FDA Express

FDA Express    Vol. 31, No. 2, May 30, 2019

All issues: http://jsstam.org.cn/fda/

Editors: http://jsstam.org.cn/fda/Editors.htm

Institute of Soft Matter Mechanics, Hohai University
For contribution: suxianglong1303@hhu.edu.cn, fdaexpress@hhu.edu.com

For subscription: http://jsstam.org.cn/fda/subscription.htm

PDF download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol31_No2_2019.pdf


↑  Latest SCI Journal Papers on FDA

(Searched on May 30, 2019)

  Call for Papers

Winter school on Computational Models of Heterogeneous Media

↑  Books

HAUSDORFF CALCULUS: Applications to Fractal Systems

↑  Journals

Computer Methods in Applied Mechanics and Engineering

Physical Review E

  Paper Highlight

A physical interpretation of fractional viscoelasticity based on the fractal structure of media: Theory and experimental validation

A spatial structural derivative model for the characterization of superfast diffusion/dispersion in porous media

  Websites of Interest

Fractal derivative and operators and their applications

Fractional Calculus & Applied Analysis

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 Latest SCI Journal Papers on FDA

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(Searched on May 30, 2019)



Lattice Boltzmann model for time sub-diffusion equation in Caputo sense

By: Du, Rui; Sun, Dongke; Shi, Baochang; etc.

APPLIED MATHEMATICS AND COMPUTATION Volume: 358 Pages: 80-90 Published: OCT 1 2019

Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction-diffusion equations
By: Zhang, Qifeng; Ren, Yunzhu; Lin, Xiaoman; etc.
APPLIED MATHEMATICS AND COMPUTATION Volume: 358 Pages: 91-110 Published: OCT 1 2019


Exponentially fitted methods for solving time fractional nonlinear reaction-diffusion equation
By: Zahra, W. K.; Nasr, M. A.; Van Daele, M.
APPLIED MATHEMATICS AND COMPUTATION Volume: 358 Pages: 468-490 Published: OCT 1 2019


Convergence analysis of the Chebyshev-Legendre spectral method for a class of Fredholm fractional integro-differential equations
By: Yousefi, A.; Javadi, S.; Babolian, E.; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 358 Pages: 97-110 Published: OCT 1 2019


On chaos in the fractional-order Grassi-Miller map and its control
By: Ouannas, Adel; Khennaoui, Amina-Aicha; Grassi, Giuseppe; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 358 Pages: 293-305 Published: OCT 1 2019


Non-polynomial spline approach in two-dimensional fractional sub-diffusion problems
By: Li, Xuhao; Wong, Patricia J. Y.
APPLIED MATHEMATICS AND COMPUTATION Volume: 357 Pages: 222-242 Published: SEP 15 2019


Radius of starlikeness of p-valent lambda-fractional operator
By: Aydogan, S. M.; Sakar, F. M.
APPLIED MATHEMATICS AND COMPUTATION Volume: 357 Pages: 374-378 Published: SEP 15 2019


Global synchronization between two fractional-order complex networks with non-delayed and delayed coupling via hybrid impulsive control
By: Li, Hong-Li; Cao, Jinde; Hu, Cheng; etc.
NEUROCOMPUTING Volume: 356 Pages: 31-39 Published: SEP 3 2019


A fast finite-difference algorithm for solving space-fractional filtration equation with a generalised Caputo derivative
By: Bohaienko, V. O.
COMPUTATIONAL & APPLIED MATHEMATICS Volume: 38 Issue: 3 Document number: UNSP 105 Published: SEP 2019


A high-order compact difference method for time fractional Fokker-Planck equations with variable coefficients
By: Ren, Lei; Liu, Lei
COMPUTATIONAL & APPLIED MATHEMATICS Volume: 38 Issue: 3 Document number: UNSP 101 Published: SEP 2019


Can we split fractional derivative while analyzing fractional differential equations?
By: Bhalekar, Sachin; Patil, Madhuri
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 76 Pages: 12-24 Published: SEP 2019


Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting
By: Plociniczak, Lukasz
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 76 Pages: 66-70 Published: SEP 2019


Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations
By: Garrappa, Roberto
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 76 Pages: 138-139 Published: SEP 2019


Performance evaluation of fractional OFDM for extending transmission distance without reducing spectral efficiency
By: Yamasaki, Y.; Nagashima, T.; Cincotti, G.; etc.
OPTICS COMMUNICATIONS Volume: 446 Pages: 100-105 Published: SEP 1 2019


A piecewise spectral-collocation method for solving fractional Riccati differential equation in large domains
By: Azin, H.; Mohammadi, F.; Tenreiro Machado, J. A.
COMPUTATIONAL & APPLIED MATHEMATICS Volume: 38 Issue: 3 Document number: UNSP 96 Published: SEP 2019


Robust type-2 fuzzy fractional order PID controller for dynamic stability enhancement of power system having RES based microgrid penetration
By: Abdulkhader, Haseena Kuttomparambil; Jacob, Jeevamma; Mathew, Abraham T.
INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS Volume: 110 Pages: 357-371 Published: SEP 2019


Forecasting short-term renewable energy consumption of China using a novel fractional nonlinear grey Bernoulli model
By: Wu, Wenqing; Ma, Xin; Zeng, Bo; etc.
RENEWABLE ENERGY Volume: 140 Pages: 70-87 Published: SEP 2019

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Call for Papers

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Winter school on Computational Models of Heterogeneous Media

(QUEENSLAND UNIVERSITY OF TECHNOLOGY

1-12 JULY 2019)



The study of multiphase flow in heterogeneous media finds application across a number of important industrial and biological processes, including drying of foods for preservation, converting biomass into biofuels, using fractional dynamic models for MRI to probe tissue microstructure, studying viscoelastic non-Newtonian fluids, and understanding the role of heterogeneity for treating diseases of the heart. A significant challenge to modelling these processes is to understand how the strongly coupled heat and mass transfer phenomena evolve and interact in the complicated porous microstructure. To elucidate the complex physics, exposure to a broad cross-section of sophisticated numerical methods is essential and we will explore some of these methods in the Winter School. The School will feature modules on multiscale modelling; computational homogenization; fractional calculus; finite volume, finite element, spectral and meshless methods; Stokes flow; parameter estimation; and Krylov subspace methods.

Program
Hosted over two weeks, this program offers a range of specialist topics with overarching themes including computational homogenisation, fractional calculus, multiscale modelling and stokes flow. This year*s impressive expert speaker line-up draws upon the knowledge of national and international lecturers at the forefront of their fields, and attracts students from all around Australia.

To maximise the experience, the school aims to feature prominent international and domestic speakers, researchers and lecturers as well as a number of program extras including social events, a special guest public lecture and a diversity in STEM panel event.

Detailed information: https://ws.amsi.org.au/


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Books

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HAUSDORFF CALCULUS: Applications to Fractal Systems

(Editors: Yingjie Liang, Wen Chen, Wei Cai)

Details: https://www.degruyter.com/view/product/506187#?tdsourcetag=s_pctim_aiomsg

Introduction

This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.

-Presents the theory and applications of Hausdorff calculus.
-Covers applications in dynamics, statistics, mechanics, and computation.
-Of interest to mathematicians and physicists as well as to engineers.

Chapters


-Introduction

-Hausdorff diffusion equation

-Statistics on fractals

-Lyapunov stability of Hausdorff derivative non-linear systems

-Hausdorff radial basis function

-Hausdorff PDE modeling

-Local structural derivative

-Perspectives


The Contents is available at: https://www.degruyter.com/view/product/506187#?tdsourcetag=s_pctim_aiomsg

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 Journals

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Computer Methods in Applied Mechanics and Engineering

 (Selected)

Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations

Tinggang Zhao, Zhiping Mao, George Em Karniadakis

A meshfree approach for solving 2D variable-order fractional nonlinear diffusion-wave equation

Younes Shekari, Ali Tayebi, Mohammad Hossein Heydari

Fractional Gray每Scott model: Well-posedness, discretization, and simulations

Tingting Wang, Fangying Song, Hong Wang, George Em Karniadakis

High-order central difference scheme for Caputo fractional derivative

Yuping Ying, Yanping Lian, Shaoqiang Tang, Wing Kam Liu

A Petrov每Galerkin finite element method for the fractional advection每diffusion equation

Yanping Lian, Yuping Ying, Shaoqiang Tang, Stephen Lin, Wing Kam Liu

Fractional-order uniaxial visco-elasto-plastic models for structural analysis

J. L. Suzuki, M. Zayernouri, M. L. Bittencourt, G. E. Karniadakis

Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview

Bangti Jin, Raytcho Lazarov, Zhi Zhou

Adaptive finite element method for fractional differential equations using hierarchical matrices

Xuan Zhao, Xiaozhe Hu, Wei Cai, George Em Karniadakis

A tunable finite difference method for fractional differential equations with non-smooth solutions

Xuejuan Chen, Fanhai Zeng, George Em Karniadakis

A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations

Fangying Song, Chuanju Xu, George Em Karniadakis

Aspects of an adaptive finite element method for the fractional Laplacian: A priori and a posteriori error estimates, efficient implementation and multigrid solver

Mark Ainsworth, Christian Glusa

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

Fanhai Zeng, Zhongqiang Zhang, George Em Karniadakis

A unified Petrov每Galerkin spectral method for fractional PDEs

Mohsen Zayernouri, Mark Ainsworth, George Em Karniadakis

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Physical Review E

 (Selected)

Fractional Langevin equation from damped bath dynamics

Alex V. Plyukhin

Statistical testing approach for fractional anomalous diffusion classification

Aleksander Weron, Joanna Janczura, Ewa Boryczka, Titiwat Sungkaworn, and Davide Calebiro

Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries

Jae-Hyung Jeon and Ralf Metzler

Fractional superstatistics from a kinetic approach

Kamel Ourabah and Mouloud Tribeche

Fractional Brownian motors and stochastic resonance

Igor Goychuk and Vasyl Kharchenko

Fractional diffusion on a fractal grid comb

Trifce Sandev, Alexander Iomin, and Holger Kantz

Fractional Langevin equations of distributed order

C. H. Eab and S. C. Lim

Fractional Brownian motion with a reflecting wall

Alexander H. O. Wada and Thomas Vojta

Nonlinear subdiffusive fractional equations and the aggregation phenomenon

Sergei Fedotov

Variational principle for fractional kinetics and the L谷vy Ansatz

Sumiyoshi Abe

Fractional Brownian motion run with a nonlinear clock

Daniel O*Malley and John H. Cushman

Fractional entropy decay and the third law of thermodynamics

Chun-Yang Wang, Xue-Mei Zong, Hong Zhang, and Ming Yi

Fractional dynamics using an ensemble of classical trajectories

Zhaopeng Sun , Hao Dong , and Yujun Zheng

First passage in an interval for fractional Brownian motion

Kay Jörg Wiese

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 Paper Highlight

A physical interpretation of fractional viscoelasticity based on the fractal structure of media: Theory and experimental validation

Somayeh Mashayekhi, M. Yousuff Hussaini, William Oates 

Publication information: Journal of the Mechanics and Physics of Solids, Volume 128, July 2019, Pages 137-150

https://www.sciencedirect.com/science/article/pii/S0022509619300766/pdfft?md5=a73022abf527d972dbc08583fd8e63bc&pid=1-s2.0-S0022509619300766-main.pdf

Abstract

In this work, a physical connection between the fractional time derivative and fractal geometry of fractal media is developed and applied to viscoelasticity and thermal diffusion in elastomers. Integral to this formulation is the application of both the fractal dimension and the spectral dimension which characterizes diffusion in fractal media. The methodology extends the generalized molecular theory of Rouse and Zimm where generalized Gaussian structures (GGSs) replace the Rouse matrix with the generalized Gaussian Rouse matrix (GRM). Importantly, the Zimm model is extended to fractal media where the new relaxation formulation contains internal state variables that naturally depend on the fractional time derivative of deformation. Through the use of thermodynamic laws in fractal media, we derive the linear fractional model of viscoelasticity based on both spectral and fractal dimensions. This derivation shows how the order of the fractional derivative in the linear fractional model of viscoelasticity is a rate dependent material property that is strongly correlated with fractal and spectral dimensions in fractal media. To validate the correlation between fractional rates and fractal material structure, we measure the viscoelasticity and thermal diffusion of two different dielectric elastomers: Very High Bond (VHB) 4910 and VHB 4949. Using Bayesian uncertainty quantification (UQ) based on uniaxial stress每strain measurements, the fractional order of the derivative in the linear fractional model of viscoelasticity is quantified. Two dimensional fractal dimensions are also independently quantified using the box counting method. Lastly, the diffusion equation in fractal media is inferred from experiments using Bayesian UQ to quantify the spectral dimension by heating the polymer locally with a laser beam and quantifying thermal diffusion. Comparing theory to experiments, a strong correlation is found between the viscoelastic fractional order obtained from stress每strain measurements in comparisons with independent predictions of fractional viscoelasticity based on the fractal structure and fractional thermal diffusion rates.


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A spatial structural derivative model for the characterization of superfast diffusion/dispersion in porous media

 Wei Xu, Yingjie Liang, Wen Chen, John H. Cushman

Publication information: International Journal of Heat and Mass Transfer, Volume 139, August 2019, Pages 39-45
https://www.sciencedirect.com/science/article/pii/S0017931019302820/pdfft?md5=ac5224d5774839f00f3045a243554784&pid=1-s2.0-S0017931019302820-main.pdf

Abstract

Many theoretical and experimental results show that anomalous diffusion/dispersion occurs in porous media. To exactly solve anomalously fast dispersion, we introduce a structural derivative diffusion model to present superfast diffusion via a logarithmic structural function in space. The fundamental solution of the diffusion model is a form of log-normal distribution, and the corresponding analytical mean squared displacement grows like et/汕2, 0<汕<1. Compared with the existing models, the proposed model is more effective and accurate in fitting experimental data.

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