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anomalous diffusion IN FRACTAL POROUS MEDIUM

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Applied Mathematics and Mechanics(English Edition) 2000年第10期21卷 1145-1152页

作者：王子亭 Department of Applied Mathematics University of Petroleum Dongying P R China

Fractal media has many characteristics different from those of homogeneous media, it has a correlated self-similar structure. The particle diffusion in pore fractal is different from Fick' s diffusion, and its mean-squared displacement follows fractal scaling law. The model of particle diffusion in pore fractal by means of the statistics method of stochastic process is structured and some fractal characteristics and non-Markov property are proved.

关键词： fractal anomalous diffusion porous media

anomalous diffusion on the Percolating Networks

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Communications in Nonlinear Science and Numerical Simulation 1997年第4期2卷 220-225页

作者： De L IU,Houqiang LI,Fuxuan CHANG &Libin L IN (Department of Physics &Open laboratory of Radiation Physics and technology,Sichuan Union university,Cheng Du,6 1 0 0 6 4,China) 1The paper was received on Dec.2 0 th.,1997 Department of Physics & Open laboratory of Radiation Physics and technology Sichuan Union university Chengdu 610064 China

According to the standard diffusion equation,by introducing reasonably into a anomalous diffusion coefficient,the generalized diffusion equation,which describes anomalous diffusion on the percolating networks with a power- law distribution of waiting times,is derived in this paper.The solution of the generalized diffusion equation is obtained by using the method,which is used by Barta.The problems of anomalous diffusion on percolating networks with a power- law distribution of waiting times,which aren’tsolved by Barta,are resolved.

关键词： anomalous diffusion percolating networks the critical point a power- law distribution of waiting times

anomalous diffusion IN FINITE LENGTH FINGERS COMB FRAME WITH THE EFFECTS OF TIME AND SPACE RIESZ FRACTIONAL CATTANEO-CHRISTOV FLUX AND POISEUILLE FLOW

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Journal of Computational Mathematics 2018年第4期36卷 563-578页

作者： Lin Liu Liancun Zheng Fawang Liu Xinxin Zhang School of Mathematics and Physics and School of Energy and Environmental Engineering University of Science and Technology Beijing Beijing 100083 China School of Energy and Environmental Engineering Queensland University of Technology GPO Box 2434 Brisbane Qld. 4001 Australia School of Mechanical Engineering University of Science and Technology Beijing Beijing 100083 China

This paper presents an investigation on the anomalous diffusion in finite length fingers comb frame, the time and space Riesz fractional Cattaneo-Christov flux is introduced with the Oldroyds＇ upper convective derivative and the effect of Poiseuille flow is also taken into account. Formulated governing equation possesses the coexisting characteristics of parabolicity and hyperbolicity. Numerical solution is obtained by the Ll-scheme and shifted Griinwald formulae, which is verified by introducing a source item to construct an exact solution. The effects, such as time and space fractional parameters, relaxation parameter and the ratio of the pressure gradient and viscosity coefficient, on the spatial and temporal evolution of particles distribution and dynamic characteristics are shown graphically and analyzed in detail.

关键词： anomalous diffusion Cattaneo-Christov flux Fractional derivative Poiseuille flow Distribution

Analysis of Anisotropic Nonlocal diffusion Models:Well-Posedness of Fractional Problems for anomalous Transport

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Numerical Mathematics(Theory,Methods and Applications) 2022年第4期15卷 851-875页

作者： Marta D’Elia Mamikon Gulian Data Science and Computing Sandia National LaboratoriesCAUSA

We analyze the well-posedness of an anisotropic,nonlocal diffusion equation.Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus,we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation.Furthermore,we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s∈[0.5,1).We also present an application of the advection-diffusion equation to anomalous transport of solutes.

关键词： Nonlocal models fractional models anomalous diffusion anisotropic diffusion solute transport

CONCENTRATION DISTRIBUTION OF FRACTIONAL anomalous diffusion CAUSED BY AN INSTANTANEOUS POINT SOURCE

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Applied Mathematics and Mechanics(English Edition) 2003年第11期24卷 1302-1308页

作者：段俊生徐明瑜 Department of Basic Sciences Tianjin University of Commerce Tianjin 300134 P.R.China Institute of Mathematics and Systematical Science Shandong University Jinan 250100 P. R. Chinahe Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1 2 or 3) are derived by means of the condition of mass conservation the time-space similarity of the solution Mellin transform and the properties of the Fox function . And the asymptotic behaviors for the solutions are also given .

The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by means of the condition of mass conservation , the time-space similarity of the solution , Mellin transform and the properties of the Fox function . And the asymptotic behaviors for the solutions are also given .

关键词： instantaneous point source anomalous diffusion fractional calculus Fox function Mellin transform

Memory dependent anomalous diffusion in comb structure under distributed order time fractional dual-phase-lag model

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International Journal of Biomathematics 2021年第8期14卷 33-53页

作者： Lin Liu Shuo Yang Libo Feng Qian Xu Liancun Zheng Fawang Liu School of Mathematics and Physics University of Science and Technology BeijingBeijing 100083P.R.China School of Mathematical Sciences Queensland University of TechnologyGPO Box 2434BrisbaneQueensland 4001Australia School of Energy and Environmental Engineering University of Science and Technology BeijingBeijing 100083P.R.China

This paper considers a novel distributed order time fractional dual-phase-lag model to analyze the anomalous diffusion in a comb structure,which has a widespread application in medicine and biology.The newly proposed constitution model is a generalization of the dual-phase-lag model,in which a spectrum of the time fractional derivatives with the memory characteristic governed by the weight coefficient is considered and the formulated governing equation contains both the diffusion and wave characteristics.With the L1-formula to discrete the time Caputo fractional derivatives,the finite difference method is used to discretize the model and the related numerical results are plotted graphically.By adding a source term,an exact solution is defined to verify the correctness of the numerical scheme and the convergence order of the error in spatial direction is presented.Finally,the dynamic characteristics of the particle distributions and the effects of involved parameters on the total number of particles in the x-direction are analyzed in detail.

关键词： anomalous diffusion distributed order time fractional derivative constitutive relationship relaxation parameter

Fractional single-phase-lagging heat conduction model for describing anomalous diffusion

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Propulsion and Power Research 2016年第1期5卷 45-54页

作者： T.N.Mishra K.N.Rai DST-CIMS Faculty of SciencesBHUVaranasiUP 221005India Mathematical Sciences IIT BHUVaranasiUP 221005India

The fractional single-phase-lagging(FSPL)heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging(SPL)heat conduction model.Based on the FSPL heat conduction model,anomalous diffusion within a finite thin film is investigated.The effect of different parameters on solution has been observed and studied the asymptotic behavior of the FSPL model.The analytical solution is obtained using Laplace transform method.The whole analysis is presented in dimensionless form.Numerical examples of particular interest have been studied and discussed in details.

关键词： Single-phase-lagging(SPL)heat conduction model Fractional single-phase-lagging(FSPL)heat conductionmodel Laplace transform Fractional conservation equation Asymptotic behavior anomalous diffusion

SCALE-INVARIANT SOLUTION FOR FRACTIONAL anomalous diffusion EOUATION

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Annals of Differential Equations 2006年第1期22卷 21-26页

作者： Duan Junsheng Temuer Chaolu College of Science Tianjin University of Commerce Tianjin 300134 College of Science Inner Mongolia Uiversity of Technology Huhhot 010062

Fractional diffusion equation for transport phenomena in fractal media is an integro-partial differential equation. For solving the problem of this kind of equation the invariants of the group of scaling transformations are given and then used for deriving the integro-ordinary differential equation for the scale-invariant solution. With the help of Mellin transform the scale-invariant solution is obtained in terms of Fox functions. And the series and asymptotic representations for the solution are considered.

关键词： fractional calculus anomalous diffusion scale-invariant solution. Fox functions

anomalous diffusion and dynamic disorder in biomolecular systems based on mesoscopic statistical modeling

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Anomalous diffusion and dynamic disorder in biomolecular sys...