Sample path large deviations for single and multi class queues in the many sources asymptotic

In this thesis we consider prove large deviations results for two kinds of queuing systems. In the first case, we consider a queuing system fed by traffic from N independent and identically distributed marked point processes. We establish novel one-dimensional large deviations results for such a system in the previously unexplored lightly loaded case (the load vanishes as N → ∞). This case requires the introduction of novel speed scalings for such queueing systems. We also prove some important properties about the sample paths of such systems in the scaled uniform topology. However, we are unable to prove sample path large deviations principles in this case because the log moment-generating function in this case is not steep, and we are unable to find tools in the literature that enable us to deal with such scenarios. This part of the work is done using the framework introduced by Cruise [1] and Cruise et al. [2] to explore this scaling. In the second case, we consider a two-class queuing network, with each class fed by traffic from N independent and identically distributed marked point processes. We introduce a new, probabilistic interpretation of state-space collapse, and show that under a given scaling of the system, the probability of the vector of stationary queue lengths being a given distance from the identity line in R2 decreases exponentially as the distance increases, and therefore the most likely sample paths are those which stay close to the identity line in R2.James Watt scholarshi

Process-Based Statistical Models Predict Dynamic Estuarine Salinity

Climate change is increasing variation in freshwater input and the intensity of this variation in estuarine systems throughout the world. Estuarine salinity responds to dynamic meteorological and hydrological processes with important consequences to physical features, such as vertical stratification, as well as living resources, such as the distribution, abundance and diversity of species. We developed and evaluated two space-time statistical models to predict bottom salinity in Pamlico Sound, NC: (i) process and (ii) time models. Both models used 20-years of observed salinity and contained a deterministic component designed to represent four key processes that affect salinity: (1) recent and long-term fresh water influx (FWI) from four rivers, (2) mixing with the ocean through inlets, (3) hurricane incidence, and (4) interactions among these variables. Freshwater discharge and distance from an inlet to the Atlantic Ocean explained the most variance in dynamic salinity. The final process model explained 89% of spatiotemporal variability in salinity in a withheld dataset, whereas the final time model explained 87% of the variability within the same withheld data set. This study provides a methodological template for modeling salinity and other normally-distributed abiotic variables in this lagoonal estuary

Interstellar Turbulence II: Implications and Effects

Interstellar turbulence has implications for the dispersal and mixing of the elements, cloud chemistry, cosmic ray scattering, and radio wave propagation through the ionized medium. This review discusses the observations and theory of these effects. Metallicity fluctuations are summarized, and the theory of turbulent transport of passive tracers is reviewed. Modeling methods, turbulent concentration of dust grains, and the turbulent washout of radial abundance gradients are discussed. Interstellar chemistry is affected by turbulent transport of various species between environments with different physical properties and by turbulent heating in shocks, vortical dissipation regions, and local regions of enhanced ambipolar diffusion. Cosmic rays are scattered and accelerated in turbulent magnetic waves and shocks, and they generate turbulence on the scale of their gyroradii. Radio wave scintillation is an important diagnostic for small scale turbulence in the ionized medium, giving information about the power spectrum and amplitude of fluctuations. The theory of diffraction and refraction is reviewed, as are the main observations and scintillation regions.Comment: 46 pages, 2 figures, submitted to Annual Reviews of Astronomy and Astrophysic

Faint extended Lyalpha emission due to star formation at the centre of high-column density QSO absorption systems

We use detailed Lyalpha radiative transfer calculations to further test the claim of Rauch et al. (2008) that they have detected spatially extended faint Lyalpha emission from the elusive host population of Damped Lyalpha Absorption systems (DLAs) in their recent ultra-deep spectroscopic survey. We investigate the spatial and spectral distribution of Lyalpha emission due to star-formation at the centre of DLAs, and its dependence on the spatial and velocity structure of the gas. Our model simultaneously reproduces the observed properties of DLAs and the faint Lyalpha emitters, including the velocity width and column density distribution of DLAs and the large spatial extent of the emission of the faint emitters. Our modelling confirms previous suggestions that DLAs are predominately hosted by Dark Matter (DM) halos in the mass range 10^{9.5}-10^{12} M_sun, and are thus of significantly lower mass than those inferred for L_* Lyman Break Galaxies (LBGs). Our modelling suggests that DM halos hosting DLAs retain up to 20% of the cosmic baryon fraction in the form of neutral hydrogen, and that star formation at the centre of the halos is responsible for the faint Lyalpha emission. The scattering of a significant fraction of the Lyalpha emission to the observed radii, which can be as large as 50 kpc or more, requires the amplitude of the bulk motions of the gas at the centre of the halos to be moderate. The observed space density and size distribution of the emitters together with the incidence rate of DLAs suggests that the Lyalpha emission due to star formation has a duty cycle of ~ 25%.Comment: 17 pages, 13 figures, Accepted for publication in Monthly Notices of the Royal Astronomical Societ

The Effect of Static Pressure on the Inertial Cavitation Threshold and Collapse Strength

The amplitude of the acoustic pressure required to nucleate a gas and/or vapor bubble in a fluid, and to have that bubble undergo an inertial collapse, is termed the inertial cavitation threshold. The hydrostatic dependence of the inertial cavitation threshold was measured up to 30 MPa in ultrapure water using a high quality factor spherical resonator. The threshold increased linearly with the hydrostatic pressure and was found to be temperature dependent. The strength of the bubble collapse at the threshold was measured in terms of shock waves and light emissions. The shock amplitudes increased linearly with the hydrostatic pressure, while the number of photons increased quadratically. The increase of the collapse strength was attributed to the increased threshold, and therefore to the amount of available acoustic energy

Wind power prediction models

Investigations were performed to predict the power available from the wind at the Goldstone, California, antenna site complex. The background for power prediction was derived from a statistical evaluation of available wind speed data records at this location and at nearby locations similarly situated within the Mojave desert. In addition to a model for power prediction over relatively long periods of time, an interim simulation model that produces sample wind speeds is described. The interim model furnishes uncorrelated sample speeds at hourly intervals that reproduce the statistical wind distribution at Goldstone. A stochastic simulation model to provide speed samples representative of both the statistical speed distributions and correlations is also discussed

Statistical multiplexing and connection admission control in ATM networks

Asynchronous Transfer Mode (ATM) technology is widely employed for the transport of network traffic, and has the potential to be the base technology for the next generation of global communications. Connection Admission Control (CAC) is the effective traffic control mechanism which is necessary in ATM networks in order to avoid possible congestion at each network node and to achieve the Quality-of-Service (QoS) requested by each connection. CAC determines whether or not the network should accept a new connection. A new connection will only be accepted if the network has sufficient resources to meet its QoS requirements without affecting the QoS commitments already made by the network for existing connections. The design of a high-performance CAC is based on an in-depth understanding of the statistical characteristics of the traffic sources

Field Measurements at River and Tidal Current Sites for Hydrokinetic Energy Development: Best Practices Manual

In this report, existing data collection techniques and protocols for characterizing open channel flows are reviewed and refined to further address the needs of the MHK industry. The report provides an overview of the hydrodynamics of river and tidal channels, and the working principles of modern acoustic instrumentation, including best practices in remote sensing methods that can be applied to hydrokinetic energy site characterization. Emphasis is placed upon acoustic Doppler velocimeter (ADV) and acoustic-Doppler current profiler (ADCP) instruments, as these represent the most practical and economical tools for use in the MHK industry. Incorporating the best practices as found in the literature, including the parameters to be measured, the instruments to be deployed, the instrument deployment strategy, and data post-processing techniques. The data collected from this procedure aims to inform the hydro-mechanical design of MHK systems with respect to energy generation and structural loading, as well as provide reference hydrodynamics for environmental impact studies. The standard metrics and protocols defined herein can be utilized to guide field experiments with MHK systems

Fast-response measurement of the concentration of sulphur (and phosphorus) compounds in the atmosphere

Imperial Users onl

A study of the groundwater travel time distribution at a rural watershed in Iowa: A systems theory approach to groundwater flow analysis

This dissertation is a study of groundwater-surface water interaction in terms of the travel time distribution framework applied to a tile-drained, agricultural landscape at the watershed scale. Specifically, we examined the two dimensional, steady state groundwater flow characterizing a shallow, unconfined aquifer at a representative watershed. A groundwater flow model of the aquifer was constructed using MODFLOW (Harbaugh et al., 2000). Hypothetical particles were then tracked through the simulated groundwater flow field using MODPATH (Pollock, 1994) to determine travel times associated with advective solute transport. The resultant distribution of travel times was represented by an exponential decay function with a mean travel time of 20.51 years. We further examined the impact of various control variables on groundwater travel times. First, the influence of the model selection on the travel time distribution results was examined by comparing results obtained from three models - analytic, GIS-based, and MODFLOW. Distributions obtained from all three models were represented by exponential decays, with the mean travel time varying between 16.22 and 20.51 years. The agreement between the MODFLOW and GIS models was probed by analyzing their flowpath length and velocity distributions. The spatial distributions of travel times obtained from the two models were analyzed, and conclusions of the impact of model selection on travel times were drawn. We also examined the impact of depth of flow on groundwater travel times. The analysis, conducted using the sink strength threshold parameter as a surrogate to depth showed that travel times, and structure of the effective sink network, are significantly impacted by depth. We examined the impact of variable tile drainage density and incision depth on travel times and baseflow. The marginal impact of tile drainage density on travel times and baseflow volumes was observed to diminish with increasing density, while the impact of tile incision depth on the two variables was observed to be linear. Overall, tile drainage density was observed to have a stronger impact on travel times than baseflow, while tile incision depth impacted baseflow more than travel times. The impact of aquifer recharge on travel times was observed to vary based on landscape position