Classical Statistical Mechanics with Nested Sampling

Robert John Nicholas Baldock (Autor)

Buch | Hardcover

XII, 144 Seiten

2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-66768-3 (ISBN)

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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.

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.

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.

Erscheinungsdatum	08.12.2017
Reihe/Serie	Springer Theses
Zusatzinfo	XII, 144 p. 30 illus., 25 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	361 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
	Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
Schlagworte	Aluminium P-T Phase Diagram • Blind Search Algorithms • Calculation of Partition Function • Clone and Decorrelate • Complex Systems • Condensed matter physics (liquid state & solid sta • Condensed matter physics (liquid state & solid sta • dynamics & statics • Dynamics & statics • Efficient Derivation of Phase Diagram • Lennard-Jonesium • Mathematical Physics • Nested Sampling Algorithm • Numerical and Computational Physics, Simulation • Phase Transitions and Multiphase Systems • Physics • Physics and Astronomy • Statistical Physics • Statistical Physics and Dynamical Systems • Unexpected Collective Phenomena
ISBN-10	3-319-66768-8 / 3319667688
ISBN-13	978-3-319-66768-3 / 9783319667683
Zustand	Neuware