# 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 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.

## 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 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.

## 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.

## 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.

## Functional Fractional Calculus

Author | : Shantanu Das |

Publsiher | : Springer Science & Business Media |

Total Pages | : 612 |

Release | : 2011-06-01 |

ISBN 10 | : 3642205453 |

ISBN 13 | : 9783642205453 |

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

**Functional Fractional Calculus Book Review:**

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. The normal physical laws like, transport theory, electrodynamics, equation of motions, elasticity, viscosity, and several others of are based on ‘ordinary’ calculus. In this book these physical laws are generalized in fractional calculus contexts; taking, heterogeneity effect in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, physics of random delay in computer network; and several others; mapping the reality of nature closely. The concept of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically with examples. The practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function is deliberated. Practical results of viscoelastic experiments, fractional order controls experiments, design of fractional controller and practical circuit synthesis for fractional order elements are elaborated in this book. The book also maps theory of classical integer order differential equations to fractional calculus contexts, and deals in details with conflicting and demanding initialization issues, required in classical techniques. The book presents a modern approach to solve the ‘solvable’ system of fractional and other differential equations, linear, non-linear; without perturbation or transformations, but by applying physical principle of action-and-opposite-reaction, giving ‘approximately exact’ series solutions. Historically, Sir Isaac Newton and Gottfried Wihelm Leibniz independently discovered calculus in the middle of the 17th century. In recognition to this remarkable discovery, J.von Neumann remarked, “...the calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more equivocally than anything else the inception of modern mathematical analysis which is logical development, still constitute the greatest technical advance in exact thinking.” This XXI century has thus started to ‘think-exactly’ for advancement in science & technology by growing application of fractional calculus, and this century has started speaking the language which nature understands the best.

## Introduction to Fractional Differential Equations

Author | : Constantin Milici,Gheorghe Drăgănescu,J. Tenreiro Machado |

Publsiher | : Springer |

Total Pages | : 188 |

Release | : 2018-10-28 |

ISBN 10 | : 3030008959 |

ISBN 13 | : 9783030008956 |

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

**Introduction to Fractional Differential Equations Book Review:**

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.

## 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.

## 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.

## The International Conference on Advanced Machine Learning Technologies and Applications AMLTA2019

Author | : Aboul Ella Hassanien,Ahmad Taher Azar,Tarek Gaber,Roheet Bhatnagar,Mohamed F. Tolba |

Publsiher | : Springer |

Total Pages | : 960 |

Release | : 2019-03-16 |

ISBN 10 | : 3030141187 |

ISBN 13 | : 9783030141189 |

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

**The International Conference on Advanced Machine Learning Technologies and Applications AMLTA2019 Book Review:**

This book presents the peer-reviewed proceedings of the 4th International Conference on Advanced Machine Learning Technologies and Applications (AMLTA 2019), held in Cairo, Egypt, on March 28–30, 2019, and organized by the Scientific Research Group in Egypt (SRGE). The papers cover the latest research on machine learning, deep learning, biomedical engineering, control and chaotic systems, text mining, summarization and language identification, machine learning in image processing, renewable energy, cyber security, and intelligence swarms and optimization.

## Fractional Dynamical Systems

Author | : Piotr Kulczycki |

Publsiher | : Springer Nature |

Total Pages | : 398 |

Release | : 2022 |

ISBN 10 | : 3030899721 |

ISBN 13 | : 9783030899721 |

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

**Fractional Dynamical Systems Book Review:**

This book presents a wide and comprehensive spectrum of issues and problems related to fractional-order dynamical systems. It is meant to be a full-fledge, comprehensive presentation of many aspects related to the broadly perceived fractional-order dynamical systems which constitute an extension of the traditional integer-order-type descriptions. This implies far-reaching consequences, both analytic and algorithmic, becausein generalproperties of the traditional integer-order systems cannot be directly extended by a straightforward generalization to fractional-order systems, modeled by fractional-order differential equations involving derivatives of an non-integer order. This can be useful for describing and analyzing, for instance, anomalies in the behavior of various systems, chaotic behavior, etc. The book contains both analytic contributions with state-of-the-art and theoretical foundations, algorithmic implementation of tools and techniques, andfinallysome examples of relevant and successful practical applications.

## Scientific and Technical Aerospace Reports

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 1992-05 |

ISBN 10 | : 1928374650XXX |

ISBN 13 | : UFL:31262082066480 |

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

**Scientific and Technical Aerospace Reports Book Review:**

## Linear and Non linear Stability Analysis in Boiling Water Reactors

Author | : Alfonso Prieto Guerrero,Gilberto Espinosa Paredes |

Publsiher | : Woodhead Publishing |

Total Pages | : 471 |

Release | : 2018-10-15 |

ISBN 10 | : 0081024460 |

ISBN 13 | : 9780081024461 |

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

**Linear and Non linear Stability Analysis in Boiling Water Reactors Book Review:**

Linear and Non-Linear Stability Analysis in Boiling Water Reactors: The Design of Real-Time Stability Monitors presents a thorough analysis of the most innovative BWR reactors and stability phenomena in one accessible resource. The book presents a summary of existing literature on BWRs to give early career engineers and researchers a solid background in the field, as well as the latest research on stability phenomena (propagation phenomena in BWRs), nuclear power monitors, and advanced computer systems used to for the prediction of stability. It also emphasizes the importance of BWR technology and embedded neutron monitoring systems (APRMs and LPRMs), and introduces non-linear stability parameters that can be used for the onset detection of instabilities in BWRs. Additionally, the book details the scope, advantages, and disadvantages of multiple advanced linear and non linear signal processing methods, and includes analytical case studies of existing plants. This combination makes Linear and Non-Linear Stability Analysis in Boiling Water Reactors a valuable resource for nuclear engineering students focusing on linear and non-linear analysis, as well as for those working and researching in a nuclear power capacity looking to implement stability methods and estimate decay ratios using non-linear techniques. Explores the nuclear stability of Boiling Water Reactors based on linear and non-linear models Evaluates linear signal processing methods such as autoregressive models, Fourier-based methods, and wavelets to calculate decay ratios Proposes novel non-linear signal analysis techniques linked to non-linear stability indicators Includes case studies of various existing nuclear power plants as well as mathematical models and simulations

## The Shock and Vibration Digest

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 1983 |

ISBN 10 | : 1928374650XXX |

ISBN 13 | : STANFORD:36105112118869 |

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

**The Shock and Vibration Digest Book Review:**

## 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:**