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Reverse Monte Carlo

2007-05-30T16:12:02Z

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'''Reverse Monte Carlo''' (RMC) [1-4] is a variation of the standard [[Metropolis Monte Carlo]] method. It is used to produce a 3 dimensional atomic model that fits a set of measurements (Neutron-, X-ray-diffraction, EXAFS etc.).
In addition to measured data a number of constraints based on prior knowledge of the system (like chemical bonds etc.) can be applied. Some examples are:

*Closest approach between atoms (hard sphere potential)
*Coordination numbers.
*Angles in triplets of atoms.

The 3 dimensional structure that is produced by RMC is not unique, it is a model consistent with the data and constraints provided.

The algorithm for RMC can be written:

#Start with a configuration of atoms with periodic boundary conditions. This can be a random or a crystalline configuration from a different simulation or model.
#Calculate the total [[radial distribution function]] <math>g_o^C(r)</math> for this old configuration (''C''=Calculated, ''o''=Old).
#Transform to the total [[Structure factor | structure factor]]:
#:<math>S_o^C (Q)-1=\frac{4\pi\rho}{Q}\int\limits_{0}^{\infty} r(g_o^C(r)-1)\sin(Qr)\, dr</math>
#:where ''Q'' is the momentum transfer and <math>\rho</math> the number density.
#Calculate the difference between the measured structure factor <math>S^E(Q)</math> (''E''=Experimental) and the one calculated from the configuration <math>S_o^C(Q)</math>:
#:<math>\chi_o^2=\sum_i(S_o^C(Q_i)-S^E(Q_i))^2/\sigma(Q_i)^2</math>
#:this sum is taken over all experimental points <math>\sigma</math> is the experimental error.
#Select and move one atom at random and calculate the new (''n''=New) distribution function, structure factor and:
#:<math>\chi_n^2=\sum_i(S_n^C(Q_i)-S^E(Q_i))^2/\sigma(Q_i)^2</math>
#If <math>\chi_n^2<\chi_o^2</math> accept the move and let the new configuration become the old. If <math>\chi_n^2 \geq \chi_o^2</math> then the move is accepted with probability <math>\exp(-(\chi_n^2-\chi_0^2)/2)</math> otherwise it is rejected.
#repeat from step 5.
When <math>\chi^2</math> have reached an equilibrium the configuration is saved and can be analysed.

== References ==
#[http://dx.doi.org/10.1080/08927028808080958 R. L. McGreevy and L. Pusztai, "Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures", Molecular Simulation, '''1''' pp. 359-367 (1988)]
#[http://dx.doi.org/10.1088/0953-8984/13/46/201 R. L. McGreevy, "Reverse Monte Carlo modelling", Journal of Physics: Condensed Matter '''13''' pp. R877-R913 (2001)]
#[http://dx.doi.org/10.1016/S1359-0286(03)00015-9 R. L. McGreevy and P. Zetterström, "To RMC or not to RMC? The use of reverse Monte Carlo modelling", Current Opinion in Solid State and Materials Science. '''7''' pp. 41-47 (2003)]
#[http://dx.doi.org/10.1088/0953-8984/17/5/001 G. Evrard, L. Pusztai, "Reverse Monte Carlo modelling of the structure of disordered materials with RMC++: a new implementation of the algorithm in C++", Journal of Physics: Condensed Matter '''17''' pp. S1-S13 (2005)]

[[Category:Monte Carlo]]

Conferences

2007-05-22T13:56:23Z

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Note: to make this page more useful, the conferences should be in '''chronological order''', with the forthcoming conference at the '''top''' of the list.
===2007===
*[http://www-thphys.physics.ox.ac.uk/users/JuliaYeomans/OxfordWorkshop/home.php Mesoscale Modelling for Complex Fluids and Flows] June 25--27, 2007 University of Oxford, UK.
*[http://www.ecns2007.org 4th European Conference on Neutron Scattering] Lund, Sweden 25-29 June 2007
*[http://www.realitygrid.org/CompSci07 Computational Science 2007] 25-26 June 2007 The Royal Society, London
*[https://www.cecam.fr/index.php?content=activities/workshop New directions in liquid state theory] CECAM workshop, 2 - 4 July, 2007 at ENS, Lyon, France.
*[http://www.cecam.fr/index.php?content=activities/workshop&action=details&wid=157 Fluid phase behaviour and critical phenomena from liquid state theories and simulations] July 05 2007 to July 07 2007 CECAM workshop, Lyon, France.
*[http://www.statphys23.org/ STATPHYS 23] Genova, Italy, from July 9 to 13, 2007.
*[http://www.iupac2007.org/ 41st IUPAC World Chemistry Conference] Turin, Italy, August 5-11th
*[http://www.srcf.ucam.org/~jae1001/ccp5_2007 CCP5 Annual Conference] 29th-31st August 2007 New Hall, Cambridge, UK
*[http://ccp2007.ulb.ac.be CCP 2007] Brussels 5-8 September 2007
*[http://www.castep.org CASTEP Workshop] 17th - 21st September 2007 University of York, UK
*[http://thermo2007.ifp.fr Thermodynamics 2007] 26-28 September 2007, IFP - Rueil-Malmaison (France)
*[http://www.iccmse.org/ ICCMSE 2007] International Conference of Computational Methods in Sciences and Engineering, HOTEL MARBELLA, Corfu, Greece, 25-30 September 2007
*[http://www.fz-juelich.de/iff/ismc2007/ ISMC 2007] International Soft Matter Conference 2007, 1 - 4 October 2007, Eurogress, Aachen (Germany)

===2008===
*[http://www.ill.fr/Events/rktsymposium/ SISMB 2008] Surfaces and Interfaces in Soft Matter and Biology : the impact and future of neutron reflectivity - A Symposium in Honor of Robert K. Thomas, 21-23 May 2008, Institut Laue-Langevin (Grenoble, France).
*[http://www.chm.bris.ac.uk/cms/ Computational Molecular Science 2008] 22nd – 25th June 2008, Cirencester, UK.
*[http://www.liquids2008.se/ 7th Liquid Matter Conference] 27 June - 1 July 2008 Lund, Sweden

===2009===
*[http://www.isis.rl.ac.uk/largescale/loq/SAS2009/SAS2009.htm SAS-2009] XIV International Conference on Small-Angle Scattering, Sunday 13 - Friday 18 September, 2009, Oxford (UK).
==Previous conferences==
*[http://www.simbioma.cecam.org/ Simulation of Hard Bodies] April 16 to April 19 2007 in Lyon.
*[http://www.math.rutgers.edu/events/smm/ 97th Statistical Mechanics Conference] May 6-8, 2007 Rutgers University
*[http://www.ucm.es/info/molecsim/workshop.htm Workshop on Theory and Computer Simulations of Inhomogenoeus Fluids] May 16-18, 2007, Universidad Complutense, Madrid.

Help:Contents

2007-04-26T09:20:57Z

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*[[How to contribute to SklogWiki]]
*[[SklogWiki style guide]]
*[[LaTeX math markup]]
*[[Tables]]
*[[Variables]]
*[[Short essays section]]

Conferences

2007-04-25T10:58:02Z

161.111.20.5:

Note: to make this page more useful, the conferences should be in '''chronological order''', with the forthcoming conference at the '''top''' of the list.
*[http://www.math.rutgers.edu/events/smm/res-formI.html 97th Statistical Mechanics Conference] May 6-8, 2007 Rutgers University
*[http://www.ecns2007.org 4th European Conference on Neutron Scattering] Lund, Sweden 25-29 June 2007.
*[http://www.realitygrid.org/CompSci07 Computational Science 2007] 25-26 June 2007 The Royal Society, London
*[https://www.cecam.fr/index.php?content=activities/workshop "New directions in liquid state theory"] CECAM workshop, 2 - 4 July, 2007 at ENS, Lyon
*[http://www.statphys23.org/ STATPHYS 23] Genova, Italy, from July 9 to 13, 2007.
*[http://www.iupac2007.org/ 41st IUPAC World Chemistry Conference] Turin, Italy, August 5-11th.
*[http://ccp2007.ulb.ac.be CCP 2007] Brussels 5-8 September 2007
*[http://www.isis.rl.ac.uk/largescale/loq/SAS2009/SAS2009.htm SAS-2009] XIV International Conference on Small-Angle Scattering, Sunday 13 - Friday 18 September, 2009, Oxford (UK).
*[http://thermo2007.ifp.fr Thermodynamics 2007] 26-28 September 2007, IFP - Rueil-Malmaison (France)
*[http://www.iccmse.org/ ICCMSE 2007] International Conference of Computational Methods in Sciences and Engineering, HOTEL MARBELLA, Corfu, Greece, 25-30 September 2007
*[http://www.fz-juelich.de/iff/ismc2007/ ISMC 2007] International Soft Matter Conference 2007, 1 - 4 October 2007, Eurogress, Aachen (Germany)
*[http://www.ill.fr/Events/rktsymposium/ SISMB 2008] Surfaces and Interfaces in Soft Matter and Biology : the impact and future of neutron reflectivity - A Symposium in Honor of Robert K. Thomas, 21-23 May 2008, Institut Laue-Langevin (Grenoble, France).
==Previous conferences==
*[http://www.simbioma.cecam.org/ Simulation of Hard Bodies] April 16 to April 19 2007 in Lyon.

Conferences

2007-03-22T15:01:25Z

161.111.20.5:

Note: to make this page more useful, the conferences should be in '''chronological order''', with the forthcoming conference at the '''top''' of the list.
*[http://www.simbioma.cecam.org/ Simulation of Hard Bodies] April 16 to April 19 2007 in Lyon.
*[http://www.math.rutgers.edu/events/smm/res-formI.html 97th Statistical Mechanics Conference] May 6-8, 2007 Rutgers University
*[http://www.ecns2007.org 4th European Conference on Neutron Scattering] Lund, Sweden 25-29 June 2007.
*[http://ccp2007.ulb.ac.be CCP 2007] Brussels 5-8 September 2007
*[http://www.isis.rl.ac.uk/largescale/loq/SAS2009/SAS2009.htm SAS-2009] XIV International Conference on Small-Angle Scattering, Sunday 13 - Friday 18 September, 2009, Oxford (UK).
*[http://thermo2007.ifp.fr Thermodynamics 2007] 26-28 September 2007, IFP - Rueil-Malmaison (France)
*[http://www.iccmse.org/ ICCMSE 2007] International Conference of Computational Methods in Sciences and Engineering, HOTEL MARBELLA, Corfu, Greece, 25-30 September 2007
*[http://www.fz-juelich.de/iff/ismc2007/ ISMC 2007] International Soft Matter Conference 2007, 1 - 4 October 2007, Eurogress, Aachen (Germany)

Conferences

2007-03-21T09:45:10Z

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