Fractional Calculus With Applications For Nuclear Reactor Dynamics

Fractional Calculus With Applications For Nuclear Reactor Dynamics Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Fractional Calculus With Applications For Nuclear Reactor Dynamics book. This book definitely worth reading, it is an incredibly well-written.

Fractional Calculus with Applications for Nuclear Reactor Dynamics

Santanu Saha Ray
Fractional Calculus with Applications for Nuclear Reactor Dynamics Book PDF

Author : Santanu Saha Ray
Publisher : CRC Press
Page : 235 pages
File Size : 45,5 Mb
Release : 2015-07-29
Category : Mathematics
ISBN : 9781498727280

Get Book

Fractional Calculus with Applications for Nuclear Reactor Dynamics by Santanu Saha Ray Pdf

Introduces Novel Applications for Solving Neutron Transport Equations While deemed nonessential in the past, fractional calculus is now gaining momentum in the science and engineering community. Various disciplines have discovered that realistic models of physical phenomenon can be achieved with fractional calculus and are using them in numerous ways. Since fractional calculus represents a reactor more closely than classical integer order calculus, Fractional Calculus with Applications for Nuclear Reactor Dynamics focuses on the application of fractional calculus to describe the physical behavior of nuclear reactors. It applies fractional calculus to incorporate the mathematical methods used to analyze the diffusion theory model of neutron transport and explains the role of neutron transport in reactor theory. The author discusses fractional calculus and the numerical solution for fractional neutron point kinetic equation (FNPKE), introduces the technique for efficient and accurate numerical computation for FNPKE with different values of reactivity, and analyzes the fractional neutron point kinetic (FNPK) model for the dynamic behavior of neutron motion. The book begins with an overview of nuclear reactors, explains how nuclear energy is extracted from reactors, and explores the behavior of neutron density using reactivity functions. It also demonstrates the applicability of the Haar wavelet method and introduces the neutron diffusion concept to aid readers in understanding the complex behavior of average neutron motion. This text: Applies the effective analytical and numerical methods to obtain the solution for the NDE Determines the numerical solution for one-group delayed neutron FNPKE by the explicit finite difference method Provides the numerical solution for classical as well as fractional neutron point kinetic equations Proposes the Haar wavelet operational method (HWOM) to obtain the numerical approximate solution of the neutron point kinetic equation, and more Fractional Calculus with Applications for Nuclear Reactor Dynamics thoroughly and systematically presents the concepts of fractional calculus and emphasizes the relevance of its application to the nuclear reactor.

Fractional-Order Models for Nuclear Reactor Analysis

Gilberto Espinosa Paredes
Fractional Order Models for Nuclear Reactor Analysis Book PDF

Author : Gilberto Espinosa Paredes
Publisher : Woodhead Publishing
Page : 404 pages
File Size : 47,7 Mb
Release : 2020-10-22
Category : Technology & Engineering
ISBN : 9780128236666

Get Book

Fractional-Order Models for Nuclear Reactor Analysis by Gilberto Espinosa Paredes Pdf

Fractional-Order Models for Nuclear Reactor Analysis presents fractional modeling issues in the context of anomalous diffusion processes in an accessible and practical way. The book emphasizes the importance of non-Fickian diffusion in heterogeneous systems as the core of the nuclear reactor, as well as different variations of diffusion processes in nuclear reactors which are presented to establish the importance of nuclear and thermohydraulic phenomena and the physical side effects of feedback. In addition, the book analyzes core issues in fractional modeling in nuclear reactors surrounding phenomenological description and important analytical sub-diffusive processes in the transport neutron. Users will find the most innovative modeling techniques of nuclear reactors using operator differentials of fractional order and applications in nuclear design and reactor dynamics. Proposed methods are tested with Boltzmann equations and non-linear order models alongside real data from nuclear power plants, making this a valuable resource for nuclear professionals, researchers and graduate students, as well as those working in nuclear research centers with expertise in mathematical modeling, physics and control. Presents and analyzes a new paradigm of nuclear reactor phenomena with fractional modeling Considers principles of fractional calculation, methods of solving differential equations of fractional order, and their applications Includes methodologies of linear and nonlinear analysis, along with design and dynamic analyses

Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications

Esteban Tlelo-Cuautle,Ana Dalia Pano-Azucena,Omar Guillén-Fernández,Alejandro Silva-Juárez
Analog Digital Implementation of Fractional Order Chaotic Circuits and Applications Book PDF

Author : Esteban Tlelo-Cuautle,Ana Dalia Pano-Azucena,Omar Guillén-Fernández,Alejandro Silva-Juárez
Publisher : Springer Nature
Page : 212 pages
File Size : 49,7 Mb
Release : 2019-11-11
Category : Technology & Engineering
ISBN : 9783030312503

Get Book

Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications by Esteban Tlelo-Cuautle,Ana Dalia Pano-Azucena,Omar Guillén-Fernández,Alejandro Silva-Juárez Pdf

This book details the simulation and optimization of integer and fractional-order chaotic systems, and how they can be implemented in the analog and digital domains using FPAAs and FPGAs. Design guidelines are provided to use commercially available electronic devices, and to perform hardware descriptions of integer/fractional-order chaotic systems programming in VHDL. Finally, several engineering applications oriented to cryptography, internet of things, robotics and chaotic communications, are detailed to highlight the usefulness of FPAA/FPGA based integer/fractional-order chaotic systems. Provides guidelines to implement fractional-order derivatives using commercially available devices; Describes details on using FPAAs to approach fractional-order chaotic systems; Includes details on using FPGAs to approach fractional-order chaotic systems, programming in VHDL and reducing hardware resources; Discusses applications to cryptography, internet of things, robotics and chaotic communications.

Fractional Order Control and Synchronization of Chaotic Systems

Ahmad Taher Azar,Sundarapandian Vaidyanathan,Adel Ouannas
Fractional Order Control and Synchronization of Chaotic Systems Book PDF

Author : Ahmad Taher Azar,Sundarapandian Vaidyanathan,Adel Ouannas
Publisher : Springer
Page : 877 pages
File Size : 55,8 Mb
Release : 2017-02-27
Category : Technology & Engineering
ISBN : 9783319502496

Get Book

Fractional Order Control and Synchronization of Chaotic Systems by Ahmad Taher Azar,Sundarapandian Vaidyanathan,Adel Ouannas Pdf

The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional control and stability, the book also discusses key applications of fractional order chaotic systems, as well as multidisciplinary solutions developed via control modeling. As such, it offers the perfect reference guide for graduate students, researchers and practitioners in the areas of fractional order control systems and fractional order chaotic systems.

Introduction to Fractional Differential Equations

Constantin Milici,Gheorghe Drăgănescu,J. Tenreiro Machado
Introduction to Fractional Differential Equations Book PDF

Author : Constantin Milici,Gheorghe Drăgănescu,J. Tenreiro Machado
Publisher : Springer
Page : 188 pages
File Size : 54,5 Mb
Release : 2018-10-28
Category : Technology & Engineering
ISBN : 9783030008956

Get Book

Introduction to Fractional Differential Equations by Constantin Milici,Gheorghe Drăgănescu,J. Tenreiro Machado Pdf

This book introduces a series of problems and methods insufficiently discussed in the field of Fractional Calculus – a major, emerging tool relevant to all areas of scientific inquiry. The authors present examples based on symbolic computation, written in Maple and Mathematica, and address both mathematical and computational areas in the context of mathematical modeling and the generalization of classical integer-order methods. Distinct from most books, the present volume fills the gap between mathematics and computer fields, and the transition from integer- to fractional-order methods.

Generalized Fractional Order Differential Equations Arising in Physical Models

Santanu Saha Ray,Subhadarshan Sahoo
Generalized Fractional Order Differential Equations Arising in Physical Models Book PDF

Author : Santanu Saha Ray,Subhadarshan Sahoo
Publisher : CRC Press
Page : 191 pages
File Size : 45,6 Mb
Release : 2018-11-13
Category : Mathematics
ISBN : 9780429771781

Get Book

Generalized Fractional Order Differential Equations Arising in Physical Models by Santanu Saha Ray,Subhadarshan Sahoo Pdf

This book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models.

Nonlinear Differential Equations in Physics

Santanu Saha Ray
Nonlinear Differential Equations in Physics Book PDF

Author : Santanu Saha Ray
Publisher : Springer Nature
Page : 409 pages
File Size : 49,5 Mb
Release : 2019-12-28
Category : Mathematics
ISBN : 9789811516566

Get Book

Nonlinear Differential Equations in Physics by Santanu Saha Ray Pdf

This book discusses various novel analytical and numerical methods for solving partial and fractional differential equations. Moreover, it presents selected numerical methods for solving stochastic point kinetic equations in nuclear reactor dynamics by using Euler–Maruyama and strong-order Taylor numerical methods. The book also shows how to arrive at new, exact solutions to various fractional differential equations, such as the time-fractional Burgers–Hopf equation, the (3+1)-dimensional time-fractional Khokhlov–Zabolotskaya–Kuznetsov equation, (3+1)-dimensional time-fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov equation, fractional (2+1)-dimensional Davey–Stewartson equation, and integrable Davey–Stewartson-type equation. Many of the methods discussed are analytical–numerical, namely the modified decomposition method, a new two-step Adomian decomposition method, new approach to the Adomian decomposition method, modified homotopy analysis method with Fourier transform, modified fractional reduced differential transform method (MFRDTM), coupled fractional reduced differential transform method (CFRDTM), optimal homotopy asymptotic method, first integral method, and a solution procedure based on Haar wavelets and the operational matrices with function approximation. The book proposes for the first time a generalized order operational matrix of Haar wavelets, as well as new techniques (MFRDTM and CFRDTM) for solving fractional differential equations. Numerical methods used to solve stochastic point kinetic equations, like the Wiener process, Euler–Maruyama, and order 1.5 strong Taylor methods, are also discussed.

Basic Theory

Anatoly Kochubei,Yuri Luchko
Basic Theory Book PDF

Author : Anatoly Kochubei,Yuri Luchko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 489 pages
File Size : 42,5 Mb
Release : 2019-02-19
Category : Mathematics
ISBN : 9783110571622

Get Book

Basic Theory by Anatoly Kochubei,Yuri Luchko Pdf

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

Numerical Analysis with Algorithms and Programming

Santanu Saha Ray
Numerical Analysis with Algorithms and Programming Book PDF

Author : Santanu Saha Ray
Publisher : CRC Press
Page : 391 pages
File Size : 42,8 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781498741835

Get Book

Numerical Analysis with Algorithms and Programming by Santanu Saha Ray Pdf

Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization Approximation of functions and least square approximation Numerical differentiation and divided differences Numerical quadrature and integration Numerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs) The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.

Novel Methods for Solving Linear and Nonlinear Integral Equations

Santanu Saha Ray,Prakash Kumar Sahu
Novel Methods for Solving Linear and Nonlinear Integral Equations Book PDF

Author : Santanu Saha Ray,Prakash Kumar Sahu
Publisher : CRC Press
Page : 242 pages
File Size : 54,7 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429777387

Get Book

Novel Methods for Solving Linear and Nonlinear Integral Equations by Santanu Saha Ray,Prakash Kumar Sahu Pdf

This book deals with the numerical solution of integral equations based on approximation of functions and the authors apply wavelet approximation to the unknown function of integral equations. The book's goal is to categorize the selected methods and assess their accuracy and efficiency.

Stochastic Integral And Differential Equations In Mathematical Modelling

Santanu Saha Ray
Stochastic Integral And Differential Equations In Mathematical Modelling Book PDF

Author : Santanu Saha Ray
Publisher : World Scientific
Page : 319 pages
File Size : 49,6 Mb
Release : 2023-04-25
Category : Mathematics
ISBN : 9781800613591

Get Book

Stochastic Integral And Differential Equations In Mathematical Modelling by Santanu Saha Ray Pdf

The modelling of systems by differential equations usually requires that the parameters involved be completely known. Such models often originate from problems in physics or economics where we have insufficient information on parameter values. One important class of stochastic mathematical models is stochastic partial differential equations (SPDEs), which can be seen as deterministic partial differential equations (PDEs) with finite or infinite dimensional stochastic processes — either with colour noise or white noise. Though white noise is a purely mathematical construction, it can be a good model for rapid random fluctuations.Stochastic Integral and Differential Equations in Mathematical Modelling concerns the analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes. It also provides a theoretical basis for working with SDEs and stochastic processes.This book is written in a simple and clear mathematical logical language, with basic definitions and theorems on stochastic calculus provided from the outset. Each chapter contains illustrated examples via figures and tables. The reader can also construct new wavelets by using the procedure presented in the book. Stochastic Integral and Differential Equations in Mathematical Modelling fulfils the existing gap in the literature for a comprehensive account of this subject area.

Simulation and Modeling Methodologies, Technologies and Applications

Mohammad S. Obaidat,Tuncer Ören,Janusz Kacprzyk,Joaquim Filipe
Simulation and Modeling Methodologies Technologies and Applications Book PDF

Author : Mohammad S. Obaidat,Tuncer Ören,Janusz Kacprzyk,Joaquim Filipe
Publisher : Springer
Page : 352 pages
File Size : 52,9 Mb
Release : 2016-01-14
Category : Computers
ISBN : 9783319264707

Get Book

Simulation and Modeling Methodologies, Technologies and Applications by Mohammad S. Obaidat,Tuncer Ören,Janusz Kacprzyk,Joaquim Filipe Pdf

The present book includes a set of selected extended papers from the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2014), held in Vienna, Austria, from 28 to 30 August 2014. The conference brought together researchers, engineers and practitioners interested in methodologies and applications of modeling and simulation. New and innovative solutions are reported in this book. SIMULTECH 2014 received 167 submissions, from 45 countries, in all continents. After a double blind paper review performed by the Program Committee, 23% were accepted as full papers and thus selected for oral presentation. Additional papers were accepted as short papers and posters. A further selection was made after the Conference, based also on the assessment of presentation quality and audience interest, so that this book includes the extended and revised versions of the very best papers of SIMULTECH 2014. Commitment to high quality standards is a major concern of SIMULTECH that will be maintained in the next editions, considering not only the stringent paper acceptance ratios but also the quality of the program committee, keynote lectures, participation level and logistics.

Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models

Vishwesh Vyawahare,Paluri S. V. Nataraj
Fractional order Modeling of Nuclear Reactor From Subdiffusive Neutron Transport to Control oriented Models Book PDF

Author : Vishwesh Vyawahare,Paluri S. V. Nataraj
Publisher : Springer
Page : 210 pages
File Size : 53,7 Mb
Release : 2018-02-03
Category : Technology & Engineering
ISBN : 9789811075872

Get Book

Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models by Vishwesh Vyawahare,Paluri S. V. Nataraj Pdf

This book addresses the topic of fractional-order modeling of nuclear reactors. Approaching neutron transport in the reactor core as anomalous diffusion, specifically subdiffusion, it starts with the development of fractional-order neutron telegraph equations. Using a systematic approach, the book then examines the development and analysis of various fractional-order models representing nuclear reactor dynamics, ultimately leading to the fractional-order linear and nonlinear control-oriented models. The book utilizes the mathematical tool of fractional calculus, the calculus of derivatives and integrals with arbitrary non-integer orders (real or complex), which has recently been found to provide a more compact and realistic representation to the dynamics of diverse physical systems. Including extensive simulation results and discussing important issues related to the fractional-order modeling of nuclear reactors, the book offers a valuable resource for students and researchers working in the areas of fractional-order modeling and control and nuclear reactor modeling.

General Fractional Derivatives

Xiao-Jun Yang
General Fractional Derivatives Book PDF

Author : Xiao-Jun Yang
Publisher : CRC Press
Page : 306 pages
File Size : 43,9 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9780429811524

Get Book

General Fractional Derivatives by Xiao-Jun Yang Pdf

General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.

Advances in Memristors, Memristive Devices and Systems

Sundarapandian Vaidyanathan,Christos Volos
Advances in Memristors Memristive Devices and Systems Book PDF

Author : Sundarapandian Vaidyanathan,Christos Volos
Publisher : Springer
Page : 511 pages
File Size : 44,8 Mb
Release : 2017-02-15
Category : Technology & Engineering
ISBN : 9783319517247

Get Book

Advances in Memristors, Memristive Devices and Systems by Sundarapandian Vaidyanathan,Christos Volos Pdf

This book reports on the latest advances in and applications of memristors, memristive devices and systems. It gathers 20 contributed chapters by subject experts, including pioneers in the field such as Leon Chua (UC Berkeley, USA) and R.S. Williams (HP Labs, USA), who are specialized in the various topics addressed in this book, and covers broad areas of memristors and memristive devices such as: memristor emulators, oscillators, chaotic and hyperchaotic memristive systems, control of memristive systems, memristor-based min-max circuits, canonic memristors, memristive-based neuromorphic applications, implementation of memristor-based chaotic oscillators, inverse memristors, linear memristor devices, delayed memristive systems, flux-controlled memristive emulators, etc. Throughout the book, special emphasis is given to papers offering practical solutions and design, modeling, and implementation insights to address current research problems in memristors, memristive devices and systems. As such, it offers a valuable reference book on memristors and memristive devices for graduate students and researchers with a basic knowledge of electrical and control systems engineering.