkov model. This implementation is based around the creation of individual initiators following the experimentally observed distribution for specific reactor pressure vessel steel, and determining if these initiators form voids or cause cleavage failure using the model’s improved criterion for particle failure. This implementation has been presented previously in PVP2015-45905, where it was successfully applied across different constraint conditions; in the work presented here it is applied across different irradiation conditions for a second type of steel. The model predicts the fracture toughness in a large part of the transition region, demonstrates an ability to predict the irradiation shift and shows a level of scatter similar to that observed experimentally. All results presented, for a given material, are obtained without changes in the model parameters. This suggests that the model can be used predicatively for assessing toughness changes due to constraint-, irradiation- and temperature-driven plasticity changes.

A Monte Carlo Implementation of the James-Ford-Jivkov Micro-Structurally Informed Local Approach Applied to Predict Fracture Toughness Including Low Constraint Conditions

2015 ◽  
Author(s):  
Michael Ford ◽  
Peter James
Keyword(s):  
Fracture Toughness ◽  
Monte Carlo ◽  
Transition Region ◽  
Crack Size ◽  
Model Parameters ◽  
Local Approach ◽  
Rpv Steel ◽  
Low Constraint ◽  
Constraint Effects ◽  
Monte Carlo Implementation

The need to predict changes in fracture toughness for materials where the tensile properties change through life, such as with irradiation, whilst accounting for geometric constraint effects, such as crack size, are clearly important. Currently one of the most likely approaches by which to develop such ability are through application of local approach models. These approaches appear to be sufficient in predicting lower shelf toughness under high constraint conditions, but may fail when attempting to predict toughness in the transition region or for low constraint geometries when using the same parameters, making predictions impossible. Cleavage toughness predictions in the transition regime that are then extended to low constraint conditions are here made with a stochastic, Monte Carlo implementation of the recently proposed James-Ford-Jivkov model. This implementation is based around the creation of individual initiators following the experimentally observed distribution for specific RPV steel, and determining if these initiators form voids or cause cleavage failure using the model’s improved criterion for particle failure. The model has shown to predict experimentally measured locations of cleavage initiators. Further, initial results from the Monte Carlo implementation of the model predicts the fracture toughness in a large part of the transition region, demonstrates an ability to predict the constraint shift and shows a level of scatter similar to that observed experimentally. All results presented, for a given material, are obtained without changes in the model parameters. This suggests that the model can be used predicatively for assessing toughness changes due to constraint- and temperature-driven plasticity changes.

Sign in / Sign up

Export Citation Format

Share Document