Hierarchical quantum master equation with semiclassical Drude dissipation

We propose a nonperturbative quantum dissipation theory, in term of hierarchical quantum master equation. It may be used with a great degree of confidence to various dynamics systems in condensed phases. The theoretical development is rooted in an improved semiclassical treatment of Drude bath, beyond the conventional high temperature approximations. It leads to the new theory a simple modification but important improvement over the conventional stochastic Liouville equation theory, without extra numerical cost. Its broad range of validity and applicability is extensively demonstrated with two--level electron transfer model systems, where the new theory can be considered as the modified Zusman equation. We also present a criterion, which depends only on the system--bath coupling strength, characteristic bath memory time, and temperature, to estimate the performance of the hierarchical quantum master equation.Comment: 10 pages, 8 figures, submitted to J. Chem. Phys. on 2009-08-0

The Dark Matter Tidal Stripping History of the Sagittarius Core with N-body simulations

The infall of the Sagittarius (Sgr) Dwarf Spheroidal Galaxy in the Milky Way halo is an unique opportunity to understand how the different components of a dwarf galaxy could be tidally removed. In this work, we reconstruct the Sgr core morphology and kinematics on the basis of a model that has already successfully reproduced the Sgr stream. Here we use a very high resolution model that almost resolves individual stars in the Sgr core. It reproduces most of the observed morphology and kinematic properties, without specific fine-tuning. We also show that the dark matter may have been almost entirely stripped by Milky Way tides after two passages at pericenter. Finally the model predicts that the Sgr core will be fully disrupted within the next 2 Gyr.Comment: 9 pages, 5 figures,1 table. Accepted for publication in ApJ

Envy-Free House Allocation with Minimum Subsidy

House allocation refers to the problem where $m$ houses are to be allocated to $n$ agents so that each agent receives one house. Since an envy-free house allocation does not always exist, we consider finding such an allocation in the presence of subsidy. We show that computing an envy-free allocation with minimum subsidy is NP-hard in general, but can be done efficiently if $m$ differs from $n$ by an additive constant or if the agents have identical utilities

Multiple-bounce Smith Microfacet BRDFs using the Invariance Principle

Smith microfacet models are widely used in computer graphics to represent materials. Traditional microfacet models do not consider the multiple bounces on microgeometries, leading to visible energy missing, especially on rough surfaces. Later, as the equivalence between the microfacets and volume has been revealed, random walk solutions have been proposed to introduce multiple bounces, but at the cost of high variance. Recently, the position-free property has been introduced into the multiple-bounce model, resulting in much less noise, but also bias or a complex derivation. In this paper, we propose a simple way to derive the multiple-bounce Smith microfacet bidirectional reflectance distribution functions (BRDFs) using the invariance principle. At the core of our model is a shadowing-masking function for a path consisting of direction collections, rather than separated bounces. Our model ensures unbiasedness and can produce less noise compared to the previous work with equal time, thanks to the simple formulation. Furthermore, we also propose a novel probability density function (PDF) for BRDF multiple importance sampling, which has a better match with the multiple-bounce BRDFs, producing less noise than previous naive approximations

Analysis of the Dielectric Constant of Saline-Alkali Soils and the Effect on Radar Backscattering Coefficient: A Case Study of Soda Alkaline Saline Soils in Western Jilin Province Using RADARSAT-2 Data

Soil salinity is a global problem, especially in developing countries, which affects the environment and productivity of agriculture areas. Salt has a significant effect on the complex dielectric constant of wet soil. However, there is no suitable model to describe the variation in the backscattering coefficient due to changes in soil salinity content. The purpose of this paper is to use backscattering models to understand behaviors of the backscattering coefficient in saline soils based on the analysis of its dielectric constant. The effects of moisture and salinity on the dielectric constant by combined Dobson mixing model and seawater dielectric constant model are analyzed, and the backscattering coefficient is then simulated using the AIEM. Simultaneously, laboratory measurements were performed on ground samples. The frequency effect of the laboratory results was not the same as the simulated results. The frequency dependence of the ionic conductivity of an electrolyte solution is influenced by the ion’s components. Finally, the simulated backscattering coefficients measured from the dielectric constant with the AIEM were analyzed using the extracted backscattering coefficient from the RADARSAT-2 image. The results show that RADARSAT-2 is potentially able to measure soil salinity; however, the mixed pixel problem needs to be more thoroughly considered