# Fractional Order Models For Nuclear Reactor Analysis

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## Fractional Order Models for Nuclear Reactor Analysis

Author | : Gilberto Espinosa Paredes |

Publsiher | : Woodhead Publishing |

Total Pages | : 402 |

Release | : 2020-10-22 |

ISBN 10 | : 0128236663 |

ISBN 13 | : 9780128236666 |

Language | : EN, FR, DE, ES & NL |

**Fractional Order Models for Nuclear Reactor Analysis Book Review:**

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

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

Author | : Vishwesh Vyawahare,Paluri S. V. Nataraj |

Publsiher | : Springer |

Total Pages | : 200 |

Release | : 2018-02-03 |

ISBN 10 | : 9811075875 |

ISBN 13 | : 9789811075872 |

Language | : EN, FR, DE, ES & NL |

**Fractional order Modeling of Nuclear Reactor From Subdiffusive Neutron Transport to Control oriented Models Book Review:**

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.

## Simulation and Modeling Methodologies Technologies and Applications

Author | : Mohammad S. Obaidat,Tuncer Ören,Janusz Kacprzyk,Joaquim Filipe |

Publsiher | : Springer |

Total Pages | : 352 |

Release | : 2016-01-14 |

ISBN 10 | : 3319264702 |

ISBN 13 | : 9783319264707 |

Language | : EN, FR, DE, ES & NL |

**Simulation and Modeling Methodologies Technologies and Applications Book Review:**

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 Calculus with Applications for Nuclear Reactor Dynamics

Author | : Santanu Saha Ray |

Publsiher | : CRC Press |

Total Pages | : 235 |

Release | : 2015-07-29 |

ISBN 10 | : 149872728X |

ISBN 13 | : 9781498727280 |

Language | : EN, FR, DE, ES & NL |

**Fractional Calculus with Applications for Nuclear Reactor Dynamics Book Review:**

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 Calculus

Author | : Varsha Daftardar-Gejji |

Publsiher | : ALPHA SCIENCE INTERNATIONAL LIMITED |

Total Pages | : 232 |

Release | : 2013-07-26 |

ISBN 10 | : 8184874782 |

ISBN 13 | : 9788184874785 |

Language | : EN, FR, DE, ES & NL |

**Fractional Calculus Book Review:**

FRACTIONAL CALCULUS: Theory and Applications deals with differentiation and integration of arbitrary order. The origin of this subject can be traced back to the end of seventeenth century, the time when Newton and Leibniz developed foundations of differential and integral calculus. Nonetheless, utility and applicability of FC to various branches of science and engineering have been realized only in last few decades. Recent years have witnessed tremendous upsurge in research activities related to the applications of FC in modeling of real-world systems. Unlike the derivatives of integral order, the non-local nature of fractional derivatives correctly models many natural phenomena containing long memory and give more accurate description than their integer counterparts.The present book comprises of contributions from academicians and leading researchers and gives a panoramic overview of various aspects of this subject: Introduction to Fractional Calculus Fractional Differential Equations Fractional Ordered Dynamical Systems Fractional Operators on Fractals Local Fractional Derivatives Fractional Control Systems Fractional Operators and Statistical Distributions Applications to Engineering

## Fractional Calculus and Fractional Differential Equations

Author | : Varsha Daftardar-Gejji |

Publsiher | : Springer |

Total Pages | : 180 |

Release | : 2019-08-10 |

ISBN 10 | : 9811392277 |

ISBN 13 | : 9789811392276 |

Language | : EN, FR, DE, ES & NL |

**Fractional Calculus and Fractional Differential Equations Book Review:**

This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed. The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.

## Analog Digital Implementation of Fractional Order Chaotic Circuits and Applications

Author | : Esteban Tlelo-Cuautle,Ana Dalia Pano-Azucena,Omar Guillén-Fernández,Alejandro Silva-Juárez |

Publsiher | : Springer Nature |

Total Pages | : 212 |

Release | : 2019-11-11 |

ISBN 10 | : 303031250X |

ISBN 13 | : 9783030312503 |

Language | : EN, FR, DE, ES & NL |

**Analog Digital Implementation of Fractional Order Chaotic Circuits and Applications Book Review:**

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.

## Basic Theory

Author | : Anatoly Kochubei,Yuri Luchko |

Publsiher | : Walter de Gruyter GmbH & Co KG |

Total Pages | : 489 |

Release | : 2019-02-19 |

ISBN 10 | : 3110571625 |

ISBN 13 | : 9783110571622 |

Language | : EN, FR, DE, ES & NL |

**Basic Theory Book Review:**

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.

## Investigation of Spatial Control Strategies with Application to Advanced Heavy Water Reactor

Author | : Ravindra Munje,Balasaheb Patre,Akhilanand Tiwari |

Publsiher | : Springer |

Total Pages | : 168 |

Release | : 2017-10-13 |

ISBN 10 | : 9811030146 |

ISBN 13 | : 9789811030147 |

Language | : EN, FR, DE, ES & NL |

**Investigation of Spatial Control Strategies with Application to Advanced Heavy Water Reactor Book Review:**

This book examines the different spatial control techniques for regulation of spatial power distribution in advanced heavy water reactors (AHWR). It begins with a review of the literature pertinent to the modeling and control of large reactors. It also offers a nodal-core model based on finite difference approximation since the AHWR core is considered to be divided into 17 relatively large nodes. Further, it introduces a nonlinear model characterizing important thermal hydraulics parameters of AHWR and integrates it into the neutronics model to obtain a coupled neutronics-thermal hydraulics model of AHWR. The book also presents a vectorized nonlinear model of AHWR and implements it in MATLAB/Simulink environment. The model of the reactor is then linearized at the rated power and put into standard state variable form. It is characterized by 90 states, 5 inputs and 18 outputs. Lastly, it discusses control techniques for a nonlinear model of AHWR. This book will prove to be a valuable resource for professional engineers and implementation specialists, researchers and students.

## Artificial Intelligence and Soft Computing

Author | : Leszek Rutkowski,Rafał Scherer,Marcin Korytkowski,Witold Pedrycz,Ryszard Tadeusiewicz,Jacek M. Zurada |

Publsiher | : Springer Nature |

Total Pages | : 728 |

Release | : 2020-10-20 |

ISBN 10 | : 3030614018 |

ISBN 13 | : 9783030614010 |

Language | : EN, FR, DE, ES & NL |

**Artificial Intelligence and Soft Computing Book Review:**

The two-volume set LNCS 12415 and 12416 constitutes the refereed proceedings of of the 19th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2020, held in Zakopane, Poland*, in October 2020. The 112 revised full papers presented were carefully reviewed and selected from 265 submissions. The papers included in the first volume are organized in the following six parts: neural networks and their applications; fuzzy systems and their applications; evolutionary algorithms and their applications; pattern classification; bioinformatics, biometrics and medical applications; artificial intelligence in modeling and simulation. The papers included in the second volume are organized in the following four parts: computer vision, image and speech analysis; data mining; various problems of artificial intelligence; agent systems, robotics and control. *The conference was held virtually due to the COVID-19 pandemic.

## Intelligent Engineering Systems and Computational Cybernetics

Author | : J.A. Tenreiro Machado,Béla Pátkai,Imre J. Rudas |

Publsiher | : Springer Science & Business Media |

Total Pages | : 460 |

Release | : 2008-12-18 |

ISBN 10 | : 1402086784 |

ISBN 13 | : 9781402086786 |

Language | : EN, FR, DE, ES & NL |

**Intelligent Engineering Systems and Computational Cybernetics Book Review:**

Engineering practice often has to deal with complex systems of multiple variable and multiple parameter models almost always with strong non-linear coupling. The conventional analytical techniques-based approaches for describing and predicting the behaviour of such systems in many cases are doomed to failure from the outset, even in the phase of the construction of a more or less appropriate mathematical model. These approaches normally are too categorical in the sense that in the name of “modelling accuracy” they try to describe all the structural details of the real physical system to be modelled. This can significantly increase the intricacy of the model and may result in a enormous computational burden without achieving considerable improvement of the solution. The best paradigm exemplifying this situation may be the classic perturbation theory: the less significant the achievable correction, the more work has to be invested to obtain it. A further important component of machine intelligence is a kind of “structural uniformity” giving room and possibility to model arbitrary particular details a priori not specified and unknown. This idea is similar to the ready-to-wear industry, which introduced products, which can be slightly modified later on in contrast to tailor-made creations aiming at maximum accuracy from the beginning. These subsequent corrections can be carried out by machines automatically. This “learning ability” is a key element of machine intelligence. The past decade confirmed that the view of typical components of the present soft computing as fuzzy logic, neural computing, evolutionary computation and probabilistic reasoning are of complementary nature and that the best results can be applied by their combined application. Today, the two complementary branches of Machine Intelligence, that is, Artificial Intelligence and Computational Intelligence serve as the basis of Intelligent Engineering Systems. The huge number of scientific results published in Journal and conference proceedings worldwide substantiates this statement. The present book contains several articles taking different viewpoints in the field of intelligent systems.

## British Technology Index

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 1981 |

ISBN 10 | : 1928374650XXX |

ISBN 13 | : UOM:39015024228697 |

Language | : EN, FR, DE, ES & NL |

**British Technology Index Book Review:**

## Fractional Differential Equations

Author | : Juan J. Nieto,Rosana Rodríguez-López |

Publsiher | : MDPI |

Total Pages | : 172 |

Release | : 2019-11-19 |

ISBN 10 | : 3039217321 |

ISBN 13 | : 9783039217328 |

Language | : EN, FR, DE, ES & NL |

**Fractional Differential Equations Book Review:**

Fractional calculus provides the possibility of introducing integrals and derivatives of an arbitrary order in the mathematical modelling of physical processes, and it has become a relevant subject with applications to various fields, such as anomalous diffusion, propagation in different media, and propogation in relation to materials with different properties. However, many aspects from theoretical and practical points of view have still to be developed in relation to models based on fractional operators. This Special Issue is related to new developments on different aspects of fractional differential equations, both from a theoretical point of view and in terms of applications in different fields such as physics, chemistry, or control theory, for instance. The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields.

## Fractional Order Nonlinear Systems

Author | : Ivo Petráš |

Publsiher | : Springer Science & Business Media |

Total Pages | : 218 |

Release | : 2011-05-30 |

ISBN 10 | : 3642181015 |

ISBN 13 | : 9783642181016 |

Language | : EN, FR, DE, ES & NL |

**Fractional Order Nonlinear Systems Book Review:**

"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.

## Fundamentals of Nuclear Reactor Physics

Author | : Elmer E. Lewis |

Publsiher | : Elsevier |

Total Pages | : 280 |

Release | : 2008-01-18 |

ISBN 10 | : 9780080560434 |

ISBN 13 | : 0080560431 |

Language | : EN, FR, DE, ES & NL |

**Fundamentals of Nuclear Reactor Physics Book Review:**

Fundamentals of Nuclear Reactor Physics offers a one-semester treatment of the essentials of how the fission nuclear reactor works, the various approaches to the design of reactors, and their safe and efficient operation . It provides a clear, general overview of atomic physics from the standpoint of reactor functionality and design, including the sequence of fission reactions and their energy release. It provides in-depth discussion of neutron reactions, including neutron kinetics and the neutron energy spectrum, as well as neutron spatial distribution. It includes ample worked-out examples and over 100 end-of-chapter problems. Engineering students will find this applications-oriented approach, with many worked-out examples, more accessible and more meaningful as they aspire to become future nuclear engineers. A clear, general overview of atomic physics from the standpoint of reactor functionality and design, including the sequence of fission reactions and their energy release In-depth discussion of neutron reactions, including neutron kinetics and the neutron energy spectrum, as well as neutron spatial distribution Ample worked-out examples and over 100 end-of-chapter problems Full Solutions Manual

## The Analysis of Fractional Differential Equations

Author | : Kai Diethelm |

Publsiher | : Springer |

Total Pages | : 247 |

Release | : 2010-08-18 |

ISBN 10 | : 3642145744 |

ISBN 13 | : 9783642145742 |

Language | : EN, FR, DE, ES & NL |

**The Analysis of Fractional Differential Equations Book Review:**

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

## Accounting for Core Burnup in Reactor Analysis of the University of WIsconsin Nuclear Reactor

Author | : Benjamin J. Schmitt |

Publsiher | : Unknown |

Total Pages | : 65 |

Release | : 2006 |

ISBN 10 | : 1928374650XXX |

ISBN 13 | : WISC:89091506675 |

Language | : EN, FR, DE, ES & NL |

**Accounting for Core Burnup in Reactor Analysis of the University of WIsconsin Nuclear Reactor Book Review:**

## Generalized Fractional Order Differential Equations Arising in Physical Models

Author | : Santanu Saha Ray,Subhadarshan Sahoo |

Publsiher | : CRC Press |

Total Pages | : 314 |

Release | : 2018-11-13 |

ISBN 10 | : 0429771789 |

ISBN 13 | : 9780429771781 |

Language | : EN, FR, DE, ES & NL |

**Generalized Fractional Order Differential Equations Arising in Physical Models Book Review:**

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.

## Functional Fractional Calculus for System Identification and Controls

Author | : Shantanu Das |

Publsiher | : Springer Science & Business Media |

Total Pages | : 240 |

Release | : 2007-09-26 |

ISBN 10 | : 3540727035 |

ISBN 13 | : 9783540727033 |

Language | : EN, FR, DE, ES & NL |

**Functional Fractional Calculus for System Identification and Controls Book Review:**

In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.

## Nonlinear Differential Equations in Physics

Author | : Santanu Saha Ray |

Publsiher | : Springer Nature |

Total Pages | : 388 |

Release | : 2019-12-28 |

ISBN 10 | : 9811516561 |

ISBN 13 | : 9789811516566 |

Language | : EN, FR, DE, ES & NL |

**Nonlinear Differential Equations in Physics Book Review:**

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.