A radio frequency field guide using field induced adiabatic potential

We study the behaviour of atoms in a field with both static magnetic field and radio frequency (rf) magnetic field. We calculate the adiabatic potential of atoms numerically beyond the usually rotating wave approximation, and it is pointed that there is a great difference between using these two methods. We find the preconditions when RWA is valid. In the extreme of static field almost parallel to rf field, we reach an analytic formula. Finally, we apply this method to Rb-87 and propose a guide based on an rf field on atom chip.

Study of dynamical behaviour and fermionization of a bosonic gas in funnel potential

This paper presents a funnel external potential model to investigate dynamic properties of ultracold Bose gas. By using variational method, we obtain the ground-state energy and density properties of ultracold Bose atoms. The results show that the ultracold Bose gas confined in a funnel potential experiences the transition from three-dimensional regime to quasi-one-dimensional regime in a small aspect ratio, and undergoes fermionization process as the aspect ratio increases.

Logarithmic Potential Theory on Riemann Surfaces

We develop a logarithmic potential theory on Riemann surfaces which generalizes logarithmic potential theory on the complex plane. We show the existence of an equilibrium measure and examine its structure. This leads to a formula for the structure of the equilibrium measure which is new even in the plane. We then use our results to study quadrature domains, Laplacian growth, and Coulomb gas ensembles on Riemann surfaces. We prove that the complement of the support of the equilibrium measure satisfies a quadrature identity. Furthermore, our setup allows us to naturally realize weak solutions of Laplacian growth (for a general time-dependent source) as an evolution of the support of equilibrium measures. When applied to the Riemann sphere this approach unifies the known methods for generating interior and exterior Laplacian growth. We later narrow our focus to a special class of quadrature domains which we call Algebraic Quadrature Domains. We show that many of the properties of quadrature domains generalize to this setting. In particular, the boundary of an Algebraic Quadrature Domain is the inverse image of a planar algebraic curve under a meromorphic function. This makes the study of the topology of Algebraic Quadrature Domains an interesting problem. We briefly investigate this problem and then narrow our focus to the study of the topology of classical quadrature domains. We extend the results of Lee and Makarov and prove (for n ≥ 3) c ≤ 5n-5, where c and n denote the connectivity and degree of a (classical) quadrature domain. At the same time we obtain a new upper bound on the number of isolated points of the algebraic curve corresponding to the boundary and thus a new upper bound on the number of special points. In the final chapter we study Coulomb gas ensembles on Riemann surfaces.

Invertebrate communities in northern Lake Victoria, with reference to their potential for fishery production

The zooplankton and macrobenthic communities of Lake Victoria were sampled by lift net and Ponar grab, respectively. The zooplankton comprised copepods and cladocerans, rotifers and aquatic insect larvae. Most taxa exhibited wide distribution in the lake, with the exception of rotifers which were rare in deep offshore waters. The main components in the macro-benthos were chaoborid and chironomid larvae and molluscs. Caridina nilotica (Roux) and other groups were rare in the samples. Zooplankton density ranged from 100000 or more to 4 million ind. m2 and increased from the shallow inshore to deep offshore waters. Numerical dominance of cyclopoids and nauplius larvae was a common feature at all stations sampled. Most macrobenthic taxa were also widely distributed, although chaoborid and chironomid larvae were rare in the samples. Rastrineobola argentea (Pellegrin) and larval Lates niloticus (L.) ate mainly cyclopoid copepods, while cichlids showed a strong preference for adult insects. High ecological stability of the cyclopoids, and the zooplankton community in general, despite radical ecosystem changes in recent years, coupled with what appears to be high predation pressure, offers good prospects for the pelagic fishery in the lake.

Aerodynamics of vertical-axis wind turbines in full-scale and laboratory-scale experiments

Within a wind farm, multiple turbine wakes can interact and have a substantial effect on the overall power production. This makes an understanding of the wake recovery process critically important to optimizing wind farm efficiency. Vertical-axis wind turbines (VAWTs) exhibit features that are amenable to dramatically improving this efficiency. However, the physics of the flow around VAWTs is not well understood, especially as it pertains to wake interactions, and it is the goal of this thesis to partially fill this void. This objective is approached from two broadly different perspectives: a low-order view of wind farm aerodynamics, and a detailed experimental analysis of the VAWT wake.

One of the contributions of this thesis is the development of a semi-empirical model of wind farm aerodynamics, known as the LRB model, that is able to predict turbine array configurations to leading order accuracy. Another contribution is the characterization of the VAWT wake as a function of turbine solidity. It was found that three distinct regions of flow exist in the VAWT wake: (1) the near wake, where periodic blade shedding of vorticity dominates; (2) a transition region, where growth of a shear-layer instability occurs; (3) the far wake, where bluff-body oscillations dominate. The wake transition can be predicted using a new parameter, the dynamic solidity, which establishes a quantitative connection between the wake of a VAWT and that of a circular cylinder. The results provide insight into the mechanism of the VAWT wake recovery and the potential means to control it.

Wave induced oscillations in harbors of arbitrary shape

Theoretical and experimental studies were conducted to investigate the wave induced oscillations in an arbitrary shaped harbor with constant depth which is connected to the open-sea.

A theory termed the “arbitrary shaped harbor” theory is developed. The solution of the Helmholtz equation, ∇²f + k²f = 0, is formulated as an integral equation; an approximate method is employed to solve the integral equation by converting it to a matrix equation. The final solution is obtained by equating, at the harbor entrance, the wave amplitude and its normal derivative obtained from the solutions for the regions outside and inside the harbor.

Two special theories called the circular harbor theory and the rectangular harbor theory are also developed. The coordinates inside a circular and a rectangular harbor are separable; therefore, the solution for the region inside these harbors is obtained by the method of separation of variables. For the solution in the open-sea region, the same method is used as that employed for the arbitrary shaped harbor theory. The final solution is also obtained by a matching procedure similar to that used for the arbitrary shaped harbor theory. These two special theories provide a useful analytical check on the arbitrary shaped harbor theory.

Experiments were conducted to verify the theories in a wave basin 15 ft wide by 31 ft long with an effective system of wave energy dissipators mounted along the boundary to simulate the open-sea condition.

Four harbors were investigated theoretically and experimentally: circular harbors with a 10° opening and a 60° opening, a rectangular harbor, and a model of the East and West Basins of Long Beach Harbor located in Long Beach, California.

Theoretical solutions for these four harbors using the arbitrary shaped harbor theory were obtained. In addition, the theoretical solutions for the circular harbors and the rectangular harbor using the two special theories were also obtained. In each case, the theories have proven to agree well with the experimental data.

It is found that: (1) the resonant frequencies for a specific harbor are predicted correctly by the theory, although the amplification factors at resonance are somewhat larger than those found experimentally,(2) for the circular harbors, as the width of the harbor entrance increases, the amplification at resonance decreases, but the wave number bandwidth at resonance increases, (3) each peak in the curve of entrance velocity vs incident wave period corresponds to a distinct mode of resonant oscillation inside the harbor, thus the velocity at the harbor entrance appears to be a good indicator for resonance in harbors of complicated shape, (4) the results show that the present theory can be applied with confidence to prototype harbors with relatively uniform depth and reflective interior boundaries.

A potential approach to claims problems

Hart and Mas Colell (1989) introduce the potential function for cooperative TU games. In this paper, we extend this approach to claims problems, also known as bankruptcy or rationing problems. We show that for appropriate subproblems, the random arrival rule, the rules in the TAL-family (which include the uniform gains rule, the uniform losses rule and the Talmud rule), the minimal overlap rule, and the proportional rule admit a potential. We also study the balanced contributions property for these rules. By means of a potential, we introduce a generalization of the random arrival rule and mixtures of the minimal overlap rule and the uniform losses rule.

Relativistic velocity - potential hydrodynamics and stellar stability

The equations of relativistic, perfect-fluid hydrodynamics are cast in Eulerian form using six scalar "velocity-potential" fields, each of which has an equation of evolution. These equations determine the motion of the fluid through the equation

U_ʋ=µ^-1 (ø,_ʋ + αβ,_ʋ + ƟS,_ʋ).

Einstein's equations and the velocity-potential hydrodynamical equations follow from a variational principle whose action is

I = (R + 16π p) (-g)^1/2 d⁴x,

where R is the scalar curvature of spacetime and p is the pressure of the fluid. These equations are also cast into Hamiltonian form, with Hamiltonian density –T₀⁰ (-g^oo)^-1/2.

The second variation of the action is used as the Lagrangian governing the evolution of small perturbations of differentially rotating stellar models. In Newtonian gravity this leads to linear dynamical stability criteria already known. In general relativity it leads to a new sufficient condition for the stability of such models against arbitrary perturbations.

By introducing three scalar fields defined by

ρ ᵴ = ∇λ + ∇x(xi + ∇xɣi)

(where ᵴ is the vector displacement of the perturbed fluid element, ρ is the mass-density, and i, is an arbitrary vector), the Newtonian stability criteria are greatly simplified for the purpose of practical applications. The relativistic stability criterion is not yet in a form that permits practical calculations, but ways to place it in such a form are discussed.

Classical and Quantum Effects in Plasmonic Metals

The field of plasmonics exploits the unique optical properties of metallic nanostructures to concentrate and manipulate light at subwavelength length scales. Metallic nanostructures get their unique properties from their ability to support surface plasmons– coherent wave-like oscillations of the free electrons at the interface between a conductive and dielectric medium. Recent advancements in the ability to fabricate metallic nanostructures with subwavelength length scales have created new possibilities in technology and research in a broad range of applications.

In the first part of this thesis, we present two investigations of the relationship between the charge state and optical state of plasmonic metal nanoparticles. Using experimental bias-dependent extinction measurements, we derive a potential- dependent dielectric function for Au nanoparticles that accounts for changes in the physical properties due to an applied bias that contribute to the optical extinction. We also present theory and experiment for the reverse effect– the manipulation of the carrier density of Au nanoparticles via controlled optical excitation. This plasmoelectric effect takes advantage of the strong resonant properties of plasmonic materials and the relationship between charge state and optical properties to eluci- date a new avenue for conversion of optical power to electrical potential.

The second topic of this thesis is the non-radiative decay of plasmons to a hot-carrier distribution, and the distribution’s subsequent relaxation. We present first-principles calculations that capture all of the significant microscopic mechanisms underlying surface plasmon decay and predict the initial excited carrier distributions so generated. We also preform ab initio calculations of the electron-temperature dependent heat capacities and electron-phonon coupling coefficients of plasmonic metals. We extend these first-principle methods to calculate the electron-temperature dependent dielectric response of hot electrons in plasmonic metals, including direct interband and phonon-assisted intraband transitions. Finally, we combine these first-principles calculations of carrier dynamics and optical response to produce a complete theoretical description of ultrafast pump-probe measurements, free of any fitting parameters that are typical in previous analyses.

The kingdom of the shore: achievement of good ecological potential in reservoirs

The European Water Framework Directive requires member states to restore aquatic habitats to good ecological status (quality) by 2015. Good ecological status is defined as slightly different from high status, which, according to the Directive, means negligible human influence. This poses problems enough for restoration of natural habitats but artificial reservoirs are not excluded from the Directive. They must be restored to good ecological potential. The meaning of good ecological status is linked to that of 'high' ecological status, the pristine reference condition for aquatic habitats under the Directive. From the point of view of an ecologist, this is taken to mean the presence of four fundamental characteristics: nutrient parsimony, characteristic biological and physical structure, connectivity within a wider system and adequate size to give resilience of the biological communities to environmental change. These characteristics are strongly interrelated. Ecological potential must bear some relationship to ecological status but since the reference state for ecological quality is near absence of human impact, it is difficult to see how the criteria for ecological status can be applied to a completely man-made entity where the purpose of the dam is deliberately to interfere with the natural characteristics of a river or former natural lake. Rservoirs are disabled lakes, ususally lakcing the diversity and function provided by a littoral zone. Nonetheless, pragmatic approaches to increasing the biodiversity of reservours are reviewed and conclusions drawn as to the likely effectivemess of the legislation.

The potential of RIVPACS for predicting the effects of environmental change

RIVPACS has been used successfully for biological assessment of river water quality but its potential in forecasting the effects of environmental change has not been investigated. This study has shown that it is possible to simulate faunal changes in response to environmental disturbance, provided that the disturbance directly involves the environmental variables used in RIVPACS predictions. These variables relate to channel shape, discharge and substratum. Many impacts, particularly those associated with pollution, will not affect these variables and therefore RIVPACS cannot simulate the effects of pollution. RIVPACS was sensitive only to major changes in substratum. It was concluded that, because of the static nature of RIVPACS, it cannot respond to the dynamic effects and processes associated with environmental disturbance. Thus RIVPACS, while showing direction of change and indicating sensitive taxa, cannot be used to predict or forecast the effects of environmental impacts.

Progressive Decrease in the Potential Usefulness of Meningococcal Serogroup B Vaccine (4CMenB, Bexsero (R)) in Gipuzkoa, Northern Spain

The effectiveness of a vaccine is determined not only by the immunogenicity of its components, but especially by how widely it covers the disease-causing strains circulating in a given region. Because vaccine coverage varies over time, this study aimed to detect possible changes that could affect vaccine protection during a specific period in a southern European region. The 4CMenB vaccine is licensed for use in Europe, Canada, and Australia and is mainly directed against Neisseria meningitidis serogroup B. This vaccine contains four main immunogenic components: three recombinant proteins, FHbp, Nhba and NadA, and an outer membrane vesicle [PorA P1.4]. The allelic distribution of FHbp, Nhba, NadA, and PorA antigens in 82 invasive isolates (B and non-B serogroups) isolated from January 2008 to December 2013 were analyzed. 4CMenB was likely protective against 61.8% and 50% of serogroup B and non-B meningococci, respectively, in the entire period, but between 2012 and 2013, the predicted protection fell below 45% (42.1% for serogroup B isolates). The observed decreasing trend in the predicted protection during the 6 years of the study (X-2 for trend = 4.68, p=0.03) coincided with a progressive decrease of several clonal complexes (e. g., cc11, cc32 and cc41/44), which had one or more antigens against which the vaccine would offer protection.