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

Gaussian Process Planning with Lipschitz Continuous Reward Functions: Towards Unifying Bayesian Optimization, Active Learning, and Beyond

This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountable set of candidate observations. A key contribution of our work here thus lies in exploiting the Lipschitz continuity of the reward functions to solve for a nonmyopic adaptive epsilon-optimal GPP (epsilon-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of epsilon-GPP with performance guarantee. We empirically demonstrate the effectiveness of our epsilon-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.Comment: 30th AAAI Conference on Artificial Intelligence (AAAI 2016), Extended version with proofs, 17 page

Electron field emission from carbons and their emission mechanism.

This thesis is concerned with the research of the electron field emission properties of carbon based materials. Low emission threshold fields have been observed from both amorphous carbon thin films and carbon nanotubes. The emission mechanism can be subdivided into two groups depending on the type of electric field enhancement. These are the amorphous carbon flat films with non-geometric field enhancement and carbon nanotubes with high surface geometric field enhancement. Amorphous carbon thin films are deposited using an rf-plasma enhanced chemical vapour deposition technique. Changing the deposition conditions such as the addition of Argon or Nitrogen modifies the electronic properties. This induces variations in the sp2 concentration and its distribution within the films. The electron field emission properties from amorphous carbon thin films show a close relationship to its sp2 configuration. A model based on non-geometric field enhancement is proposed to explain the variation in the field emission characteristics. Nano-structured amorphous carbon films custom "designed" using ion beam assisted deposition with sp2 cluster sizes of around 60 nm have also been investigated. The field emission threshold field was shown to be controlled by the film's intrinsic stress and the local carbon density. With increasing stress, there is a concomitant increase in the local density, which is postulated to decrease the distance between the carbon graphitic "planes". This results in enhancement of the electron emission at lower fields. Stress within the films also induces changes to the band structure of the nano-structured carbon which are beneficial to the field emission process. Field emission from carbon nanotubes that are embedded in a polymer matrix has been investigated. The emission threshold fields are observed to be dependent on the nanotube density. The effect of electric field screening is used to explain the reduction of field enhancement observed in these films with increasing nanotube density. The field emission properties are compared with those films which have vertically aligned and in e-beam fabricated nanotube arrays. Results indicate that field emission properties from non-aligned nanotube films are comparable in performance to the best designed arrays in the literature. Although this study shows carbon based materials to have superior field emission properties, integrating the cathodes to fabricate commercial devices could prove to be very challenging

Anomaly-safe discrete groups

We show that there is a class of finite groups, the so-called perfect groups, which cannot exhibit anomalies. This implies that all non-Abelian finite simple groups are anomaly-free. On the other hand, non-perfect groups generically suffer from anomalies. We present two different ways that allow one to understand these statements.Comment: 11 page

Gaussian Process Planning with Lipschitz Continuous Reward Functions

This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountable set of candidate observations. A key contribution of our work here thus lies in exploiting the Lipschitz continuity of the reward functions to solve for a nonmyopic adaptive ε-optimal GPP (ε-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of ε-GPP with performance guarantee. We empirically demonstrate the effectiveness of our ε-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.Singapore-MIT Alliance for Research and Technology (SMART) (52 R-252-000-550-592