Scaling analysis of nonequilibrium processes in random media = 마구잡이 매질에서 일어나는 비평형 과정의 눈금잡기 분석

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Statistical physics has the simplest form in the thermodynamic limit. However, especially in the uncharted territory of nonequilibrium phenomena and disordered systems, finding the thermodynamic limit is often made difficult by the absence of general formalism and strong finite-size effects. In order to overcome such difficulties, a systematic scaling analysis must be performed to filter out irrelevant properties. This thesis discusses a few examples of nonequilibrium processes in random media in which such scaling analysis provides useful information about the thermodynamic limit. Chapter 2 discusses the graphicaliy problem of scale-free networks, which is related to the geometric constraint on key structural parameters of many complex systems, namely the degree exponent $\gamma$ and the upper cutoff exponent $\alpha$. Using the graphicality criterion proved by Erd\H{o}s and Gallai, the realizable $\alpha$ is shown to be lower than $1/\gamma$ for $\gamma < 2$, whereas any upper cutoff is possible for $\gamma > 2$. This result is also numerically verified by random and deterministic samplings of degree sequences. Chapter 3 discusses the metastable states of zero-temperature Glauber dynamics on Erd\H{o}s--R\`{e}nyi networks, which concerns the fate of curvature-driven coarsening process in the quenched random media. Previous studies have been inconclusive about how close the system can approach the ground state after the quench from infinite to zero temperature. Simulations at various system sizes reveal that there exist two different self-averaging subgroups of metastable states, one approaching close to the ground state and the other staying far away. Scaling analysis suggests that the latter type might be asymptotically dominant, which implies the existence of large stable domain walls in the quenched random media. Chapter 4 discusses the totally asymmetric simple exclusion process (TASEP) on directed random regular networks, which is a simple model of activ...
Jeong, Ha-Woongresearcher정하웅
한국과학기술원 : 물리학과,
Issue Date
568466/325007  / 020098044

학위논문(박사) - 한국과학기술원 : 물리학과, 2014.2, [ x, 91 p. ]


scaling; 능동 수송; 자기 구역 확대; 연결 가능성; 연결망; 눈금잡기; network; graphicality; coarsening; active transport

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