The application of statistical mechanics on the study of selfish behaviors in transportation networks and energy landscapes in models of combinatorial optimization problems /

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Student Theses

2021

Po, Ho Fai

Hong Kong : The Education University of Hong Kong

Thesis

Knowledge and techniques from statistical physics have been extensively applied in many areas of study, including complex networks and optimization problems. In this thesis, we study two interdisciplinary problems using methods from statistical physics, underlining the broad applicability of statistical methods. The first corresponds to a problem in transportation systems, in which selfish users exist and choose alternative routes to minimize their individual costs instead of using the optimal paths provided. The dynamics of selfish routing have been extensively studied and yet their impact on an initially optimized transportation network have not yet been discussed. We apply the cavity method in spin glass theory with probabilistic modeling to reveal the rerouting behaviors of selfish users as well as their impacts. We also extend to the case of multiple rounds of selfish rerouting, to study the Nash equilibrium of the system via simulation. The second problem corresponds to the study of the energy landscapes of complex disordered systems. These systems exhibit glassy behaviors which are believed to be characterized by the energy landscapes. However, most existing methods describing the energy landscapes have omitted important features. We introduce a method to reveal the complete energy landscape of complex disordered systems, taking spin glasses and K−Satisfiability problems as examples. The energy landscape is used to derive the non-equilibrium dynamics of these systems analytically, which is computationally infeasible by simulations. Physical pictures of the glassy behaviors of these systems are also discussed

LG51.H43 Dr 2021eb Pohf

https://educoll.lib.eduhk.hk/records/jPtmBd4u