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Galerkin Method for Wave Equations with Uncertain Coefficients

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Communications in Computational Physics 2008年第2期3卷 505-518页

作者： david gottlieb Dongbin Xiu Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA Department of Mathematics Purdue UniversityWest LafayetteIN 47907USA.

Polynomial chaos methods(and generalized polynomial chaos methods)have been extensively applied to analyze PDEs that contain *** this approach is rarely applied to hyperbolic *** this paper we analyze the properties of the resulting deterministic system of equations obtained by stochastic Galerkin *** consider a simple model of a scalar wave equation with random wave *** show that when uncertainty causes the change of characteristic directions,the resulting deterministic system of equations is a symmetric hyperbolic system with both positive and negative eigenvalues.A consistent method of imposing the boundary conditions is proposed and its convergence is *** examples are presented to support the analysis.

关键词： Generalized polynomial chaos stochastic PDE Galerkin method hyperbolic equation uncertainty quantification.

A Weighted Multi-Domain Spectral Penalty Method with Inhomogeneous Grid for Supersonic Injective Cavity Flows

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Communications in Computational Physics 2009年第5期5卷 986-1011页

作者： Wai-Sun Don david gottlieb Jae-Hun Jung Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA Department of Mathematics University of Massachusetts at DartmouthNorth DartmouthMA 02747-2300USA

In[***.192(1),pp.325-354(2003)],we have developed a multidomain spectral method with stable and conservative penalty interface conditions for the numerical simulation of supersonic reactive recessed cavity flows with homogeneous *** this work,the previously developed methodology is generalized to inhomogeneous grid to simulate the two dimensional supersonic injector-cavity ***-physical modes in the solution generated at the domain interfaces due to the spatial grid inhomogeneity are minimized using the new weighted multi-domain spectral penalty *** proposed method yields accurate and stable solutions of the injector-cavity system which agree well with experiments *** the direct numerical simulation of the injector-cavity system using the weighted method,the geometric effect of the cavity wall on pressure fluctuations is *** is shown that the recessed slanted cavity attenuates pressure fluctuations inside cavity enabling the cavity to act potentially as a stable flameholder for scramjet engine.

关键词： Penalty interface conditions weighted multi-domain spectral penalty methods supersonic recessed cavity flame-holder compressible Navier-Stokes equations

Two-Dimensional Multi-Domain Hybrid Spectral-WENO Methods for Conservation Laws

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Communications in Computational Physics 2006年第3期1卷 548-574页

作者： Bruno Costa Wai Sun Don david gottlieb Radislav Sendersky Departamento de Matem´atica Aplicada IM-UFRJCaixa Postal 68530Rio de JaneiroRJC.E.P.21945-970Brazil Division of Applied Mathematics Brown UniversityProvidenceRhode Island 02912USA

The multi-domain hybrid Spectral-WENO method(Hybrid)is introduced for the numerical solution of two-dimensional nonlinear hyperbolic systems in a Cartesian physical domain which is partitioned into a grid of rectangular *** main idea of the Hybrid scheme is to conjugate the spectral and WENO methods for solving problems with shock or high gradients such that the scheme adapts its solver spatially and temporally depending on the smoothness of the solution in a given *** as a multi-domain method,an adaptive algorithm is used to keep the solutions parts exhibiting high gradients and discontinuities always inside WENO subdomains while the smooth parts of the solution are kept inside spectral ones,avoiding oscillations related to the well-known Gibbs phenomenon and increasing the numerical efficiency of the overall scheme.A higher order version of the multi-resolution analysis proposed by Harten is used to determine the smoothness of the solution in each *** also discuss interface conditions for the two-dimensional problem and the switching procedure between WENO and spectral *** Hybrid method is applied to the two-dimensional Shock-Vortex Interaction and the Richtmyer-Meshkov Instability(RMI)problems.

关键词： Spectral WENO multi-resolution multi-domain hybrid conservation laws

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时间相关问题的谱方法

国外科技新书评介 2008年第5期 8-9页

作者： Jan S. Hesthaven Sigal gottlieb david gottlieb 吴永礼 Brown University University of Massachusetts Dartmouth 中国科学院力学研究所

本书是《剑桥应用和计算数学专著》系列丛书第21册。谱方法是非常适用于以时间相关的偏微分方程来模拟的问题。此方法快速、有效而精确，已为广大的数学家和专业人员所应用。在书中，作者论述了谱方法的基本理论，并通过严格的推理和许... 详细信息

本书是《剑桥应用和计算数学专著》系列丛书第21册。谱方法是非常适用于以时间相关的偏微分方程来模拟的问题。此方法快速、有效而精确，已为广大的数学家和专业人员所应用。在书中，作者论述了谱方法的基本理论，并通过严格的推理和许多实例使读者理解谱方法的技术，此外，还在福里叶展开和正交多项式的基础上，提供详细的处理方法，时域积分的计算技术则用Runge-Kutta法。

关键词：解谱方法时间相关 Runge-Kutta法计算技术偏微分方程正交多项式计算数学数学家

A Strong Stability Preserving Analysis for Explicit Multistage Two-Derivative Time-Stepping Schemes Based on Taylor Series Conditions

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Communications on Applied Mathematics and Computation 2019年第1期1卷 21-59页

作者： Zachary Grant Sigal gottlieb david C.Seal Department of Computational and Applied Mathematics Oak Ridge National LaboratoryOak RidgeUSA Department of Mathematics University of Massachusetts DartmouthDartmouthUSA Department of Mathematics U.S.Naval AcademyAnnapolisUSA

High-order strong stability preserving(SSP)time discretizations are often needed to ensure the nonlinear(and sometimes non-inner-product)strong stability properties of spatial discretizations specially designed for the solution of hyperbolic ***-derivative time-stepping methods have recently been increasingly used for evolving hyperbolic PDEs,and the strong stability properties of these methods are of *** our prior work we explored time discretizations that preserve the strong stability properties of spatial discretizations coupled with forward Euler and a second-derivative ***,many spatial discretizations do not satisfy strong stability properties when coupled with this second-derivative formulation,but rather with a more natural Taylor series *** this work we demonstrate sufficient conditions for an explicit two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and Taylor series *** call these strong stability preserving Taylor series(SSP-TS)*** also prove that the maximal order of SSP-TS methods is p=6,and define an optimization procedure that allows us to find such SSP *** types of these methods are presented and their efficiency ***,these methods are tested on several PDEs to demonstrate the benefit of SSP-TS methods,the need for the SSP property,and the sharpness of the SSP time-step in many cases.

关键词： Strong stability preserving Taylor series.Hyperbolic conservation laws Two derivative Runge Kutta

Transrectal EUS-guided FNA biopsy of a presacral chordoma-report of a case and review of the literature

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World Journal of Gastroenterology 2008年第16期14卷 2586-2589页

作者： Klaus gottlieb Paul H Lin david M Liu Karl Anders Endoscopic Ultrasound and Interventional Endoscopy Spokane WA 99202 United States Surgical Specialists of Spokane Spokane WA 99202 United States Inland Imaging Spokane WA 99202 United States Deaconess Pathology Spokane WA 99202 United States

Chordomas are rare tumors which originate from the remnants of the notochord. These tumors are locally aggressive and have a predilection for the ends of the axial skeleton. An important prerequisite for optimal management of these tumors is a correct preoperative diagnosis. The present case is the first report of the use of endoscopic ultrasound to obtain transrectal fine needle aspiration biopsy of a presacral chordoma. A review of the prior computer tomography (CT) scans allowed us to calculate the tumor volume doubling time (18.3 mo). Transrectal biopsy of chordomas is controversial, however we believe that such concerns are not justified.

关键词： Chordoma Endoscopic ultrasound Spinaltumors Trans-rectal biopsies

Sucrose-responsive osmoregulation of plant cell size by a long non-coding RNA

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Molecular Plant 2024年第11期17卷 1719-1732页

作者： Jakub Hajný Tereza Trávnícková Martina pundová Michelle Roenspies R.M.Imtiaz Karim Rony Sebastian Sacharowski Michal Krzyszton david Zalabák Christian S.Hardtke Ales Pecinka Holger Puchta Szymon Swiezewski Jaimie M.van Norman Ondrej Novák Laboratory of Growth Regulators Czech Academy of SciencesInstitute of Experimental Botany and Palacky UniversitySlechtitelu 2777900 OlomoucCzech Republic Department of Biophysics Faculty of SciencePalacky UniversitySlechtitelu 2777900 OlomoucCzech Republic Joseph gottlieb Kölreuter Institute for Plant Sciences(JKIP)–Molecular Biology Karlsruhe Institute of Technology76131 KarlsruheGermany Department of Molecular Celland Systems BiologyUniversity of CaliforniaRiversideCA 92521USA Laboratory of Seeds Molecular Biology Institute of Biochemistry and Biophysics Polish Academy of SciencesPawinskiego 5a02-106 WarsawPoland Department of Plant Molecular Biology University of Lausanne1015 LausanneSwitzerland Center of Plant Structural and Functional Genomics Institute of Experimental BotanyCzech Academy of SciencesSlechtitelu 3177900 OlomoucCzech Republic Department of Molecular Celland Developmental BiologyUniversity of CaliforniaLos AngelesLos AngelesCA 90095USA

In plants,sugars are the key source of energy and metabolic building *** systemic transport of sugars is essential for plant growth and *** evolved intricate molecular networks to effectively distribute *** dynamic distribution of these osmotically active compounds is a handy tool for regulating cell turgor pressure,an instructive force in developmental *** this study,we have investigated the molecular mechanism behind the dual role of the receptor-like kinase *** functionally characterized a long non-coding RNA,CARMA,as a negative regulator of *** CARMA specifically fine-tunes CANAR expression in the phloem,the route of sugar *** genetic,molecular,microscopy,and biophysical data suggest that the CARMA–CANAR module controls the shoot-to-root phloem transport of sugars,allows cells to flexibly adapt to the external osmolality by appropriate water uptake,and thus adjust the size of vascular cell types during organ growth and *** study identifies a nexus of plant vascular tissue formation with cell internal pressure monitoring,revealing a novel functional aspect of long non-coding RNAs in developmental biology.

关键词： lncRNA auxin turgor sugar transport cell size