FDA Express

The study of fluctuations in statistical physics has a long history, and a general theory is well established, connecting fluctuations to response properties of equilibrium systems. Remarkably, this framework fails as soon as some current is flowing across the system, driving it out of equilibrium.

The presence of currents is quite common in nature and produces rich phenomena which are far from being included in a general framework. This thesis focuses on this general problem by studying different models such as granular materials and systems exhibiting anomalous diffusion and shows how the generalized response techniques can be successfully used to catch the relevant degrees of freedom that drive the systems out of equilibrium.

This study paves the way to the use of the generalized fluctuation relations in an operative way, in order to extract information from a non-equilibrium system and to build the corresponding phenomenological theory.

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

http://www.springer.com/physics/complexity/book/978-3-319-01771-6

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Limits, Series, and Fractional Part Integrals

Furdui, Ovidiu

Book Description

Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis features original problems in classical analysis that invite the reader to explore a host of strategies and mathematical tools used for solving real analysis problems. The book is designed to fascinate the novice, puzzle the expert, and trigger the imaginations of all. The text is geared toward graduate students in mathematics and engineering, researchers, and anyone who works on topics at the frontier of pure and applied mathematics. Moreover, it is the first book in mathematical literature concerning the calculation of fractional part integrals and series of various types.

Most problems are neither easy nor standard and deal with modern topics of classical analysis. Each chapter has a section of open problems that may be considered as research projects for students who are taking advanced calculus classes. The intention of having these problems collected in the book is to stimulate the creativity and the discovery of new and original methods for proving known results and establishing new ones.

The book is divided into three parts, each of them containing a chapter dealing with a particular type of problems. The first chapter contains problems on limits of special sequences and Riemann integrals; the second chapter deals with the calculation of special classes of integrals involving a fractional part term; and the third chapter hosts a collection of problems on the calculation of series (single or multiple) involving either a numerical or a functional term.

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

http://www.springer.com/mathematics/analysis/book/978-1-4614-6761-8

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Journals

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Communications in Nonlinear Science and Numerical Simulation

Volume 19, Issue 12

Stochastic resonance in a single-well anharmonic oscillator with coexisting attractors

S. Arathi, S. Rajasekar

The difference between a class of discrete fractional and integer order boundary value problems

Yi Chen, Xianhua Tang

Structure properties of one-mode collaboration network model based on rate equation approach

Long Wang, Yinghong Ma

Detection of quasi-periodic processes in repeated measurements: New approach for the fitting and clusterization of different data

R. Nigmatullin, R. Rakhmatullin

An efficient self-adaptive model for chaotic image encryption algorithm

Xiaoling Huang, Guodong Ye

Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks

Diyi Chen, Runfan Zhang, Xinzhi Liu, Xiaoyi Ma

Global dissipativity of mixed time-varying delayed neural networks with discontinuous activations

Lian Duan, Lihong Huang

Optimal control of information epidemics modeled as Maki Thompson rumors

Kundan Kandhway, Joy Kuri

Stability analysis of dynamic collaboration model with control signals on two lanes

Zhipeng Li, Run Zhang, Shangzhi Xu, Yeqing Qian, Juan Xu

Switching control and time-delay identification

Qi Chen, Xiang Li, Zhi-Chang Qin, Shun Zhong, J.Q. Sun

Spread of a disease and its effect on population dynamics in an eco-epidemiological system

Ranjit Kumar Upadhyay, Parimita Roy

A note on oscillation criteria for second-order neutral dynamic equations on isolated time scales

Tongxing Li, S.H. Saker

An open problem on the optimality of an asymptotic solution to Duffing’s nonlinear oscillation problem

Songxin Liang, Sijia Liu

Multi-harmonic measurements and numerical simulations of nonlinear vibrations of a beam with non-ideal boundary conditions

M. Claeys, J.-J. Sinou, J.-P. Lambelin, B. Alcoverro

Response to “Comments on the concept of existence of solution for impulsive fractional differential equations [Commun Nonlinear Sci Numer Simul 2014;19:401–3.]”

Michal Fec̆kan, Yong Zhou, JinRong Wang

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Computers & Mathematics with Applications

Volume 68, Issue 1-3 (selected)

Convergence analysis of Bernoulli matrix approach for one-dimensional matrix hyperbolic equations of the first order

Emran Tohidi, Faezeh Toutounian

Obtaining artificial boundary conditions for fractional sub-diffusion equation on space two-dimensional unbounded domains

Rezvan Ghaffari, S. Mohammad Hosseini

Free boundary problems and optimal control of axisymmetric polymer crystallization processes

Ramón Escobedo, Luis A. Fernández

An accelerated alternating procedure for the Cauchy problem for the Helmholtz equation

F. Berntsson, V.A. Kozlov, L. Mpinganzima, B.O. Turesson

Structural stability of subsonic irrotational flows in two-dimensional infinitely long nozzles

Mingshu Fan, Shan Li, Lei Zhang

A high-order exponential ADI scheme for two dimensional time fractional convection–diffusion equations

Zhibo Wang, Seakweng Vong

A solution of the parabolized Navier–Stokes stability model in discrete space by two-directional differential quadrature and application to swirl intense flows

Diana A. Bistrian

Trusting computations: A mechanized proof from partial differential equations to actual program

Sylvie Boldo, François Clément, Jean-Christophe Filliâtre, Micaela Mayero, Guillaume Melquiond, Pierre Weis

A global minimization hybrid active contour model with applications to oil spill images

Hui Wang, Ting-Zhu Huang, Ying-Qiong Du

Implicit–explicit methods for models for vertical equilibrium multiphase flow

R. Donat, F. Guerrero, P. Mulet

Monotone iterative technique for the elastic systems with structural damping in Banach spaces

Hongxia Fan, Yongxiang Li

Financial options pricing with regime-switching jump-diffusions

Younhee Lee

Dynamics of a general prey–predator model with prey-stage structure and diffusive effects

Shenghu Xu

D-pullback attractor for a non-autonomous wave equation with additive noise on unbounded domains

Fuqi Yin, Linfang Liu

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Paper Highlight
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Comparision of fractional wave equations for power law attenuation in ultrasound and elastography

Sverre Holm, Sven Peter Nasholm

Publication information: Sverre Holm, Sven Peter Nasholm. Comparision of fractional wave equations for power law attenuation in ultrasound and elastography. Ultrasound in Med. & Biol.40 (2014) 695-703.

http://dx.doi.org/10.1016/j.ultrasmedbio.2013.09.033

Abstract

A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones. (E-mail: sverre@ifi.uio.no)

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Continuous time random walk in homogeneous porous media

Jianguo Jiang, Jichun Wu

Publication information: Jianguo Jiang, Jichun Wu. Continuous time random walk in homogeneous porous media. Journal of Contaminant Hydrology, 155 (2013) 82-86.

http://www.sciencedirect.com/science/article/pii/S0169772213001241

Abstract

Continuous time random walk (CTRW) has been successfully applied in the description of anomalous transport in porous media in recent years.We simulate solute transport in randomly packed spheres with the same diameter and use CTRW to analyze the simulated results. From analysis, we find that there exists weak anomalous transport in the approximately homogeneous porous media. The anomaly becomes more apparent with the increase of Pe. This conclusion consists with previous simulations in two-dimensional homogeneous media and experimental data. We also calculate the trapping probabilities of solute particles in stagnant regions, which could give a physically based explanation for this non-Gaussian behavior.

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Fractional dispersion in a sand bed river

D.N. Bradley , G. E. Tucker and D. A. Benson

Publication information: D.N. Bradley, G. E. Tucker and D. A. Benson (2010), Fractional dispersion in a sand bed river, J. Geophys. Res., 115, F00A09, doi:10.1029/2009JF001268.

http://onlinelibrary.wiley.com/doi/10.1029/2009JF001268/abstract

Abstract

Random walk models of fluvial bed load transport use probability distributions to describe the distance a grain travels during an episode of transport and the time it rests after deposition. These models typically employ probability distributions with finite first and second moments, reflecting an underlying assumption that all the factors that influence sediment transport tend to combine in such a way that the length of a step or the duration of a rest can be characterized by a mean value surrounded by a specific amount of variability. The observation that many transport systems exhibit apparent scale-dependent behavior and non-Fickian dispersion suggests that this assumption is not always valid. We revisit a nearly 50 year old tracer experiment in which the tracer plume exhibits the hallmarks of dispersive transport described by a step length distribution with a divergent second moment and no characteristic dispersive size. The governing equation of this type of random walk contains fractional-order derivatives. We use the data from the experiment to test two versions of a fractional-order model of dispersive fluvial bed load transport. The first version uses a heavy-tailed particle step length distribution with a divergent second moment to reproduce the anomalously high fraction of tracer mass observed in the downstream tail of the spatial distribution. The second version adds a feature that partitions mass into a detectable mobile phase and an undetectable, immobile phase. This two-phase transport model predicts other features observed in the data: a decrease in the amount of detected tracer mass over the course of the experiment and enhanced particle retention near the source. The fractional-order models match the observed plume shape and growth rates better than prior attempts with classical models.

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The End of This Issue

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