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Theory of Phase Transitions and Critical Phenomena
Published in Hung T. Diep, Physics of Magnetic Thin Films, 2021
Phase transitions of second order are distinguished by their “universality class.” Phase transitions having the same values of critical exponents belong to the same university class. Renormalization group analysis shows that the universality class depends only on a few very general parameters such as the space dimension, the symmetry of the order parameter and the nature of the interaction. So, for example, Ising spin systems with short-range ferromagnetic interaction in two dimensions belong to the same universality class whatever the lattice structure is. Of course, the critical temperature Tc is not the same for square, hexagonal, rectangular, honeycomb, …, lattices, but Tc is not a universal quantity. It depends on the interaction value, the coordination number, … but these quantities do not affect the values of the critical exponents.
Introduction to Human Factors Methods in Land Use Planning and Urban Design
Published in Nicholas J. Stevens, Paul M. Salmon, Guy H. Walker, Neville A. Stanton, Human Factors in Land Use Planning and Urban Design, 2018
Nicholas J. Stevens, Paul M. Salmon, Guy H. Walker, Neville A. Stanton
A complex system, in its simplest sense, is a system with a large number of elements that exchange stimuli with each other and with their environment (Batty, 2007; Ottino, 2003). As such any complex system, including cities, will display specific properties. For demonstrating city complexity, Batty (2007) refers to Durlauf (2005) who states these properties are nonergodicity, phase transition, emergence, and universality. Nonergodicity is defined as a system that lacks probable behavior over time and, in the context of cities, can be characterized by exogenous shocks—for example, economic, environmental, social (Durlauf, 2005). Phase transition refers to a complex system having tipping points in which a convergence of elements can change the system. In recognizing the first two properties, emergence refers to the new systems properties that arise from the interaction of system components. It is the evolution of the system and is true to the notion that a system is greater than the sum of its parts (Batty, 2007). It is emergent changes that, from a positive perspective, can lead to innovation, novelty, and surprise, whereas from an HF safety and risk management approach may represent adverse events or accidents within the system (Rasmussen, 1997). Finally, universality refers to the system property that when examined at different times and spatial scales, the system is able to be recognized as the same (Durlauf, 2005).
Intelligent optimization of a bolt support scheme for a single-stage slope
Published in Engineering Optimization, 2023
Guang Han, Wenlu Li, Xiaoyun Sun, Shenyi Jin, Haiqing Zheng, Xiaoxue Wang
The previous research on bolt support can be divided into traditional and modern forms. In the traditional optimization method, researchers analyse the relationship between the stress of different bolt support structures and the degree of rock mass deformation through the finite element method. This takes a long time, the accuracy of optimization results is low and the engineering adaptability is poor, or the researchers establish data tables by enumeration for comparison or use orthogonal experiments to obtain data and conduct multiple linear regression analysis to explore the law of slope bolting. When the selected bolt parameters have many characteristics, because the bolt layout parameters have the characteristic of coexisting continuous and discrete quantities, these methods cannot realize the detailed enumeration of the slope bolting form, and the range of the corresponding solution space is very limited, so it is impossible to traverse all the bolting parameters. Modern optimization methods such as support vector machine, genetic algorithm, ANN and PSO have strong universality. These methods are often used in the field of tunnel engineering, such as in subway and coal-mine roadways, where structural design and optimization design are carried out to increase the bearing capacity of the bolts and reduce the displacement of the surrounding rock. However, research on the bolt support parameter optimization in the field of slope engineering is rare.