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**Partner:**UNT Libraries

**Degree Discipline:**Physics

**Degree Level:**Doctoral

**Collection:**UNT Theses and Dissertations

### Complexity as Aging Non-Poisson Renewal Processes

**Date:**May 2007

**Creator:**Bianco, Simone

**Description:**The search for a satisfactory model for complexity, meant as an intermediate condition between total order and total disorder, is still subject of debate in the scientific community. In this dissertation the emergence of non-Poisson renewal processes in several complex systems is investigated. After reviewing the basics of renewal theory, another popular approach to complexity, called modulation, is introduced. I show how these two different approaches, given a suitable choice of the parameter involved, can generate the same macroscopic outcome, namely an inverse power law distribution density of events occurrence. To solve this ambiguity, a numerical instrument, based on the theoretical analysis of the aging properties of renewal systems, is introduced. The application of this method, called renewal aging experiment, allows us to distinguish if a time series has been generated by a renewal or a modulation process. This method of analysis is then applied to several physical systems, from blinking quantum dots, to the human brain activity, to seismic fluctuations. Theoretical conclusions about the underlying nature of the considered complex systems are drawn.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc3706/

### The Concept of Collision Strength and Its Applications

**Date:**May 2004

**Creator:**Chang, Yongbin

**Description:**Collision strength, the measure of strength for a binary collision, hasn't been defined clearly. In practice, many physical arguments have been employed for the purpose and taken for granted. A scattering angle has been widely and intensively used as a measure of collision strength in plasma physics for years. The result of this is complication and unnecessary approximation in deriving some of the basic kinetic equations and in calculating some of the basic physical terms. The Boltzmann equation has a five-fold integral collision term that is complicated. Chandrasekhar and Spitzer's approaches to the linear Fokker-Planck coefficients have several approximations. An effective variable-change technique has been developed in this dissertation as an alternative to scattering angle as the measure of collision strength. By introducing the square of the reduced impulse or its equivalencies as a collision strength variable, many plasma calculations have been simplified. The five-fold linear Boltzmann collision integral and linearized Boltzmann collision integral are simplified to three-fold integrals. The arbitrary order linear Fokker-Planck coefficients are calculated and expressed in a uniform expression. The new theory provides a simple and exact method for describing the equilibrium plasma collision rate, and a precise calculation of the equilibrium relaxation time. It generalizes ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc4530/

### Cooperation-induced Criticality in Neural Networks

**Date:**August 2013

**Creator:**Zare, Marzieh

**Description:**The human brain is considered to be the most complex and powerful information-processing device in the known universe. The fundamental concepts behind the physics of complex systems motivate scientists to investigate the human brain as a collective property emerging from the interaction of thousand agents. In this dissertation, I investigate the emergence of cooperation-induced properties in a system of interacting units. I demonstrate that the neural network of my research generates a series of properties such as avalanche distribution in size and duration coinciding with the experimental results on neural networks both in vivo and in vitro. Focusing attention on temporal complexity and fractal index of the system, I discuss how to define an order parameter and phase transition. Criticality is assumed to correspond to the emergence of temporal complexity, interpreted as a manifestation of non-Poisson renewal dynamics. In addition, I study the transmission of information between two networks to confirm the criticality and discuss how the network topology changes over time in the light of Hebbian learning.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc283813/

### Criticality in Cooperative Systems

**Date:**May 2012

**Creator:**Vanni, Fabio

**Description:**Cooperative behavior arises from the interactions of single units that globally produce a complex dynamics in which the system acts as a whole. As an archetype I refer to a flock of birds. As a result of cooperation the whole flock gets special abilities that the single individuals would not have if they were alone. This research work led to the discovery that the function of a flock, and more in general, that of cooperative systems, surprisingly rests on the occurrence of organizational collapses. In this study, I used cooperative systems based on self-propelled particle models (the flock models) which have been proved to be virtually equivalent to sociological network models mimicking the decision making processes (the decision making model). The critical region is an intermediate condition between a highly disordered state and a strong ordered one. At criticality the waiting times distribution density between two consecutive collapses shows an inverse power law form with an anomalous statistical behavior. The scientific evidences are based on measures of information theory, correlation in time and space, and fluctuation statistical analysis. In order to prove the benefit for a system to live at criticality, I made a flock system interact with another similar ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc271910/

### Decoherence, Master Equation for Open Quantum Systems, and the Subordination Theory

**Date:**August 2005

**Creator:**Giraldi, Filippo

**Description:**This thesis addresses the problem of a form of anomalous decoherence that sheds light into the spectroscopy of blinking quantum dots. The system studied is a two-state system, interacting with an external environment that has the effect of establishing an interaction between the two states, via a coherence generating coupling, called inphasing. The collisions with the environment produce also decoherence, named dephasing. Decoherence is interpreted as the entanglement of the coherent superposition of these two states with the environment. The joint action of inphasing and dephasing generates a Markov master equation statistically equivalent to a random walker jumping from one state to the other. This model can be used to describe intermittent fluorescence, as a sequence of "light on" and "light off" states. The experiments on blinking quantum dots indicate that the sojourn times are distributed with an inverse power law. Thus, a proposal to turn the model for Poisson fluorescence intermittency into a model for non-Poisson fluorescence intermittency is made. The collision-like interaction of the two-state system with the environment is assumed to takes place at random times rather than at regular times. The time distance between one collision and the next is given by a distribution, called the ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc4812/

### A Determination of the Fine Structure Constant Using Precision Measurements of Helium Fine Structure

**Date:**August 2010

**Creator:**Smiciklas, Marc

**Description:**Spectroscopic measurements of the helium atom are performed to high precision using an atomic beam apparatus and electro-optic laser techniques. These measurements, in addition to serving as a test of helium theory, also provide a new determination of the fine structure constant α. An apparatus was designed and built to overcome limitations encountered in a previous experiment. Not only did this allow an improved level of precision but also enabled new consistency checks, including an extremely useful measurement in 3He. I discuss the details of the experimental setup along with the major changes and improvements. A new value for the J = 0 to 2 fine structure interval in the 23P state of 4He is measured to be 31 908 131.25(30) kHz. The 300 Hz precision of this result represents an improvement over previous results by more than a factor of three. Combined with the latest theoretical calculations, this yields a new determination of α with better than 5 ppb uncertainty, α-1 = 137.035 999 55(64).

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc31547/

### Distribution of Nighttime F-region Molecular Ion Concentrations and 6300 Å Nightglow Morphology

**Date:**December 1970

**Creator:**Brasher, William Ernest, 1939-

**Description:**The purpose of this study is two-fold. The first is to determine the dependence of the molecular ion profiles on the various ionospheric and atmospheric parameters that affect their distributions. The second is to demonstrate the correlation of specific ionospheric parameters with 6300 Å nightglow intensity during periods of magnetically quiet and disturbed conditions.

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc278620/

### A dynamic and thermodynamic approach to complexity.

**Date:**August 2003

**Creator:**Yang, Jin

**Description:**The problem of establishing the correct approach to complexity is a very hot and crucial issue to which this dissertation gives some contributions. This dissertation considers two main possibilities, one, advocated by Tsallis and co-workers, setting the foundation of complexity on a generalized, non-extensive , form of thermodynamics, and another, proposed by the UNT Center for Nonlinear Science, on complexity as a new condition that, for physical systems, would be equivalent to a state of matter intermediate between dynamics and thermodynamics. In the first part of this dissertation, the concept of Kolmogorov-Sinai entropy is introduced. The Pesin theorem is generalized in the formalism of Tsallis non-extensive thermodynamics. This generalized form of Pesin theorem is used in the study of two major classes of problems, whose prototypes are given by the Manneville and the logistic map respectively. The results of these studies convince us that the approach to complexity must be made along lines different from those of the non-extensive thermodynamics. We have been convinced that the Lévy walk can be used as a prototype model of complexity, as a condition of balance between order and randomness that yields new phenomena such as aging, and multifractality. We reach the conclusions that ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc4276/

### The dynamic foundation of fractal operators.

**Date:**May 2003

**Creator:**Bologna, Mauro

**Description:**The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation of the fractal calculus on the basis of either classical or quantum mechanics is still unknown, and the second part of this dissertation aims at this important task. This dissertation proves that the adoption of a master equation approach, and so of probabilistic as well as dynamical argument yields a satisfactory solution of the problem, as shown in a work by the candidate already published. At the same time, this dissertation shows that the foundation of Levy statistics is compatible with ordinary statistical mechanics and thermodynamics. The problem of the connection with the Kolmogorov-Sinai entropy is a delicate problem that, however, can be successfully solved. The derivation from a microscopic Liouville-like approach based on densities, however, is shown to be impossible. ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc4235/

### EEG, Alpha Waves and Coherence

**Date:**May 2010

**Creator:**Ascolani, Gianluca

**Description:**This thesis addresses some theoretical issues generated by the results of recent analysis of EEG time series proving the brain dynamics are driven by abrupt changes making them depart from the ordinary Poisson condition. These changes are renewal, unpredictable and non-ergodic. We refer to them as crucial events. How is it possible that this form of randomness be compatible with the generation of waves, for instance alpha waves, whose observation seems to suggest the opposite view the brain is characterized by surprisingly extended coherence? To shed light into this apparently irretrievable contradiction we propose a model based on a generalized form of Langevin equation under the influence of a periodic stimulus. We assume that there exist two different forms of time, a subjective form compatible with Poisson statistical physical and an objective form that is accessible to experimental observation. The transition from the former to the latter form is determined by the brain dynamics interpreted as emerging from the cooperative interaction among many units that, in the absence of cooperation would generate Poisson fluctuations. We call natural time the brain internal time and we make the assumption that in the natural time representation the time evolution of the EEG variable ...

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**Permallink:**digital.library.unt.edu/ark:/67531/metadc28389/