Kac regular sets and Sobolev spaces in geometry, probability and quantum physics

Let Ω ⊂ M be an open subset of a Riemannian manifold M and let V: M→ R be a Kato decomposable potential. With W01,2(M;V) the natural form domain of the Schrödinger operator - Δ + V in L2(M) , in this paper we study systematically the following question: Under which assumption on Ω is the statement for allf∈W01,2(M;V)withf=0a.e. inMΩone hasf|Ω∈W01,2(Ω;V)true for every such V? Generalizing a classical result by Herbst and Zhao, who treat the Euclidean Rm and V= 0 , we prove that without any further assumptions on V, the above property is satisfied, if Ω is Kac regular, a probabilistic property which means that the first exit time of Brownian motion on M from Ω is equal to its first penetration time to M Ω. In fact, we treat more general covariant Schrödinger operators acting on sections in metric vector bundles, allowing new results concerning the harmonicity of Dirac spinors on singular subsets. Finally, we prove that locally Lipschitz regular Ω ’s are Kac regular

On the space of connections having non-trivial twisted harmonic spinors

We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yield an invertible operator has infinitely many connected components if the untwisted Dirac operator is invertible and the dimension of the twisting bundle is sufficiently large

Nonequilibrium Quantum Field Theory

Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this 2008 book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts are applied to research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. This self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics. It has been reissued as an Open Access publication

Impacts of urban expansion on relatively smaller surrounding cities during heat waves

Urban-induced thermal stress can threaten human health, especially during heat waves (HWs). The growth of cities further exacerbates this effect. Here, weather research and forecasting (WRF) with an urban canopy model (UCM) is used to assess the effects of megacities and their growth on the thermal regime of proximal cities during heat waves. Analysis of the heat fluxes shows that advection impacts cities downwind. Results indicate that as urban areas change size (50%−100% and 100−150% of their current size), the local 2 m temperature increases by 2.7 and 1.7 °C, and the 2 m specific humidity decreases by 2.1 and 1.4 g kg−1, respectively. A small city downwind is impacted with a 0.3−0.4 °C increase in 2 m temperature. Green roof is a potential mitigation strategy for these regions (i.e., beyond the megacity). With 50% green roofs in an urban area, a 0.5 °C decrease in 2 m temperature and 0.6 g kg−1 increase in specific humidity is simulated. Urbanization upwind of a megacity will contribute to regional climate change

Nonequilibrium Quantum Field Theory

Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this 2008 book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts are applied to research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. This self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics. It has been reissued as an Open Access publication

A general model for collaboration networks

In this paper, we propose a general model for collaboration networks. Depending on a single free parameter "{\bf preferential exponent}", this model interpolates between networks with a scale-free and an exponential degree distribution. The degree distribution in the present networks can be roughly classified into four patterns, all of which are observed in empirical data. And this model exhibits small-world effect, which means the corresponding networks are of very short average distance and highly large clustering coefficient. More interesting, we find a peak distribution of act-size from empirical data which has not been emphasized before of some collaboration networks. Our model can produce the peak act-size distribution naturally that agrees with the empirical data well.Comment: 10 pages, 10 figure

Seismic Performance Evaluation of a Submarine Gas Pipeline

Analyses were conducted on the seismic performance of a proposed offshore gas flowline, which connects a manifold in 830-m water depth to a riser platform in shallow waters of the outer continental shelf. Climbing a 10-degree continental slope, the flowline will be installed on the seafloor underlain by deep carbonate sediments of sands and silty clays. Two types of analyses were performed for a critical segment of the flowline, where it traverses a narrow ridge flanked by two deep submarine canyons: (1) probabilistic analyses using simplified empirical methods; and (2) deterministic 2D and 3D analyses with FLAC using a nonlinear, effective-stress soil model fully coupled with an empirical pore-pressure generation scheme. Soil properties were derived from PCPT and T-bar data, Bender element tests, and monotonic and cyclic direct simple shear tests. The analysis results indicated an extremely small likelihood of liquefaction along the flowline, with only small deformations predicted to occur for ground motions with a return period of 5,000 years

Evaluation of WRF mesoscale simulations and particle trajectory analysis for the MILAGRO field campaign

Accurate numerical simulations of the complex wind flows in the Mexico City Metropolitan Area (MCMA) can be an invaluable tool for interpreting the MILAGRO field campaign results. This paper uses three methods to evaluate numerical simulations of basin meteorology using the MM5 and WRF models: statistical comparisons with observations, "Concentration Field Analysis" (CFA) using measured air pollutant concentrations, and comparison of flow features using cluster analysis. CFA is shown to be a better indication of simulation quality than statistical metrics, and WRF simulations are shown to be an improvement on the MM5 ones. Comparisons with clusters identifies an under-representation of the drainage flows into the basin and an over-representation of wind shear in the boundary layer. Particle trajectories simulated with WRF-FLEXPART are then used to analyse the transport of the urban plume and show rapid venting and limited recirculation during MILAGRO. Lagrangian impacts were identified at the campaign supersites, and age spectra of the pollutants evaluated at those same sites. The evaluation presented in the paper show that mesoscale meteorological simulations are of sufficient accuracy to be useful for MILAGRO data analysis.National Science Foundation (U.S.) (Award ATM-0511803)National Science Foundation (U.S.) (Award ATM-0810950)National Science Foundation (U.S.) (Award ATM-0810931)Molina Center for Energy and the Environmen

Using 3DVAR data assimilation system to improve ozone simulations in the Mexico City basin

This study investigates the improvement of ozone (O<sub>3</sub>) simulations in the Mexico City basin using a three-dimensional variational (3DVAR) data assimilation system in meteorological simulations during the MCMA-2003 field measurement campaign. Meteorological simulations from the NCAR/Penn State mesoscale model (MM5) are used to drive photochemical simulations with the Comprehensive Air Quality Model with extensions (CAMx) during a four-day episode on 13–16 April 2003. The simulated wind circulation, temperature, and humidity fields in the basin with the data assimilation are found to be more consistent with the observations than those from the reference deterministic forecast. This leads to improved simulations of plume position, peak O<sub>3</sub> timing, and peak O<sub>3</sub> concentrations in the photochemical model. The improvement in O<sub>3</sub> simulations is especially strong during the daytime. The results demonstrate the importance of applying data assimilation in meteorological simulations for air quality studies in the Mexico City basin