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Quasi-Monte Carlo Simulation of Diffusion

Christian Lécot, Faysal El Khettabi
1999 Journal of Complexity  
A particle method adapted to the simulation of diffusion problems is presented. Time is discretized into increments of length 2t.  ...  Quasi-random samples are used and the particles are relabeled according to their position at each time step. Convergence is proved for the pure initial-value problem in s space dimensions.  ...  We also thank the referees for their constructive criticism on the first version of this paper and for several valuable suggestions.  ... 
doi:10.1006/jcom.1999.0509 fatcat:wehq72faijdo7ddsndbbhxrfcu

Quasi-Spin Ising Model and Monte Carlo Simulation of Ferroelastic Phase Transition: 3D Diffuse Scattering and Displacement Short-Range Ordering in Pre-Martensitic State [article]

Xiaoxu Guo, Yongmei M. Jin, Yang Ren, Yu U. Wang
2019 arXiv   pre-print
A quasi-spin Ising model of ferroelastic phase transition is developed and employed to perform atomic-scale Monte Carlo simulation of thermoelastic martensitic transformation.  ...  The simulated diffuse scattering is compared and agrees with the complementary synchrotron X-ray single-crystal diffuse scattering experiment.  ...  Computer simulations were performed on XSEDE supercomputers. Use of Advanced Photon Source at Argonne National Laboratory was supported by DOE DE-AC02-06CH11357.  ... 
arXiv:1912.10295v1 fatcat:oali4tpbhrfy3mmxhzdif2s2ou

Page 2686 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
(English summary) IMACS Seminar on Monte Carlo Methods (Brussels, 1997). Math. Comput. Simulation 47 (1998), no. 2-5, 153-163. Summary: “We present a method for computer simulation of diffusion.  ...  (RS-AOS-MD; Moscow) On quasi-Monte Carlo integrations. (English summary) IMACS Seminar on Monte Carlo Methods (Brussels, 1997). Math. Comput. Simulation 47 (1998), no. 2-5, 103-112.  ... 

Page 4353 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
In the third step the diffu- sion is simulated using a quasi-Monte Carlo approximation in the 2s-dimensional unit cube. We prove a convergence theorem in the context of the diffusion equation.  ...  (English summary) Monte Carlo and quasi-Monte Carlo methods 1998 (Claremont, CA), 296-310, Springer, Berlin, 2000.  ... 

Subject Index [chapter]

2007 Advances in Chemical Physics  
characteristics of, 16 Monte Carlo simulations, 31-34 Quaternary structure prediction, protein folding, 227-228 Monte Carlo, 260-263,268-269 integration, 430-432 Schrodinger equation : diffusion Monte  ...  , 510-513 Persistent configuration, diffusion Monte Carlo, 107-109 Perturbation theory, thermodynamic properties, 118-120 Phase coupling, Gibbs-Duhem integration, Phase equilibria, Monte Carlo simulation  ... 
doi:10.1002/9780470141649.indsub fatcat:uwedjpuxzzcn3hiphjzgbdr65e

Page 1262 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
{Some of the papers are being reviewed individually. } 2002b:65005 65-06 65C05 %* Monte Carlo and quasi-Monte Carlo methods 1998 Proceedings of the 3rd International Conference on Monte Carlo and Quasi-Monte  ...  Owen, Monte Carlo, quasi-Monte Carlo, and randomized quasi- Monte Carlo (86-97); Jerome Spanier, Geometrically convergent learning algorithms for global solutions of transport problems (98-113); Henryk  ... 

Adsorbate order-disorder effects on recombinative thermal desorption: Equivalence between dynamic Monte Carlo simulations and self-consistent cluster approximations

Sieghard Weinketz, G. G. Cabrera
1997 Journal of Chemical Physics  
within dynamic Monte Carlo simulations.  ...  calculated structure forms, reproducing quantitatively the temperature-programmed desorption spectra simulated with the Monte Carlo procedure.  ...  This last set of figures shows that the quasi-equilibrium local order obtained by the Monte Carlo simulation can be very well approximated by the C 2 approximation, except in the regions immediately left  ... 
doi:10.1063/1.473229 fatcat:6745v33gabf5zjjarvhaas6in4

Page 2050 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
Summary: “Quasi-Monte Carlo methods can be described as de- terministic versions of Monte Carlo methods.  ...  We combine the flexibility of Monte Carlo methods with the effectiveness and fast convergence of quasi-Monte Carlo methods.  ... 

Page 7757 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
We consider in this paper two different approaches which combine Monte Carlo and quasi-Monte Carlo methods.  ...  Spanier (1-CGS; Claremont, CA) 65C Numerical simulation 97m:65020 97m:65017 65COS 65M06 76M35 76Rxx Simonoy, N. A. (RS-AOSSI-C; Novosibirsk) Monte Carlo methods for convective diffusion equations.  ... 

A 3-dimensional particle device simulator; HyDeLEOSMC and its application to a FinFET

Y. Ohkura, C. Suzuki, T. Enda, H. Takashino, H. Ishikawa, T. Kojima, T. Wada
2005 2005 International Conference On Simulation of Semiconductor Processes and Devices  
A 2 and 3 dimensional ensemble Monte Carlo device simulator is developed and applied to FinFET analysis by using 'realistic' number of electrons within the channel of actual device.  ...  The result of transient fluctuation of electron numbers, currents, and distributions of potential and electron are shown.  ...  Thus we developed 3 dimensional ensemble Monte Carlo device simulator.  ... 
doi:10.1109/sispad.2005.201529 fatcat:3twgwgy3fnaq7blh4jse5zjbvq

Page 3583 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
This 49-page article is not comprehensive enough to qualify as a 65C Probabilistic methods, simulation and stochastic differential equations 2000e:65019 survey of Monte Carlo and quasi-Monte Carlo methods  ...  based) Monte Carlo and that of quasi-Monte Carlo methods, which are based on the use of low discrepancy sequences.  ... 

Mobility and energy-transport in degenerate hopping systems [article]

Dan Mendels, Nir Tessler
2012 arXiv   pre-print
While we revisit the drift diffusion process in the context of degenerate hopping systems, a considerable part of the argumentation put forward can be applied generally to degenerate systems.  ...  Revisiting charge transport in degenerate hopping systems we present a modification to the drift diffusion equation where instead of employing the generalized Einstein relation we add an energy flux term  ...  is matched to the Monte Carlo simulations, we employed Monte Carlo simulations and solved equation (2) using several boundary conditions that would induce charge density gradients.  ... 
arXiv:1206.5482v2 fatcat:6vc5p2ktpne2zkieuxp43hvxea

Modeling of the surface-to-surface radiation exchange using a Monte Carlo method

A Frank, W Heidemann, K Spindler
2016 Journal of Physics, Conference Series  
Several variations for grid spacing, the number of emitted photons and a quasi-Monte Carlo method are discussed.  ...  of the plane, grey, diffuse surfaces.  ...  For most simulations the results obtained with the quasi-Monte Carlo method are more accurate than the values obtained with the Monte Carlo method for a corresponding grid spacing and number of emitted  ... 
doi:10.1088/1742-6596/745/3/032143 fatcat:tyfura32gze6peldpvffkx6scq

Page 1222 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
The accuracy of the quasi-Monte Carlo scheme is compared with a standard Monte Carlo algorithm.  ...  A particle simulation is described. It combines an Euler scheme in time with quasi-Monte Carlo inte- gration in velocity space.  ... 

Coupling the Monte-Carlo method with semi-analytical solutions of the Boltzmann transport equation

S. C. Brugger, V. Peikert, A. Schenk
2008 2008 International Conference on Simulation of Semiconductor Processes and Devices  
This paper presents an important improvement of the current-based one-particle Monte-Carlo method.  ...  By regionwise coupling a semi-analytical solution of the Boltzmann equation to a full solution, the usage of computationally intensive Monte Carlo Boltzmann solvers can be limited to only those regions  ...  INTRODUCTION The Monte Carlo (MC) method is a well known approach to solve the Boltzmann transport equation (BTE) .  ... 
doi:10.1109/sispad.2008.4648296 fatcat:7slol6a3kzceno3p7ivouwzuqe
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