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

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**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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### 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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### 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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### 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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### Fractional Brownian motion and dynamic approach to complexity.

**Date:**August 2007

**Creator:**Cakir, Rasit

**Description:**The dynamic approach to fractional Brownian motion (FBM) establishes a link between non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a non-vanishing memory of their past time evolution. It is well known that the recrossing times of the origin by an ordinary 1D diffusion trajectory generates a distribution of time distances between two consecutive origin recrossing times with an inverse power law with index m=1.5. However, with theoretical and numerical arguments, it is proved that this is the special case of a more general condition, insofar as the recrossing times produced by the dynamic FBM generates process with m=2-H. Later, the model of ballistic deposition is studied, which is as a simple way to establish cooperation among the columns of a growing surface, to show that cooperation generates memory properties and, at same time, non-Poisson renewal events. Finally, the connection between trajectory and density memory is discussed, showing that the trajectory memory does not necessarily yields density memory, and density memory might be compatible with the existence of abrupt jumps resetting to zero the system's memory.

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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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### 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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### A Non-equilibrium Approach to Scale Free Networks

**Date:**August 2012

**Creator:**Hollingshad, Nicholas W.

**Description:**Many processes and systems in nature and society can be characterized as large numbers of discrete elements that are (usually non-uniformly) interrelated. These networks were long thought to be random, but in the late 1990s, Barabási and Albert found that an underlying structure did in fact exist in many natural and technological networks that are now referred to as scale free. Since then, researchers have gained a much deeper understanding of this particular form of complexity, largely by combining graph theory, statistical physics, and advances in computing technology. This dissertation focuses on out-of-equilibrium dynamic processes as they unfold on these complex networks. Diffusion in networks of non-interacting nodes is shown to be temporally complex, while equilibrium is represented by a stable state with Poissonian fluctuations. Scale free networks achieve equilibrium very quickly compared to regular networks, and the most efficient are those with the lowest inverse power law exponent. Temporally complex diffusion also occurs in networks with interacting nodes under a cooperative decision-making model. At a critical value of the cooperation parameter, the most efficient scale free network achieves consensus almost as quickly as the equivalent all-to-all network. This finding suggests that the ubiquity of scale free networks in nature ...

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### Theoretical and Experimental Investigations Concerning Microgels of Varied Spherical Geometries

**Date:**August 2012

**Creator:**Wahrmund, Joshua Joseph

**Description:**Polymer gels have been studied extensively due to their ability to simulate biological tissues and to swell or collapse reversibly in response to external stimuli. This work presents a variety of studies using poly-N-isopropylacrylamide (PNIPA) hydrogels. The projects have been carried out both in the lab of Dr. Zhibing Hu and in collaboration with others outside of UNT: (1) an analysis of the swelling kinetics of microgel spherical shells prepared using a novel design of microfluidic devices; (2) a comparison of the drug-release rates between nanoparticle structures having either core or core-with-shell (core-shell) designs; (3) an investigation into the thermodynamics of swelling for microgels of exceedingly small size.

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### Temporal Properties Of Dynamic Processes On Complex Networks

**Date:**December 2011

**Creator:**Turalska, Malgorzata A.

**Description:**Many social, biological and technological systems can be viewed as complex networks with a large number of interacting components. However despite recent advancements in network theory, a satisfactory description of dynamic processes arising in such cooperative systems is a subject of ongoing research. In this dissertation the emergence of dynamical complexity in networks of interacting stochastic oscillators is investigated. In particular I demonstrate that networks of two and three state stochastic oscillators present a second-order phase transition with respect to the strength of coupling between individual units. I show that at the critical point fluctuations of the global order parameter are characterized by an inverse-power law distribution and I assess their renewal properties. Additionally, I study the effect that different types of perturbation have on dynamical properties of the model. I discuss the relevance of those observations for the transmission of information between complex systems.

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### Electrostatic Mechanism of Emission Enhancement in Hybrid Metal-semiconductor Light-emitting Heterostructures

**Date:**May 2012

**Creator:**Llopis, Antonio

**Description:**III-V nitrides have been put to use in a variety of applications including laser diodes for modern DVD devices and for solid-state white lighting. Plasmonics has come to the foreground over the past decade as a means for increasing the internal quantum efficiency (IQE) of devices through resonant interaction with surface plasmons which exist at metal/dielectric interfaces. Increases in emission intensity of an order of magnitude have been previously reported using silver thin-films on InGaN/GaN MQWs. the dependence on resonant interaction between the plasmons and the light emitter limits the applications of plasmonics for light emission. This dissertation presents a new non-resonant mechanism based on electrostatic interaction of carriers with induced image charges in a nearby metallic nanoparticle. Enhancement similar in strength to that of plasmonics is observed, without the restrictions imposed upon resonant interactions. in this work we demonstrate several key features of this new interaction, including intensity-dependent saturation, increase in the radiative recombination lifetime, and strongly inhomogeneous light emission. We also present a model for the interaction based on the aforementioned image charge interactions. Also discussed are results of work done in the course of this research resulting in the development of a novel technique for strain measurement ...

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### 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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### Electrostatic Effects in III-V Semiconductor Based Metal-optical Nanostructures

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**Date:**May 2012

**Creator:**Gryczynski, Karol Grzegorz

**Description:**The modification of the band edge or emission energy of semiconductor quantum well light emitters due to image charge induced phenomenon is an emerging field of study. This effect observed in quantum well light emitters is critical for all metal-optics based light emitters including plasmonics, or nanometallic electrode based light emitters. This dissertation presents, for the first time, a systematic study of the image charge effect on semiconductor–metal systems. the necessity of introducing the image charge interactions is demonstrated by experiments and mathematical methods for semiconductor-metal image charge interactions are introduced and developed.

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### How Cooperative Systems Respond to External Forces

**Date:**May 2014

**Creator:**Svenkeson, Adam

**Description:**Cooperative interactions permeate through nature, bringing about emergent behavior and complexity. Using a simple cooperative model, I illustrate the mean field dynamics that occur at the critical point of a second order phase transition in the framework of Langevin equations. Through this formalism I discuss the response, both linear and nonlinear, to external forces. Emphasis is placed on how information is transferred from one individual to another in order to facilitate the collective response of the cooperative network to a localized perturbation. The results are relevant to a wide variety of systems, ranging from nematic liquid crystals, to flocks and swarms, social groups, and neural networks.

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### Fractional Calculus and Dynamic Approach to Complexity

**Date:**December 2015

**Creator:**Beig, Mirza Tanweer Ahmad

**Description:**Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. Nonlinear Langevin equation describes the mean field of a finite size complex network at criticality. Critical phenomena and temporal complexity are two very important issues of modern nonlinear dynamics and the link between them found by the author can significantly improve the understanding behavior of dynamical systems at criticality. The subject of temporal complexity addresses the challenging and especially helpful in addressing fundamental physical science issues beyond the limits of reductionism.

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### A Precise Few-nucleon Size Difference by Isotope Shift Measurements of Helium

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**Date:**August 2015

**Creator:**Hassan Rezaeian, Nima

**Description:**We perform high precision measurements of an isotope shift between the two stable isotopes of helium. We use laser excitation of the 2^3 S_1-2^3 P_0 transition at 1083 nm in a metastable beam of 3He and 4He atoms. A newly developed tunable laser frequency selector along with our previous electro-optic frequency modulation technique provides extremely reliable, adaptable, and precise frequency and intensity control. The intensity control contributes negligibly to overall experimental uncertainty by stabilizing the intensity of the required sideband and eliminating the unwanted frequencies generated during the modulation of 1083 nm laser carrier frequency. The selection technique uses a MEMS based fiber switch and several temperature stabilized narrow band (~3 GHz) fiber gratings. A fiber based optical circulator and an inline fiber amplifier provide the desired isolation and the net gain for the selected frequency. Also rapid (~2 sec.) alternating measurements of the 2^3 S_1-2^3 P_0 interval for both species of helium is achieved with a custom fiber laser for simultaneous optical pumping. A servo-controlled retro-reflected laser beam eliminates residual Doppler effects during the isotope shift measurement. An improved detection design and software control makes negligible subtle potential biases in the data collection. With these advances, combined with new ...

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### Electromagnetically Modulated Sonic Structures

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**Date:**May 2014

**Creator:**Walker, Ezekiel Lee

**Description:**Phononic crystals are structures composed of periodically arranged scatterers in a background medium that affect the transmission of elastic waves. They have garnered much interest in recent years for their macro-scale properties that can be modulated by the micro-scale components. The elastic properties of the composite materials, the contrast in the elastic properties of the composite materials, and the material arrangement all directly affect how an elastic wave will behave as it propagates through the sonic structure. The behavior of an elastic wave in a periodic structure is revealed in its transmission bandstructure, and modification of any the elastic parameters will result in tuning of the band structure. In this dissertation, a phononic crystal with properties that can be modulated using electromagnetic radiation, and more specifically, radio-frequency (RF) light will be presented.

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### Temporal Complexity and Stochastic Central Limit Theorem

**Date:**August 2014

**Creator:**Pramukkul, Pensri

**Description:**Complex processes whose evolution in time rests on the occurrence of a large and random number of intermittent events are the systems under study. The mean time distance between two consecutive events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that explains why the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories, each of which fits the stochastic central limit theorem and the condition for the Mittag-Leffler universality. Additionally, the effect of noise on the generation of the Mittag-Leffler function is discussed. Fluctuations of relatively weak intensity can conceal the asymptotic inverse power law behavior of the Mittag-Leffler function, providing a reason why stretched exponentials are frequently found in nature. These results afford a more unified picture of complexity resting on the Mittag-Leffler function and encompassing the standard inverse power law definition.

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### Studying Interactions of Gas Molecules with Nanomaterials Loaded in a Microwave Resonant Cavity

**Date:**August 2007

**Creator:**Anand, Aman

**Description:**A resonant cavity operating in TE011 mode was used to study the adsorption response of single walled carbon nanotubes (SWCNTs) and other nanomaterials for different types of gas molecules. The range of the frequency signal as a probe was chosen as geometry dependent range between 9.1 -9.8 GHz. A highly specific range can be studied for further experiments dependent on the type of molecule being investigated. It was found that for different pressures of gases and for different types of nanomaterials, there was a different response in the shifts of the probe signal for each cycle of gassing and degassing of the cavity. This dissertation suggests that microwave spectroscopy of a complex medium of gases and carbon nanotubes can be used as a highly sensitive technique to determine the complex dielectric response of different polar as well as non-polar gases when subjected to intense electromagnetic fields within the cavity. Also, as part of the experimental work, a range of other micro-porous materials was tested using the residual gas analysis (RGA) technique to determine their intrinsic absorption/adsorption characteristics when under an ultra-high vacuum environment. The scientific results obtained from this investigation, led to the development of a chemical biological sensor prototype. ...

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