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GLOBAL EXPONENTIAL NONLINEAR STABILITY FOR DOUBLE diffusive CONVECTION IN POROUS MEDIUM

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Acta Mathematica Scientia 2019年第1期39卷 119-126页

作者： Lanxi XU Ziyi LI Department of Mathematics Beijing University of Chemical Technology

Nonlinear stability of the motionless double-diffusive solution of the problem of an infinite horizontal fluid layer saturated porous medium is studied. The layer is heated and salted from below. By introducing two balance fields and through defining new energy functionals it is proved that for CLe ≥ R, Le ≤ 1 the motionless double-diffusive solution is always stable and for CLe < R, Le < 1 the solution is globally exponentially and nonlinearly stable whenever R < 4π~2+ Le C, where Le, C and R are the Lewis number, Rayleigh number for solute and heat, respectively. Moreover, the nonlinear stability proved here is global and exponential, and the stabilizing effect of the concentration is also proved.

关键词： energy method energy functional nonlinear stability diffusive convection porous medium

Dynamics of a diffusive predator–prey system with ratio-dependent functional response and time delay

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International Journal of Biomathematics 2020年第6期13卷 1-21页

作者： Xin Jiang Ran Zhang Zhikun She School of Mathematical Sciences Beihang University Beijing 100191P.R.China School of Mathematics Harbin Institute of Technology Harbin 150001P.R.China

In this paper,we investigate the qualitative behaviors of a predator–prey system with ratio-dependent *** system accommodates the diffusion effect to model the migration of individuals and the time delay induced by *** start with some basic properties of the *** the sufficient condition independent of time delay and diffusion effect for global asymptotical stability of the boundary equilibrium is obtained by using the comparison ***,based on the LaSalle’s invariance principle and Lyapunov functional,we investigate the global attractiveness of the positive equilibrium,arriving at its global asymptotical ***,Hopf bifurcation induced by time delay around the positive equilibrium is ***,numerical examples are listed to verify the corresponding analytical results.

关键词： Predator-prey model diffusive time delay global asymptotical stability Hopf bifurcation

Analysis of a delayed diffusive model with Beddington-DeAngelis functional response

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International Journal of Biomathematics 2019年第4期12卷 277-300页

作者： Xin-You Meng Jiao-Guo Wang School of Science Lanzhou University of Technology Lanzhou Gansu 730050 P. R.China

In this paper, a delayed diffusive phytoplankton-zooplankton model with Beddington DeAngelis functional response and toxins is investigated. Existence of equilibria of the system are solved. The global asymptotic stability of the zooplankton-free equilibrium is obtained. The local stability of the coexistent equilibrium and existence of Hopf bifurcation are discussed. In addition, the properties of the Hopf bifurcation are studied based on the center manifold and normal form theory for partial differential equations. Finally, some numerical simulations are also carried out to confirm our theoretical analysis.

关键词： Phytoplankton-zooplankton time delay stability Hopf bifurcation diffusive Beddington-DeAngelis

Numerical Simulation of Double diffusive Mixed Convection in a Horizontal Annulus with Finned Inner Cylinder

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Fluid Dynamics & Materials Processing 2019年第2期15卷 153-169页

作者： Cherfi Ryad Sadaoui Djamel Sahi Adel Mouloud Smail Laboratoire de Mécanique Matériaux et Energétique(L2ME)Facultéde TechnologieUniversitéde Bejaia06000BejaiaAlgérie

The present work relates to a numerical investigation of double diffusive mixed convection around a horizontal annulus with a finned inner *** solutal and thermal buoyancy forces are sustained by maintaining the inner and outer cylinders at uniform temperatures and *** effects are also considered,with the Boussinesq *** forced convection effect is induced by the outer cylinder rotating with an angular velocity(ω)in an anti-clockwise *** studies are made for various combinations of dimensionless numbers;buoyancy ratio number(N),Lewis number(Le),Richardson number(Ri)and Grashof number(Gr).The isotherms,isoconcentrations and streamlines as well as both average and local Nusselt and Sherwood numbers were studied.A finite volume scheme is adopted to solve the transport equations for continuity,momentum,energy and mass *** results indicate that the use of fins on the inner cylinder with outer cylinder rotation,significantly improves the heat and mass transfer in the annulus.

关键词： Finned inner cylinder double diffusive flow heat and mass transfer rotating annulus mixed convection numerical simulation

THE CRITERIA OF ULTIMATE BOUNDEDNESS FOR NONAUTONOMOUS diffusive LOTKA-VOLTERRA SYSTEMS IN TWO HETEROGENEOUS PATCHES

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Journal of Systems Science & Complexity 2001年第2期14卷 179-188页

作者： LI Xuezhi (Department of Mathematics, Xinyang Teachers College, Henan 464000, China) GENI Gupur (Deportment of Mathematics, Xinjiang University, Urumqi 830046, China) ZHU Guangtian (Institute of Systems Science, Academy of Mathematics and Systems Science, 信阳师范学院河南 464000 新疆大学新疆乌鲁木齐 830046 中科院系统科学所北京 100080

In this paper, a set of sufficient conditions is obtained for the ultimate boundedness of nonautonomous n-species diffusive Lotka-Volterra sub-models in two heterogeneous patches. The sub-models are the Lotka-Volterra tree systems, including the Lotka-Volterra chain systems and the Lotka-Volterra models between one and multispecies. The criteria in this paper are in explicit forms of the parameters and thus are easily verifiable.

关键词： Ultimate boundedness diffusive Lotka-Volterra systems patches.

diffusive modelling of glioma evolution: a review

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Journal of Biomedical Science and Engineering 2010年第5期3卷 501-508页

作者： Alexandros Roniotis Kostas Marias Vangelis Sakkalis Michalis Zervakis 不详

Gliomas, the most aggressive form of brain cancer, are known for their widespread invasion into the tissue near the tumor lesion. Exponential models, which have been widely used in other types of cancers, cannot be used for the simulation of tumor growth, due to the diffusive behavior of glioma. diffusive models that have been proposed in the last two decades seem to better approximate the expansion of gliomas. This paper covers the history of glioma diffusive modelling, starting from the simplified initial model in 90s and describing how this have been enriched to take into account heterogenous brain tissue, anisotropic migration of glioma cells and adjustable proliferation rates. Especially, adjustable proliferation rates are very important for modelling therapy plans and personalising therapy to different patients.

关键词： Glioma Brain Tumor diffusive Models Proliferation Invasion

Effect of Non-Uniform Basic Concentration Gradient on the Onset of Double-diffusive Convection in Micropolar Fluid

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Applied Mathematics 2012年第5期3卷 417-424页

作者： Subbarama Pranesh Arun Kumar Narayanappa Department of Mathematics Christ University Bangalore India Department of Mathematics Faculty of Engineering Christ University Bangalore India

The effect of non-uniform basic concentration gradient on the onset of double diffusive convection in a micropolar fluid layer heated and saluted from below and cooled from above has been studied. The linear stability analysis is performed. The eigen value of the problem is obtained using Galerkian method. The eigen values are obtained for 1) free-free 2) rigid-free 3) rigid-rigid velocity boundary combination with isothermal temperature condition on spin-vanishing permeable boundaries. The influence of various micropolar parameters on the onset of convection has been analyzed. One linear and five non linear concentration profiles are considered and their comparative influence on onset is discussed and results are depicted graphically. It is observed that fluid layer with suspended particles heated and soluted from below is more stable compare to the classical fluid without suspended particles.

关键词： Double diffusive Convection Micropolar Fluid Rayleigh Benard Convection and Non Uniform Concentration Gradients

Information-Driven Collaborative Processing for diffusive Source Estimation in Wireless Sensor Networks

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Wireless Sensor Network 2010年第7期2卷 562-570页

作者： Hossein Khonsari Mohammad Hossein Kahaei 不详

This paper discusses an accurate distributed algorithm for diffusive source localization while maintaining the low energy consumption of sensor nodes in wireless sensor networks. In this algorithm, the sensor selection scheme based on the information utility measure is used. To update the estimation in each selected node, a neighborhood radius equal to the communication range of the sensor nodes is defined and all sensors located in the neighborhood circle, whose radius is equal to the neighborhood radius and the selected node is its centre, collaborate their information. To decrease the energy consumption, the neighborhood radius is reduced gradually based on the error covariance value of the estimation. In addition, this paper includes a new method for the initial point calculation which is important in the recursive methods used for distributed algorithms in wireless sensor networks. Numerical examples are used to study the performance of the algorithms. Simulation results show the accuracy of the new algorithm becomes better while its energy consumption is low enough.

关键词： Information-Driven Collaborative Processing Wireless Sensor Network diffusive Source Localization

Effects of Non-Uniform Temperature Gradients on Triple diffusive Marangoni Convection in a Composite Layer

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Open Journal of Applied Sciences 2019年第8期9卷 640-660页

作者： Narayanappa Manjunatha Ramakrishna Sumithra School of Applied Sciences REVA University Bengaluru India Department of Mathematics Government Science College Bengaluru India

The problem of triple diffusive Marangoni convection is investigated in a composite layer comprising an incompressible three component fluid saturated, sparsely packed porous layer over which lies a layer of the same fluid. The lower rigid surface of the porous layer and the upper free surface are considered to be insulating to temperature, insulating to both salute concentration perturbations. At the upper free surface, the surface tension effects depending on temperature and salinities are considered. At the interface, the normal and tangential components of velocity, heat and heat flux, mass and mass flux are assumed to be continuous. The resulting eigenvalue problem is solved exactly for linear, parabolic and inverted parabolic temperature profiles and analytical expressions of the thermal Marangoni number are obtained. The effects of variation of different physical parameters on the thermal Marangoni numbers for the profiles are compared.

关键词： Triple diffusive Thermal Marangoni Convection Composite Layer Temperature Profiles