Global Hilbert Expansion for the Vlasov-Poisson-Boltzmann System

We study the Hilbert expansion for small Knudsen number $\varepsilon$ for the Vlasov-Boltzmann-Poisson system for an electron gas. The zeroth order term takes the form of local Maxwellian: $ F_{0}(t,x,v)=\frac{\rho_{0}(t,x)}{(2\pi \theta_{0}(t,x))^{3/2}} e^{-|v-u_{0}(t,x)|^{2}/2\theta_{0}(t,x)},\text{\ }\theta_{0}(t,x)=K\rho_{0}^{2/3}(t,x).$Our main result states that if the Hilbert expansion is valid at$t=0$for well-prepared small initial data with irrotational velocity$u_0$, then it is valid for$0\leq t\leq \varepsilon ^{-{1/2}\frac{2k-3}{2k-2}},$where$\rho_{0}(t,x)$and$ u_{0}(t,x)$satisfy the Euler-Poisson system for monatomic gas$\gamma=5/3$

How relative prices affect fuel use patterns in manufacturing : plant - level evidence from Chile

Some economists have urged reliance on fuel taxes and other fiscal incentives to reduce air pollution in semi-industrialized countries. They argue that policies that act on relative prices are easier to enforce than those based on emission monitoring, create less misallocation of resources, and are relatively free of the rent-seeking and corruption that accompany regulations administered at the plant level. To be effective, however, fuel specific taxes and subsidies must inspire manufacturers to significantly adjust their input use as relative prices change. Moreover, these policies must not create politically unacceptable income redistribution. The authors shed light on both issues by analyzing detailed panel data on Chilean manufacturing plants. Overall, their estimates suggest that there is substantial scope for fuel taxes to encourage fuel substitution, but that the response will be very uneven - not only across sectors but across producers of different sizes. Although others may be correct in arguing that fiscal incentives are easier to implement that are direct emission controls, the costs of adjustment are likely to be concentrated fairly narrowly for some fuels. The authors found bakeries, for example, to be very responsive to changes in the relative prices of alternative fuels. By contrast, energy demand in metal products plants appears to be very insensitive to relative prices, no matterwhat estimates are used. Meatpackers fall somewhere between the two - with little price responsiveness in electricity demand, but more in the demand for energy from other sources, especially if coherency-constrained figures are used. It seems that the effects of fuel taxes would depend in significant measure on the sectoral composition varies and some sectors have little flexibility.Energy and Environment,Economic Theory&Research,Transport and Environment,Access to Markets,Environmental Economics&Policies

Thermal performance and energy savings of white and sedum-tray garden roof: A case study in a Chongqing office building

This study presents the experimental measurement of the energy consumption of three top-floor air-conditioned rooms in a typical office building in Chongqing, which is a mountainous city in the hot-summer and cold-winter zone of China, to examine the energy performance of white and sedum-tray garden roofs. The energy consumption of the three rooms was measured from September 2014 to September 2015 by monitoring the energy performance (temperature distributions of the roofs, evaporation, heat fluxes, and energy consumption) and indoor air temperature. The rooms had the same construction and appliances, except that one roof top was black, one was white, and one had a sedum-tray garden roof. This study references the International Performance Measurement and Verification Protocol (IPMVP) to calculate and compare the energy savings of the three kinds of roofs. The results indicate that the energy savings ratios of the rooms with the sedum-tray garden roof and with the white roof were 25.0% and 20.5%, respectively, as compared with the black-roofed room, in the summer; by contrast, the energy savings ratios were −9.9% and −2.7%, respectively, in the winter. Furthermore, Annual conditioning energy savings of white roof (3.9 kWh/m2) were 1.6 times the energy savings for the sedum-tray garden roof. It is evident that white roof is a preferable choice for office buildings in Chongqing. Additionally, The white roof had a reflectance of 0.58 after natural aging owing to the serious air pollution worsened its thermal performance, and the energy savings reduced by 0.033 kWh/m2·d. Evaporation was also identified to have a significant effect on the energy savings of the sedum-tray garden roof

Decay and Continuity of Boltzmann Equation in Bounded Domains

Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: inflow, bounce-back reflection, specular reflection, and diffuse reflection. We establish exponential decay in $L^{\infty}$ norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set of the velocity at the boundary. Our contribution is based on a new $L^{2}$ decay theory and its interplay with delicate $$ decay analysis for the linearized Boltzmann equation, in the presence of many repeated interactions with the boundary.Comment: 89 pages

Optimization of cool roof and night ventilation in office buildings: A case study in Xiamen, China

Increasing roof albedo (using a “cool” roof) and night ventilation are passive cooling technologies that can reduce the cooling loads in buildings, but existing studies have not comprehensively explored the potential benefits of integrating these two technologies. This study combines an experiment in the summer and transition seasons with an annual simulation so as to evaluate the thermal performance, energy savings and thermal comfort improvement that could be obtained by coupling a cool roof with night ventilation. A holistic approach integrating sensitivity analysis and multi-objective optimization is developed to explore key design parameters (roof albedo, night ventilation air change rate, roof insulation level and internal thermal mass level) and optimal design options for the combined application of the cool roof and night ventilation. The proposed approach is validated and demonstrated through studies on a six-storey office building in Xiamen, a cooling-dominated city in southeast China. Simulations show that combining a cool roof with night ventilation can significantly decrease the annual cooling energy consumption by 27% compared to using a black roof without night ventilation and by 13% compared to using a cool roof without night ventilation. Roof albedo is the most influential parameter for both building energy performance and indoor thermal comfort. Optimal use of the cool roof and night ventilation can reduce the annual cooling energy use by 28% during occupied hours when air-conditioners are on and reduce the uncomfortable time slightly during occupied hours when air-conditioners are off

Entanglement detection beyond the CCNR criterion for infinite-dimensions

In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion which is strictly stronger than the computable cross-norm or realignment (CCNR) criterion.Comment: 11 page

de Sitter geodesics: reappraising the notion of motion

The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de Sitter spacetime which cannot be joined to each other by any one of these geodesics. By taking into account the appropriate transitivity properties in the variational principle, a new family of maximizing trajectories is obtained, whose members are able to connect any two points of the de Sitter spacetime. These geodesics introduce a new notion of motion, given by a combination of translations and proper conformal transformations, which may possibly become important at very-high energies, where conformal symmetry plays a significant role.Comment: 9 pages. V2: Presentation changes aiming at clarifying the text; version accepted for publication in Gen. Rel. Gra