The cerebral cortex contains many neurons. The neuron is part of the nervous system and it receives and transmits the electrical signals. These signals are significant to a human's behaviour. Since the neurons are charged, these charges produce electrical fields, so these neural signals can be measured by using scalp electrodes in electroencephalography (EEG). As long as the brain is not dead, the spontaneous activities of neurons will produce a series of EEG signals. There are many models that have been developed for simulating the cortical signal, and mostly each model is focused towards a different purpose or application. Often, a different computer code has to be written for each different application, and this can be inefficient. Therefore, this project aims to develop a software system for simulating cortical signals where the model used for the system can be changed easily. Furthermore, the system is requested to be versatile and easy-to-use for many applications. The developed system is written in MATLAB in response to a user requirement and mostly applies to any model which uses a mean-field approach. Only the specific inputs need to be modified for changing the model. This thesis details how this system is developed. The main limitation of the system is computational resources, much the same as other cortical modelling. However, all the user requirements had been satisfied. The system can simulate the response of the neurons for any condition and generate simulated EEG data to the user. The user can analyze the cortical activities using the standard signal processing techniques such as a power spectrum. This software is very helpful for the research of sleep and anaesthesia.

published_or_final_version / abstract / Physics / Master / Master of Philosophy

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The dynamics of a quantum system with a large number $N$ of identical bosonic particles interacting by means of weak two-body potentials can be simplified by using mean-field equations in which all interactions to any one body have been replaced with an average or effective interaction in the mean-field limit $N \rightarrow \infty$. In order to show these mean-field equations are accurate, one needs to show convergence of the quantum $N$-body dynamics to these equations in the mean-field limit. Previous results on convergence in the mean field limit have been derived for certain initial conditions in the case of one species of bosonic particles, but no results have yet been shown for multi-species. In this thesis, we look at a quantum bosonic system with two species of particles. For this system, we derive a formula for the rate of convergence in the mean-field limit in the case of an initial coherent state, and we also show convergence in the mean-field limit for the case of an initial factorized state. The analysis for two species can then be extended to multiple species.

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Jorge Piekarewicz, Florida State University, College of Arts and Sciences, Dept. of Physics. Title and description from dissertation home page (viewed June 15, 2004). Includes bibliographical references.

Thesis (M. Phil.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf [74]-81).

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 48). Also available in electronic version. Access restricted to campus users.

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