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Classical Statistical Mechanics with Nested Sampling: Springer Theses

Autor Robert John Nicholas Baldock
en Limba Engleză Hardback – 28 noi 2017
This thesis develops a nested sampling algorithm into a black box tool for directly calculating the partition function, and thus the complete phase diagram of a material, from the interatomic potential energy function. It represents a significant step forward in our ability to accurately describe the finite temperature properties of materials. In principle, the macroscopic phases of matter are related to the microscopic interactions of atoms by statistical mechanics and the partition function. In practice, direct calculation of the partition function has proved infeasible for realistic models of atomic interactions, even with modern atomistic simulation methods. The thesis also shows how the output of nested sampling calculations can be processed to calculate the complete PVT (pressure–volume–temperature) equation of state for a material, and applies the nested sampling algorithm to calculate the pressure–temperature phase diagrams of aluminium and a model binary alloy.
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Specificații

ISBN-13: 9783319667683
ISBN-10: 3319667688
Pagini: 144
Ilustrații: XII, 144 p. 30 illus., 25 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.4 kg
Ediția:1st ed. 2017
Editura: Springer International Publishing
Colecția Springer
Seria Springer Theses

Locul publicării:Cham, Switzerland

Cuprins

Introduction.- A Primer in Probability.- Phase Space Probability Distributions for Various External Conditions.- Relating Probability Density Functions to the Behaviour of Systems.- The Strategy of Nested Sampling.- Nested Sampling for Materials.- Equations of State.- Parallelising Nested Sampling.- Hamiltonian Monte Carlo for the Canonical Distribution.- Hamiltonian Monte Carlo for Nested Sampling.- Conclusion of Thesis and Further Work.

Notă biografică

Robert Baldock completed his doctoral studies in Physics at the University of Cambridge, UK, in the Theory of Condensed Matter Group in the Cavendish Laboratory (supervised by Dr Gábor Csányi and Prof Michael Payne FRS). He is currently a Postdoc at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland.

Textul de pe ultima copertă

This thesis develops a nested sampling algorithm into a black box tool for directly calculating the partition function, and thus the complete phase diagram of a material, from the interatomic potential energy function. It represents a significant step forward in our ability to accurately describe the finite temperature properties of materials. In principle, the macroscopic phases of matter are related to the microscopic interactions of atoms by statistical mechanics and the partition function. In practice, direct calculation of the partition function has proved infeasible for realistic models of atomic interactions, even with modern atomistic simulation methods. The thesis also shows how the output of nested sampling calculations can be processed to calculate the complete PVT (pressure–volume–temperature) equation of state for a material, and applies the nested sampling algorithm to calculate the pressure–temperature phase diagrams of aluminium and a model binary alloy.

Caracteristici

Nominated as an outstanding PhD thesis by the University of Cambridge, UK Enables the calculation of partition functions as explicit functions of temperature for realistic models of materials directly from atomic interactions Allows the determination of complete phase diagrams and pressure–volume–temperature equations of state Illustrates the efficiency of the algorithm which paves the way for the automated calculation of phase diagrams Includes supplementary material: sn.pub/extras