FDA Express

Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion ProThis 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.springer.com/engineering/control/book/978-3-319-04833-8

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Fractional Derivatives for Physicists and Engineers

Uchaikin Vladimir V

Book Description

The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics.

The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular.

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

http://www.springer.com/physics/theoretical,+mathematical+&+computational+physics/book/978-3-642-33910-3

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Journals

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Entropy

Volume 16, Issue 6

Reaction Kinetics Path Based on Entropy Production Rate and Its Relevance to Low-Dimensional Manifolds

Shinji Kojima

Information Geometric Complexity of a Trivariate Gaussian Statistical Model

Domenico Felice, Carlo Cafaro and Stefano Mancini

How to Determine Losses in a Flow Field: A Paradigm Shifttowards the Second Law Analysis

Heinz Herwig and Bastian Schmandt

Constraints of Compound Systems: Prerequisites for Thermodynamic Modeling Based on Shannon Entropy

Martin Pfleger, Thomas Wallek and Andreas Pfennig

Tsallis Wavelet Entropy and Its Application in Power Signal Analysis

Jikai Chen and Guoqing Li

Asymptotically Constant-Risk Predictive Densities When the Distributions of Data and Target Variable Are Different

by Keisuke Yano and Fumiyasu Komaki

Using Permutation Entropy to Measure the Changes in EEG Signals During Absence Seizures

Jing Li, Jiaqing Yan, Xianzeng Liu and Gaoxiang Ouyang

Entropy Content During Nanometric Stick-Slip Motion

Paul Creeger and Fredy Zypman

Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions

Samuel Livingstone and Mark Girolami

Analysis and Optimization of a Compressed Air Energy Storage—Combined Cycle System

Wenyi Liu, Linzhi Liu, Luyao Zhou, Jian Huang, Yuwen Zhang, Gang Xu and Yongping Yang

Quantum Flows for Secret Key Distribution in the Presence of the Photon Number Splitting Attack

Luis A. Lizama-Pérez, J. Mauricio López, Eduardo De Carlos-López and Salvador E. Venegas-Andraca

Minimum Entropy-Based Cascade Control for Governing Hydroelectric Turbines

Mifeng Ren, Di Wu, Jianhua Zhang and Man Jiang

A Derivation of a Microscopic Entropy and Time Irreversibility From the Discreteness of Time

Roland Riek

Relative Entropy, Interaction Energy and the Nature of Dissipation

Bernard Gaveau, Léo Granger, Michel Moreau and Lawrence S. Schulman

On the Fisher Metric of Conditional Probability Polytopes

Guido Montúfar, Johannes Rauh and Nihat Ay

On Spatial Covariance, Second Law of Thermodynamics and Configurational Forces in Continua

Vassilis P. Panoskaltsis and Dimitris Soldatos

Density Reconstructions with Errors in the Data

Erika Gomes-Gonçalves, Henryk Gzyl and Silvia Mayoral

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Nonlinear dynamics

Volume 76, Issue 4

Hyperchaos synchronization of fractional-order arbitrary dimensional dynamical systems via modified sliding mode control

Ling Liu, Wen Ding, Chongxin Liu, Huigang Ji, Chuqing Cao

Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity

Leipo Liu, Jiexin Pu, Xiaona Song, Zhumu Fu, Xiaohong Wang

Primary and secondary resonance analyses of clamped–clamped micro-beams

D. Younesian, M. Sadri, E. Esmailzadeh

Nonlinear vibrations of a single-walled carbon nanotube for delivering of nanoparticles

Keivan Kiani

Highly efficient nonlinear energy sink

Mohammad A. AL-Shudeifat

The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets

Yun Zeng, Lixiang Zhang, Yakun Guo, Jing Qian, Chenli Zhang

Types of coefficient constraints of coupled nonlinear Schrödinger equations for elastic and inelastic interactions between spatial solitons with symbolic computation

Wen-Jun Liu, Ming Lei

A new image alternate encryption algorithm based on chaotic map

Xingyuan Wang, Kang Guo

Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice

Jun Ma, Xinyi Wu, Runtong Chu, Liping Zhang

Bifurcation analysis of a nonlinear pendulum using recurrence and statistical methods: applications to fault diagnostics

C. A. Kitio Kwuimy, M. Samadani, C. Nataraj

Actuator fault diagnosis for uncertain T–S fuzzy systems with local nonlinear models

Huimin Wang, Dan Ye, Guang-Hong Yang

Algebraic analysis of a RGB image encryption algorithm based on DNA encoding and chaotic map

Akram Belazi, Houcemeddine Hermassi, Rhouma Rhouma, Safya Belghith

Postbuckling instability of nonlinear nanobeam with geometric imperfection embedded in elastic foundation

Hossein Mohammadi, Mojtaba Mahzoon, Mohsen Mohammadi…

A new car-following model with consideration of inter-vehicle communication

Tieqiao Tang, Weifang Shi, Huayan Shang, Yunpeng Wang

Nonlinear behavior analysis of geared rotor bearing system featuring confluence transmission

Haodong Gao, Yidu Zhang

Distributed proportional plus second-order spatial derivative control for distributed parameter systems subject to spatiotemporal uncertainties

Jun-Wei Wang, Han-Xiong Li, Huai-Ning Wu

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Paper Highlight
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Nondiffusive Transport in Plasma Turbulence: A Fractional Diffusion Approach

Nondiffusive Transport in Plasma Turbulence: A Fractional Diffusion Approach

Publication information: D. del-Castillo-Negrete, B. A. Carreras, and V. E. Lynch. Nondiffusive Transport in Plasma Turbulence: A Fractional Diffusion Approach. Physical Review Letters, 94, 065003 (2005).

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.94.065003

Abstract

Numerical evidence of nondiffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of tracer particles’ radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time that incorporate in a unified way space-time nonlocality (non-Fickian transport), non-Gaussianity, and nondiffusive scaling. The fractional diffusion model reproduces the shape and space time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed superdiffusive scaling.

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Multifractality of the Feigenbaum Attractor and Fractional Derivatives

U. Frisch, K. Khanin and T. Matsumoto

Publication information: U. Frisch, K. Khanin and T. Matsumoto. Multifractality of the Feigenbaum Attractor and Fractional Derivatives. Journal of Statistical Physics, 2005, 121(5/6), 671-695.

http://link.springer.com/article/10.1007/s10955-005-7011-4

Abstract

It is shown that fractional derivatives of the (integrated) invariant measure of the Feigenbaum map at the onset of chaos have power-law tails in their cumulative distributions, whose exponents can be related to the spectrum of singularities (f(α). This is a new way of characterizing multifractality in dynamical systems, so far applied only to multifractal random functions [Frisch and Matsumoto, J. Stat. Phys. 108:1181, 2002]. The relation between the thermodynamic approach [Vul, Sinai and Khanin, Russian Math. Surveys 39:1, 1984] and that based on singularities of the invariant measures is also examined. The theory for fractional derivatives is developed from a heuristic point view and tested by very accurate simulations.

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