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A REDUCED ORDER SCHWARZ METHOD FOR NONLINEAR MULTISCALE ELLIPTIC EQUATIONS BASED ON TWO-LAYER NEURAL NETWORKS

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journal of Computational Mathematics 2024年第2期42卷 570-596页

作者： Shi Chen Zhiyan Ding Qin Li Stephen j.Wright Mathematics Department University of Wisconsin-MadisonMadisonWI 53706USA Department of Mathematics University of California-BerkeleyBerkeley CA 94720USA Mathematics Department and Discovery Institute University of Wisconsin-Madison MadisonWI 53706USA Computer Sciences Department University of WisconsinMadisonWI 53706USA

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts,including solution of partial differential equations(PDEs).We describe a solver for multiscale fully nonlinear elliptic equations that makes use of domain decomposition,an accelerated Schwarz framework,and two-layer neural networks to approximate the boundary-to-boundarymap for the subdomains,which is the key step in the Schwarz ***,the boundary-to-boundary map requires solution of boundary-value elliptic problems on each *** leveraging the compressibility of multiscale problems,our approach trains the neural network offline to serve as a surrogate for the usual implementation of the boundary-to-boundary *** method is applied to a multiscale semilinear elliptic equation and a multiscale p-Laplace *** both cases we demonstrate significant improvement in efficiency as well as good accuracy and generalization performance.

关键词： Nonlinear homogenization Multiscale elliptic problem Neural networks Do-main decomposition

Transabdominal intestinal ultrasound and its parameters used in the assessment of pediatric inflammatory bowel disease

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World journal of Clinical Pediatrics 2024年第3期13卷 137-140页

作者： Kevan j English Department of Medicine-Pediatrics St.George's University School of MedicineSaint George's 33334Saint GeorgeGrenada

This article extends on the use of transabdominal intestinal ultrasound in diagnosing pediatric inflammatory bowel *** of the more essential features used in assessing bowel inflammation,such as hyperemia and wall thickness on ultrasound,are expanded upon from the publication on imaging and endoscopic tools in pediatric inflammatory bowel disease.

关键词： Inflammatory bowel disease Intestinal ultrasound Limberg score Hyperemia Bowel wall thickness

Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

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Applied Mathematics and Mechanics(English Edition) 2024年第1期45卷 197-216页

作者： C.G.PAVITHRA B.j.GIREESHA M.L.KEERTHI Department of PG Studies and Research in Mathematics Kuvempu UniversityShankaraghatta 577451India Department of Mathematics and Statistics M.S.Ramaiah University of Applied SciencesBengaluru 560058India

The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.

关键词： convection radiation moving longitudinal fin Adomian decomposition Sumudu transform method(ADSTM) trihybrid nanofluid magnetic field

Attitude control of multi-spacecraft systems on SO(3)with stochastic links failure

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Chinese journal of Aeronautics 2024年第3期37卷 320-331页

作者： KANG Zeyu SHEN Qiang WU Shufan Chris j.DAMAREN MU Zhongcheng School of Aeronautics and Astronautics Shanghai Jiao Tong UniversityShanghai 200240China Institute for Aerospace Studies University of TorontoTorontoOntario M3H 5T6Canada

In this paper,for Multi-Spacecraft System(MSS)with a directed communication topology link and a static virtual leader,a controller is proposed to realize attitude consensus and attitude stabilization with stochastic links failure and actuator ***,an MSS attitude error model suitable for a directed topology link and with a static virtual leader based on SO(3)is derived,which considers that the attitude error on SO(3)cannot be defined based on algebraic ***,we design a controller to realize the MSS on SO(3)with attitude consensus and attitude stabilization under stochastic links failure and actuator ***,the simulation results of a multi-spacecraft system with stochastic links failure and a static virtual leader spacecraft are demonstrated to illustrate the efficiency of the attitude controller.

关键词： Multi-spacecraft systems Attitude consensus Attitude stabilization Stochastic links failure Super-martingale convergence

On an isotropic porous solid cylinder:the analytical solution and sensitivity analysis of the pressure

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Applied Mathematics and Mechanics(English Edition) 2024年第9期45卷 1499-1522页

作者： H.ASGHARI L.MILLER R.PENTA j.MERODIO Departamento de Matematica Aplicada a las TIC ETS de Ingenieria de Sistemas InformaticosUniversidad Politecnica de MadridMadrid 28031Spain School of Mathematics and Statistics University of GlasgowGlasgow G128QQU.K.

Within this work,we perform a sensitivity analysis to determine the influence of the material input parameters on the pressure in an isotropic porous solid *** provide a step-by-step guide to obtain the analytical solution for a porous isotropic elastic cylinder in terms of the pressure,stresses,and elastic *** obtain the solution by performing a Laplace transform on the governing equations,which are those of Biot's poroelasticity in cylindrical polar *** enforce radial boundary conditions and obtain the solution in the Laplace transformed domain before reverting back to the time *** sensitivity analysis is then carried out,considering only the derived pressure *** analysis finds that the time t,Biot's modulus M,and Poisson's ratio ν have the highest influence on the pressure whereas the initial value of pressure P_(0) plays a very little role.

关键词： sensitivity analysis Laplace transform cylindrical polar coordinate Biot's modulus cylinder

Ycf1/Tic214 Is Not Essential for the Accumulation of Plastid Proteins

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Molecular Plant 2017年第1期10卷 219-221页

作者： Bettina Bölter j.rgen Soll Department Biologie I-Botanik Ludwig-Maximilians-Universität Großhadernerstraße 2-4 82152 Planegg-Martinsried Germany

Dear Editor,Protein import into chloroplasts is an essential process for plant survival. Numerous studies in recent years have revealed many facts about the components involved and mechanistic features, but have also turned up some controversies. Especially the composition and function of the Tic （translocon at the inner enve- lope of chloroplasts） complex（es） are vividly debated. Whereas the importance of one central Tic component,

关键词： Essential Accumulation Proteins

Universal insertion of molecules in ionic compounds under pressure

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National Science Review 2024年第1期11卷 120-128页

作者： Feng Peng Yanming Ma Chris j.Pickard Hanyu Liu Maosheng Miao College of Physics and Electronic Information Luoyang Normal University Department of Chemistry and Biochemistry California State University Northridge State Key Laboratory of Superhard Materials & Key Laboratory of Material Simulation Methods and Software of Ministry of Education College of Physics Jilin University International Center of Future Science Jilin University Department of Materials Science & Metallurgy University of Cambridge Advanced Institute for Materials Research Tohoku University Department of Earth Science University of California Santa Barbara

Using first-principles calculations and crystal structure search methods, we found that many covalently bonded molecules such as H2, N2, CO2, NH3, H2O and CH4may react with NaC l, a prototype ionic solid,and form stable compounds under pressure while retaining their molecular structure. These molecules,despite whether they are homonuclear or heteronuclear, polar or non-polar, small or large, do not show strong chemical interactions with surrounding Na and Cl ions. In contrast, the most stable molecule among all examples, N2, is found to transform into cyclo-N5-anions while reacting with NaC l under high pressures. It provides a new route to synthesize pentazolates, which are promising green energy materials with high energy density. Our work demonstrates a unique and universal hybridization propensity of covalently bonded molecules and solid compounds under pressure. This surprising miscibility suggests possible mixing regions between the molecular and rock layers in the interiors of large planets.

关键词： molecule-solid hybrid materials high-pressure crystal structure prediction density functional theory planet interior

Cell Polarity and Development

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journal of Integrative Plant Biology 2013年第9期55卷 786-788页

作者： Remko Offringa j.rgen Kleine‐Vehn Molecular and Developmental Genetics Institute Biology Leiden Leiden University Sylvius Laboratory Universitt für Bodenkultur Wien (BOKU) Institute of Applied Genetics and Cell Biology (IAGZ)

All ceiis show some degree of poiarity, either by asymmetrically distributed membrane or cytosolic components. Even in bacterial cells that do not have the eukaryotic membrane compartmentalization of the cytoplasm, proteins can be localized at specific areas. In rod-shaped bacteria, many processes such as signaling, flagella formation, and DNA uptake occur at the cell poles. In addition,

关键词： Cell Polarity Membrane Curvature

Model evaluation for the prediction of solubility of active pharmaceutical ingredients(APIs) to guide solid–liquid separator design

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Asian journal of Pharmaceutical Sciences 2018年第3期13卷 265-278页

作者： Kuveneshan Moodley j.rgen Rarey Deresh Ramjugernath Thermodynamics Research Unit School of Engineering University of KwaZulu-Natal Howard College Campus Industrial Chemistry Carl von Ossietzky University Oldenburg

The assumptions and models for solubility modelling or prediction in systems using nonpolar solvents, or water and complex triterpene and other active pharmaceutical ingredients as solutes aren't well studied. Furthermore, the assumptions concerning heat capacity effects(negligibility, experimental values or approximations) are explored, using non-polar solvents(benzene), or water as reference solvents, for systems with solute melting points in the range of 306–528 K and molecular weights in the range of 90–442 g/mol. New empirical estimation methods for the Δ_(fus)C_(pi) of APIs are presented which correlate the solute molecular masses and van der Waals surface areas with Δ_(fus)C_(pi). Separate empirical parameters were required for oxygenated and non-oxygenated solutes. Subsequently, the predictive capabilities of the various approaches to solubility modelling for complex pharmaceuticals,for which data is limited, are analysed. The solute selection is based on a principal component analysis, considering molecular weights, fusion temperatures, and solubilities in a non-polar solvent, alcohol, and water, where data was available. New NRTL-SAC parameters were determined for selected steroids, by regression. The original UNIFAC, modified UNIFAC(Dortmund), COSMO-RS(OL), and COSMO-SAC activity coefficient predictions are then conducted, based on the availability of group constants and sigma profiles. These are undertaken to assess the predictive capabilities of these models when each assumption concerning heat capacity is employed. The predictive qualities of the models are assessed, based on the mean square deviation and provide guidelines for model selection, and assumptions concerning phase equilibrium, when designing solid–liquid separators for the pharmaceutical industry on process simulation software. The most suitable assumption regarding Δ_(fus)C_(pi) was found to be system specific, with modified UNIFAC(Dortmund) performing well in benzene as a solvent system,

关键词： Solubility Solid–Liquid Equilibrium Model prediction Active pharmaceutical ingredients