Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

de Sitter Tunneling,Emission Spectrum and Entropy/Area Quantum

The Banerjee-Majhi's recent work shows that the Hawking radiation and entropy/area quantum of the black hole horizon (EH) can be well described in the tunneling picture. In this paper, we develop this idea to the case o a de Sitter tunneling from the cosmological horizon (CH), and obtain the Hawking emission spectrum and entropy/area spectroscopy from the CH of the purely de Sitter black hole as well as the Schwarzschild-de Sitter black hole. It i interestingly found that the area of the CH is quantized by A = 4l 2 pl , as was given by Hod for the area quantum of -the EH by considering the Heisenberg uncertainty principle and Schwinger-type emission process. Also, we conclude from our derivation that the entropy/area quantum of the CH is universal in the sense that it is independent of the black hole parameters. This realization implies that, (at least) at a semiclassical level, the de Sitter gravity shares the similar quantum behavior as the usual gravity without presence of a cosmological constant.     

A note on approximate Bayesian credible sets based on modified loglikelihood ratios

Higher-order asymptotic arguments for a scalar parameter of interest have been widely investigated for Bayesian inference. In this paper the theory of asymptotic expansions is discussed for a vector parameter of interest. A modified loglikelihood ratio is suggested, which can be used to derive approximate Bayesian credible sets with accurate frequentist coverage. Three examples are illustrated.     

Optimal Approximation of the Second Iterated Integral of Brownian Motion

Abstract

In this article, a theorem is proved that describes the optimal approximation (in the L ²(?)-sense) of the second iterated integral of a standard two-dimensional Wiener process, W, by a function of finitely many elements of the Gaussian Hilbert space generated by W. This theorem has some interesting corollaries: First of all, it implies that Euler's method has the optimal rate of strong convergence among all algorithms that depend solely on linear functionals of the Wiener process, W; second, it shows that the approximation of the second iterated integral based on Karhunen–Loève expansion of the Brownian bridge is asymptotically optimal.     

场致爆炸发射阴极有效发射面积研究

通过改变阴阳极间隙,得到在不同外加电场情况下,场致爆炸发射石墨阴极有效发射面积随时间变化的实验结果。结果表明,在起始的一定时间内,阴极有效发射面积随时间的增加而增大。阴极有效发射面积达到1.0的时间随阴阳极间隙内电场的增加而减小;当二极管阴阳极之间的平均电场约为100 kV/cm时,阴极有效发射面积达到1.0的时间约为20 ns;阴极有效发射面积相对电压波形的延迟时间随电场的变化近似呈指数衰减曲线。     

Littlewood–Paley characterizations of higher‐order Sobolev spaces via averages on balls

In this article, the authors characterize higher‐order Sobolev spaces , with , and , or with , and , via the Lusin area function and the Littlewood–Paley ‐function in terms of ball averages, where denotes the maximal integer not greater than . Moreover, the authors also complement the above results in the endpoint cases of p via establishing some weak type estimates. These improve and develop the corresponding known results for Sobolev spaces with smoothness order .     

Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one‐dimensional second‐order wave equation

In this article, we analyze a residual‐based a posteriori error estimates of the spatial errors for the semidiscrete local discontinuous Galerkin (LDG) method applied to the one‐dimensional second‐order wave equation. These error estimates are computationally simple and are obtained by solving a local steady problem with no boundary condition on each element. We apply the optimal L² error estimates and the superconvergence results of Part I of this work [Baccouch, Numer Methods Partial Differential Equations 30 (2014), 862–901] to prove that, for smooth solutions, these a posteriori LDG error estimates for the solution and its spatial derivative, at a fixed time, converge to the true spatial errors in the L²‐norm under mesh refinement. The order of convergence is proved to be , when p‐degree piecewise polynomials with are used. As a consequence, we prove that the LDG method combined with the a posteriori error estimation procedure yields both accurate error estimates and superconvergent solutions. Our computational results show higher convergence rate. We further prove that the global effectivity indices, for both the solution and its derivative, in the L²‐norm converge to unity at rate while numerically they exhibit and rates, respectively. Numerical experiments are shown to validate the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1461–1491, 2015     

煤炭矿区植被冠层光谱土地复垦敏感性分析

煤矿区土地复垦及复垦监测工作,对于我国土地利用和生态环境治理具有重要意义。微生物复垦技术能够促进植物吸收利用矿质养分和水分,增强土壤肥力,对矿区生态恢复具有显著作用。监测和评价土地复垦效应对植物生长影响的传统方法,通常采用野外采集植物和土壤样本并进行室内分析,但这些方法不仅破坏植物根系原状土壤,造成植株损伤,而且耗费人力、物力,时效性差。高光谱遥感技术具有数据获取速度快、信息量大、精度高且无须离体破坏植株等优点,对于土地复垦监测有非常大的潜力。目前,土地复垦效应遥感监测相关研究仍以观测盆栽大豆、玉米等作物的叶片光谱分析为主。实际上,卫星遥感数据观测到的是冠层光谱,并非叶片光谱,但目前还没有通过植被冠层光谱对矿区土地复垦进行监测的研究成果出现。植被冠层光谱不仅受到叶片光谱的影响,还受到植株长势、下垫面等其他因素的影响,光谱特征变化更为复杂。矿区植被冠层光谱特征对于土地复垦效应的敏感度分析,是对矿区植被理化参量进行定量反演的基础,也是限制高光谱技术应用于大面积土地复垦监测的主要瓶颈。于煤炭矿区土地复垦实验基地开展野外冠层光谱观测实验,获取了接菌组和对照组野外植株冠层光谱数据,并从光谱波形变化和光谱特征参量变化两方面综合分析了植被冠层光谱对土地复垦的敏感性。冠层光谱波形方面,分别采用标准差和光谱敏感度作为组内和组间光谱波形差异的有效指标;冠层光谱特征参量方面,选取了植被红边、黄边、蓝边、绿峰、红谷等典型光谱特征,计算获取其位置、斜率、面积等特征参量,并通过描述性统计和单因素方差分析研究了这些冠层光谱特征参量对土地复垦效应的敏感性,挑选出矿区土地复垦监测的有效特征参量。研究表明,接菌组和对照组冠层光谱的主要波形变化趋势一致,但接菌组植株的生长状况更稳定,不同植株之间差异较小,且绿峰和红谷两个特征更突出。这说明土地复垦能够减少植株间冠层光谱差异,增强植被典型光谱特征,而绿峰和红谷对土地复垦有较高的光谱敏感度。光谱特征参量方面,绿峰、红谷、红边波长在土地复垦作用下显著向长波方向移动,而此前叶片光谱研究中对土地复垦较敏感的红边、蓝边斜率变化并不显著。这说明,野外植被冠层光谱分析结果与实验室植被叶片光谱分析的结果并不完全一致,这可能和植被类型、生长周期、土壤背景光谱干扰等因素相关。在采用卫星或航拍遥感数据进行矿区植被环境监测时,所获取的都是植被冠层光谱,因此本研究所得到的结论具有更强的参考意义和实际应用价值。     

一种高精度的修正Hermite-ENO格式

设计一种基于三单元具有六阶精度的修正Hermite-ENO格式（CHENO）,求解一维双曲守恒律问题.CHENO格式利用有限体积法进行空间离散,在空间层上,使用ENO格式中的Newton差商法自适应选择模板.在重构半节点处的函数值及其一阶导数值时,利用Taylor展开给出修正Hermite插值使其提高到六阶精度,并设计了间断识别法与相应的处理方法以抑制间断处的虚假振荡;在时间层上采用三阶TVD Runge-Kutta法进行函数值及一阶导数值的推进.其主要优点是在达到高阶精度的同时具有紧致性.数值实验表明对一维双曲守恒律问题的求解达到了理论分析结果,是有效可行的.