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Book Chapter

Reverse Monte Carlo methods

By
Martin T. Dove
Martin T. Dove
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.
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Matthew G. Tucker
Matthew G. Tucker
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.
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Stephen A. Wells
Stephen A. Wells
Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.
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David A. Keen
David A. Keen
ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, U.K.
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Published:
January 01, 2002

Abstract

Most modelling techniques in the solid-state sciences are what would be called forward modelling. The starting point is an exact expression for a Hamiltonian or free energy, together with a way of using this to generate numerical quantities that can be compared with experiment. The starting expression could be a representation of the Schrödinger equation, or a numerical approximation to the forces between atoms. The models can also be based on differential equations to incorporate time-dependence (e.g. the Lagrangian of classical mechanics), or the partition function to obtain thermodynamic averages. The solutions to the models can be exact in some cases (particularly when the models are used to describe a system at zero temperature), but may frequently have some degree of statistical uncertainty. For example, in molecular dynamics, the dynamic equations are solved using discrete time steps over a limited time span, and in Monte Carlo simulations only a portion of the total phase space available to a system is sampled. Whatever approach is taken, the end point of forward modelling may be to provide new insights, to predict behaviour, or to interpret observations. A key point towards this end is to be able to reproduce some experimental data in order to check that the simulations are representative of reality, even though the true value of a simulation is to provide information, insight or understanding that cannot be extracted from experimental data.

In this chapter we will consider a second type of modelling technique, which is called inverse modelling. This is best described by comparison with forward modelling.

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Contents

European Mineralogical Union Notes in Mineralogy

Energy Modelling in Minerals

Carlo Maria Gramaccioli
Carlo Maria Gramaccioli
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Mineralogical Society of Great Britain and Ireland
Volume
4
ISBN electronic:
9780903056397
Publication date:
January 01, 2002

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