http://dspace.cityu.edu.hk:80/handle/2031/775 2013-04-30T06:23:19Z 2013-04-30T06:23:19Z Guo, Wenxuan ( 郭文軒) http://dspace.cityu.edu.hk:80/handle/2031/6633 2012-08-07T07:48:01Z 2010-01-01T00:00:00Z

Title: Anomalous phenomena and intermittency in the dynamics of multiple particles in a funnel Authors: Guo, Wenxuan ( 郭文軒) Abstract: In this thesis, we investigate a granular system of multiple inelastic, frictionless, spherical particles falling under gravity through a symmetric two-dimensional funnel with different particle injection frequencies. Intuitively, one might expect that the average durations which particles spend in the funnel would increase monotonically as the particle injection frequency increases, since, due to inter-particle collisions, the more particles in the funnel, the more likely the particles would slow down and consequently more difficult to pass through the funnel. However we show surprisingly that the duration is not a monotonic function of the injection frequency. We provide an explanation for the seemingly counterintuitive phenomena. We further conduct detailed studies on how the coefficient of restitution and dynamics of inter-particle collisions affect the duration. We also identify the phenomena of intermittency in the system with steep walls. Namely, the behaviors of the system keep altering between two completely different states at certain range of injection frequency. In one state, the particles have very few inter-particle collisions, short durations and simple trajectories; in the other, they have considerably more inter-particle collisions, much longer durations and more complicated trajectories. We provide an explanation for these phenomena, and develop a method of classifying these two states. Notes: CityU Call Number: TA418.78 .G86 2010; iv, 36 leaves : ill. 30 cm.; Thesis (M.Phil.)--City University of Hong Kong, 2010.; Includes bibliographical references (leaves [35]-36)

2010-01-01T00:00:00Z Xu, Chen (徐晨) http://dspace.cityu.edu.hk:80/handle/2031/6259 2011-05-25T01:19:35Z 2010-01-01T00:00:00Z

Title: Convergence to shared lexicons for multi-object domains Authors: Xu, Chen (徐晨) Abstract: In recent years, consensus problems have attracted increasing attention from researchers in various fields. Consensus problems in language emergence and evolution are always raised in the following form: how might a group of agents reach a shared communication system under certain patterns of interaction despite the absence of a centralized coordinator? In this thesis, consensus problems of a multi-agent model for multi-object domains in discrete time are considered. We first propose a generalization of Liberman’s model and study how a group of agents produce a common lexicon to describe the same collection objects despite their different initial beliefs on word usage. At each time, all agents meet together, select an object, exchange messages with a name for this object, and update their beliefs, based on these messages, according to a designed protocol. We study the dynamics for this model and analyze convergence and homonymy phenomena. Then we study a different situation on which each agent can select its own individual object. In contrast with the previous case, however, we now assume that agents can exchange their beliefs (instead of only pairs (object, word)). We prove that all beliefs will converge to the same belief provided each object is selected frequently enough. Finally, computer simulations are attached to support the mathematical proofs of the above two cases. Notes: CityU Call Number: P326 .X8 2010; iv, 65 leaves : ill. 30 cm.; Thesis (M.Phil.)--City University of Hong Kong, 2010.; Includes bibliographical references (leaves [50]-52)

2010-01-01T00:00:00Z Ng, Kwok-tim (伍國添) http://dspace.cityu.edu.hk:80/handle/2031/6257 2011-05-25T01:19:31Z 2010-01-01T00:00:00Z

Title: On a nonlinear model for stress-induced phase transitions in a slender compressible hyperelastic cylinder : analytical solutions and stability Authors: Ng, Kwok-tim (伍國添) Abstract: In this thesis, some methodology in nonlinear dynamics is used to study a boundary-value problem of a nonlinear model arisen in phase transitions in a slender cylinder composed of a compressible hyperelastic material. We transform the original system of boundary value problem to an initial-value (dynamical) problem of finding periodic solutions of coupled nonlinear autonomous oscillators in a four-dimensional space. Hopf-like bifurcation analysis of the periodic solutions of the system is studied. Both analytical and numerical solutions are obtained by using a nonlinear transformation formulation. The analytical solutions are obtained by the perturbation method incorporate with a nonlinear transformation while the numerical solutions are obtained by the perturbation-incremental method. In addition, the accuracy of analytical solutions is investigated by comparing with the numerical solutions. The engineering stress-strain curve is plotted and compared with that from the normal form equation, which is a simplification of the original system. The stability of periodic solutions is also discussed in this thesis. Notes: CityU Call Number: QA379 .N39 2010; iii, 99 leaves : ill. 30 cm.; Thesis (M.Phil.)--City University of Hong Kong, 2010.; Includes bibliographical references (leaves 78-80)

2010-01-01T00:00:00Z Huang, Chi (黃遲) http://dspace.cityu.edu.hk:80/handle/2031/6253 2011-05-25T01:19:22Z 2009-01-01T00:00:00Z

Title: Synchronization analysis of polytopic complex dynamical network Authors: Huang, Chi (黃遲) Abstract: Complex dynamical networks are ubiquitous in our real world, ranging from biological, physical, to social networks. Over the past decade, much of the interesting dynamical behaviour of complex dynamical networks, such as synchronization, spatiotemporal chaos, auto-waves and spiral waves, has recently attracted increasing attention from researchers in different areas. Among these, synchronization has been a hot research topic in recent years. Synchronization behaviour of networks is a universal phenomenon in nature; while, synchronization techniques have been widely applied in our daily life. Hence, there is a great demand to study synchronization behaviour of complex dynamical networks. There are some common phenomena in most real-world networks including the diversity of complex networks, structural uncertainty and time-varying links. Research on the corresponding concerned issues of synchronization analysis of complex dynamical networks will be presented in this thesis. The research problems are as follows: (a) Is it possible to establish synchronization criteria of a group of complex networks? (b) How does one establish synchronization criteria of complex networks with structural uncertainty? (c) How does one propose synchronization criteria of time-varying complex networks? Problem (a) arises from the fact that in practice people always have to investigate the synchronization of many different networks. The existing results can check the synchronization behaviour for only one complex network, which motivates the research of Problem (a). In this thesis, the concept of the polytopic complex network family is first defined. The models of inner and outer network families are constructed. The coupling delay, a common phenomenon of real life networks, is also considered in these models. The delay independent and delay dependent synchronization criteria are derived for inner and outer network families, respectively. Compared with the existing results, the proposed synchronization criteria in this thesis are satisfied by a set of complex networks within the same family, rather than being applied for only single complex network. Since intrinsic physical disturbances exist in real-life networks, the structural uncertainty of complex networks is unavoidable. Thus, Problem (b) arises, which few results have addressed. In this thesis, some sufficient conditions to guarantee the synchronization of complex networks with structural uncertainty will be derived. The uncertainty is considered in inner and outer coupling matrices of complex networks, which represent the network structure. Both polytopic and norm-bounded representations of uncertainty are discussed in detail. It is widely known that many real networks have time-varying structure. Hence, Problem (c) is investigated. In this thesis, the time-varying polytopic complex network is constructed. Based on the parameter-dependent Lyapunov function, the global synchronization criterion is proposed. In our result, the condition on the negative definition of some time-varying matrices has been removed, thus providing a more convenient way to verify the condition when compared with existing results. Notes: CityU Call Number: QA402 .H825 2009; vii, 77 leaves 30 cm.; Thesis (M.Phil.)--City University of Hong Kong, 2009.; Includes bibliographical references (leaves [66]-77)

2009-01-01T00:00:00Z