THEORETICAL PHYSICIST
Derek J. Daniel BSc Hons PhD
Assistant Professor of Physics & Mathematics
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University of The Bahamas-North
School of Mathematics, Physics and Technology, Room A204
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Office Phone: +1-242-688 5929
Email: derek.daniel@ub.edu.bs
This monograph presents new classes of exact solutions for three formidable and unsolvable problems in theoretical physics. The simple pendulum, the Markovian birth-and-death equations, and the simple harmonic oscillator are among the problems covered.
Computational Projects
The following computational projects are ongoing, but originally began at the Dept. of Applied Physics, University of Technology, Sydney (Australia), with former Head of the Dept. Dr Geoff Anstis.
The project manuscripts below contain detailed analyses, mathematical algorithms and computer codes of each nonlinear dynamical system (or complex system) studied, incorporating a suite of Mathematica software subroutines. The systems, themselves, involved applying:
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i. numerical analysis and finite-element modelling techniques
ii. time-series, random probability and forecasting algorithms
iii. chaos theory
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Chaos Theory of Mandelbrot Sets
Abstract: Fractal sets, defined with the viewpoint as being irregular geometric shapes, are studied as part of computational complexity, with emphasis on understanding basic concepts in chaos theory, as far as is required for science graduates to begin implementing computer algorithms in Mathematica, which itself aims to provide graduates with an easy-to-use simulation tool for understanding and replicating the fractal nature of the Julia and Mandelbrot sets.
Volatility in Economics Forecasting
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Abstract: Simulation of “Foreign exchange rate volatility” is performed under Mathematica to demonstrate computational complexity, in which random walk models and Markov chains, as developed by Rose [Ros] with and without white noise, have been adopted as examples of stochastic processes inherent in many of the economic forecast models found in the literature, including those with a rational bubble component. Time series and phase-space plots are analysed using first-order autoreg-ressive models, which are finite-differ-ence equations implemented within Mathem-atica to further identify another type of fractal common in economic systems, namely, that of clusters and aggregation as formed from the data points.
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Cellular Automata Model for
Earthquakes.
Abstract: The fractal procedure known as cellular automata is applied to the mechanical model of an earthquake fault, based on Carlson and Langer’s [CL] extension of the Burridge and Knopoff (BK) earthquake model, which adopts a slip-stick friction velocity dependent force to describe the Netwonian dynamics of earth-quakes as a system of elastically coupled chain of masses in contact with a moving rough surface subject to slipping. Numerical simulations of this system are performed with Mathematica on a “Newtonian Lattice”, to effect a “crumpling” dynamical behaviour from Newton’s equation of the motion for the chain of masses subject to the slip-stick law, so that “space” and “time” are both discretized to formulate an “earthquake-automaton” that is considered ideal for cellular-automata calculations, since only neighbouring sites (discrete cells) are able to interact due to the nature of the friction force being velocity dependent. Results for the 3-dimensional phase-space dynamics of this earthquake model are also presented