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Maxwell's Equations from Electrostatics and Einstein's Gravitational Field Equation from Newton's Universal Law of Gravitation Using Tensors

Description: Maxwell's equations are obtained from Coulomb's Law using special relativity. For the derivation, tensor analysis is used, charge is assumed to be a conserved scalar, the Lorentz force is assumed to be a pure force, and the principle of superposition is assumed to hold. Einstein's gravitational field equation is obtained from Newton's universal law of gravitation. In order to proceed, the principle of least action for gravity is shown to be equivalent to the maximization of proper time along a geodesic. The conservation of energy and momentum is assumed, which, through the use of the Bianchi identity, results in Einstein's field equation.
Date: May 2004
Creator: Burns, Michael E.
Partner: UNT Libraries

Characterizing Spontaneous Neurophysiological Activity with Measures of Statistical Serial Dependence: a Summary Statistic and an Extension of the Joint Interval Histogram

Description: Two measures which indicate statistical serial dependence were evaluated. The n-dimensional Average Stored Information index (ndASI) is a measure of conditional information, which compares the entropies of higher order conditional distributions to estimate average statistical serial dependence. The generalized ranked joint interval histogram (RJIH-o) is a new nonparametric graphical analysis method. It extends the joint interval histogram by depicting longer interval sequences and can be interpereted precisely analagously to the joint interval histogram. The generalized ranked joint interval histogram correctly represents independence in a Poisson process model and statistical serial dependence in a directionally reinforced Markov model. The generalized ranked joint interval histogram correctly depicts the underlying periodic and strange attractors in a standard map model. Both measures can be used to effectively analyze interspike interval sequences from spontaneous neurophsyiological activity effectively.
Date: August 1994
Creator: Weil, Jon C. (Jon Christopher)
Partner: UNT Libraries

Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor

Description: The de Broglie-Bohm (BB) approach to quantum mechanics gives trajectories similar to classical trajectories except that they are also determined by a quantum potential. The quantum potential is a "fictitious potential" in the sense that it is part of the quantum kinetic energy. We use quantum trajectories to treat quantum chaos in a manner similar to classical chaos. For the kicked rotor, which is a bounded system, we use the Benettin et al. method to calculate both classical and quantum Lyapunov exponents as a function of control parameter K and find chaos in both cases. Within the chaotic sea we find in both cases nonchaotic stability regions for K equal to multiples of π. For even multiples of π the stability regions are associated with classical accelerator mode islands and for odd multiples of π they are associated with new oscillator modes. We examine the structure of these regions. Momentum diffusion of the quantum kicked rotor is studied with both BB and standard quantum mechanics (SQM). A general analytical expression is given for the momentum diffusion at quantum resonance of both BB and SQM. We obtain agreement between the two approaches in numerical experiments. For the case of nonresonance the quantum potential is not zero and must be included as part of the quantum kinetic energy for agreement. The numerical data for momentum diffusion of classical kicked rotor is well fit by a power law DNβ in the number of kicks N. In the anomalous momentum diffusion regions due to accelerator modes the exponent β(K) is slightly less than quadratic, except for a slight dip, in agreement with an upper bound (K2/2)N2. The corresponding coefficient D(K) in these regions has three distinct sections, most likely due to accelerator modes with period greater than one. We also show that the local ...
Date: August 2005
Creator: Zheng, Yindong
Partner: UNT Libraries

Deterministic Brownian Motion

Description: The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscpoic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism - the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous ...
Date: August 1993
Creator: Trefán, György
Partner: UNT Libraries

Magneto-Optical and Chaotic Electrical Properties of n-InSb

Description: This thesis investigation concerns the optical and nonlinear electrical properties of n-InSb. Two specific areas have been studied. First is the magneto-optical study of magneto-donors, and second is the nonlinear dynamic study of nonlinear and chaotic oscillations in InSb. The magneto-optical study of InSb provides a physical picture of the magneto-donor levels, which has an important impact on the physical model of nonlinear and chaotic oscillations. Thus, the subjects discussed in this thesis connect the discipline of semiconductor physics with the field of nonlinear dynamics.
Date: December 1991
Creator: Song, Xiang-Ning
Partner: UNT Libraries

Synchronous Chaos, Chaotic Walks, and Characterization of Chaotic States by Lyapunov Spectra

Description: Four aspects of the dynamics of continuous-time dynamical systems are studied in this work. The relationship between the Lyapunov exponents of the original system and the Lyapunov exponents of induced Poincare maps is examined. The behavior of these Poincare maps as discriminators of chaos from noise is explored, and the possible Poissonian statistics generated at rarely visited surfaces are studied.
Date: August 1993
Creator: Albert, Gerald (Gerald Lachian)
Partner: UNT Libraries

The Fractal Stochastic Point Process Model of Molecular Evolution and the Multiplicative Evolution Statistical Hypothesis

Description: A fractal stochastic point process (FSPP) is used to model molecular evolution in agreement with the relationship between the variance and mean numbers of synonymous and nonsynonymous substitutions in mammals. Like other episodic models such as the doubly stochastic Poisson process, this model accounts for the large variances observed in amino acid substitution rates, but unlike other models, it also accounts for the results of Ohta's (1995) analysis of synonymous and nonsynonymous substitutions in mammalian genes. That analysis yields a power-law increase in the index of dispersion and an inverse power-law decrease in the coefficient of variation with the mean number of substitutions, as predicted by the FSPP model but not by the doubly stochastic Poisson model. This result is compatible with the selection theory of evolution and the nearly-neutral theory of evolution.
Date: May 1997
Creator: Bickel, David R. (David Robert)
Partner: UNT Libraries

Two-Fold Role of Randomness: A Source of Both Long-Range Correlations and Ordinary Statistical Mechanics

Description: The role of randomness as a generator of long range correlations and ordinary statistical mechanics is investigated in this Dissertation. The difficulties about the derivation of thermodynamics from mechanics are pointed out and the connection between the ordinary fluctuation-dissipation process and possible anomalous properties of statistical systems is highlighted.
Date: December 1998
Creator: Rocco, A. (Andrea)
Partner: UNT Libraries

On Delocalization Effects in Multidimensional Lattices

Description: A cubic lattice with random parameters is reduced to a linear chain by the means of the projection technique. The continued fraction expansion (c.f.e.) approach is herein applied to the density of states. Coefficients of the c.f.e. are obtained numerically by the recursion procedure. Properties of the non-stationary second moments (correlations and dispersions) of their distribution are studied in a connection with the other evidences of transport in a one-dimensional Mori chain. The second moments and the spectral density are computed for the various degrees of disorder in the prototype lattice. The possible directions of the further development are outlined. The physical problem that is addressed in the dissertation is the possibility of the existence of a non-Anderson disorder of a specific type. More precisely, this type of a disorder in the one-dimensional case would result in a positive localization threshold. A specific type of such non-Anderson disorder was obtained by adopting a transformation procedure which assigns to the matrix expressing the physics of the multidimensional crystal a tridiagonal Hamiltonian. This Hamiltonian is then assigned to an equivalent one-dimensional tight-binding model. One of the benefits of this approach is that we are guaranteed to obtain a linear crystal with a positive localization threshold. The reason for this is the existence of a threshold in a prototype sample. The resulting linear model is found to be characterized by a correlated and a nonstationary disorder. The existence of such special disorder is associated with the absence of Anderson localization in specially constructed one-dimensional lattices, when the noise intensity is below the non-zero critical value. This work is an important step towards isolating the general properties of a non-Anderson noise. This gives a basis for understanding of the insulator to metal transition in a linear crystal with a subcritical noise.
Date: May 1998
Creator: Bystrik, Anna
Partner: UNT Libraries

Microscopic Foundations of Thermodynamics and Generalized Statistical Ensembles

Description: This dissertation aims at addressing two important theoretical questions which are still debated in the statistical mechanical community. The first question has to do with the outstanding problem of how to reconcile time-reversal asymmetric macroscopic laws with the time-reversal symmetric laws of microscopic dynamics. This problem is addressed by developing a novel mechanical approach inspired by the work of Helmholtz on monocyclic systems and the Heat Theorem, i.e., the Helmholtz Theorem. By following a line of investigation initiated by Boltzmann, a Generalized Helmholtz Theorem is stated and proved. This theorem provides us with a good microscopic analogue of thermodynamic entropy. This is the volume entropy, namely the logarithm of the volume of phase space enclosed by the constant energy hyper-surface. By using quantum mechanics only, it is shown that such entropy can only increase. This can be seen as a novel rigorous proof of the Second Law of Thermodynamics that sheds new light onto the arrow of time problem. The volume entropy behaves in a thermodynamic-like way independent of the number of degrees of freedom of the system, indicating that a whole thermodynamic-like world exists at the microscopic level. It is also shown that breaking of ergodicity leads to microcanonical phase transitions associated with nonanalyticities of volume entropy. The second part of the dissertation deals with the problem of the foundations of generalized ensembles in statistical mechanics. The starting point is Boltzmann's work on statistical ensembles and its relation with the Heat Theorem. We first focus on the nonextensive thermostatistics of Tsallis and the associated deformed exponential ensembles. These ensembles are analyzed in detail and proved (a) to comply with the requirements posed by the Heat Theorem, and (b) to interpolate between canonical and microcanonical ensembles. Further they are showed to describe finite systems in contact with finite heat baths. ...
Date: May 2008
Creator: Campisi, Michele
Partner: UNT Libraries

The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes

Description: We show that the nonadditive open systems can be studied in a consistent manner by using a generalized version of S-theorem. This new generalized S-theorem can further be considered as an indication of self-organization in nonadditive open systems as prescribed by Haken. The nonadditive S-theorem is then illustrated by using the modified Van der Pol oscillator. Finally, Tsallis entropy as an equilibrium entropy is studied by using Boltzmann's method of orthodes. This part of dissertation shows that Tsallis ensemble is on equal footing with the microcanonical, canonical and grand canonical ensembles. However, the associated entropy turns out to be Renyi entropy.
Date: August 2008
Creator: Bagci, Gokhan Baris
Partner: UNT Libraries

Model for Long-range Correlations in DNA Sequences

Description: We address the problem of the DNA sequences developing a "dynamical" method based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic, with long-range correlations, and the other random and delta correlated. The generator of the deterministic evolution is a nonlinear map, belonging to a class of maps recently tailored to mimic the processes of weak chaos responsible for the birth of anomalous diffusion. It is assumed that the deterministic process corresponds to unknown biological rules which determine the DNA path, whereas the noise mimics the influence of an infinite-dimensional environment on the biological process under study. We prove that the resulting diffusion process, if the effect of the random process is neglected, is an a-stable Levy process with 1 < a < 2. We also show that, if the diffusion process is determined by the joint action of the deterministic and the random process, the correlation effects of the "deterministic dynamics" are cancelled on the short-range scale, but show up in the long-range one. We denote our prescription to generate statistical sequences as the Copying Mistake Map (CMM). We carry out our analysis of several DNA sequences, and of their CMM realizations, with a variety of techniques, and we especially focus on a method of regression to equilibrium, which we call the Onsager Analysis. With these techniques we establish the statistical equivalence of the real DNA sequences with their CMM realizations. We show that long-range correlations are present in exons as well as in introns, but are difficult to detect, since the exon "dynamics" is shown to be determined by theentaglement of three distinct and independent CMM's. Finally we study the validity of the stationary assumption in DNA sequences and we discuss a biological model for the ...
Date: December 1996
Creator: Allegrini, Paolo
Partner: UNT Libraries

A Study of Quantum Electron Dynamics in Periodic Superlattices under Electric Fields

Description: This thesis examines the quantum dynamics of electrons in periodic semiconductor superlattices in the presence of electric fields, especially uniform static fields. Chapter 1 is an introduction to this vast and active field of research, with an analysis and suggested solutions to the fundamental theoretical difficulties. Chapter 2 is a detailed historical review of relevant theories, and Chapter 3 is a historical review of experiments. Chapter 4 is devoted to the time-independent quantum mechanical study of the electric-field-induced changes in the transmission properties of ballistic electrons, using the transfer matrix method. In Chapter 5, a new time-dependent quantum mechanical model free from the fundamental theoretical difficulties is introduced, with its validity tested at various limiting cases. A simplified method for calculating field-free bands of various potential models is designed. In Chapter 6, the general features of "Shifting Periodicity", a distinctive feature of this new model, is discussed, and a "Bloch-Floquet Theorem" is rigorously proven. Numerical evidences for the existence of Wannier-Stark-Ladders are presented, and the conditions for its experimental observability is also discussed. In Chapter 7, an analytical solution is found for Bloch Oscillations and Wannier-Stark-Ladders at low electric fields. In Chapter 8, a new quantum mechanical interpretation for Bloch Oscillations and Wannier-Stark-Ladders is derived from the analytical result. The extension of this work to the cases of time-dependent electric fields is also discussed.
Date: May 1996
Creator: Yuan, Daiqing
Partner: UNT Libraries

Functional Properties and Organization of Primary Somatosensory Cortex

Description: The physiological characteristics and organization of cat primary somatosensory cortex (SI) were studied in electrophysiological and anatomical experiments. In single cell recording experiments, quantitatively controlled mechanical stimuli were used to examine the responses of SI cortical neurons to the velocity component of skin or hair displacement. The firing frequency of most rapidly adapting neurons increased as stimulus velocity was increased. Rapidly adapting neurons were classified based on their response patterns to constant-velocity ramp stimuli. Neurons in these classes differed significantly in sensitivity to stimulus velocity and amplitude, adaptation rate, and spontaneous firing rate. The results suggest that frequency coding of stimulus displacement velocity could be performed by individual SI rapidly adapting neurons, and that the classes of rapidly adapting neurons may play different roles in sensation of tactile stimuli. Tract-tracing experiments were used to investigate the ipsilateral corticocortical connections of areas 3b and 2 in SI. Different patterns of connections were found for these areas: area 2 projects to areas 3b, 1, 3a, 5a, 4 and second somatosensory cortex (SII), and area 3b projects to areas 2, 1, 3a and SII. To further compare the organization of these areas, the thalamic input to the forepaw representation within each area was studied. The forepaw region in area 3b receives thalamic input exclusively from ventroposteriopr lateral nucleus (VPL), while area 2 receives input from VPL, medial division of the posterior complex (PoM), and lateral posterior nucleus (LP). These results suggest that area 2 lies at a higher position in the hierarchy of somatosensory information flow.
Date: December 1993
Creator: Esteky, Hossein
Partner: UNT Libraries

Scaling Behaviors and Mechanical Properties of Polymer Gels

Description: Polymer gels undergo a volume phase transition in solvent in response to an infinitesimal environmental change. This remarkable phenomenon has resulted in many potential applications of polymer gels. The understanding of its mechanical properties has both scientific and technological importance. For this purpose, we have developed a novel method for measuring Poisson's ratio, which is one of the most important parameters determining the mechanical property of gels. Using this method, Poisson's ratio in N-isopropyacrylamide (NIPA) and polyacrylamide (PAAM) gels has been studied.
Date: May 1994
Creator: Li, Chʻun-fang
Partner: UNT Libraries

Quantitative Analysis of the Gabaergic System in Cat Primary Somatosensory Cortex and Its Relation to Receptive Field Properties

Description: Sensory neocortex contains a significant number of inhibitory neurons that use gamma-aminobutyric acid (GABA) as their neurotransmitter. Functional roles for these neurons have been identified in physiological studies. For example, in primary somatosensory cortex (SI), blockade of GABAa receptors with bicuculline leads to expansion of receptive fields (RFs). The magnitude of RF enlargement varies between SIpopulations of GABAergic neurons were identified by labeling specific calcium binding proteins.
Date: May 1995
Creator: Li, Jianying
Partner: UNT Libraries

Nonlinear Dynamics of Semiconductor Device Circuits and Characterization of Deep Energy Levels in HgCdTe by Using Magneto-Optical Spectroscopy

Description: The nonlinear dynamics of three physical systems has been investigated. Diode resonator systems are experimentally shown to display a period doubling route to chaos, quasiperiodic states, periodic locking states, and Hopf bifurcation to chaos. Particularly, the transition from quasiperiodic states to chaos in line-coupled systems agrees well with the Curry-Yorke model. The SPICE program has been modified to give realistic models for the diode resonator systems.
Date: May 1994
Creator: Yü, Chi
Partner: UNT Libraries

Studies of Classically Chaotic Quantum Systems within the Pseudo-Probablilty Formalism

Description: The evolution of classically chaotic quantum systems is analyzed within the formalism of Quantum Pseudo-Probability Distributions. Due to the deep connections that a quantum system shows with its classical correspondent in this representation, the Pseudo-Probability formalism appears to be a useful method of investigation in the field of "Quantum Chaos." In the first part of the thesis we generalize this formalism to quantum systems containing spin operators. It is shown that a classical-like equation of motion for the pseudo-probability distribution ρw can be constructed, dρw/dt = (L_CL + L_QGD)ρw, which is rigorously equivalent to the quantum von Neumann-Liouville equation. The operator L_CL is undistinguishable from the classical operator that generates the semiclassical equations of motion. In the case of the spin-boson system this operator produces semiclassical chaos and is responsible for quantum irreversibility and the fast growth of quantum uncertainty. Carrying out explicit calculations for a spin-boson Hamiltonian the joint action of L_CL and L_QGD is illustrated. It is shown that the latter operator, L_QGD makes the spin system 'remember' its quantum nature, and competes with the irreversibility induced by the former operator. In the second part we test the idea of the enhancement of the quantum uncertainty triggered by the classical chaos by investigating the analogous effect of diffusive excitation in periodically kicked quantum systems. The classical correspondents of these quantum systems exhibit, in the chaotic region, diffusive behavior of the unperturbed energy. For the Quantum Kicked Harmonic Oscillator, in the case of quantum resonances, we provide an exact solution of the quantum evolution. This proves the existence of a deterministic drift in the energy increase over time of the system considered. More generally, this "superdiffusive" excitation of the energy is due to coherent quantum mechanical tunnelling between degenerate tori of the classical phase space. In conclusion we find ...
Date: August 1992
Creator: Roncaglia, Roberto
Partner: UNT Libraries

L-Shell X-Ray Production Cross Sections for ₂₀Ca, ₂₆Fe, ₂₈Ni, ₂₉Cu, ₃₀Zn, ₃₁Ga, and ₃₂Ge by Hydrogen, Helium, and Lithium Ions

Description: L-shell x-ray production cross sections are presented for Fe, Ni, Cu, Zn, Ga, and Ge by 0.5- to 5.0-MeV protons and by 0.5- to 8.0-MeV helium ions and Ca, Fe, Ni, Cu, and Ge by 0.75- to 4.5-MeV lithium ions. These measurements are compared to the first Born theory and the perturbed-stationary- state theory with energy-loss, Coulomb deflection, and relativistic corrections (ECPSSR). The results are also compared to previous experimental investigations. The high precision x-ray measurements were performed with a windowless Si(Li) detector. The efficiency of the detector was determined by the use of thin target atomic-field bremsstrahlung produced by 66.5 keV electrons. The measured bremsstrahlung spectra were compared to theoretical bremsstrahlung distributions in order to obtain an efficiency versus energy curve. The targets for the measurement were manufactured by the vacuum evaporation of the target element onto thin foils of carbon. Impurities in the carbon caused interferences inthe L-shell x-ray peaks. Special cleansing procedures were developed that reduced the impurity concentrations in the carbon foil, making the use of less than 5 μg/cm^2 targets possible. The first Born theory is seen to greatly overpredict the data at low ion energies. The ECPSSR theory matches the data very well at the high energy region. At low energies, while fitting the data much more closely than the first Born theory, the ECPSSR theory does not accurately predict the trend of the data. This is probably due to the onset of molecular-orbital effects, a mechanism not accounted for in the ECPSSR theory.
Date: May 1992
Creator: McNeir, Michael Ridge
Partner: UNT Libraries