Potential Vorticity Mixing in a Tangled Magnetic Field

A theory of potential vorticity (PV) mixing in a disordered (tangled) magnetic field is presented. The analysis is in the context of $\beta$-plane MHD, with a special focus on the physics of momentum transport in the stably stratified, quasi-2D solar tachocline. A physical picture of mean PV evolution by vorticity advection and tilting of magnetic fields is proposed. In the case of weak-field perturbations, quasi-linear theory predicts that the Reynolds and magnetic stresses balance as turbulence Alfv\'enizes for a larger mean magnetic field. Jet formation is explored quantitatively in the mean field-resistivity parameter space. However, since even a modest mean magnetic field leads to large magnetic perturbations for large magnetic Reynolds number, the physically relevant case is that of a strong but disordered field. We show that numerical calculations indicate that the Reynolds stress is modified well before Alfv\'enization -- i.e. before fluid and magnetic energies balance. To understand these trends, a double-average model of PV mixing in a stochastic magnetic field is developed. Calculations indicate that mean-square fields strongly modify Reynolds stress phase coherence and also induce a magnetic drag on zonal flows. The physics of transport reduction by tangled fields is elucidated and linked to the related quench of turbulent resistivity. We propose a physical picture of the system as a resisto-elastic medium threaded by a tangled magnetic network. Applications of the theory to momentum transport in the tachocline and other systems are discussed in detail.Comment: 17 pages, 10 figures, 2 table

Calibrating an ice sheet model using high-dimensional binary spatial data

Rapid retreat of ice in the Amundsen Sea sector of West Antarctica may cause drastic sea level rise, posing significant risks to populations in low-lying coastal regions. Calibration of computer models representing the behavior of the West Antarctic Ice Sheet is key for informative projections of future sea level rise. However, both the relevant observations and the model output are high-dimensional binary spatial data; existing computer model calibration methods are unable to handle such data. Here we present a novel calibration method for computer models whose output is in the form of binary spatial data. To mitigate the computational and inferential challenges posed by our approach, we apply a generalized principal component based dimension reduction method. To demonstrate the utility of our method, we calibrate the PSU3D-ICE model by comparing the output from a 499-member perturbed-parameter ensemble with observations from the Amundsen Sea sector of the ice sheet. Our methods help rigorously characterize the parameter uncertainty even in the presence of systematic data-model discrepancies and dependence in the errors. Our method also helps inform environmental risk analyses by contributing to improved projections of sea level rise from the ice sheets

Visible Cascade Higgs Decays to Four Photons at Hadron Colliders

The presence of a new singlet scalar particle a can open up new decay channels for the Higgs boson, through cascades of the form h -> 2a -> X, possibly making discovery through standard model channels impossible. If a is CP-odd, its decay products are particularly sensitive to physics beyond the standard model. Quantum effects from heavy fields can naturally make gluonic decay, a -> 2g, the dominant decay mode, resulting in a h -> 4 g decay which is difficult to observe at hadron colliders, and is allowed by LEP for m_h > 82 GeV. However, there are usually associated decays with photons, either h -> 2g 2gamma or h -> 4gamma, which are more promising. The decay h -> 2g 2gamma only allows discovery of the a particle and not the Higgs whereas h -> 4gamma is a clean channel that can discover both particles. We determine what branching ratios are required for discovery at LHC and find that with 300 fb^-1 of luminosity, a branching ratio of order 10^-4 is sufficient for a large region of Higgs masses. Due to a lower expected luminosity of ~ 8 fb^-1, discovery at the Tevatron requires more than 5 x 10^-3 in branching ratio.Comment: 6 pages, 2 color figures, revtex4 forma

An improved size, matching, and scaling synthesis method for the design of meso-scale truss structures

The recent improvement of additive manufacturing has allowed designers to achieve a level of complexity and customizability that is difficult or impossible to accomplish using traditional manufacturing processes. As a result, much research has been conducted on developing new methods to utilize the larger design space brought by additive manufacturing. One such research area is in the design of mesoscale lattice structures. Mesoscale lattice structures are a type of cellular structure with support element sizes on the order of magnitude of centimeters. These types of structures are engineered for high performance and have applications in industries where both low weight and high strength are desired. However, due to the small size of their struts, these structures can easily have hundreds to thousands of individual struts. As a result, design poses a unique challenge. Current methods approach design of mesoscale lattice structures as a topological optimization problem, treating each strut diameter in the structure as a design variable. For structures with a fewer number struts, these optimization methods can converge, but will generally be very time-consuming. For structures with a large number of struts, the optimization problem becomes too large for current algorithms to solve. In previous research, a new, highly efficient design method for mesoscale lattice structures was presented that eliminates the need for global size or topological optimization. This method, termed the Size, Matching and Scaling method, used a unique combination of a solid-body finite element analysis and a library of pre-defined lattice configurations, termed the "unit-cell library," to generate lattice topologies. The results from this method were highly promising: design time was significantly reduced when compared to optimization methods. Furthermore, lattices designed using the SMS method had performance results that were either comparable or better than their optimized counterparts. However, the method developed was highly conceptual, lacking a true systematic methodology for generating topologies and suffering from some gaps in implementation. In this research, we present a modified Size Matching and Scaling (SMS) design method. Firstly, we introduce and outline the modified methodology. This methodology particularly includes an optimization step for determining strut diameters that replaces the manual search used in the original method. Secondly, we expand and explore the unit-cell library in an attempt to improve the performance of lattices generated using the SMS method. In particular, we optimize several unit-cell configurations and compare their performance in the context of the SMS method. Finally, we test the updated SMS methodology and unit-cell library using various design examples. Results from the various example problems indicate that optimization is not only a viable systematic method for determining diameter values, but is actually preferred to the manual, iterative process used in the original method. Furthermore, various optimization algorithms and approaches yield different results. Between the two optimization algorithms utilized in this method: constrained optimization and least-squares minimization, constrained minimization converges faster, but least-squares minimization yields slightly improved performance results. In addition to these algorithms, a one-variable approach using an untested, simplifying assumption, dubbed the "28% approach," was tested. Results indicate that this assumption was incorrect and cannot be utilized. Finally, results from the expanded unit-cell library indicate that the best unit-cell configuration is still the same original unit-cell configuration utilized in the first SMS method. The addition of more unit-cell does not improve the performance of structures generated using the SMS method. In fact, both performance and design time worsen when additional configurations are utilized.M.S.Committee Chair: Rosen, David; Committee Member: Choi, Seung-Kyum; Committee Member: Paredis, Christiaa

Fourier instantaneous estimators and the Epps effect

We compare the Malliavin-Mancino and Cuchiero-Teichmann Fourier instantaneous estimators to investigate the impact of the Epps effect arising from asynchrony in the instantaneous estimates. We demonstrate the instantaneous Epps effect under a simulation setting and provide a simple method to ameliorate the effect. We find that using the previous tick interpolation in the Cuchiero-Teichmann estimator results in unstable estimates when dealing with asynchrony, while the ability to bypass the time domain with the Malliavin-Mancino estimator allows it to produce stable estimates and is therefore better suited for ultra-high frequency finance. An empirical analysis using Trade and Quote data from the Johannesburg Stock Exchange illustrates the instantaneous Epps effect and how the intraday correlation dynamics can vary between days for the same equity pair.Comment: 17 pages, 10 figures, 2 tables. Link to the supporting Julia code: https://github.com/CHNPAT005/PC-FI

High-frequency correlation dynamics: Is the Epps effect a bias?

We tackle the question of whether Trade and Quote data from high-frequency finance are representative of discrete connected events, or whether these measurements can still be faithfully represented as random samples of some underlying Brownian diffusion in the context of modelling correlation dynamics. In particular, if the implicit notion of instantaneous correlation dynamics that are independent of the time-scale a reasonable assumption. To this end, we apply kernel averaging non-uniform fast Fourier transforms in the context of the Malliavin-Mancino integrated and instantaneous volatility estimators to speed up the estimators. We demonstrate the implicit time-scale investigated by the estimator by comparing it to the theoretical Epps effect arising from asynchrony. We compare the Malliavin-Mancino and Cuchiero-Teichmann Fourier instantaneous estimators and demonstrate the relationship between the instantaneous Epps effect and the cutting frequencies in the Fourier estimators. We find that using the previous tick interpolation in the Cuchiero-Teichmann estimator results in unstable estimates when dealing with asynchrony, while the ability to bypass the time domain with the Malliavin-Mancino estimator allows it to produce stable estimates and is therefore better suited for ultra high-frequency finance. We derive the Epps effect arising from asynchrony and provide a refined approach to correct the effect. We compare methods to correct for the Epps effect arising from asynchrony when the underlying process is a Brownian diffusion, and when the underlying process is from discrete connected events (proxied using a D-type Hawkes process). We design three experiments using the Epps effect to discriminate the underlying processes. These experiments demonstrate that using a Hawkes representation recovers the empiricism reported in the literature under simulation conditions that cannot be achieved when using a Brownian representation. The experiments are applied to Trade and Quote data from the Johannesburg Stock Exchange and the evidence suggests that the empirical measurements are from a system of discrete connected events where correlations are an emergent property of the time-scale rather than an instantaneous quantity that exists at all time-scales

The Perceptions of Macao Undergraduates Regarding Help Websites for Problem Gambling

This study conducted a web-surfing exercise and a questionnaire survey among a group of Macao undergraduate students regarding the websites that offered help with problem gambling. The results of this study found that most help websites in Macao and Hong Kong provided basic information-sharing service. The students indicated that they would choose their preferred help organization based on factors such as trust, familiarity, and the characteristics of the websites. They also gave comments/suggestions related to the publicity, design, contents, and focus of the websites. This study discussed the results and their implications for future research and practice

Design, implementation and evaluation of a QoS-aware transport protocol

In the context of a reconfigurable transport protocol framework, we propose a QoS-aware Transport Protocol (QSTP), specifically designed to operate over QoS-enabled networks with bandwidth guarantee. QSTP combines QoS-aware TFRC congestion control mechanism, which takes into account the network-level bandwidth reservations, with a Selective ACKnowledgment (SACK) mechanism in order to provide a QoS-aware transport service that fill the gap between QoS enabled network services and QoS constraint applications. We have developed a prototype of this protocol in the user-space and conducted a large range of measurements to evaluate this proposal under various network conditions. Our results show that QSTP allows applications to reach their negotiated QoS over bandwidth guaranteed networks, such as DiffServ/AF network, where TCP fails. This protocol appears to be the first reliable protocol especially designed for QoS network architectures with bandwidth guarantee