Fast and Accurate Computation of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

This paper is concerned with fast and accurate computation of exterior wave equations truncated via exact circular or spherical nonreflecting boundary conditions (NRBCs, which are known to be nonlocal in both time and space). We first derive analytic expressions for the underlying convolution kernels, which allow for a rapid and accurate evaluation of the convolution with $O(N_t)$ operations over $N_t$ successive time steps. To handle the onlocality in space, we introduce the notion of boundary perturbation, which enables us to handle general bounded scatters by solving a sequence of wave equations in a regular domain. We propose an efficient spectral-Galerkin solver with Newmark's time integration for the truncated wave equation in the regular domain. We also provide ample numerical results to show high-order accuracy of NRBCs and efficiency of the proposed scheme.Comment: 22 pages with 9 figure

A new two-component sasa-satuma equation: large-time asymaptotics on the line

We consider the initial value problem for a new two-component Sasa-Satsuma equation associated with the fourth-order Lax pair with decaying initial data on the line. By utilizing the spectral analysis, the solution of the new two-component Sasa-Satsuma system is transformed into the solution of a fourth-order matrix Riemann-Hilbert problem. Then the long-time asymptotics of the solution is obtained by means of the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann-Hilbert problems. We show that there are three main regions in the half-plane, where the asymptotics has qualitatively different forms: a left fast decaying sector, a central Painleve sector where the asymptotics is described in terms of the solution of a new coupled Painleve II equation which is related to a fourth-order matrix Riemann-Hilbert problem, and a right slowly decaying oscillatory sector

The impacts of air pollution on human and natural capital in China: A look from a provincial perspective

Abstract Air quality has a significant impact on human health and natural systems worldwide. China, as one of the largest developing countries, faces very much serious air pollution and requires much attention. While the influences of air pollution on human or nature have been extensively investigated, few scholars considered the two effects of air pollution on human health and nature simultaneously based on the same framework. Indeed, human and nature coexist in the same biosphere on which they depend for their development and the impacts of air pollution on human health and nature occur at the same time with different and synergic effects. Only by considering both impacts we can develop a more comprehensive understanding of air pollution impacts, in particular including SO2, NO2, CO, PM10 and PM2.5. Impacts can be looked at from the point of view of damage provided and damage repair (health recovery, replacement cost). Therefore, considering the different pollutants and sectors, the influences of air pollution on human health and nature are accounted for in this study by applying the Emergy Accounting and Life Cycle Assessment Eco-indicator 99 methods under a unified framework in 31 provinces of China taken as case study. While LCA provides an accurate assessment of the direct consequences of pollution on human and natural capital (human health and biodiversity losses), the Emergy Accounting approach quantifies the biosphere work associated to repair or replace such losses over time. Furthermore, the spatial agglomeration characteristics of emissions, human and natural capital losses analyzed by means of Moran's I index. Results show that: (1) Concerning human capital losses, the amount of emissions of PM10 and PM2.5 only account for 10% of total impacts, compared to SO2, NO2, and CO emissions, but in some provinces cause more than 70% of human capital losses. And more than 80% of PM2.5 and PM10 that cause human capital losses come from the industrial and civil sectors. (2) As far as natural capital losses are concerned, compared with SO2, the losses caused by NO2 account for 80% in most provinces. And the power, industrial and transportation sectors are the three major sources of NO2 causing natural capital losses. (3) The spatial agglomeration characteristics, such as high-high cluster, high-low cluster, low-low cluster and low–high cluster, are different for air pollution emissions, human and natural capital losses. A comprehensive and detailed understanding of the impacts of air pollution is crucial for policy makers to take informed decisions