Thesis (Ph.D.)--Brown University, 2008. / Advisor: Xinsheng S. Ling. Includes bibliographical references (leaves 111-125).

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.

The twin questions of how and why protein molecules fold into the specific topologies which enable them to fulfill their biological function have been the subject of continuous scientific investigation since the early twentieth century. Interactions between biological macromolecules and water are obviously crucial to both folding and function but attempts to gain understanding are impeded by the size and complexity of these systems. A useful approach is to consider much simpler model systems which capture some essential element of real biological systems but are experimentally and theoretically tractable. N-methylacetamide (NMA) is a minimal model of the peptide linkage which forms the backbone of protein molecules. Its behaviour in aqueous solution therefore captures the important competition between peptide - peptide and peptide - water hydrogen bonds which arises in protein hydration. In this thesis aqueous NMA solutions are studied across the full concentration range using classical molecular dynamics simulation. This gives access to the complete spectrum of behaviour between the two important limiting cases of dilute NMA in water and, conversely, dilute water in NMA. Water is now known to be an active player in biological interactions and the simple system studied here displays significant disruption of the structure and dynamics of pure water with the addition of only a small proportion of peptide groups. At dilute NMA concentrations water molecules continue to form system-size hydrogen bonded networks. Water molecules appear to optimise their local tetrahedral order by forming hydrogen bonds with a combination of NMA and water neighbours, rather than solely with members of their own species. NMA molecules hydrogen bond through the amide and carbonyl groups to form linear and branched chains in both the pure liquid and in the aqueous solutions. In the NMA rich region water molecules preferentially donate both hydrogens to chain-end or midchain carbonyl oxygens, forming bridges between NMA chains which resemble buried water configurations found in protein cavities. These bridge structures are thought to contribute to the observed slowing of the system dynamics at these concentrations. The investigation of dynamics by classical simulation is complemented by a quasielastic neutron scattering study of NMA in its liquid and aqueous phases.

<p> Micro- and nano-mechanical resonators with low mass and high vibrational frequency are often studied for applications in mass and force detection where they can offer unparalleled precision. They are also excellent systems with which to study nonlinear phenomena and fundamental physics due to the numerous routes through which they can couple to each other or to external systems. </p><p> In this work we study the structural, thermal, and nonlinear properties of various micro-mechanical systems. First, we present a study of graphene-coated silicon nitride membranes; the resulting devices demonstrate the high quality factors of silicon nitride as well as the useful electrical and optical properties of graphene. We then study nonlinear mechanics in pure graphene membranes, where all vibrational eigenmodes are coupled to one another through the membrane tension. This effect enables coherent energy transfer from one mechanical mode to another, in effect creating a graphene mechanics-based frequency mixer. In another experiment, we measure the resonant frequency of a graphene membrane over a wide temperature range, 80K - 550K, to determine whether or not it demonstrates the negative thermal expansion coefficient predicted by prevailing theories; our results indicate that this coefficient is positive at low temperatures &ndash; possibly due to polymer contaminants on the graphene surface &ndash; and negative above room temperature. Lastly, we study optically-induced self-oscillation in metal-coated silicon nitride nanowires. These structures exhibit self-oscillation at extremely low laser powers (~1&mu;W incident on the nanowire), and we use this photo-thermal effect to counteract the viscous air-damping that normally inhibits micro-mechanical motion.</p>

Single crystals of l-ascorbic acid and partially deuterated l-ascorbic acid were irradiated in the temperature range of 77K to 300K by either x-rays from a 3 Mev Van de Graaff electron accelerator or UV radiation (337.1 nm) from a pulsed nitrogen gas laser having a peak power of 240 KW. Several types of free radicals were produced by the radiation and were studied by X-band and Q-band ESR from 4.2K to 300K. The kinds of radicals produced by the UV and x-irradiation were the same. The relative intensities of the spectral lines of the different types of radicals depend upon both the temperature and the type of radiation. Four radicals were identified: two oxidation products (radicals I and IV), one neutralized anion (radical III), and one adduct (radical II). Radicals I, III, and IV are present at 77K after irradiation at 77K. Upon annealing to 140K, radical I changes to dehydroascorbic acid and proton adduction creates radical II. Upon annealing to 300K, radicals II, III, and IV remain and are stable at 300K for at least several months. All four radicals are carbon based radicals and are located on the furan ring. All hyperfine couplings are to (beta)-protons. No carbon-13 hyperfine couplings were observed. ENDOR was tried at 4.2K, 77K, and 300K after x-irradiation at 77K or 300K. In all cases a matrix ENDOR line was observed, but no hyperfine ENDOR lines were observed. UV bleaching was attempted at 300K on a deuterated crystal which had been x-irradiated previously. The UV laser radiation had no observable effect on the ESR spectra in which radicals II, III, and IV were already present. / Source: Dissertation Abstracts International, Volume: 41-10, Section: B, page: 3822. / Thesis (Ph.D.)--The Florida State University, 1980.

Energy studies of the constituents of a mass-selected Gallium Liquid Metal Ion Source (LMIS) are presented. Results were obtained showing double energy loss peaks for Ga$\sbsp{2}{+},$ Ga$\sbsp{3}{+},$ and Ga$\sbsp{4}{+}$ which have not previously been reported in the literature. These loss peaks coincided with higher LMIS emission current, and some of the heavier mass peaks in the LMIS mass spectrum were observed to simultaneously diminish. The relationship of these two observations is discussed in terms of classical liquid drop fission theory. This theory predicts classical fissioning barriers and gives a range of possible parents. The fissioning times of various assumed parents for the given daughters is calculated and inferences concerning the manner of fissioning--asymmetric or symmetric--and their viability are presented. The apparatus used to perform the experiment and its implementation is discussed. / Source: Dissertation Abstracts International, Volume: 55-08, Section: B, page: 3383. / Major Professor: David M. Lind. / Thesis (Ph.D.)--The Florida State University, 1994.

Experimental results concerning the multiphonon scattering of He from the LiF(001) surface, the structure of the NiO(001) surface probed by $\sp3$He scattering, and the structure and dynamics of the CoO(001) surface are presented. Experiments measuring the multiphonon background of He scattered from the LiF surface were used to model the form factor of the interaction for the atom-surface system. This modeling yielded a surface Debye frequency of $\omega\sb{D} = 6.8\times10\sp{13}$ rad/s, the stiffness parameter in the Mott-Jackson matrix element $\beta\ =\ 9.5\ {\rm\A}\sp{-1}$, and a parallel "cutoff" factor $Q\sb{c}\ =\ 8.5\ {\rm\A}\sp{-1}$ for this system. Experiments to determine the structure of NiO using $\sp3$He as the incident probe atom were performed to search for an interaction between the antiferromagnetic ordering in the NiO surface and the nuclear spin in the $\sp3$He. These experiments showed no evidence of any magnetic scattering. It was shown that the mixing of $\sp3$He and $\sp4$He can be used to produce $\sp3$He beams with velocity distributions unobtainable from pure $\sp3$He. Experiments scattering He from the surface of a single crystal CoO sample were used to estimate the peak-to-peak corrugation of CoO for He with an incident wave vector of 6.7 A$\sp{-1}$ at 0.19 A. In addition, the Rayleigh phonon surface dispersion was measured over approximately half of the Brillouin zone. / Source: Dissertation Abstracts International, Volume: 55-09, Section: B, page: 3953. / Major Professor: James G. Skofronick. / Thesis (Ph.D.)--The Florida State University, 1994.

High resolution helium atom scattering (HAS) experiments were performed on the disordered surface of KCN(001) in the rhombohedral phase and on expitaxial grown layers of KBr on RbCl(001). The experiments on KCN used the time-of-flight (TOF) method to measure multiphonon interactions of the incident helium atoms with the crystal surface as a function of incident energy and crystal temperature. These measurements were used to model a cutoff factor ($Q\sb{c} = 4.5{\rm\A}\sp{-1}$) for parallel momentum transfer, a range parameter ($\beta$ = 4.5A$\sp{-1}$) of an exponential potential $V\propto$ exp(-$\beta z$), and a surface Debye temperature ($\Theta\sb{S}$ = 195K). / The experiments with RbCl involved the deposition of one to three monolayers of KBr onto the RbCl(001) surface, which was monitored in situ by attenuation of the atomic helium beam. Inelastic scattering experiments were performed on each atomic layer to determine the surface phonon dispersion curves as a function of coverage. This experiment was performed to validate and also, to provide additional results that will extend the shell model for ionic insulators. Measurements were made in both the ${\overline{\Gamma M}}$ and ${\overline{\Gamma X}}$ high symmetry directions for coverages of one, two, and three monolayers. The KBr/RbCl system which is nearly perfectly lattice matched is compared to the KBr/NaCl system which has lattice registry of 6 KBr to 7 NaCl. / Source: Dissertation Abstracts International, Volume: 55-09, Section: B, page: 3955. / Major Professor: J. G. Skofronick. / Thesis (Ph.D.)--The Florida State University, 1994.

The two-dimensional antiferromagnetic Heisenberg model and $t - J$ model are studied on the square lattice aimed to understand certain normal state properties of the high-temperature copper-oxide superconductors. Fundamental physical issues such as the role of quantum spin fluctuations, and hole dynamics are addressed. We constructed a variational wave function for the Heisenberg model, which includes spin-spin correlations and possesses antiferromagnetic long range order. Long and short wave length spin excitations are calculated using this wave function and compared with neutron scattering and Raman scattering experiments. Loop-expansions up to two-loop level are applied to study the spectral function of a single hole described by the $t - J$ model. Our numerical solutions extrapolated to the thermodynamical limit show that the hole spectral function consists of a sharp lowest-energy quasihole peak and a series of well defined peaks above it, which correspond to the "string" excitations. The single hole spectral weight of the t-J model is also calculated using the Green's function Monte Carlo method to further clarify the controversial question of whether or not the Fermi liquid theory breaks down in this model due to a vanishing spectral weight. / Source: Dissertation Abstracts International, Volume: 54-03, Section: B, page: 1473. / Major Professor: Efstratios Manousakis. / Thesis (Ph.D.)--The Florida State University, 1993.

The penetration of a quasistatic electric field into an epitaxial film of Yba$\sb2$Cu$\sb3$O$\sb{\rm 7-x}$ was studied around the film's transition temperature. The electric field penetration into the YBa$\sb2$Cu$\sb3$O$\sb{\rm 7-x}$ electrode was shown to vary by as much as 100A in the temperature regime 60K $<$ T $<$ 110K. The distance between the physical interface and the effective electrical interface is at least 100A at temperatures within 25K of T$\sb{\rm c}$. The direction of interfacial movement is reversed at T$\sb{\rm c}$. The data are consistent with the continuous movement, with changing temperature, of an interface between two regions, one penetrated by the electric field and one devoid of electric field. / The data indicate far stronger temperature dependance and magnitude of the delocalization forces along the c-axis of the material in both the superconducting and normal state than could be expected from any conventional theory of metals. / Applying a dc bias to the films, the effect of charge carrier concentration on T$\sb{\rm c}$ was studied. The first and second derivatives of T$\sb{\rm c}$ with respect to surface carrier concentration were determined to be, respectively, near zero and negative. / Source: Dissertation Abstracts International, Volume: 54-03, Section: B, page: 1471. / Major Professor: Louis R. Testardi. / Thesis (Ph.D.)--The Florida State University, 1993.