Potential energy landscape of particulate matter
Item
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Title
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Potential energy landscape of particulate matter
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Identifier
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d_2009_2013:c010e7b2b245:11222
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identifier
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11528
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Creator
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Wang, Kun,
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Contributor
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Hernan A. Makse
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Date
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2012
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Language
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English
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Publisher
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City University of New York.
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Subject
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Plasma physics | Condensed matter physics | angoricity | Edwards ensemble | granular materials | jamming | network | potential energy landscape
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Abstract
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The application of concepts from equilibrium statistical mechanics to out of equilibrium systems has a long history of describing diverse systems ranging from glasses to granular materials [1, 2, 3]. These systems are considered "complex" since equilibrium statistics is insufficient in its attempt to describe the system dynamics. An appealing approach for understanding these complex systems is to study the properties of the system's "potential energy landscape" (PEL), described by the 3 N-coordinates of all particles in the multi-dimensional configuration space, or landscape, of the potential energy of the system (N is the number of particles).;For dissipative jammed systems-- granular materials or droplets-- a key concept introduced by S. Edwards in 1989 is to replace the energy ensemble describing conservative systems by the volume ensemble [3]. However, this approach is not able to describe the jamming critical point (J-point) for deformable particles like emulsions [4, 5, 6], whose geometric configurations are influenced by the applied external stress. Therefore, the volume ensemble requires augmentation by the ensemble of stresses [7, 8, 9, 10]. Just as volume fluctuations in the Edwards ensemble can be described by compactivity, the stress fluctuations give rise to an angoricity, another analogue of temperature in equilibrium systems. In this Thesis, we test the combined volume-stress ensemble for granular matter by comparing the statistical properties of jammed configurations obtained by dynamics with those averaged over the ensemble as a test of ergodicity. Agreement between both methods suggests the idea of "thermalization" at a given angoricity and compactivity. These intensive variables elucidate the thermodynamic order of the jamming phase transition by showing the absence of critical fluctuations above jamming in static observables like pressure and volume. Our results demonstrate the possibility of calculating important observables such as the entropy, volume, pressure, coordination number and the distribution of interparticle forces to fully characterize the scaling laws near the jamming transition from a statistical mechanics point of view.;We also study the energy-landscape network. We find the stable basins and the first order saddles connecting them, and identify them with the network nodes and links, respectively. We analyze the network properties and model the system's evolution.
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Type
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dissertation
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Source
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2009_2013.csv
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degree
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Ph.D.
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Program
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Physics
