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asymptotic analysis OF DYNAMIC PROBLEMS FOR LINEARLY ELASTIC SHELLS--JUSTIFICATION OF EQUATIONS FOR DYNAMIC FLEXURAL SHELLS

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Chinese Annals of Mathematics,Series B 2001年第3期22卷 13-22页

作者： XIAO LIMING Institute of Mathematics Fudan University Shanghai 200433 China Department of Computer Science Guangdong Normal Polytechnic Guangzhou 510665 China

Under certain conditions, starting from the three-dimensional dynamic equations of elastic shells the author gives the justification of dynamic equations of flexural shells by means of the method of asymptotic analysis.

关键词： Dynamics for elastic shells asymptotic analysis Flexural shells Space of inextensional displacement Body force density

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asymptotic analysis of Quantum Dynamics in Crystals: the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 465-476页

作者： Weinan E Jian-feng LU Xu YANG Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University School of Mathematical Sciences Peking University

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.

关键词： semiclassical limit Bloch-Wigner transform Bloch dynamics Berry phase asymptotic analysis

asymptotic analysis OF LINEARLY ELASTIC SHALLOW SHELLS WITH VARIABLE THICKNESS

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Chinese Annals of Mathematics,Series B 2001年第4期22卷 405-416页

作者： N. SABU Laboratoire d’Analyse Numerique, Universite Pierre et Marie Curie, 4 Place Jussieu, 75005, Paris, France.E-mail: sabu@ann.jussieu.fr Laboratoire d'Analyse Numerique Université Pierre et Marie Curie 4 Place Jussieu 75005 Paris France

The author considers a linearly elastic shallow shell with variable thickness and shows that, as the thickness of the shell goes to zero, the solution of the three-dimensional equations converges to the solution of th... 详细信息

关键词： asymptotic analysis Elastic shallow shells Vaiable thickness

asymptotic analysis of multi-valley dark soliton solutions in defocusing coupled Hirota equations

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Communications in Theoretical Physics 2023年第11期75卷 38-48页

作者： Ziwei Jiang Liming Ling Department of Mathematics South China University of TechnologyGuangzhou 510641China

We construct uniform expressions of such dark soliton solutions encompassing both single-valley and double-valley dark solitons for the defocusing coupled Hirota equation with high-order nonlinear effects utilizing the uniform Darboux transformation,in addition to proposing a sufficient condition for the existence of the above dark soliton ***,the asymptotic analysis we perform reveals that collisions for single-valley dark solitons typically exhibit elastic behavior;however,collisions for double-valley dark solitons are generally *** light of this,we further propose a sufficient condition for the elastic collisions of double-valley dark soliton *** results offer valuable insights into the dynamics of dark soliton solutions in the defocusing coupled Hirota equation and can contribute to the advancement of studies in nonlinear optics.

关键词： coupled Hirota equation uniform Darboux transformation dark soliton solution asymptotic analysis

asymptotic analysis of Lattice Boltzmann Outflow Treatments

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Communications in Computational Physics 2011年第5期9卷 1117-1127页

作者： Michael Junk Zhaoxia Yang FB Mathematik und Statistik Universität KonstanzPostfach D19478457 KonstanzGermany

We show the methodology and advantages of asymptotic analysis when applied to lattice Boltzmann outflow *** the one hand,one can analyze outflow algorithms formulated directly in terms of the lattice Boltzmann variables,like the extrapolation method,to find the induced outflow conditions in terms of the NavierStokes *** the other hand,one can check the consistency and accuracy of lattice Boltzmann outflow treatments to given hydrodynamic outflow conditions like the Neumann or average pressure *** example how the gained insight can be used,we propose an improvement of the well known extrapolation method.

关键词： Outflow condition asymptotic analysis lattice Boltzmann method

asymptotic　analysis　OF　A　CLASS　OF　NONLINEAR　OSCILLATION　EQUATION　IN　ELECTRICAL　ENGINEERING

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Applied Mathematics and Mechanics(English Edition) 1994年第1期15卷 7-12页

作者：程友良戴世强 Department of Fundamental Courses North China Institute of Electric Power Baoding Shanghai Institute of Applied Mathematics and Mechanics Shanghai University of Technology Shanghai

ＡＳＹＭＰＴＯＴＩＣＡＮＡＬＹＳＩＳＯＦＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＯＳＣＩＬＬＡＴＩＯＮＥＱＵＡＴＩＯＮＩＮＥＬＥＣＴＲＩＣＡＬＥＮＧＩＮＥＥＲＩＮＧＣｈｅｎｇＹｏｕ－ｌｉａｎｇ（程友良）（Ｄｅｐａｒｔｍｅｎ... 详细信息

ＡＳＹＭＰＴＯＴＩＣＡＮＡＬＹＳＩＳＯＦＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＯＳＣＩＬＬＡＴＩＯＮＥＱＵＡＴＩＯＮＩＮＥＬＥＣＴＲＩＣＡＬＥＮＧＩＮＥＥＲＩＮＧＣｈｅｎｇＹｏｕ－ｌｉａｎｇ（程友良）（ＤｅｐａｒｔｍｅｎｔｏｆＦｕｎｄａｍｅｎｔａｌＣｏｕ...

关键词： nonlinear oscillation limit cycle asymptotic analysis modified Krylov-Bogolyubov method

Exact Controllability and asymptotic analysis for Shallow Shells

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Chinese Annals of Mathematics,Series B 2007年第1期28卷 93-122页

作者： S.KAIZU N.SABU Department of Mathematics Faculty of Education Ibaraki University 2-1-1BunkyoMitoJapanDepartment of Mathematics Faculty of EducationIbaraki University2-1-1BunkyoMitoJapan

The authors consider the exact controllability of the vibrations of a thin shallow shell, of thickness 2ε with controls imposed on the lateral surface and at the top and bottom of the shell. Apart from proving the existence of exact controls, it is shown that the solutions of the three dimensional exact controllability problems converge, as the thickhess of the shell goes to zero, to the solution of an exact controllability problem in two dimensions.

关键词： Exact controllability asymptotic analysis Shallow shells

Bounded multi-soliton solutions and their asymptotic analysis for the reversal-time nonlocal nonlinear Schrodinger equation

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Communications in Theoretical Physics 2021年第10期73卷 1-13页

作者： Wei-Jing Tang Zhang-nan Hu Liming Ling Department of Mathematics South China University of TechnologyGuangzhou510641China

In this paper, we construct the Darboux transformation(DT) for the reverse-time integrable nonlocal nonlinear Schrodinger equation by loop group method. Then we utilize the DT to derive soliton solutions with zero seed. We investigate the dynamical properties for those solutions and present a sufficient condition for the non-singularity of multi-soliton ***, the asymptotic analysis of bounded multi-solutions has also been established by the determinant formula.

关键词： nonlocal nonlinear Schrodinger equation multi-soliton solution singularity asymptotic analysis

HIGH-ORDER asymptotic analysis FOR THE CRACK IN NONLINEAR MATERIAL

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Acta Mechanica Sinica 1992年第2期8卷 156-164页

作者：夏霖王自强 Institute of Mechanics Chinese Academy of SciencesBeijing 100080China

Accurate high-order asymptotic analyses were carried out for Mode Ⅱ plane strain crack inpower hardening *** second-order crack tip fields have been *** is found that theamplitude coefficient k;of the second term of the asymptotic field is correlated to the first order field as thehardening exponent nasymptotic field has little influence on the near-crack-tip fieldand can be neglected when n<*** fact,k;directly reflects the effects of triaxiality near the crack tip,thecrack geometry and the loading mode,so that besides J-integral it can be used as another characteristicparameter in the two-parameter criterion.

关键词： asymptotic analysis nearcrack-tip field triaxiality