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.

The finite element method (FEM) is reviewed and applied to the one-dimensional eigensystems of the isotropic harmonic oscillator, finite well, infinite well and radial hydrogen atom, and the two-dimensional eigensystems of the isotropic harmonic oscillator and the propagational modes of sound in a rectangular cavity. Computer codes that I developed were introduced and utilized to find accurate results for the FEM eigensolutions. One of the computer codes was modified and applied to the one-dimensional unbound quantum mechanical system of a square barrier potential and also provided accurate results.

I: Quantum information obeys laws that subtly extend those governing classical information, making possible novel effect such as cryptography and quantum computation. Quantum computations are extremely sensitive to disruption by interaction of the computer with its environment, but this problem can be overcome by recently developed quantum versions of classical error-correcting codes and fault-tolerant circuits. Based on these ideas, the purpose of this paper is to provide an approach to quantum information by analyzing and demonstrating Bell's inequality and by discussing the problems related to decoherence and error-correcting. II: The growing need for a better understanding of complex processes has stimulated the development of new and more advanced data analysis techniques. The purpose of this research was to investigate some of the already existing techniques (Hurst's rescaled range and relative dispersion analysis), to develop a software able to process time series with these techniques, and to get familiar with the theory of diffusion processes.

Complexity can emerge from extremely simple rules. A paradigmatic example of this is the model of ballistic deposition (BD), a simple model of sedimentary rock growth. In two separate Problem-in-Lieu-of Thesis studies, BD was investigated numerically in (1+1)-D on a lattice. Both studies are combined in this document. For problem I, the global interface roughening (IR) process was studied in terms of effective scaling exponents for a generalized BD model. The model used incorporates a tunable parameter B to change the cooperation between aggregating particles. Scaling was found to depart increasingly from the predictions of Kardar-Parisi-Zhang theory both with decreasing system sizes and with increasing cooperation. For problem II, the local single column evolution during BD rock growth was studied via statistical analysis of time series. Connections were found between single column time series properties and the global IR process.

This problem in lieu of thesis is a discussion of two topics: Brownian movement and quantum computers. Brownian movement is a physical phenomenon in which the particle velocity is constantly undergoing random fluctuations. Chapters 2, 3 and 4, describe Brownian motion from three different perspectives. The next four chapters are devoted to the subject of quantum computers, which are the signal of a new era of technology and science combined together. In the first chapter I present to a reader the two topics of my problem in lieu of thesis. In the second chapter I explain the idea of Brownian motion, its interpretation as a stochastic process and I find its distribution function. The next chapter illustrates the probabilistic picture of Brownian motion, where the statistical averages over trajectories are related to the probability distribution function. Chapter 4 shows how to derive the Langevin equation, introduced in chapter 1, using a Hamiltonian picture of a bath with infinite number of harmonic oscillators. The chapter 5 explains how the idea of quantum computers was developed and how step-by-step all the puzzles for the field of quantum computers were created. The next chapter, chapter 6, discus the basic quantum unit of information …

One of the leading problems that will be carried into the 21st century is that of alternative fuels to get our planet away from the consumption of fossil fuels. There has been a growing interest in the use of nanotechnology to somehow aid in this progression. There are several unanswered questions in how to do this. It is known that carbon nanotubes will store hydrogen but it is unclear how to increase that storage capacity and how to remove this hydrogen fuel once stored. This document offers some answers to these questions. It is possible to implant more hydrogen in a nanotube sample using a technique of ion implantation at energy levels ~50keV and below. This, accompanied with the rapid removal of that stored hydrogen through the application of a microwave field, proves to be one promising avenue to solve these two unanswered questions.

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 …

The characterization, properties and applications of the novel nanostructured microgel (nanoparticle network and microgel crystal) composed of poly-N-isopropylacrylanmide-co-allylamine (PNIPAM-co-allylamine) and PNIPAM-co-acrylic acid(AA) have been investigated. For the novel nanostructured hydrogels with the two levels of structure: the primary network inside each individual particle and the secondary network of the crosslinked nanoparticles, the new shear modulus, drug release law from hydrogel with heterogeneous structure have been studied. The successful method for calculating the volume fraction related the phase transition of colloid have been obtained. The kinetics of crystallization in an aqueous dispersion of PNIPAM particles has been explored using UV-visible transmission spectroscopy. This dissertation also includes the initial research on the melting behavior of colloidal crystals composed of PNIPAM microgels. Many new findings in this study area have never been reported before. The theoretical model for the columnar crystal growth from the top to bottom of PNIPAM microgel has been built, which explains the growth mechanism of the novel columnar hydrogel colloidal crystals. Since the unique structure of the novel nanostructured hydrogels, their properties are different with the conventional hydrogels and the hard-sphere-like system. The studies and results in this dissertation have the important significant for theoretical study and valuable application …

Ion induced charge collection dynamics within Integrated Circuits (ICs) is important due to the presence of ionizing radiation in the IC environment. As the charge signals defining data states are reduced by voltage and area scaling, the semiconductor device will naturally have a higher susceptibility to ionizing radiation induced effects. The ionizing radiation can lead to the undesired generation and migration of charge within an IC. This can alter, for example, the memory state of a bit, and thereby produce what is called a "soft" error, or Single Event Upset (SEU). Therefore, the response of ICs to natural radiation is of great concern for the reliability of future devices. Immunity to soft errors is listed as a requirement in the 1997 National Technology Roadmap for Semiconductors prepared by the Semiconductor Industry Association in the United States. To design more robust devices, it is essential to create and test accurate models of induced charge collection and transport in semiconductor devices. A heavy ion microbeam produced by an accelerator is an ideal tool to study charge collection processes in ICs and to locate the weak nodes and structures for improvement through hardening design. In this dissertation, the Ion Beam Induced Charge Collection …

This dissertation addresses the delicate problem of establishing the statistical mechanical foundation of complex processes. These processes are characterized by a delicate balance of randomness and order, and a correct paradigm for them seems to be the concept of sporadic randomness. First of all, we have studied if it is possible to establish a foundation of these processes on the basis of a generalized version of thermodynamics, of non-extensive nature. A detailed account of this attempt is reported in Ignaccolo and Grigolini (2001), which shows that this approach leads to inconsistencies. It is shown that there is no need to generalize the Kolmogorov-Sinai entropy by means of a non-extensive indicator, and that the anomaly of these processes does not rest on their non-extensive nature, but rather in the fact that the process of transition from dynamics to thermodynamics, this being still extensive, occurs in an exceptionally extended time scale. Even, when the invariant distribution exists, the time necessary to reach the thermodynamic scaling regime is infinite. In the case where no invariant distribution exists, the complex system lives forever in a condition intermediate between dynamics and thermodynamics. This discovery has made it possible to create a new method of analysis …

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.

Computational techniques were employed to investigate pathways that would improve the properties and characteristics of transition metal (i.e., ruthenium) catalysts, and to explore their mechanisms. The studied catalytic pathways are particularly relevant to catalytic hydroarylation of olefins. These processes involved the +2 to +3 oxidation of ruthenium and its effect on ruthenium-carbon bond strengths, carbon-hydrogen bond activation by 1,2-addition/reductive elimination pathways appropriate to catalytic hydrogen/deuterium exchange, and the possible intermediacy of highly coordinatively unsaturated (e.g., 14-electron) ruthenium complexes in catalysis. The calculations indicate a significant decrease in the Ru-CH3 homolytic bond dissociation enthalpy for the oxidation of TpRu(CO)(NCMe)(Me) to its RuIII cation through both reactant destabilization and product stabilization. This oxidation can thus lead to the olefin polymerization observed by Gunnoe and coworkers, since weak RuIII-C bonds would afford quick access to alkyl radical species. Calculations support the experimental proposal of a mechanism for catalytic hydrogen/deuterium exchange by a RuII-OH catalyst. Furthermore, calculational investigations reveal a probable pathway for the activation of C-H bonds that involves phosphine loss, 1,2-addition to the Ru-OH bond and then reversal of these steps with deuterium to incorporate it into the substrate. The presented results offer the indication for the net addition of aromatic C-H …

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 …

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 …

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 …

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. …

The work function of hydrogen-terminated, polycrystalline diamond was studied using ultraviolet photoelectron spectroscopy. Polycrystalline diamond films were deposited onto molybdenum substrates by electrophoresis for grain sizes ranging from 0.3 to 108 microns. The work function and electron affinity were measured using 21.2 eV photons from a helium plasma source. The films were characterized by x-ray photoelectron spectroscopy to determine elemental composition and the sp2/sp3 carbon fraction. The percentage of (111) diamond was determined by x-ray diffraction, and scanning electron microscopy was performed to determine average grain size. The measured work function has a maximum of 5.1 eV at 0.3 microns, and decreases to 3.2 eV at approximately 4 microns. Then the work function increases with increasing grain size to 4.0 eV at 15 microns and then asymptotically approaches the 4.8 eV work function of single crystal diamond at 108 microns. These results are consistent with a 3-component model in which the work function is controlled by single-crystal (111) diamond at larger grain sizes, graphitic carbon at smaller grain sizes, and by the electron affinity for the intervening grain sizes.

The effects of Cs deposition on the field emission (FE) properties of single-walled carbon nanotube (SWNT) bundles were studied. In addition, a comparative study was made on the effects of O2, Ar and H2 gases on the field emission properties of SWNT bundles and multiwall carbon nanotubes (MWNTs). We observed that Cs deposition decreases the turn-on field for FE by a factor of 2.1 - 2.9 and increases the FE current by 6 orders of magnitude. After Cs deposition, the FE current versus voltage (I-V) curves showed non-Fowler-Nordheim behavior at large currents consistent with tunneling from adsorbate states. At lower currents, the ratio of the slope of the FE I-V curves before and after Cs deposition was approximately 2.1. Exposure to N2 does not decrease the FE current, while exposure to O2 decreases the FE current. Our results show that cesiated SWNT bundles have great potential as economical and reliable vacuum electron sources. We find that H2 and Ar gases do not significantly affect the FE properties of SWNTs or MWNTs. O2 temporarily reduces the FE current and increases the turn-on voltage of SWNTs. Full recovery of these properties occurred after operation in UHV. The higher operating voltages in an …

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.

Energy distribution measurements of sputtered neutral particles contribute to the general knowledge of sputtering, a common technique for surface analysis. In this work emphasis was placed on the measurement of energy distribution of sputtered neutral atoms from different depths. The liquid Ga-In eutectic alloy as a sample target for this study was ideal due to an extreme concentration ratio gradient between the top two monolayers. In pursuing this study, the method of sputter-initiated resonance ionization spectroscopy (SIRIS) was utilized. SIRIS employs a pulsed ion beam to initiate sputtering and tunable dye lasers for resonance ionization. Observation of the energy distribution was achieved with a position-sensitive detector. The principle behind the detector's energy resolution is time of flight (TOF) spectroscopy. For this specific detector, programmed time intervals between the sputtering pulse at the target and the ionizing laser pulse provided information leading to the energy distribution of the secondary neutral particles. This experiment contributes data for energy distributions of sputtered neutral particles to the experimental database, required by theoretical models and computer simulations for the sputtering phenomenon.

Statistical analysis of time series. With compelling arguments we show that the Diffusion Entropy Analysis (DEA) is the only method of the literature of the Science of Complexity that correctly determines the scaling hidden within a time series reflecting a Complex Process. The time series is thought of as a source of fluctuations, and the DEA is based on the Shannon entropy of the diffusion process generated by these fluctuations. All traditional methods of scaling analysis, instead, are based on the variance of this diffusion process. The variance methods detect the real scaling only if the Gaussian assumption holds true. We call H the scaling exponent detected by the variance methods and d the real scaling exponent. If the time series is characterized by Fractional Brownian Motion, we have H¹d and the scaling can be safely determined, in this case, by using the variance methods. If, on the contrary, the time series is characterized, for example, by Lévy statistics, H ¹ d and the variance methods cannot be used to detect the true scaling. Lévy walk yields the relation d=1/(3-2H). In the case of Lévy flights, the variance diverges and the exponent H cannot be determined, whereas the scaling d …

Living neural networks are capable of processing information much faster than a modern computer, despite running at significantly lower clock speeds. Therefore, understanding the mechanisms neural networks utilize is an issue of substantial importance. Neuronal interaction dynamics were studied using histiotypic networks growing on microelectrode arrays in vitro. Hierarchical relationships were explored using bursting (when many neurons fire in a short time frame) dynamics, pairwise neuronal activation, and information theoretic measures. Together, these methods reveal that global network activity results from ignition by a small group of burst leader neurons, which form a primary circuit that is responsible for initiating most network-wide burst events. Phase delays between leaders and followers reveal information about the nature of the connection between the two. Physical distance from a burst leader appears to be an important factor in follower response dynamics. Information theory reveals that mutual information between neuronal pairs is also a function of physical distance. Activation relationships in developing networks were studied and plating density was found to play an important role in network connectivity development. These measures provide unique views of network connectivity and hierarchical relationship in vitro which should be included in biologically meaningful models of neural networks.

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.

Carbon nanotubes were synthesized in the laboratory using chemical vapor deposition at different methane concentration. I found that a methane concentration of 4 sccm was ideal for well recognizable carbon nanotubes. A higher concentration led to fewer nanotube growth and silicon carbide structure. Coating the sample first with Fe(NO3)3 created a catalyst base on the substrate for the nanotube to adhere and grow on.