### Emergence of Complexity from Synchronization and Cooperation

**Date:**May 2008

**Creator:**Geneston, Elvis L.

**Description:**The dynamical origin of complexity is an object of intense debate and, up to moment of writing this manuscript, no unified approach exists as to how it should be properly addressed. This research work adopts the perspective of complexity as characterized by the emergence of non-Poisson renewal processes. In particular I introduce two new complex system models, namely the two-state stochastic clocks and the integrate-and-fire stochastic neurons, and investigate its coupled dynamics in different network topologies. Based on the foundations of renewal theory, I show how complexity, as manifested by the occurrence of non-exponential distribution of events, emerges from the interaction of the units of the system. Conclusion is made on the work's applicability to explaining the dynamics of blinking nanocrystals, neuron interaction in the human brain, and synchronization processes in complex networks.

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### Oligonucleotide guanosine conjugated to gallium nitride nano-structures for photonics.

**Date:**August 2008

**Creator:**Li, Jianyou

**Description:**In this work, I studied the hybrid system based on self-assembled guanosine crystal (SAGC) conjugated to wide-bandgap semiconductor gallium nitride (GaN). Guanosine is one of the four bases of DNA and has the lowest oxidation energy, which favors carrier transport. It also has large dipole moment. Guanosine molecules self-assemble to ribbon-like structure in confined space. GaN surface can have positive or negative polarity depending on whether the surface is Ga- or N-terminated. I studied SAGC in confined space between two electrodes. The current-voltage characteristics can be explained very well with the theory of metal-semiconductor-metal (MSM) structure. I-V curves also show strong rectification effect, which can be explained by the intrinsic polarization along the axis of ribbon-like structure of SAGC. GaN substrate property influences the properties of SAGC. So SAGC has semiconductor properties within the confined space up to 458nm. When the gap distance gets up to 484nm, the structure with guanosine shows resistance characteristics. The photocurrent measurements show that the bandgap of SAGC is about 3.3-3.4eV and affected by substrate properties. The MSM structure based on SAGC can be used as photodetector in UV region. Then I show that the periodic structure based on GaN and SAGC can have photonic ...

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### Mechanism and the Effect of Microwave-Carbon Nanotube Interaction

**Date:**December 2005

**Creator:**Ye, Zhou

**Description:**A series of experimental results about unusual heating of carbon nanotubes by microwaves is analyzed in this dissertation. Two of vibration types, cantilever type (one end is fixed and the other one end is free), the second type is both ends are fixed, have been studied by other people. A third type of forced vibration of carbon nanotubes under an alternating electromagnetic field is examined in this paper. Heating of carbon nanotubes (CNTs) by microwaves is described in terms of nonlinear dynamics of a vibrating nanotube. Results from the model provide a way to understand several observations that have been made. It is shown that transverse vibrations of CNTs during microwave irradiation can be attributed to transverse parametric resonance, as occurs in the analysis of Melde's experiment on forced longitudinal vibrations of a stretched elastic string. For many kinds of carbon nanotubes (SWNT, DWNT, MWNT, ropes and strands) the resonant parameters are found to be located in an unstable region of the parameter space of Mathieu's equation. Third order wave equations are used to qualitatively describe the effects of phonon-phonon interactions and energy transfer from microwaves to CNTs. This result provides another way to input energy from microwaves to carbon ...

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### Chaos and Momentum Diffusion of the Classical and Quantum Kicked Rotor

**Date:**August 2005

**Creator:**Zheng, Yindong

**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 ...

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### Random growth of interfaces: Statistical analysis of single columns and detection of critical events.

**Access:**Use of this item is restricted to the UNT Community.

**Date:**August 2004

**Creator:**Failla, Roberto

**Description:**The dynamics of growth and formation of surfaces and interfaces is becoming very important for the understanding of the origin and the behavior of a wide range of natural and industrial dynamical processes. The first part of the paper is focused on the interesting field of the random growth of surfaces and interfaces, which finds application in physics, geology, biology, economics, and engineering among others. In this part it is studied the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction g. It is argued that the main properties of Kardar-Parisi-Zhang theory are derived by identifying the distribution of return times to y(0) = 0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the model of ballistic deposition is remarkably good, in spite of the finite size effects affecting this model. The second part of the paper deals with the efficiency of the diffusion entropy analysis (DEA) when applied to the studies of stromatolites. In this case ...

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### 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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### Perturbation of renewal processes

**Date:**May 2008

**Creator:**Akin, Osman Caglar

**Description:**Renewal theory began development in the early 1940s, as the need for it in the industrial engineering sub-discipline operations research had risen. In time, the theory found applications in many stochastic processes. In this thesis I investigated the effect of seasonal effects on Poisson and non-Poisson renewal processes in the form of perturbations. It was determined that the statistical analysis methods developed at UNT Center for Nonlinear Science can be used to detect the effects of seasonality on the data obtained from Poisson/non-Poisson renewal systems. It is proved that a perturbed Poisson process can serve as a paradigmatic model for a case where seasonality is correlated to the noise and that diffusion entropy method can be utilized in revealing this relation. A renewal model making a connection with the stochastic resonance phenomena is used to analyze a previous neurological experiment, and it was shown that under the effect of a nonlinear perturbation, a non-Poisson system statistics may make a transition and end up in the of Poisson basin of statistics. I determine that nonlinear perturbation of the power index for a complex system will lead to a change in the complexity characteristics of the system, i.e., the system will reach ...

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### Multifunctional Organic-Inorganic Hybrid Nanophotonic Devices

**Date:**May 2008

**Creator:**Garner, Brett William

**Description:**The emergence of optical applications, such as lasers, fiber optics, and semiconductor based sources and detectors, has created a drive for smaller and more specialized devices. Nanophotonics is an emerging field of study that encompasses the disciplines of physics, engineering, chemistry, biology, applied sciences and biomedical technology. In particular, nanophotonics explores optical processes on a nanoscale. This dissertation presents nanophotonic applications that incorporate various forms of the organic polymer N-isopropylacrylamide (NIPA) with inorganic semiconductors. This includes the material characterization of NIPA, with such techniques as ellipsometry and dynamic light scattering. Two devices were constructed incorporating the NIPA hydrogel with semiconductors. The first device comprises a PNIPAM-CdTe hybrid material. The PNIPAM is a means for the control of distances between CdTe quantum dots encapsulated within the hydrogel. Controlling the distance between the quantum dots allows for the control of resonant energy transfer between neighboring quantum dots. Whereby, providing a means for controlling the temperature dependent red-shifts in photoluminescent peaks and FWHM. Further, enhancement of photoluminescent due to increased scattering in the medium is shown as a function of temperature. The second device incorporates NIPA into a 2D photonic crystal patterned on GaAs. The refractive index change of the NIPA hydrogel as ...

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### Anderson Localization in Two-Channel Wires with Correlated Disorder: DNA as an Application

**Date:**December 2007

**Creator:**Bagci, V. M. Kemal

**Description:**This research studied the Anderson localization of electrons in two-channel wires with correlated disorder and in DNA molecules. It involved an analytical calculation part where the formula for the inverse localization length for electron states in a two-channel wire is derived. It also involved a computational part where the localization length is calculated for some DNA molecules. Electron localization in two-channel wires with correlated disorder was studied using a single-electron tight-binding model. Calculations were within second-order Born-approximation to second-order in disorder parameters. An analytical expression for localization length as a functional of correlations in potentials was found. Anderson localization in DNA molecules were studied in single-channel wire and two-channel models for electron transport in DNA. In both of the models, some DNA sequences exhibited delocalized electron states in their energy spectrum. Studies with two-channel wire model for DNA yielded important link between electron localization properties and genetic information.

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### 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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