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Time Discrete Approximation of Weak Solutions to Stochastic Equations of Geophysical Fluid Dynamics and Applications(Dedicated to Haim Brézis on the occasion of his 70th birthday)

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Chinese Annals of Mathematics,Series B 2017年第2期38卷 425-472页

作者： Nathan GLATT-HOLTZ roger temam Chuntian WANG department of mathematics tulane universityLA 70118USA department of mathematics and the institute for scientific computing and applied mathematics indiana universityBloomingtonIN 47405USA department of mathematics university of los angelesCA 90059USA

As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and the oceans, the time discretization of these equations by an implicit Euler scheme is studied. From the deterministic point of view, the 3D primitive equations are studied in their full form on a general domain and with physically realistic boundary conditions. From the probabilistic viewpoint, this paper deals with a wide class of nonlinear, state dependent, white noise forcings which may be interpreted in either the Itor the Stratonovich sense. The proof of convergence of the Euler scheme,which is carried out within an abstract framework, covers the equations for the oceans, the atmosphere, the coupled oceanic-atmospheric system as well as other related geophysical equations. The authors obtain the existence of solutions which are weak in both the PDE and probabilistic sense, a result which is new by itself to the best of our knowledge.

关键词： Nonlinear stochastic partial differential equations, Geophysical fluid dy-namics, Primitive equations, Discrete time approximation, Martingalesolutions~ Numerical analysis of stochastic PDEs

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Numerical Resolution Near t=0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1

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Communications in Computational Physics 2011年第3期9卷 568-586页

作者： Qingshan Chen Zhen Qin roger temam Department of Scientific Computing Florida State UniversityTallahasseeFL 32306USA Institute for Scientific Computing and Applied Mathematics Indiana UniversityBloomingtonIN 47405USA

The incompatibilities between the initial and boundary data will cause singularities at the time-space corners,which in turn adversely affect the accuracy of the numerical schemes used to compute the *** study the corner singularity issue for nonlinear evolution equations in 1D,and propose two remedy procedures that effectively recover much of the accuracy of the numerical scheme in *** of the remedy procedures to the 1D viscous Burgers equation,and to the 1D nonlinear reaction-diffusion equation are *** remedy procedures are applicable to other nonlinear diffusion equations as well.

关键词： Compatibility conditions corner singularities viscous Burgers equation nonlinear convection diffusion equation finite element methods

Boundary Conditions for Limited Area Models Based on the Shallow Water Equations

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Communications in Computational Physics 2013年第8期14卷 664-702页

作者： Arthur Bousquet Madalina Petcu Ming-Cheng Shiue roger temam Joseph Tribbia The Institute for Scientific Computing and Applied Mathematics Indiana UniversityBloomingtonIN 47405USA Laboratoire de Mathematiques et Applications UMR 6086Universite de PoitiersFrance The Institute of Mathematics of the Romanian Academy BucharestRomania Department of Applied Mathematics National Chiao Tung UniversityHsinchuTaiwan National Center for Atmospheric Research BoulderColoradoUSA.

A new set of boundary conditions has been derived by rigorousmethods for the shallow water equations in a limited *** aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary *** new boundary conditions which are mildly dissipative let the waves move freely inside and outside the *** problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.

关键词： Boundary conditions finite volumes shallow water

Mathematical Analysis of the Jin-Neelin Model of El Nio-Southern-Oscillation

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Chinese Annals of Mathematics,Series B 2019年第1期40卷 1-38页

作者： Yining CAO Mickaёl D.CHEKROUN Aimin HUANG roger temam Department of Mathematics and the Institute for Scientific Computing and Applied Mathematics Indiana University Department of Atmospheric and Oceanic Sciences University of California

The Jin-Neelin model for the El Nio–Southern Oscillation(ENSO for short) is considered for which the authors establish existence and uniqueness of global solutions in time over an unbounded channel domain. The result is proved for initial data and forcing that are sufficiently small. The smallness conditions involve in particular key physical parameters of the model such as those that control the travel time of the equatorial waves and the strength of feedback due to vertical-shear currents and upwelling; central mechanisms in ENSO *** the mathematical view point, the system appears as the coupling of a linear shallow water system and a nonlinear heat equation. Because of the very different nature of the two components of the system, the authors find it convenient to prove the existence of solution by semi-discretization in time and utilization of a fractional step scheme. The main idea consists of handling the coupling between the oceanic and temperature components by dividing the time interval into small sub-intervals of length k and on each sub-interval to solve successively the oceanic component, using the temperature T calculated on the previous sub-interval, to then solve the sea-surface temperature(SST for short) equation on the current sub-interval. The passage to the limit as k tends to zero is ensured via a priori estimates derived under the aforementioned smallness conditions.

关键词： El Nio–Southern Oscillation Coupled nonlinear hyperbolic-parabolic systems Fractional step method Semigroup theory

Mathematical Analysis of the Jin-Neelin Model of El Niño-Southern-Oscillation

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Chinese Annals of Mathematics,Series B 2019年第1期40卷 1-38页

关键词： El Niño-Southern Oscillation Coupled nonlinear hyperbolic-parabolic systems Fractional step method Semigroup theory

3D shear flows driven by Lévy noise at the boundary

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Probability, Uncertainty and Quantitative Risk 2023年第1期8卷 75-94页

作者： Wai-tong(Louis)Fan Ali Pakzad Krutika Tawri roger temam Department of Mathematics Indiana University BloomingtonIN 47405USA Department of Mathematics California State University NorthridgeCA 91330USA Department of Mathematics University of California BerkeleyCA 94720USA

This paper is concerned with the stochastic incompressible Navier–Stokes equations in a layer of fluid between two flat no-slip *** fluid is driven by the noisy movement of the bottom boundary,where the noise is given by a Lévy *** establishing existence of a martingale solution,we use the background flow method to derive an upper bound on the turbulent energy dissipation *** estimate recovers one of the basic scaling ideas of turbulence theory,namely,that the dissipation rate is independent of the viscosity at high Reynolds number.

关键词： Existence Lévy noise Navier–Stokes equations 3D shear flows Upper bound

A sphingolipid message promotes neuronal health across generations

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Neural Regeneration Research 2024年第11期19卷 2325-2326页

作者： Wenyue Wang roger Pocock Development and Stem Cells Program Monash Biomedicine Discovery Institute and Department of Anatomy and Developmental BiologyMonash UniversityMelbourneVICAustralia

Maternal nutrition can affect brain function of offspring in later life(Fitzgerald et al.,2020).Emerging studies have also shown that the maternal environment can modify susceptibility to neurodegenerative disease(Boots et al.,2023).Transmission of environmental information from mother to offspring depends on maternal nutrient *** the nematode Caenorhabditis elegans,maternal yolk,which is synthesized in the intestine and transferred to nourish oocytes and early embryos,can provide extranuclear inheritance factors to mediate phenotypic plasticity across ***,the molecular mechanisms of regulating such intergenerational effects remain largely unknown.

关键词： mother intestine transferred

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Understanding antimicrobial pharmacokinetics in critically ill patients to optimize antimicrobial therapy:A narrative review

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Journal of Intensive Medicine 2024年第3期4卷 287-298页

作者： Claire roger Department of Anesthesiology and Intensive Care Pain and Emergency MedicineNîmes-Caremeau University HospitalNîmesFrance UR UM 103 IMAGINE(Initial Management and prévention of orGan failures IN critically ill patiEnts) Faculty of MedicineMontpellier UniversityMontpellierFrance

Effective treatment of sepsis not only demands prompt administration of appropriate antimicrobials but also requires precise dosing to enhance the likelihood of patient survival. Adequate dosing refers to the administration of doses that yield therapeutic drug concentrations at the infection site. This ensures a favorable clinical and microbiological response while avoiding antibiotic-related toxicity. Therapeutic drug monitoring (TDM) is the recommended approach for attaining these goals. However, TDM is not universally available in all intensive care units (ICUs) and for all antimicrobial agents. In the absence of TDM, healthcare practitioners need to rely on several factors to make informed dosing decisions. These include the patient's clinical condition, causative pathogen, impact of organ dysfunction (requiring extracorporeal therapies), and physicochemical properties of the antimicrobials. In this context, the pharmacokinetics of antimicrobials vary considerably between different critically ill patients and within the same patient over the course of ICU stay. This variability underscores the need for individualized dosing. This review aimed to describe the main pathophysiological changes observed in critically ill patients and their impact on antimicrobial drug dosing decisions. It also aimed to provide essential practical recommendations that may aid clinicians in optimizing antimicrobial therapy among critically ill patients.

关键词： Pharmacokinetics/pharmacodynamics ICU Antibiotics Dose optimization TDM

Making topological protein links using enzymatic reactions

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National Science Review 2024年第03期11卷 50-51页

作者： roger Castells-Graells Todd O.Yeates Department of Chemistry and Biochemistry University of California UCLA-DOE Institute for Genomics and Proteomics

Proteins are exceedingly complex molecules though, at their heart, they are essentially linear polymers. Pull at their ends and one obtains an extended backbone. While that is true in most cases, some natural proteins... 详细信息

关键词： DESIGN