FDA Express Vol. 5, No. 5, Dec. 15, 2012
Editors:
W. Chen H.G. Sun
H. Wei
S. Hu
Institute of Soft Matter Mechanics, Hohai University
For contribution: fdaexpress@163.com,
fdaexpress@hhu.edu.cn
For subscription:
http://em.hhu.edu.cn/fda/subscription.htm
◆ Latest SCI Journal Papers on FDA
◆ Conferences
Fractional Calculus in Vibration and Acoustics
◆ Call for Paper
◆ Books
Soft Solids: A Primer to the Theorical Mechanics of Materials
◆ Journals
Fractional Calculus &
Application Analysis
Chaos
Journal of
Computational and Nonlinear Dynamics
◆ Paper Highlight
Anomalous diffusion expressed through fractional order differential operators in
the Bloch–Torrey equation
Fractional Laplacian time-space models for linear and nonlinear lossy media
exhibiting arbitrary frequency power-law dependency
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Latest
SCI Journal Papers on FDA
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Title:
A numerical technique for solving a class of
fractional variational problems
Author(s): Lotfi, A.; Yousefi, S. A.
Source: JOURNAL OF COMPUTATIONAL AND APPLIED
MATHEMATICS Volume: 237 Issue: 1 Pages: 633-643 DOI:
10.1016/j.cam.2012.08.005 Published: JAN 1 2013
Title:
Image encryption algorithm by using
fractional Fourier transform and pixel scrambling operation based on double
random phase encoding
Author(s): Liu, Zhengjun; Li, She; Liu, Wei; et al.
Source: OPTICS AND LASERS IN ENGINEERING Volume: 51 Issue:
1 Pages: 8-14 DOI: 10.1016/j.optlaseng.2012.08.004 Published: JAN 2013
Title:
Fractional stochastic differential equations
with applications to finance
Author(s): Nguyen Tien Dung
Source: JOURNAL OF MATHEMATICAL ANALYSIS AND
APPLICATIONS Volume: 397 Issue: 1 Pages: 334-348 DOI:
10.1016/j.jmaa.2012.07.062 Published: JAN 1 2013
Title:
Simulation of Infinitely Divisible Random
Fields
Author(s): Karcher, Wolfgang; Scheffler, Hans-Peter; Spodarev,
Evgeny
Source: COMMUNICATIONS IN STATISTICS-SIMULATION AND
COMPUTATION Volume: 42 Issue: 1 Pages: 215-246 DOI:
10.1080/03610918.2011.634536 Published: 2013
Title:
Modified fractional Euler method for solving
Fuzzy Fractional Initial Value Problem
Author(s): Mazandarani, Mehran; Kamyad, Ali Vahidian
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL
SIMULATION Volume: 18 Issue: 1 Pages: 12-21 DOI:
10.1016/j.cnsns.2012.06.008 Published: JAN 2013
Title:
A semi-analytical method for the computation
of the Lyapunov exponents of fractional-order systems
Author(s): Caponetto, Riccardo; Fazzino, Stefano
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL
SIMULATION Volume: 18 Issue: 1 Pages: 22-27 DOI:
10.1016/j.cnsns.2012.06.013 Published: JAN 2013
Title:
Generalized anti-periodic boundary value
problems of impulsive fractional differential equations
Author(s): Li, Xiaoping; Chen, Fulai; Li, Xuezhu
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL
SIMULATION Volume: 18 Issue: 1 Pages: 28-41 DOI:
10.1016/j.cnsns.2012.06.014 Published: JAN 2013
Title:
The fractional q-differential transformation
and its application
Author(s): El-Shahed, Moustafa; Gaber, Mohammed; Al-Yami,
Maryam
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL
SIMULATION Volume: 18 Issue: 1 Pages: 42-55 DOI:
10.1016/j.cnsns.2012.06.016 Published: JAN 2013
Title:
Wave propagation in nonlocal
elastic continua modelled by a fractional calculus approach
Author(s): Sapora, Alberto; Cornetti, Pietro; Carpinteri,
Alberto
Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL
SIMULATION Volume: 18 Issue: 1 Pages: 63-74 DOI:
10.1016/j.cnsns.2012.06.017 Published: JAN 2013
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Conferences
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Fractional Calculus in Vibration and Acoustics
at the ASME International Design
Engineering Technical Conferences (IDETC) 25th.Conference on Mechanical
Vibration and Noise (VIB) in Portland, Oregon Aug. 4 - 7, 2013.
(Contributed by Prof. Francesco
Mainardi)
Dear Colleagues,
Please forward to others who may be
interested. We bring your attention to the following and invite your
submissions.
1)
There will be a special symposium on "Fractional Calculus in Vibration and
Acoustics" held at the ASME International Design Engineering Technical
Conferences (IDETC) 25th.Conference on Mechanical Vibration and Noise
(VIB) in Portland, Oregon Aug. 4 - 7, 2013.
Abstracts due Jan. 7, 2013 and
papers due Jan. 21, 2013. Information about the special session and how to
submit papers can be found at:
http://www.asmeconferences.org/IDETC2013/
Please click the link on "25th
Conference on Vibration and Noise" and you will see our symposium listed VIB-12.
2)
Authors of exceptional conference submissions to (1) above will also be invited
to expand upon and improve their manuscript for inclusion in a special issue of
the ASME Journal of Vibration and Acoustics guest-edited by the organizers of
this symposium(listed below). See:
http://www.asmedl.org/VibrationAcoustics and choose the link Submit Papers.
Next, select the Journal of Vibration and Acoustics and then choose the Special
Issue option for "Fractional Calculus in Vibration and Acoustics". Journal
manuscript submissions can be taken at any time up to the deadline of April 30,
2013. The target date for all articles to be accepted is August 30, 2013 and the
target publication date is December 2013 or early 2014. Note, participation in
the conference is not mandatory for submission of a manuscript for the special
issue of the journal. However, we hope you will consider submitting to both.
Sincerely,
The symposium and special issue
organizers/co-editors:
Dieter Klatt, University of Illinois
at Chicago, IL
dklatt@uic.edu
Richard L. Magin, University of
Illinois at Chicago, IL
rmagin@uic.edu
Francesco Mainardi, University of
Bologna, Italy
mainardi@bo.infn.it
Thomas J. Royston, University of
Illinois at Chicago
troyston@uic.edu
=================================
Thomas J. Royston, PhD
Professor and Head, Dept. of
Bioengineering
College of Medicine,College of
Engineering
The University of Illinois at
Chicago
851 South Morgan St. 218 SEO, MC 063
Chicago,
IL 60607-7052
www.bioe.uic.edu
Adjunct Professor, Dept. of
Mechanical & Industrial Engineering Associate Editor, ASME Journal of Vibration
& Acoustics
==========================================================================
Call for Paper
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ASME Journal of
Vibration and Acoustics Special Issue on:
Fractional Calculus in Vibration and Acoustics
(Contributed by Prof. Francesco Mainardi)
Background, Scope and Motivation
The classical acoustic models
(linear and nonlinear) of vibration involve systems of ordinary and partial
differential equations of integer order. Interpolation between first and second
order models, for example, is possible using the tools of fractional calculus
(integration and differentiation of arbitrary real order). Such tools are
increasingly being applied to model the dynamics of complex materials and
systems in mechanics, acoustics, and bioengineering. This special issue is
motivated by our desire to bring together in one place a collection of articles
that describe both the depth and breadth of fractional analysis in vibration and
acoustics. We invite researchers in the field to share their expertise and
knowledge so that others can learn how to apply fractional calculus in their
work. We seek both fundamental and applied studies spanning discrete and
continuous systems and that involve fractional derivatives defined in both space
and in time.
Fractional derivatives in time: A wide range of viscoelastic models have been proposed to interpret oscillatory motion in continuous and discrete systems. These constitutive models attempt to relate measurable phenomena to the underlying elasticity and damping of the material, both of which are typically rate (frequency) dependent. Historically, this area was first explored through the development of the ‘so‐called’ spring‐pot dynamic model, which is simply a fractional order conflation of the spring and the dashpot. Since then, many studies have extended the model by adding the spring‐pot as an element in a generalized Voigt model or Maxwell model of viscoelasticity. Such models have limitations, but in general they accurately capture dynamic phenomena over multiple time scales and/or systems with broad spectral content, particularly for biological tissues and polymeric materials comprised of long chain molecules. For example, in medicine, fractional order viscoelastic models provide new disease and treatment specific biomarkers (via, elastographic imaging) that more effectively predict underlying changes in tissue associated with developing pathology, such as liver cirrhosis and breast cancer.
Fractional derivatives in space: In principle, the wave equation can be generalized in both space and in time. The fractional order space derivatives provide specific information on nonlocal variation of material properties that influence particle motion and vibration. Surprisingly, analytical solutions to the fractional order wave equation are possible and recently, they have been applied to model both the propagation and the damping of vibrations in complex, porous and heterogeneous materials. Applications in materials testing, in vibration damping and in acoustic modeling of the lung have been published; but, the utility of this approach is not widely publicized. Another goal of this special issue is to introduce the analytical and numerical methods now available for analyzing vibration in complex materials. While the applied mathematics community and many other application‐driven researchers in mechanical engineering have begun to embrace fractional calculus – as a tool to model multiscale, complex systems – many researchers in fields of acoustics and vibrations are largely unaware of the potential impact of this advancement in analysis tools. For this reason, the ASME Journal of Vibration and Acoustics intends to publish a special issue dedicated to fractional calculus in vibration and acoustics. The goal is to bring this topic to the attention of the JVA community and beyond that, to encourage a wider interest and awareness of this powerful analytical tool.
Timeline
Deadline for submission: April 30,
2013
Target date for all Articles to be
accepted: August 30, 2013
Target publication date: December
2013 or early 2014
It is recognized that
it often takes longer to complete the review of a manuscript than expected. All
contributions accepted by August 30, 2013 are guaranteed to be included in the
special issue. Submissions that receive final acceptance after this date will be
published in a subsequent regular issue. The best strategy to increase the
chance of publication in the special issue is to submit as early as possible,
even before the April 30, 2013 deadline if possible.
Submission Information
To submit a manuscript for
consideration for the special issue, please visit the journal website at:
http://www.asmedl.org/VibrationAcoustics
and choose the link Submit Papers. Next, select the Journal of Vibration and
Acoustics and then choose the Special Issue option for “Fractional
Calculus in Vibration and Acoustics”.
Guest Associate Editors
Dieter Klatt, University of
Illinois at Chicago, IL
dklatt@uic.edu
Richard L. Magin, University of
Illinois at Chicago, IL
rmagin@uic.edu
Francesco Mainardi, University of
Bologna, Italy mainardi@bo.infn.it
Associate Editor
Thomas J. Royston, University of
Illinois at Chicago
troyston@uic.edu
Editor
Noel
C. Perkins, University of Michigan‐Ann
Arbor
ncp@umich.edu
Potential Contributors:
1) R. L. Magin,
Fractional Calculus
in Biomechanics and
Elastography
2) T. J. Royston,
Fractional Calculus
in Acoustics and Vibration
3) D. Klatt, Elastography and
Fractional Order Modeling
4) F. Mainardi,
Fractional Calculus
of Waves and Relaxation
5) M. B. Ozer,
Fractional Calculus
vibration absorber
optimization
6) Y. Yazicioglu
Fractional Calculus
models in viscoelasticity
7) S. P. Näsholm,
Fractional Calculus in Ultrasound
8) A. Shieh, Tumor
Biomechanics
9) T. Pritz,
Fractional Calculus Models in Viscoelasticity
10) O. Agrawal,
Fractional Calculus Models of Complex Materials
11) J. L. Adams,
Fractional Calculus Models
12) B. Vinagre,
Fractional Order Control of Vibration
13) N. Heymans,
Fractional Calculus Models of Discrete FO Elements
14) W. Chen,
Fractional Order Models of Materials
15) R. Gorenflo,
Fractional Order Models
16) J.A. Machado,
Fractional Order Control
17) B. Stabkovic,
Fractional Order Viscoelacticity
18) T. Atanackovic,
Fractional Order Viscoelacticity
19) J.S. Leszczynski,
Fractional Mechanics
20) I. Petras,
Fractional Control and Numerical Modeling
21) Y. Luchko,
Fractional Order Models of Materials
22) I. Podlubny,
Fractional Order Differential Equations
23) Y.Q. Chen,
Fractional Order Control
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Soft Solids: A Primer to the Theorical Mechanics of Materials
Alan D. Freed PhD (Author), Beth Jorgensen (Editor), Alyssa Hopps (Cover Design)
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Vol. 16, No 1 (2013)
CONTENTS
Editorial:
FCAA RELATED MEETINGS AND NEWS
(FCAA-Volume 16-1-2013)
ON A FRACTIONAL ZENER ELASTIC WAVE EQUATIO
N
GREEN'S THEOREM FOR GENERALIZED FRACTIONAL DERIVATIVES
T. Odzijewicz,
A.B. Malinowska, D.F.M. Torres
ANALYSIS AND SHAPING OF THE SELF-SUSTAINED
OSCILLATIONS IN RELAY CONTROLLED FRACTIONAL-ORDER SYSTEMS
R. Caponetto,
G. Maione, A. Pisano, M.R. Rapaic, E. Usai
NUMERICS FOR THE FRACTIONAL LANGEVIN EQUATION DRIVEN BY THE FRACTIONAL BROWNIAN
MOTION
P. Guo, C.B. Zeng, C.P. Li, Y.Q.
Chen
MICROSCOPIC MODEL OF DIELECTRIC
α-RELAXATION
IN DISORDERED MEDIA
A.A. Khamzin, R.R. Nigmatullin,
I.I. Popov, B.A. Murzaliev
BOUNDS ON THE SOLUTION OF A CAUCHY-TYPE PROBLEM INVOLVING A WEIGHTED SEQUENTIAL FRACTIONAL DERIVATIVE
K.M. Furati
STOCHASTIC DYNAMICS AND FRACTIONAL OPTIMAL CONTROL OF QUASI INTEGRABLE
HAMILTONIAN SYSTEMS WITH FRACTIONAL DERIVATIVE DAMPING
L.C. Chen, F. Hu, W.Q. Zhu
WELL-POSEDNESS FOR THE NONLINEAR FRACTIONAL SCHRÄODINGER EQUATION AND INVISCID LIMIT BEHAVIOR OF SOLUTION FOR THE FRACTIONAL GINZBURG-LANDAU EQUATION
B. Guo, Z. Huo
REFLECTION SYMMETRIC FORMULATION OF GENERALIZED FRACTIONAL VARIATIONAL CALCULUS
M. Klimek, M. Lupa
FRACTIONAL WAVE EQUATIONS WITH ATTENUATION
P. Straka, M.M. Meerschaert, R.J. McGough, Y. Zhou
DIFFERENTIATION
SIMILARITIES IN FRACTIONAL PSEUDO-STATE SPACE REPRESENTATIONS AND THE
SUBSPACE-BASED METHODS
R. Malti, M. Thomassin
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Volume 22, Issue 4, December 2012
Shape analysis using fractal dimension: A curvature based approach
Reduced dynamics for delayed systems with harmonic or stochastic forcing
Effects of weak ties on epidemic predictability on community networks
Outer synchronization between two complex dynamical networks with discontinuous coupling
Convergence time and speed of multi-agent systems in noisy environments
Dynamical topology and statistical properties of spatiotemporal chaos
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Volume 8, Issue 3
A Model for Highly Strained DNA Compressed Inside a Protein CavityModeling of a Flexible Instrument to Study its Sliding Behavior Inside a Curved Endoscope
Effect of Noise on Generalized Synchronization: An Experimental Perspective
A Continuum Based Three-Dimensional Modeling of Wind Turbine Blades
Adaptive Sliding Mode Control for Synchronization of a Fractional-Order Chaotic System
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Volume 46, In Progress (January 2013)
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Richard L. Magin, Osama Abdullah, Dumitru Baleanu, Xiaohong Joe Zhou
Publication information: Richard L. Magin, Osama Abdullah, Dumitru Baleanu, Xiaohong Joe Zhou. Anomalous diffusion expressed through fractional order differential operators in the Bloch–Torrey equation. Journal of Magnetic Resonance 190 (2008) 255–270.
http://www.sciencedirect.com/science/article/pii/S1090780707003473#
Abstract
Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on diffusion-weighted pulse sequences to probe biophysical models of molecular diffusion—typically exp[−(bD)]—where D is the apparent diffusion coefficient (mm2/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model—exp[−(bD)α], where α is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch–Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch–Torrey equation is replaced by a Riemann–Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology.
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W. Chen, S. Holm
Publication information: W. Chen, S. Holm. Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency. J. Acoust. Soc. Am. 115 (4), April 2004, 1424–1430
http://link.aip.org/link/jasman/v115/i4/p1424/s1
Abstract
Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often called the anomalous attenuation. In this study, a linear integro-differential equation wave model was developed for the anomalous attenuation by using the space-fractional Laplacian operation, and the strategy is then extended to the nonlinear Burgers equation. A new definition of the fractional Laplacian is also introduced which naturally includes the boundary conditions and has inherent regularization to ease the hypersingularity in the conventional fractional Laplacian. Under the Szabo’s smallness approximation, where attenuation is assumed to be much smaller than the wave number, the linear model is found consistent with arbitrary frequency power-law dependency.
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The End of This Issue
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