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dc.contributor.authorMartiniani, Stefano
dc.date.accessioned2017-08-21T17:12:52Z
dc.date.available2017-08-21T17:12:52Z
dc.date.issued2017-04-12
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/266695
dc.description.abstractWhen the states of a system can be described by the extrema of a high-dimensional function, the characterisation of its complexity, i.e. the enumeration of the accessible stable states, can be reduced to a sampling problem. In this thesis a robust numerical protocol is established, capable of producing numerical estimates of the total number of stable states for a broad class of systems, and of computing the a-priori probability of observing any given state. The approach is demonstrated within the context of the computation of the configurational entropy of two and three-dimensional jammed packings. By means of numerical simulation we show the extensivity of the granular entropy as proposed by S.F. Edwards for three-dimensional jammed soft-sphere packings and produce a direct test of the Edwards conjecture for the equivalent two dimensional systems. We find that Edwards’ hypothesis of equiprobability of all jammed states holds only at the (un)jamming density, that is precisely the point of practical significance for many granular systems. Furthermore, two new recipes for the computation of high-dimensional volumes are presented, that improve on the established approach by either providing more statistically robust estimates of the volume or by exploiting the trajectories of the paths of steepest descent. Both methods also produce as a natural by-product unprecedented details on the structures of high-dimensional basins of attraction. Finally, we present a novel Monte Carlo algorithm to tackle problems with fluctuating weight functions. The method is shown to improve accuracy in the computation of the ‘volume’ of high dimensional ‘fluctuating’ basins of attraction and to be able to identify transition states along known reaction coordinates. We argue that the approach can be extended to the optimisation of the experimental conditions for observing certain phenomena, for which individual measurements are stochastic and provide little guidance.
dc.description.sponsorshipGates Cambridge scholarship, St John's Benefactors scholarship
dc.language.isoen
dc.rightsNo Creative Commons licence (All rights reserved)
dc.rightsAll Rights Reserveden
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/en
dc.subjectenergy landscapes
dc.subjectMonte Carlo
dc.subjectbasins of attraction
dc.subjectgranular physics
dc.subjectEdwards conjecture
dc.subjectstochastic optimisation
dc.subjectfree energy calculations
dc.titleOn the complexity of energy landscapes: algorithms and a direct test of the Edwards conjecture
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.publisher.departmentChemistry
dc.date.updated2017-08-18T19:46:50Z
dc.identifier.doi10.17863/CAM.12772
dc.contributor.orcidMartiniani, Stefano [0000-0003-2028-2175]
dc.publisher.collegeSt John's
dc.type.qualificationtitleChemistry
cam.supervisorFrenkel, Daan
cam.supervisor.orcidFrenkel, Daan [0000-0002-6362-2021]
rioxxterms.freetoread.startdate2017-08-18


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