Two mathematical problems in disordered systems are studied: geodesics in first-passage percolation and conductivity of random resistor networks. In first-passage percolation, we consider a translation-invariant ergodic family {t(b): b bond of Z²} of nonnegative random variables, where t(b) represent bond passage times. Geodesics are paths in Z², infinite in both directions, each of whose finite segments is time-minimizing. We prove part of the conjecture that geodesics do not exist in any fixed half-plane and that they have to intersect all straight lines with rational slopes. In random resistor networks, we consider an independent and identically distributed family {C(b): b bond of a hierarchical lattice H} of nonnegative random variables, where C(b) represent bond conductivities. A hierarchical lattice H is a sequence {H(n): n = 0, 1, 2} of lattices generated in an iterative manner. We prove a central limit theorem for a sequence x(n) of effective conductivities, each of which is defined on lattices H(n), when a system is in a percolating regime. At a critical point, it is expected to have non-Gaussian behavior.

Using data from the Next Generation Virgo Cluster Survey and high-resolution simulations of Virgo cluster-like halos, we determine the stellar-to-halo mass relation (SHMR) for subhalos, using the technique of abundance matching. The subhalo SHMR differs markedly from its field galaxy counterpart, regardless of how the subhalo mass is defined (mass at z = 0, mass at infall, or maximum mass while in the field). The slope of the relation at low mass (M⋆<10^10 Msun) is in all cases steeper than the same for the field. We find conflicting indicators of whether this difference in slope indicates an increasing or decreasing dark-to-stellar ratio; further modelling is required to reach a definitive conclusion. We also find evidence for the existence of a measurable age gradient in velocity, such that older subhalos have lower velocities than their younger peers. This opens the possibility that good quality redshifts of the lower mass galaxies of the Virgo cluster might provide additional constraints on the SHMR at high redshift and its evolution. Finally, we investigate the degree to which mergers, particularly major mergers, cause mixing of old and new material in halos, which has implications for the robustness of any implied radial age gradient. We find only a slight increase in mixing for major mergers over minor mergers, and little evidence for any large amount of mixing being induced by mergers of any ratio.

Thesis (Ph.D.) - University of St Andrews, June 2009. / Restricted until 1st December 2009.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 225-232).

<p>The following dissertation shows the results of a series of inelastic neutron scattering experiments on the geometrically frustrated pyrochlore system Tb2Sn2-xTixO7 for x=0, 0.1, 0.2, 0.5, 1, 1.5 and 2. Inelastic neutron scattering measurements were performed on the SEQUOIA direct geometry time-of-flight spectrometer at the Spallation Neutron Source of Oak Ridge National Laboratory. For the two end members, x=0, Tb2Sn2O7 and x=2, Tb2Ti2O7 , they display related, but different exotic ground states, with Tb2Sn2O7 displaying “soft” spin ice order below T_N~0.87K, while Tb2Ti2O7 enters a glassy antiferromagnetic spin ice state below T_g~0.2K.</p> <p>The first two chapters give a brief introduction to the physics of geometrically frustrated magnetism and neutron scattering. Chapter 3 studies the two end members Tb2Ti2O7 and Tb2Sn2O7 experimentally and theoretically. Inelastic neutron scattering measurements and appropriate crystal field calculations together probe the crystal field states associated with the J=6 states of Tb^3+ within the appropriate Fd3m pyrochlore environment. These crystal field states determine the size and anisotropy of the Tb^3+ magnetic moment in each material’s ground state, information that is an essential starting point for any description of the low temperature phase behavior and spin dynamics in Tb2Ti2O7 and Tb2Sn2O7. Chapter 4 treats neutron scattering, as well as accompanying AC magnetic susceptibility and muSR measurements performed by our collaborators on a series of solid solutions Tb2Sn2-xTixO7 showing a novel, dynamic spin liquid state for all x other than the end members x=0 and x=2. This state is the result of disorder in the low lying Tb^3+ crystal field environments which de-stabilizes the mechanism by which quantum fluctuations contribute to ground state selection in Tb2Sn2-xTixO7.</p> / Master of Science (MSc)

<p> Atomically thin, semiconducting transition metal dichalogenides (TMDs), a special class of layered semiconductors, that can be shaped as a perfect two dimensional material, have garnered a lot of attention owing to their fascinating electronic properties which are achievable at the extreme nanoscale. In contrast to graphene, the most celebrated two-dimensional (2D) material thus far; TMDs exhibit a direct band gap in the monolayer regime. The presence of a non-zero bandgap along with the broken inversion symmetry in the monolayer limit brands semiconducting TMDs as the perfect candidate for future optoelectronic and valleytronics-based device application. These remarkable discoveries demand exploration of different materials that possess similar properties alike TMDs. Recently, III-VI layered semiconducting materials (example: InSe, GaSe etc.) have also emerged as potential materials for optical device based applications as, similar to TMDs, they can be shaped into a perfect two-dimensional form as well as possess a sizable band gap in their nano-regime. The perfect 2D character in layered materials cause enhancement of strong Coulomb interaction. As a result, excitons, a coulomb bound quasiparticle made of electron-hole pair, dominate the optical properties near the bandgap. The basis of development for future optoelectronic-based devices requires accurate characterization of the essential properties of excitons. Two fundamental parameters that characterize the quantum dynamics of excitons are: a) the dephasing rate, &gamma;, which represents the coherence loss due to the interaction of the excitons with their environment (for example- phonons, impurities, other excitons, etc.) and b) excited state population decay rate arising from radiative and non-radiative relaxation processes. The dephasing rate is representative of the time scale over which excitons can be coherently manipulated, therefore accurately probing the source of exciton decoherence is crucial for understanding the basic unexplored science as well as creating technological developments. The dephasing dynamics in semiconductors typically occur in the picosecond to femtosecond timescale, thus the use of ultrafast laser spectroscopy is a potential route to probe such excitonic responses. </p><p> The focus of this dissertation is two-fold: firstly, to develop the necessary instrumentation to accurately probe the aforementioned parameters and secondly, to explore the quantum dynamics and the underlying many-body interactions in different layered semiconducting materials. A custom-built multidimensional optical non-linear spectrometer was developed in order to perform two-dimensional spectroscopic (2DFT) measurements. The advantages of this technique are multifaceted compared to regular one-dimensional and non-linear incoherent techniques. 2DFT technique is based on an enhanced version of Four wave mixing experiments. This powerful tool is capable of identifying the resonant coupling, probing the coherent pathways, unambiguously extracting the homogeneous linewidth in the presence of inhomogeneity and decomposing a complex spectra into real and imaginary parts. It is not possible to uncover such crucial features by employing one dimensional non-linear technique. </p><p> Monolayers as well as bulk TMDs and group III-VI bulk layered materials are explored in this dissertation. The exciton quantum dynamics is explored with three pulse four-wave mixing whereas the phase sensitive measurements are obtained by employing two-dimensional Fourier transform spectroscopy. Temperature and excitation density dependent 2DFT experiments unfold the information associated with the many-body interactions in the layered semiconducting samples. </p>

No description available.

<p> Surface plasmons are collective oscillations of free charge carriers confined in interface between two dielectrics, where the real part of the dielectric changes sign (e.g a metal-insulator interface such as gold film and air). The study of surface plasmon has been a popular research theme with potential applications utilizing the fact that the wavelength of plasmons can be many order smaller than that of the incident lights. The potential applications include transfer of information in hundreds of terahertz instead of upper limit of gigahertz in traditional wires, photodetectors with frequency range from terahertz to mid-IR, and nano-imaging. In our experiment, we use an IR near-field microscopy with resolution as low as 10nm but energy scale of micron range. This is achieved by shinning an AFM tip with infrared laser on top of the sample and collecting the scattered light from the sample. The spatial resolution proportional to where a is the size of the tip and the resolution can reach 10nm. This technique beats the diffraction limit of near-IR (10um) by over 1000x. The wavelength and amplitude damping of plasmon greatly depends on the property of free carriers in the material. While metals such as gold had been widely studied and shown promising results, a better platform with longer propagation length and shorter wavelength is needed for application. Graphenes supreme electronic transport property makes it apiii pears to be an excellent candidate for plasmonic. Graphene plasmon across a p-n junction will be discussed. Oxygen doping of graphene with different dosage via UV ozone is studied. Oxygen doping has shown promising results for graphene plasmon guide. Plasmon fringes are developed in the interior breaking the limit of boundary condition. The UV ozone treatment can be fine controlled and without damaging the graphene sheet. One can, in theory, mask and selectively dope to create a robust graphene plasmon circuit that is stable in room temperature. </p>

<p> Exchange spring based superconducting heterostructures and Josephson junctions are studied to search for evidence of odd-triplet superconductivity. Cooper pairs from a superconductor can leak into a nonhomogeneous ferromagnet a much greater distance than they leak into a homogeneous ferromagnet. This is a result of a conversion of the superconducting condensate at the superconductor-nonhomogeneous ferromagnet interface from the singlet and triplet states to the odd-triplet state. The odd-triplet state is insensitive to the exchange field of the ferromagnet. </p><p> To generate the nonhomogeneous magnetic region, an exchange spring is used. The exchange spring consists of coupled hard and soft magnetic layers that are used to produce a nonhomogeneous magnetization. The system studied consists of superconducting Niobium (Nb) and a Samarium-Cobalt/Permalloy (SmCo/Py) exchange spring.</p><p> Initial samples of Niobium had a critical temperature lower than that obtainable in our laboratory (&lt; 1.8 K). Preliminary work was done to find the cause of the suppressed critical temperature of Nb and to increase it. This work resulted in obtaining Niobium thin films with critical temperatures as high as 6 K.</p><p> Indirect evidence of the odd-triplet component is searched for by looking at the critical temperature of superconductor/exchange spring bi-layers. As the nonhomogeneity of the magnetization is increased, it is expected that the critical temperature will decrease as the condensate leaks further into the exchange spring. In Nb/Py/SmCo systems, this behavior was observed, along with a modulation in the resistance that is attributed to the anisotropic magnetoresistance of the permalloy layer. A decrease in the critical temperature with increasing nonhomogeneity of the exchange spring was also observed in Nb/SmCo/Py layers, provided the SmCo layer is not too thick.</p><p> Direct evidence of the odd-triplet component is searched for by looking at the modulation of the critical current through exchange spring based Josephson junctions as exchange spring magnetization becomes more nonhomogeneous. As the nonhomogeneity of the magnetization increases, the critical current through the junction should increase as well. Fabrication of Josephson junctions with exchange spring interlayers was performed at Oak Ridge National Laboratory, and the procedure is presented here. The critical current through these junctions was observed to increase with increasing nonhomogeneity of the exchange spring magnetization, although more tests are needed to verify this is due to the odd-triplet component of the superconducting condensate.</p>

A method for separation and characterization of individual anthocyanins was developed. High Performance Liquid Chromatography (HPLC) with a polymer based reversed-phase column was used to separate the pigments while on-line Photodiode Array Detection (PDA) was employed to record the UV and Visible spectrum of the individual peaks. Spectral information obtained from on-line PDA detection provided information about: 1) the nature of the aglycone, 2) the sugar substitution pattern and 3) the presence or absence of hydroxy aromatic organic acids. The nature of the glycosidation can be determined from the HPLC retention characteristics. The HPLC/PDA methods were employed to characterize the anthocyanin profiles of the pigments in cranberry, roselle, cherry, bilberry, grape, red cabbage, black raspberry, blackberry, elderberry, plum, blackcurrant and strawberry. The anthocyanidin profiles were also determined for the samples for purposes of confirmation of the anthocyanin data. In addition to the anthocyanin and anthocyanidin profiles, the general coloring properties for most of the samples were also determined. Included were Hunter L, a, b values, total anthocyanin pigment concentration, wavelength maxima, percent tannin measurements, tinctoral strength, pH measurements and titratable acidity. / Graduation date: 1988