FDA Express

FDA Express    Vol. 10, No. 2&3, Feb. 15, 2014

 

Editors: http://em.hhu.edu.cn/fda/Editors.htm

Institute of Soft Matter Mechanics, Hohai University
For contribution: fdaexpress@163.com, pangguofei2008@126.com

For subscription: http://em.hhu.edu.cn/fda/subscription.htm

PDF download: http://em.hhu.edu.cn/fda/

 

◆  Latest SCI Journal Papers on FDA

(Searched on 15th February 2014)

  Conference

The 22nd European Signal Processing Conference

  Call for papers

Special Issue on ''Fractional Dynamics: Theory and Applications''

Special Issue on "New Challenges in Fractional Systems 2014 (NCFS14)"

Special session: "Fractional Signal Processing and Applications" in the 22nd European Signal Processing Conference

◆  Books

Lévy Processes and Infinitely Divisible Distributions

Microphysics of Cosmic Plasmas

The Realization Problem for Positive and Fractional Systems (Studies in Systems, Decision and Control)

Spectral and High Order Methods for Partial Differential Equations

◆  Journals

Entropy

Computers & Mathematics with Applications

Journal of Applied Nonlinear Dynamics

  Paper Highlight

Generalization of a theoretical basis for the application of fractional calculus to viscoelasticity

A Matlab toolbox for positive fractional time derivative modeling of arbitrarily frequency-dependent viscosity

Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena

  Websites of Interest

Fractional Calculus & Applied Analysis

International Conference on Fractional Differentiation and Its Applications (ICFDA'14)

 

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 Latest SCI Journal Papers on FDA

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(Searched on 15th February 2014)

 

Adaptive synchronization of drive-response fractional-order complex dynamical networks with uncertain parameters

By: Yang, Li-xin; Jiang, Jun

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION  Volume: 19   Issue: 5   Pages: 1496-1506   Published: MAY 2014

A comment on "Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations"

By: Salahshour, S.; Abbasbandy, S.

 COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION  Volume: 19   Issue: 5   Pages: 1256-1258   Published: MAY 2014

ON THE ORBITAL STABILITY OF FRACTIONAL SCHRODINGER EQUATIONS

By: Cho, Yonggeun; Hajaiej, Hichem; Hwang, Gyeongha; et al.

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS  Volume: 13   Issue: 3   Pages: 1267-1282   Published: MAY 2014

UNIFORM HOLDER REGULARITY WITH SMALL EXPONENT IN COMPETITION-FRACTIONAL DIFFUSION SYSTEMS

By: Terracini, Susanna; Verzini, Gianmaria; Zilio, Alessandro

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS  Volume: 34   Issue: 6   Special Issue: SI   Pages: 2669-2691   Published: JUN 2014

RIGIDITY RESULTS FOR NONLOCAL PHASE TRANSITIONS IN THE HEISENBERG GROUP H

By: Lopez, Luis F.; Sire, Yannick

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS  Volume: 34   Issue: 6   Special Issue: SI   Pages: 2639-2656   Published: JUN 2014

A new 4-D non-equilibrium fractional-order chaotic system and its circuit implementation

By: Zhou, Ping; Huang, Kun

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION  Volume: 19   Issue: 6   Pages: 2005-2011   Published: JUN 2014

Abundant bursting patterns of a fractional-order Morris-Lecar neuron model

By: Shi, Min; Wang, Zaihua

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION  Volume: 19   Issue: 6   Pages: 1956-1969   Published: JUN 2014

Periodic solutions of quadratic Weyl fractional integral equations

By: Chen, Qian; Wang, JinRong; Chen, Fulai; et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION  Volume: 19   Issue: 6   Pages: 1945-1955   Published: JUN 2014

Existence results for fractional q-difference equations of order alpha is an element of]2, 3[ with three-point boundary conditions

By: Almeida, Ricardo; Martins, Natalia

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION  Volume: 19   Issue: 6   Pages: 1675-1685   Published: JUN 2014

Existence and uniqueness of solutions of initial value problems for nonlinear langevin equation involving two fractional orders

By: Yu, Tao; Deng, Ke; Luo, Maokang

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION  Volume: 19   Issue: 6   Pages: 1661-1668   Published: JUN 2014

 

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Conference

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The 22nd European Signal Processing Conference

September 1 -5, 2014, Lisbon, Portugal

http://www.eusipco2014.org/

(Contributed by Prof. Manuel Duarte Ortigueira)

 

Organization: Instituto de Telecomunicações and INESC-ID, Portugal
European Association for Signal Processing (EURASIP)
Technical co-sponsorship: IEEE Signal Processing Society
IEEE Aerospace & Electronic Systems Society

Important Dates
Proposal for tutorials: February 17, 2014
Electronic submission of full papers: February 17, 2014
Notification of acceptance: May 26, 2014
Submission of camera-ready papers and copyright forms: June 23, 2014

Plenary Talks
Yonina Eldar, Technion - Israel Institute of Technology, Israel
Jan Rabaey, University of California, Berkeley, USA
Roger Dannenberg, Carnegie Mellon University, USA
Guillermo Sapiro, Duke University, USA

Call for Papers
EUSIPCO 2014 will be held on September 1- 5, 2014, in Lisbon, Portugal. This is one of the largest international conferences in the field of signal processing and will address all the latest developments in research and technology. The conference will bring together individuals from academia, industry, regulation bodies, and government, to exchange and discuss ideas in all the areas and applications of signal processing. EUSIPCO 2014 will feature world-class keynote speakers, special sessions, plenary talks, tutorials, and technical sessions.

We invite the submission of original, unpublished technical papers on signal processing topics, including but not limited to:
• Audio and acoustic signal processing
• Design and implementation of signal processing systems
• Multimedia signal processing
• Speech processing
• Image and video processing
• Machine learning
• Signal estimation and detection
• Sensor array and multichannel signal processing
• Signal processing for communications including wireless and optical communications and networking
• Signal processing for location, positioning and navigation
• Nonlinear signal processing
• Signal processing applications including health and biosciences

Procedure to submit papers, proposals for special sessions, and tutorials are detailed at http://www.eusipco2014.org/. Submitted papers must be camera-ready, up to five pages long, and conform to the format specified on the EUSIPCO'2014 website.

We look forward to seeing you at the conference.
 

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Call for papers

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Special Issue on " Fractional Dynamics: Theory and Applications "

--- in the Journal of Statistical Mechanics: Theory and Experiment

http://iopscience.iop.org/1742-5468/focus/extra.special5

 (Contributed by Prof. Yong Zhou)

 

Fractional Calculus is simultaneously a new and old research issue. During the few decades, fractional calculus has been recognized as one of the best tools to describe long-memory processes. Such models are interesting for physicists and dynamicists but also for mathematicians. The most important among such models are those described by complex systems containing fractional derivatives. Their evolutions behave in a much more complex way than in the classical integer-order case. The objective of this special issue is to report and review the latest progresses in the field of fractional dynamics, which covers fractional statistical mechanics, fractional quantum dynamics and related topics. We hope that one can learn the recent developments from the special issue, including theoretical, numerical and experimental results in this area.

Journal of Statistical Mechanics: Theory and Experiment is published by IOP, indexed in SCI with impact factor: 1.866.

Guest Editors

Prof. Yong Zhou

Faculty of Mathematics and Computational Science

Xiangtan University

P.R. China

Email: yzhou@xtu.edu.cn

Prof. Vasily E. Tarasov

Skobeltsyn Institute of Nuclear Physics

Moscow State University 119991 Moscow

Russia

Email: tarasov@theory.sinp.msu.ru

Prof. J. A. Tenreiro Machado

Department of Electrical Engineering

ISEP-Institute of Engineering Polytechnic of Porto

Portugal

Email: jtenreiromachado@gmail.com

Submission Deadline: June 30th, 2014.

Submission of Manuscripts

When your contribution is ready for submission, please follow the instructions below:

1. Connect to http://jstat.sissa.it , register (if needed) and login;

2. In the “Submit” section of the JSTAT home page click on “submit a paper for a special issue”;

3. Select “Fractional Dynamics: Theory and Applications” from the list;

4. Follow the step-by-step procedure for submission. In case of need, please click on the "HELP" link available at the top of the submission pages ( http://jstat.sissa.it/jstat/help/helpLoader.jsp?pgType=author )

 

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Special Issue on "New Challenges in Fractional Systems 2014 (NCFS14)"

--- in Mathematical Problems in Engineering

Website: http://www.hindawi.com/journals/mpe/si/262360/cfp/
 (contributed by Prof. Guido Maione)

Fractional order differentiation consists in the generalization of classical integer differentiation to real or complex orders. From a mathematical point of view, several interpretations of fractional differentiation were proposed, but there is still a deep debate about it. The fractional differentiation and fractional integration are nonlocal operations based on an integral with a singular kernel. This explains why these operators are still not well defined and that several definitions still coexist. Since the first recorded reference work in 1695 up to the present day, many papers have been published on this subject, but much progress still to be done particularly on the relationship of these different definitions with the physical reality of a system.

A fractional order system is a system described by an integrodifferential equation involving fractional order derivatives of its input(s) and/or output(s). From a physical point of view, linear fractional derivatives and integrals order systems are not classical linear systems and not quite conventional distributed parameter systems. They are in fact halfway between these two classes of systems and are a modelling tool well suited to a wide class of phenomena with nonstandard dynamic behaviour, and the applications of fractional order systems are now well accepted in the following disciplines. Potential topics include, but are not limited to:

The goal of the present special issue is to address the latest developments in the area of fractional calculus application in signals and systems. Papers describing original research work that reflects the recent theoretical advances and experimental results as well as open new avenues for research are invited on all aspects of object tracking.

Before submission authors should carefully read over the journal's Author Guidelines, which are located at  http://www.hindawi.com/journals/mpe/guidelines/.
Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at  http://mts.hindawi.com/ according to the following timetable:

Manuscript Due  ;June 13, 2014
First Round of Reviews  September 5, 2014
Publication Date         October 31, 2014

Lead Guest Editor

Guido Maione, Politecnico di Bari, Italy;
ggmaione@poliba.it

 

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Special session: Fractional Signal Processing and Applications

---- in the 22nd European Signal Processing Conference

September 1 -5, 2014, Lisbon, Portugal

http://www.eusipco2014.org/

(Contributed by Prof. Manuel Duarte Ortigueira)

Fractional Calculus is the generalisation of the classic integer order calculus to real or complex orders having as base the definition of fractional derivative. The mutual influence Fractional Calculus/Signal Processing has been increasing in the last fifteen years with insertion of current signal processing tools, nomenclature and system interpretations into Fractional Calculus and bringing from it the fractional concepts.    

Fractional calculus is being applied in an increasing number of fields, from Physics to Control Engineering, or modeling long range processes that we find in our daily life as internet traffic, economy and finance. Other systems and devices difficult to study and model fall into the fractional framework as ultra capacitors, batteries, dielectric materials, muscles, etc.    

The development of Fractional Signals and Systems theory has led to a new set of tools that began substituting classic procedures and implementations. In fact the success of the fractional methodology is unquestionable with a lot of applications, namely in nonlinear and complex system dynamics and image processing. The advantages of fractional filters led to an increment in the research of new design methods.    

Also important as referred above was the enrichment of Fractional Calculus done by the Signal Processing view, interpretation, and procedures.   

This special session addresses the interplay between Fractional Calculus and signal processing, which brings new challenges since the involved mathematical tools are more involved and hard to compute than the classic ones, but are also richer allowing better models, behaviours, and performances.

 

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Books

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Lévy Processes and Infinitely Divisible Distributions

Ken-iti Sato

Book Description

Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book is intended to provide the reader with comprehensive basic knowledge of Lévy processes, and at the same time serve as an introduction to stochastic processes in general. No specialist knowledge is assumed and proofs are given in detail. Systematic study is made of stable and semi-stable processes, and the author gives special emphasis to the correspondence between Lévy processes and infinitely divisible distributions. All serious students of random phenomena will find that this book has much to offer. Now in paperback, this corrected edition contains a brand new supplement discussing relevant developments in the area since the book's initial publication.

More information on this book can be found by the following link:

http://books.google.com.hk/books/about/Lévy_Processes_and_Infinitely_Divisible.html?id=CwT5BNG0-owC

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Microphysics of Cosmic Plasmas

André Balogh , Andrei Bykov , Peter Cargill, Richard Dendy, Thierry Dudok de Wit , John Raymond

Book Description

This title presents a review of the detailed aspects of the physical processes that underlie the observed properties, structures and dynamics of cosmic plasmas. An assessment of the status of understanding of microscale processes in all astrophysical collisionless plasmas is provided. The topics discussed include turbulence in astrophysical and solar system plasmas as a phenomenological description of their dynamic properties on all scales; observational, theoretical and modelling aspects of collisionless magnetic reconnection; the formation and dynamics of shock waves; and a review and assessment of microprocesses, such as the hierarchy of plasma instabilities, non-local and non-diffusive transport processes and ionisation and radiation processes. In addition, some of the lessons that have been learned from the extensive existing knowledge of laboratory plasmas as applied to astrophysical problems are also covered. This volume is aimed at graduate students and researchers active in the areas of cosmic plasmas and space science. Originally published in Space Science Reviews journal, Vol. 278/2-4, 2013.

More information on this book can be found by the following link:

http://www.springer.com/astronomy/extraterrestrial+physics,+space+sciences/book/978-1-4899-7412-9

 

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The Realization Problem for Positive and Fractional Systems (Studies in Systems, Decision and Control)

Tadeusz Kaczorek, Lukasz Sajewski

Book Description

This book addresses the realization problem of positive and fractional continuous-time and discrete-time linear systems. Roughly speaking the essence of the realization problem can be stated as follows: Find the matrices of the state space equations of linear systems for given their transfer matrices. This first book on this topic shows how many well-known classical approaches have been extended to the new classes of positive and fractional linear systems. The modified Gilbert method for multi-input multi-output linear systems, the method for determination of realizations in the controller canonical forms and in observer canonical forms are presented. The realization problem for linear systems described by differential operators, the realization problem in the Weierstrass canonical forms and of the descriptor linear systems for given Markov parameters are addressed. The book also presents a method for the determination of minimal realizations of descriptor linear systems and an extension for cone linear systems. This monographs summarizes recent original investigations of the authors in the new field of the positive and fractional linear systems.

More information on this book can be found by the following link:

http://www.amazon.com/Realization-Problem-Positive-Fractional-Decision/dp/3319048333/ref=sr_1_4?s=books&ie=UTF8&qid=1392363403&sr=1-4&keywords=fractional+model

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Spectral and High Order Methods for Partial Differential Equations

---- ICOSAHOM 2012: Selected papers from the ICOSAHOM conference, June 25-29, 2012, in Computational Science and Engineering)

Book Description

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2012), and provides an overview of the depth and breath of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.

More information on this book can be found by the following link:

http://www.springer.com/mathematics/computational+science+&+engineering/book/978-3-642-15336-5

 

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 Journals

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Entropy

Volume 16, Issue 1(partial)

Entropy and Equilibria in Competitive Systems

A. Y. Klimenko

What is a Multiscale Problem in Molecular Dynamics?

Luigi Delle Site

Computing Equilibrium Free Energies Using Non-Equilibrium Molecular Dynamics

Christoph Dellago and Gerhard Hummer

Nonadiabatic Molecular Dynamics Based on Trajectories

by Felipe Franco de Carvalho, Marine E. F. Bouduban, Basile F. E. Curchod and Ivano Tavernelli

Approximating Time-Dependent Quantum Statistical Properties

by Sara Bonella and Giovanni Ciccotti

Analysis of Time Reversible Born-Oppenheimer Molecular Dynamics

by Lin Lin, Jianfeng Lu and Sihong Shao

Time Integrators for Molecular Dynamics

by Nawaf Bou-Rabee

Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration

Cameron Abrams and Giovanni Bussi

Correlation Functions in Open Quantum-Classical Systems

Chang-Yu Hsieh and Raymond Kapral

Malliavin Weight Sampling: A Practical Guide

Patrick B. Warren and Rosalind J. Allen

Dynamical Non-Equilibrium Molecular Dynamics

Giovanni Ciccotti and Mauro Ferrario

Markov State Models for Rare Events in Molecular Dynamics

Marco Sarich, Ralf Banisch, Carsten Hartmann and Christof Schütte

First Principles Methods: A Perspective from Quantum Monte Carlo

Miguel A. Morales, Raymond Clay, Carlo Pierleoni and David M. Ceperley

Modeling Potential Energy Surfaces: From First-Principle Approaches to Empirical Force Fields

Pietro Ballone

Characterization of Rare Events in Molecular Dynamics

Carsten Hartmann, Ralf Banisch, Marco Sarich, Tomasz Badowski and Christof Schütte

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

Xiaobing Zhou, Lianglin Xiong and Xiaomei Cai

A Novel Approach to Extracting Casing Status Features Using Data Mining

Jikai Chen, Haoyu Li, Yanjun Wang, Ronghua Xie and Xingbin Liu

Nanomechanical Properties and Deformation Behaviors of Multi-Component (AlCrTaTiZr)NxSiy High-Entropy Coatings

Shao-Yi Lin, Shou-Yi Chang, Chia-Jung Chang and Yi-Chung Huang

Quantifying Compressibility and Slip in Multiparticle Collision (MPC) Flow Through a Local Constriction

Tahmina Akhter and Katrin Rohlf

Entropy Estimation of Generalized Half-Logistic Distribution (GHLD) Based on Type-II Censored Samples

Jung-In Seo and Suk-Bok Kang

Dynamics of Correlation Structure in Stock Market

Maman Abdurachman Djauhari and Siew Lee Gan

Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

Omar Abu Arqub, Ahmad El-Ajou, Zeyad Al Zhour and Shaher Momani

 

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Computers & Mathematics with Applications

Volume 67, Issue 1(partial)

Convergence analysis of a new multiscale finite element method for the stationary Navier–Stokes problem

Juan Wen, Yinnian He

A simple solution of the Bratu problem

A.    Mohsen

A novel model for biofilm growth and its resolution by using the hybrid immersed interface-level set method

Patricio Cumsille, Juan A. Asenjo, Carlos Conca

The effect of mixed convection on particle laden flow analysis in a cavity using a Lattice Boltzmann method

Che Sidik Nor Azwadi, Leila Jahanshaloo, Arman Safdari

Unconditionally stable numerical method for a nonlinear partial integro-differential equation

Nisha Sharma, Kapil K. Sharma

A penalty method for a fractional order parabolic variational inequality governing American put option valuation

Wen Chen, Song Wang

Stokes equations with small parameters in half plane

Veli B. Shakhmurov

Efficient numerical solution of discrete multi-component Cahn–Hilliard systems

P. Boyanova, M. Neytcheva

An equation error approach for the elasticity imaging inverse problem for predicting tumor location

E. Crossen, M.S. Gockenbach, B. Jadamba, A.A. Khan, B. Winkler

Nonnegative splittings for rectangular matrices

Debasisha Mishra

Weak solution of the equation for a fractional porous medium with a forcing term

Mingshu Fan, Shan Li, Lei Zhang

Hopf bifurcation in spatially homogeneous and inhomogeneous autocatalysis models

Gaihui Guo, Bingfang Li, Xiaolin Lin

Time-fractional heat equations and negative absolute temperatures

Wei Zhang, Xing Cai, Sverre Holm

Stability analysis for Zakharov–Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma

A.R. Seadawy

Coupling discontinuous Galerkin discretizations using mortar finite elements for advection–diffusion–reaction problems

Mi-Young Kim, Mary F. Wheeler

Minimizing synchronizations in sparse iterative solvers for distributed supercomputers

Sheng-Xin Zhu, Tong-Xiang Gu, Xing-Ping Liu

Numerical approximation of time evolution related to Ginzburg–Landau functionals using weighted Sobolev gradients

Nauman Raza, Sultan Sial, Asma Rashid Butt

A Nyström flavored Calderón Calculus of order three for two dimensional waves, time-harmonic and transient

Víctor Domínguez, Sijiang L. Lu, Francisco-Javier Sayas

 

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Journal of Applied Nonlinear Dynamics

Volume 2, Issue 3 & 4

https://lhscientificpublishing.com/journals/JAND-Download.aspx

 

Front/Back Materials

CRONE Control : Principles, Extensions and Applications

A. Oustaloup, P. Lanusse, J. Sabatier, and P. Melchior

Fuzzy Fractional Neural Network Approximation by Fuzzy Quasi-interpolation Operators

George A. Anastassiou

Modal Method for Solving the Nonlinear Sloshing of Two Superposed Fluids in a Rectangular Tank

Bachir Meziani and Ouerdia Ourrad

Numerical Study on Bray-Liebhafsky Oscillatory Reaction: Bifurcations

Branislav Stankovi ́c, Zˇeljko C ̆upi ́c, Nataˇsa Peji ́c and Ljiljana Kolar-Ani ́c

Bistability and Bursting Oscillations in Electromechanical Butterfly Valves

C.A. Kitio Kwuimy and C. Nataraj  

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Front/Back Materials

The Effect of Slow Flow Dynamics on the Oscillations of a Singular Damped System with an Essentially Nonlinear Attachment

J.O. Maaita, E. Meletlidou, A.F. Vakakis, and V. Rothos

Fractional Order Level Control of a System with Communicating Vessels

Cosmin Copot, Clara M. Ionescu, and Robin De Keyser

Model Reduction of Nonlinear Continuous Shallow Arch and Dynamic Buckling Simulations on Approximate Inertial Manifolds with Time Delay

Jiazhong Zhang, Liying Chen, and Sheng Ren

Control of a Hydro-electromechanical System Using Fractional-order Controllers: A Comparative Study

Roy Abi Zeid Daou, Xavier Moreau, and Clovis Francis

 Chatter Dynamics on Impulse Surfaces in Impulsive Differential Systems

Shasha Zheng, Xilin Fu

Vibrational Resonance in a Duffing System with a Generalized Delayed Feedback

J.H. Yang, Miguel A.F. Sanjuán, C.J. Wang, and H. Zhu

Fractional Differential Equations System for Commercial Fishing under Predator-Prey Interaction

G.H. Erjaee, M.H. Ostadzad, K. Okuguchi, and E. Rahimi

 

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 Paper Highlight
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Generalization of a theoretical basis for the application of fractional calculus to viscoelasticity

Andrew W. Wharmby, Ronald L. Bagley

Publication information: Andrew W. Wharmby, Ronald L. Bagley. Generalization of a theoretical basis for the application of fractional calculus to viscoelasticity. J. Rheol. 57, 1429 (2013);  http://scitation.aip.org/content/sor/journal/jor2/57/5/10.1122/1.4819083

Abstract

This work investigates the effect a fractional derivative may have on the spectrum of relaxation modes of a viscoelastic material. It is shown that the order of the fractional derivative results in a modification to the constitutive relationships that exist within the Rouse model forviscoelasticity. These relationships that are used in engineering analyses have been previously developed from an empirical standpoint. The resulting modification to these constitutive relationships further supports the inclusion of fractional calculus in models of viscoelastic materials and hence increase their level of confidence associated with their usage.

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A Matlab toolbox for positive fractional time derivative modeling of arbitrarily frequency-dependent viscosity

Wei Cai, Wen Chen, Xiaodi Zhang

Publication information: Wei Cai, Wen Chen, Xiaodi Zhang, A Matlab toolbox for positive fractional time derivative modeling of arbitrarily frequency-dependent viscosity, Journal of Vibration and Control, 2013, 1077546313479636.   http://jvc.sagepub.com/content/early/2013/05/07/1077546313479636.abstract

Abstract

The symmetric fractional derivative is introduced and its properties are studied. The Euler-Lagrange equations for models depending on sequential derivatives of type are derived using minimal action principle. The Hamiltonian for such systems is introduced following methods of classical generalized mechanics and the Hamilton’s equations are obtained. It is explicitly shown that models of fractional sequential mechanics are non-conservative. The limiting procedure recovers classical generalized mechanics of systems depending on higher order derivatives. The method is applied to fractional deformation of harmonic oscillator and to the case of classical frictional force proportional to velocity.

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Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena

A.J. Majda, P.R. Kramer

Publication information: A.J. Majda, P.R. Kramer. Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena. Physics Reports, 1999, 314: 237-574. http://www.sciencedirect.com/science/article/pii/S0370157398000830

Abstract

Several simple mathematical models for the turbulent diffusion of a passive scalar field are developed here with an emphasis on the symbiotic interaction between rigorous mathematical theory (including exact solutions), physical intuition, and numerical simulations. The homogenization theory for periodic velocity fields and random velocity fields with short-range correlations is presented and utilized to examine subtle ways in which the flow geometry can influence the large-scale effective scalar diffusivity. Various forms of anomalous diffusion are then illustrated in some exactly solvable random velocity field models with long-range correlations similar to those present in fully developed turbulence. Here both random shear layer models with special geometry but general correlation structure as well as isotropic rapidly decorrelating models are emphasized. Some of the issues studied in detail in these models are superdiffusive and subdiffusive transport, pair dispersion, fractal dimensions of scalar interfaces, spectral scaling regimes, small-scale and large-scale scalar intermittency, and qualitative behavior over finite time intervals. Finally, it is demonstrated how exactly solvable models can be applied to test and design numerical simulation strategies and theoretical closure approximations for turbulent diffusion.

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