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Asymptotic limit of the Gross-Pitaevskii equation with general initial data

Science China mathematics 2016年第6期59卷 1113-1126页

作者： LI FuCai LIN Chi-Kun WU Kung-Chien Department of Mathematics Nanjing UniversityNanjing 210093 Department of Applied Mathematics and Center of Mathematical Modeling and Scientific Computing Chiao Tung UniversityHsinchu 30010 Department of Mathematics Cheng Kung UniversityTainan 70101

This paper mainly concerns the mathematical justification of the asymptotic limit of the GrossPitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.

关键词： Gross-Pitaevskii equation asymptotic limit incompressible Euler equation general initial data

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Investigation of fractional compartmental models in pharmacokinetics with application to amiodarone drug diffusion

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scientific African 2025年

作者： Reindorf Nartey Borkor Adu Sakyi Nicholas Kwasi-Do Ohene Opoku Rhydal Esi Eghan John Amoah-Mensah Ali Abubakar Kwame Owusu Edusei Peter Amoako-Yirenkyi Department of Mathematics Kwame Nkrumah University of Science and Technology (KNUST) Ghana Center for Scientific and Technical Computing National Institute for Mathematical Sciences (NIMS) Ghana Department of Biochemistry and Biotechnology Kwame Nkrumah University of Science and Technology (KNUST) Ghana Department of Applied Mathematics Sunyani Technical University Ghana Department of Applied Mathematics and Statistics Accra Technical University Ghana

This study offers and explores fractional models derived from a classical Pharmacokinetics (PK) compartmental system. The fractional models are essentially enlarged versions of the classical model, and their distinguishing characteristics are further examined comprehensively. Through numerical simulations using the Grunwald–Letnikov finite difference method, we demonstrate that fractional PK models provide a more realistic representation of drug dynamics compared to classical model. It is demonstrated that certain model features are incompatible with the idea of mass balance. However, they appeared to surpass classical calculus theory when simulating anomalous kinetics. We demonstrate this behaviour through stability analysis of the equilibrium point under conditions of different fractional orders as well as fitting the proposed models to an experimental data set (amiodarone), thereby estimating parameters using the least-square approach. The findings reveal that fractional pharmacokinetic models provide a more accurate and physically realistic representation of drug distribution, capturing memory effects and non-exponential drug elimination. This ensures better agreement with experimental observations compared to classical integer-order models.

关键词： Fractional calculus Pharmacokinetics Grunwald–Letnikov derivative Compartmental models

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Numerical Simulation of Moving Contact Lines with Surfactant by Immersed Boundary Method

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Communications in Computational Physics 2010年第9期8卷 735-757页

作者： Ming-Chih Lai Yu-Hau Tseng Huaxiong Huang Center of Mathematical Modeling and Scientific Computing Department of Applied Mathematics National Chiao Tung University1001Ta Hsueh RoadHsinchu 300Taiwan Department of Mathematics and Statistics York UniversityTorontoOntarioM3J 1P3Canada

In this paper,we present an immersed boundary method for simulating moving contact lines with *** governing equations are the incompressible Navier-Stokes equations with the usual mixture of Eulerian fluid variables and Lagrangian interfacial *** immersed boundary force has two components:one from the nonhomogeneous surface tension determined by the distribution of surfactant along the fluid interface,and the other from unbalanced Young’s force at the moving contact *** artificial tangential velocity has been added to the Lagrangian markers to ensure that the markers are uniformly distributed at all *** corresponding modified surfactant equation is solved in a way such that the total surfactant mass is *** experiments including convergence analysis are carefully *** effect of the surfactant on the motion of hydrophilic and hydrophobic drops are investigated in detail.

关键词： Immersed boundary method interfacial flow Navier-Stokes equations surfactant moving contact line hydrophilic drop hydrophobic drop wetting

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A computational framework for Carreau nanomaterial induced by stretchy regime considering Brownian diffusion, viscous dissipation, ferromagnetism and thermophoresis

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Partial Differential Equations in applied mathematics 2025年 13卷

作者： Hussain, Iftikhar Khan, Waqar Azeem Tabrez, Muhammad Waqas, M. Ibrahim, Talib K. Saidani, Taoufik Kausar, M.S. Zamri, Nurnadiah Abdullaeva, Barno Garalleh, Hakim AL Department of Mathematics Mohi-ud-Din Islamic University Nerian Sharif Jammu and Kashmir Azad 12010 Pakistan School of Mathematics and Statistics Beijing Institute of Technology Beijing 100081 China NUTECH School of Applied Sciences and Humanities National University of Technology Islamabad 44000 Pakistan Faculty of Informatics and Computing Universiti Sultan Zainal Abidin Besut Campus Terengganu Besut 22200 Malaysia Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Department of Petroleum Engineering College of Engineering Knowledge University Erbil 44001 Iraq Department of Petroleum Engineering Al-Kitab University Altun Kupri Iraq Center for Scientific Research and Entrepreneurship Northern Border University Arar 73213 Saudi Arabia Faculty of Informatics and Computing Universiti Sultan Zainal Abidin (Kampus Gong Badak) Terengganu Kuala Terengganu 21300 Malaysia Department of Mathematics and Information Technologies Vice-Rector for Scientific Affairs Tashkent State Pedagogical University Tashkent Uzbekistan Department of Mathematical Science College of Engineering University of Business and Technology Jeddah 21361 Saudi Arabia

In recent decade, the research in nanotechnology brought the idea of nanofluids which are highly conducting materials. Some important applications of nanofluids are justified in pharmaceutical industry, coolants in vehicles engine, preparation process of various medicines for treatment of fatal diseases like cancer, aircraft industry, latest heat exchangers etc. The ferro particles are special class of nanomaterial which attract variety of interest from the researchers. The objective of current research is to perform the investigation for heat and mass transfer subject to Carreau nanofluid to observe the enhancement of heat transmission phenomena. The induction of magnetic dipole has been observed for thermal transport phenomenon. The flow is causing by stretched surface. A simplified system is obtained by utilizing the dimensionless variables. Physical interpretation of results have been presented. Result showed that temperature profile in presence of ferrofluid fluid boosts up with escalation in thermophoresis parameter, while opposite behavior is noted for power law index. The concentration of ferrofluid showing declining behavior for Schmidt numbers and rises for thermophoresis parameter. © 2024

关键词： Carreau ferrofluid Heat and mass transfer Magnetic dipole Numerical solution

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Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

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Communications in Computational Physics 2013年第10期14卷 1228-1251页

作者： Yan Li I-Liang Chern Joung-Dong Kim Xiaolin Li Department of Applied Mathematics and Statistics Stony Brook UniversityStony BrookNY 11794-3600USA Department of Applied Mathematics Center of Mathematical Modeling and Scientific ComputingNational Chiao Tung UniversityHsin Chu300Taiwan Department of Mathematics National Taiwan UniversityTaipei106Taiwan National Center for Theoretical Sciences Taipei OfficeTaipei106Taiwan

We use front tracking data structures and functions to model the dynamic evolution of fabric *** represent the fabric surface by a triangulated mesh with preset equilibrium side *** stretching and wrinkling of the surface are modeled by the mass-spring *** external driving force is added to the fabric motion through the"Impulse method"which computes the velocity of the point mass by superposition of *** mass-spring system is a nonlinear ODE *** by the numerical and computational analysis,we show that the spring system has an upper bound of the eigen *** analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the *** upper bound plays an important role in determining the numerical stability and accuracy of the ODE *** on this analysis,we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal *** used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

关键词： Front tracking spring model eigen frequency

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The Immersed Boundary Method for Two-Dimensional Foam with Topological Changes

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Communications in Computational Physics 2012年第7期12卷 479-493页

作者： Yongsam Kim Yunchang Seol Ming-Chih Lai Charles S.Peskin Department of Mathematics Chung-Ang UniversityDongjakgu HeukseokdongSeoul 156-756Korea Department of Applied Mathematics Center of Mathematical Modeling and Scientific ComputingNational Chiao Tung University1001Ta Hsueh RoadHsinchu 300Taiwan Courant Institute of Mathematical Sciences New York University251 Mercer StreetNew YorkNY 10012 USA

We extend the immersed boundary(IB)method to simulate the dynamics of a 2D dry foam by including the topological changes of the bubble *** the article[***,M.-***,and ***,***.229:5194-5207,2010],we implemented an IB method for the foam problem in the two-dimensional case,and tested it by verifying the von Neumann relation which governs the coarsening of a two-dimensional dry ***,the method implemented in that article had an important limitation;we did not allow for the resolution of quadruple or higher order junctions into triple junctions.A total shrinkage of a bubble with more than four edges generates a quadruple or higher order *** reality,a higher order junction is unstable and resolves itself into triple *** here extend the methodology previously introduced by allowing topological changes,and we illustrate the significance of such topological changes by comparing the behaviors of foams in which topological changes are allowed to those in which they are not.

关键词： Foam permeability capillary-driven motion immersed boundary method coarsening topological changes T1 and T2 processes

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Impacts of oxytactic microorganisms and viscous dissipation in Carreau nanoliquid featuring ferromagnetic nanoparticles

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Partial Differential Equations in applied mathematics 2025年 13卷

作者： Tabrez, Muhammad Hussain, I. Khan, W.A. Khan, S.U. Waqas, M. Rashid, Rzgar Farooq Anwar, M.I. Ammar, Mohamed Ben Zamri, Nurnadiah Abiyev, Ruzimurod Garalleh, Hakim AL Department of Mathematics Mohi-ud-Din Islamic University Nerian Sharif Azad Jammu and Kashmir 12010 Pakistan Department of Mathematics Namal University Mianwali 42250 Pakistan NUTECH School of Applied Sciences and Humanities National University of Technology Islamabad 44000 Pakistan Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Faculty of Informatics and Computing Universiti Sultan Zainal Abidin Besut Campus Terengganu Besut 22200 Malaysia Department of Medical Laboratory Science College of Science Knowledge University Erbil 44001 Iraq Department of Medical Laboratory Technique College of Medical Technology AL-Kitab University Kirkuk Iraq Department of Mathematics School of Sciences and Humanities Nazarbayev University Astana Kazakhstan Center for Scientific Research and Entrepreneurship Northern Border University Arar 73213 Saudi Arabia Department of Mathematics and its Teaching Methods in Primary Education Tashkent State Pedagogical University Tashkent Uzbekistan Department of Mathematical Science College of Engineering University of Business and Technology Jeddah 21361 Saudi Arabia

Owing to rapid progress in field of nanotechnology, various mathematical model has been proposed regarding the flow of nanofluids. Based on boosted thermal properties, multidisciplinary applications of such materials has been claimed in various engineering and industrial processes. In current work, a theoretical analysis is performed for bioconvective flow of Carreau fluid with applications of magnetic dipole. The significance of magnetic dipole are presented with interaction of ferrofluid. The applications of viscous dissipation have also been entertained. The flow is subject to applications of stretched surface. Similarity variables are used for making transformation to obtain set of nonlinear ODEs from set of PDEs. The numerical computation is also made by using of well-known numerical method termed as bvp4c. Influences of various non dimensional fluid parameters like Brownian motion, viscous dissipation, Curie temperature, Weissenberg number, motile difference parameter and bioconvection Paclet number are examined and expressed graphically. It is perceived that ferrofluid's concentration declines when Brownian diffusive variable is augmented while opposite characteristics are reported for Schmidt number. Current results conveying applications in the biofuels, better heat transport medium, fertilizers, catalysts, electronics, paints, semiconductors, speakers, drug delivery, fertilizers etc. © 2024 The Author(s)

关键词： Bioconvection Carreau fluid Ferromagnetic flow Magnetic dipole Viscous dissipation

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STABILITY ANALYSIS FOR NONLINEAR SCHRODINGER EQUATIONS WITH NONLINEAR ABSORBING BOUNDARY CONDITIONS

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Journal of Computational mathematics 2017年第1期35卷 1-18页

作者： Jiwei Zhang Zhenli Xu Xiaonan Wu Desheng Wang Applied and Computational Mathematics Division Beijing Computational Science Research Center China Department of Mathematics Institute of Natural Sciences and MOE Key Lab of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China Department of Mathematics Hong Kong Baptist University Kowloon Hong Kong China Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 Singapore

Local absorbing boundary conditions （LABCs） for nonlinear Schr6dinger equations have been constructed in papers [PRE 78（2008） 026709; and PRE 79 （2009） 046711] using the so-called unified approach. In this paper, we present stability analysis for the reduced problem with LABCs on the bounded computational domain by the energy estimate, and discuss a class of modified versions of LABCs. To prove the stability analysis of the re- duced problem, we turn to the technique of some auxiliary variables which reduces the higher-order derivatives in LABCs into a family of equations with lower-order derivatives. Furthermore, we extend the strategy to the stability analysis of two-dimensional problems by carefully dealing with the LABCs at corners. Numerical examples are given to demon- strate the effectiveness of our boundary conditions and validate the theoretical analysis.

关键词： Nonlinear SchrSdinger equations Energy estimates Absorbing boundaryconditions.

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Improved analysis of rectangular dielectric waveguides based on a legendre pseudospectral penalty scheme

Improved analysis of rectangular dielectric waveguides based...

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Integrated Photonics Research, Silicon and Nanophotonics, IPRSN 2010

作者： Chiang, Shun-Fan Lin, Bang-Yan Teng, Chun-Hao Chang, Hung-Chun Department of Electrical Engineering Graduate Institute of Photonics and Optoelectronics Graduate Institute of Communication Engineering National Taiwan University Taipei 10617 Taiwan Department of Applied Mathematics and Center of Mathematical Modeling and Scientific Computing National Chiao Tung University Hsinchu 30010 Taiwan

A Legendre pseudospectral method with penalty scheme is established in frequency domain for high-accuracy waveguide mode analysis. For a square dielectric waveguide, the calculated modal index is seen to converge to t... 详细信息

ISBN: (纸本)9781557528957

关键词： Frequency domain analysis

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Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes

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Communications in Computational Physics 2007年第5期2卷 933-963页

作者： Yingjie Liu Chi-Wang Shu Eitan Tadmor Mengping Zhang School of Mathematics Georgia Institute of TechnologyAtlantaGA 30332-0160USA. Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA Department of Mathematics Institute for Physical Science and Technologyand Center of Scientific Computation and Mathematical Modeling(CSCAMM)University of MarylandCollege ParkMD 20742USA Department of Mathematics University of Science and Technology of ChinaHefeiAnhui 230026China

This is the continuation of the paper”Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction”by the same *** hierarchical reconstruction introduced therein is applied to central schemes on overlapping cells and to finite volume schemes on non-staggered *** takes a new finite volume approach for approximating non-smooth solutions.A critical step for high-order finite volume schemes is to reconstruct a non-oscillatory high degree polynomial approximation in each cell out of nearby cell *** the paper this procedure is accomplished in two steps:first to reconstruct a high degree polynomial in each cell by using e.g.,a central reconstruction,which is easy to do despite the fact that the reconstructed polynomial could be oscillatory;then to apply the hierarchical reconstruction to remove the spurious oscillations while maintaining the high *** numerical computations for systems of conservation laws are performed without characteristic *** particular,we demonstrate that this new approach can generate essentially non-oscillatory solutions even for 5th-order schemes without characteristic decomposition.

关键词： Central scheme discontinuous Galerkin method ENO scheme finite volume scheme MUSCL scheme TVD scheme.

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