Transport Equations for Oscillating Neutrinos

We derive a suite of generalized Boltzmann equations, based on the density-matrix formalism, that incorporates the physics of neutrino oscillations for two- and three-flavor oscillations, matter refraction, and self-refraction. The resulting equations are straightforward extensions of the classical transport equations that nevertheless contain the full physics of quantum oscillation phenomena. In this way, our broadened formalism provides a bridge between the familiar neutrino transport algorithms employed by supernova modelers and the more quantum-heavy approaches frequently employed to illuminate the various neutrino oscillation effects. We also provide the corresponding angular-moment versions of this generalized equation set. Our goal is to make it easier for astrophysicists to address oscillation phenomena in a language with which they are familiar. The equations we derive are simple and practical, and are intended to facilitate progress concerning oscillation phenomena in the context of core-collapse supernova theory.Comment: 13 pages; Submitted to Physical Review

Global-mean Vertical Tracer Mixing in Planetary Atmospheres II: Tidally Locked Planets

In Zhang $\&$ Showman (2018, hereafter Paper I), we developed an analytical theory of 1D eddy diffusivity $K_{zz}$ for global-mean vertical tracer transport in a 3D atmosphere. We also presented 2D numerical simulations on fast-rotating planets to validate our theory. On a slowly rotating planet such as Venus or a tidally locked planet (not necessarily a slow-rotator) such as a hot Jupiter, the tracer distribution could exhibit significant longitudinal inhomogeneity and tracer transport is intrinsically 3D. Here we study the global-mean vertical tracer transport on tidally locked planets using 3D tracer-transport simulations. We find that our analytical $K_{zz}$ theory in Paper I is validated on tidally locked planets over a wide parameter space. $K_{zz}$ strongly depends on the large-scale circulation strength, horizontal mixing due to eddies and waves and local tracer sources and sinks due to chemistry and microphysics. As our analytical theory predicted, $K_{zz}$ on tidally locked planets also exhibit three regimes In Regime I where the chemical and microphysical processes are uniformly distributed across the globe, different chemical species should be transported via different eddy diffusivity. In Regime II where the chemical and microphysical processes are non-uniform---for example, photochemistry or cloud formation that exhibits strong day-night contrast---the global-mean vertical tracer mixing does not always behave diffusively. In the third regime where the tracer is long-lived, non-diffusive effects are significant. Using species-dependent eddy diffusivity, we provide a new analytical theory of the dynamical quench points for disequilibrium tracers on tidally locked planets from first principles.Comment: Accepted at ApJ, 16 pages, 12 figures. This is the part II. Part I is "Global-mean Vertical Tracer Mixing in Planetary Atmospheres I: Theory and Fast-rotating Planets

Effects of Bulk Composition on The Atmospheric Dynamics on Close-in Exoplanets

Super Earths and mini Neptunes likely have a wide range of atmospheric compositions, ranging from low-molecular mass atmospheres of H2 to higher molecular atmospheres of water, CO2, N2, or other species. Here, we systematically investigate the effects of atmospheric bulk compositions on temperature and wind distributions for tidally locked sub-Jupiter-sized planets, using an idealized 3D general circulation model (GCM). The bulk composition effects are characterized in the framework of two independent variables: molecular weight and molar heat capacity. The effect of molecular weight dominates. As the molecular weight increases, the atmosphere tends to have a larger day-night temperature contrast, a smaller eastward phase shift in the thermal phase curve and a smaller zonal wind speed. The width of the equatorial super-rotating jet also becomes narrower and the "jet core" region, where the zonal-mean jet speed maximizes, moves to a greater pressure level. The zonal-mean zonal wind is more prone to exhibit a latitudinally alternating pattern in a higher-molecular-weight atmosphere. We also present analytical theories that quantitatively explain the above trends and shed light on the underlying dynamical mechanisms. Those trends might be used to indirectly determine the atmospheric compositions on tidally locked sub-Jupiter-sized planets. The effects of the molar heat capacity are generally small. But if the vertical temperature profile is close to adiabatic, molar heat capacity will play a significant role in controlling the transition from a divergent flow in the upper atmosphere to a jet-dominated flow in the lower atmosphere.Comment: 25 pages, 22 figure

Atmospheric Circulation of Brown Dwarfs: Jets, Vortices, and Time Variability

A variety of observational evidence demonstrates that brown dwarfs exhibit active atmospheric circulations. In this study we use a shallow-water model to investigate the global atmospheric dynamics in the stratified layer overlying the convective zone on these rapidly rotating objects. We show that the existence and properties of the atmospheric circulation crucially depend on key parameters including the energy injection rate and radiative timescale. Under conditions of strong internal heat flux and weak radiative dissipation, a banded flow pattern comprising east-west jet streams spontaneously emerges from the interaction of atmospheric turbulence with the planetary rotation. In contrast, when the internal heat flux is weak and/or radiative dissipation is strong, turbulence injected into the atmosphere damps before it can self-organize into jets, leading to a flow dominated by transient eddies and isotropic turbulence instead. The simulation results are not very sensitive to the form of the forcing. Based on the location of the transition between jet-dominated and eddy-dominated regimes, we suggest that many brown dwarfs may exhibit atmospheric circulations dominated by eddies and turbulence (rather than jets) due to the strong radiative damping on these worlds, but a jet structure is also possible under some realistic conditions. Our simulated light curves capture important features from observed infrared lightcurves of brown dwarfs, including amplitude variations of a few percent and shapes that fluctuate between single-peak and multi-peak structures. More broadly, our work shows that the shallow-water system provides a useful tool to illuminate fundamental aspects of the dynamics on these worlds

High-Precision Localization Using Ground Texture

Location-aware applications play an increasingly critical role in everyday life. However, satellite-based localization (e.g., GPS) has limited accuracy and can be unusable in dense urban areas and indoors. We introduce an image-based global localization system that is accurate to a few millimeters and performs reliable localization both indoors and outside. The key idea is to capture and index distinctive local keypoints in ground textures. This is based on the observation that ground textures including wood, carpet, tile, concrete, and asphalt may look random and homogeneous, but all contain cracks, scratches, or unique arrangements of fibers. These imperfections are persistent, and can serve as local features. Our system incorporates a downward-facing camera to capture the fine texture of the ground, together with an image processing pipeline that locates the captured texture patch in a compact database constructed offline. We demonstrate the capability of our system to robustly, accurately, and quickly locate test images on various types of outdoor and indoor ground surfaces

Interregional burden-sharing of greenhouse gas mitigation in the United States

Emissions trading is an attractive candidate for implementing greenhouse gas mitigation, because it can promote both efficiency and equity. This paper analyzes the interregional impacts of alternative allocations of carbon dioxide emission permits within the U.S. The analysis is performed with the aid of a nonlinear programming model for ten EPA Regions and for six alternative permit distribution formulas. The reason that various alternatives need to be considered is that there is no universal consensus on the best definition of equity. Advance knowledge of absolute and relative regional economic impacts provides policy-makers with a stronger basis for making the choice. The analysis yields several useful results. First, the simulations indicate that no matter how permits are allocated, this policy instrument can substantially reduce the cost of greenhouse gas mitigation for the U.S. in comparison to a system of fixed quotas for each of its regions. Interestingly, the welfare impacts of several of the allocation formulas differ only slightly despite the large differences in their philosophical underpinnings. Also, the results for some equity criteria differ greatly from their application in the international domain. For example, the Egalitarian (per capita) criterion results in the relatively greatest cost burden being incurred by one of the regions of the U.S. with the lowest per capita income.Tradeable emission permits; climate policy; interregional equity

Complexity classification of two-qubit commuting hamiltonians

We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a dichotomy theorem: either this model is efficiently classically simulable or it allows one to sample from probability distributions which cannot be sampled from classically unless the polynomial hierarchy collapses. Furthermore, the only simulable Hamiltonians are those which fail to generate entanglement. This shows that generic two-qubit commuting Hamiltonians can be used to perform computational tasks which are intractable for classical computers under plausible assumptions. Our proof makes use of new postselection gadgets and Lie theory.Comment: 34 page