# 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 | : 2020-10-27 |

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

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.

## 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.

## Dynamics and Control of Energy Systems

Author | : Achintya Mukhopadhyay,Swarnendu Sen,Dipankar Narayan Basu,Sirshendu Mondal |

Publsiher | : Springer Nature |

Total Pages | : 526 |

Release | : 2019-10-14 |

ISBN 10 | : 9811505365 |

ISBN 13 | : 9789811505362 |

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

**Dynamics and Control of Energy Systems Book Review:**

This book presents recent advances in dynamics and control of different types of energy systems. It covers research on dynamics and control in energy systems from different aspects, namely, combustion, multiphase flow, nuclear, chemical and thermal. The chapters start from the basic concepts so that this book can be useful even for researchers with very little background in the area. A dedicated chapter provides an overview on the fundamental aspects of the dynamical systems approach. The book will be of use to researchers and professionals alike.

## General Fractional Derivatives

Author | : Xiao-Jun Yang |

Publsiher | : CRC Press |

Total Pages | : 364 |

Release | : 2019-05-10 |

ISBN 10 | : 0429811535 |

ISBN 13 | : 9780429811531 |

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

**General Fractional Derivatives Book Review:**

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.

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

Author | : Benjamin J. Schmitt |

Publsiher | : Anonim |

Total Pages | : 65 |

Release | : 2006 |

ISBN 10 | : |

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:**

## Theory and Applications of Non-integer Order Systems

Author | : Artur Babiarz,Adam Czornik,Jerzy Klamka,Michał Niezabitowski |

Publsiher | : Springer |

Total Pages | : 512 |

Release | : 2016-09-15 |

ISBN 10 | : 3319454749 |

ISBN 13 | : 9783319454740 |

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

**Theory and Applications of Non-integer Order Systems Book Review:**

This book collects papers from the 8th Conference on Non-Integer Order Calculus and Its Applications that have been held on September 20-21, 2016 in Zakopane, Poland. The preceding two conferences were held in Szczecin, Poland in 2015, and in Opole, Poland, in 2014. This conference provides a platform for academic exchange on the theory and application of fractional calculus between domestic and international universities, research institutes, corporate experts and scholars. The Proceedings of the 8th Conference on Non-Integer Order Calculus and Its Applications 2016 brings together rigorously reviewed contributions from leading international experts. The included papers cover novel various important aspects of mathematical foundations of fractional calculus, modeling and control of fractional systems as well as controllability, detectability, observability and stability problems for this systems.

## Nuclear-reactor Analysis

Author | : Allan F. Henry,Henry Allan F |

Publsiher | : MIT Press (MA) |

Total Pages | : 547 |

Release | : 1975 |

ISBN 10 | : |

ISBN 13 | : UCAL:B4323416 |

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

**Nuclear-reactor Analysis Book Review:**

## Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations

Author | : Santanu Saha Ray,Arun Kumar Gupta |

Publsiher | : CRC Press |

Total Pages | : 273 |

Release | : 2018-01-12 |

ISBN 10 | : 1351682229 |

ISBN 13 | : 9781351682220 |

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

**Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations Book Review:**

The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.

## Design-basis Accident Analysis Methods For Light-water Nuclear Power Plants

Author | : Martin Robert,Frepoli Cesare |

Publsiher | : World Scientific |

Total Pages | : 716 |

Release | : 2019-02-13 |

ISBN 10 | : 9813275677 |

ISBN 13 | : 9789813275676 |

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

**Design-basis Accident Analysis Methods For Light-water Nuclear Power Plants Book Review:**

This book captures the principles of safety evaluation as practiced in the regulated light-water reactor nuclear industry, as established and stabilized over the last 30 years. It is expected to serve both the current industry and those planning for the future. The work's coverage of the subject matter is the broadest to date, including not only the common topics of modeling and simulation, but also methods supporting the basis for the underlying assumptions, the extension to radiological safety, what to expect in a licensing review, historical perspectives and the implication for new designs.This text is an essential resource for practitioners and students, on the current best-practices in nuclear power plant safety and their basis. Contributors of this work are subject matter experts in their specialties, much of which was nurtured and inspired by Prof. Larry Hochreiter, a prominent nuclear safety pioneer.

## Trends in Advanced Intelligent Control, Optimization and Automation

Author | : Wojciech Mitkowski,Janusz Kacprzyk,Krzysztof Oprzędkiewicz,Paweł Skruch |

Publsiher | : Springer |

Total Pages | : 883 |

Release | : 2017-06-06 |

ISBN 10 | : 3319606999 |

ISBN 13 | : 9783319606996 |

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

**Trends in Advanced Intelligent Control, Optimization and Automation Book Review:**

This volume contains the proceedings of the KKA 2017 – the 19th Polish Control Conference, organized by the Department of Automatics and Biomedical Engineering, AGH University of Science and Technology in Kraków, Poland on June 18–21, 2017, under the auspices of the Committee on Automatic Control and Robotics of the Polish Academy of Sciences, and the Commission for Engineering Sciences of the Polish Academy of Arts and Sciences. Part 1 deals with general issues of modeling and control, notably flow modeling and control, sliding mode, predictive, dual, etc. control. In turn, Part 2 focuses on optimization, estimation and prediction for control. Part 3 is concerned with autonomous vehicles, while Part 4 addresses applications. Part 5 discusses computer methods in control, and Part 6 examines fractional order calculus in the modeling and control of dynamic systems. Part 7 focuses on modern robotics. Part 8 deals with modeling and identification, while Part 9 deals with problems related to security, fault detection and diagnostics. Part 10 explores intelligent systems in automatic control, and Part 11 discusses the use of control tools and techniques in biomedical engineering. Lastly, Part 12 considers engineering education and teaching with regard to automatic control and robotics.

## Fundamentals of Nuclear Science and Engineering Second Edition

Author | : J. Kenneth Shultis,Richard E. Faw |

Publsiher | : CRC Press |

Total Pages | : 616 |

Release | : 2007-09-07 |

ISBN 10 | : 1439894086 |

ISBN 13 | : 9781439894088 |

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

**Fundamentals of Nuclear Science and Engineering Second Edition Book Review:**

Since the publication of the bestselling first edition, there have been numerous advances in the field of nuclear science. In medicine, accelerator based teletherapy and electron-beam therapy have become standard. New demands in national security have stimulated major advances in nuclear instrumentation.An ideal introduction to the fundamentals of nuclear science and engineering, this book presents the basic nuclear science needed to understand and quantify an extensive range of nuclear phenomena. New to the Second Edition— A chapter on radiation detection by Douglas McGregor Up-to-date coverage of radiation hazards, reactor designs, and medical applications Flexible organization of material that allows for quick reference This edition also takes an in-depth look at particle accelerators, nuclear fusion reactions and devices, and nuclear technology in medical diagnostics and treatment. In addition, the author discusses applications such as the direct conversion of nuclear energy into electricity. The breadth of coverage is unparalleled, ranging from the theory and design characteristics of nuclear reactors to the identification of biological risks associated with ionizing radiation. All topics are supplemented with extensive nuclear data compilations to perform a wealth of calculations. Providing extensive coverage of physics, nuclear science, and nuclear technology of all types, this up-to-date second edition of Fundamentals of Nuclear Science and Engineering is a key reference for any physicists or engineer.

## The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order

Author | : Anonim |

Publsiher | : Elsevier |

Total Pages | : 322 |

Release | : 1974-09-05 |

ISBN 10 | : 9780080956206 |

ISBN 13 | : 0080956203 |

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

**The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order Book Review:**

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

## 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.

## Communications in Applied Analysis

Author | : Anonim |

Publsiher | : Anonim |

Total Pages | : 329 |

Release | : 2008 |

ISBN 10 | : |

ISBN 13 | : UOM:39015081659537 |

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

**Communications in Applied Analysis Book Review:**

## Fundamentals of Nuclear Models

Author | : David J Rowe,John L Wood |

Publsiher | : World Scientific Publishing Company |

Total Pages | : 676 |

Release | : 2010-03-23 |

ISBN 10 | : 9813101725 |

ISBN 13 | : 9789813101722 |

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

**Fundamentals of Nuclear Models Book Review:**

This book reviews the basic models and theories of nuclear structure and gives an in-depth analysis of their experimental and mathematical foundations. It shows the relationships between the models and exhibits the value of following the strategy of: looking for patterns in all the data available, developing phenomenological models to explain them, and finally giving the models a foundation in a fundamental microscopic theory of interacting neutrons and protons. This unique book takes a newcomer from an introduction to nuclear structure physics to the frontiers of the subject along a painless path. It provides both the experimental and mathematical foundations of the essential models in a way that is accessible to a broad range of experimental and theoretical physicists. Thus, the book provides a unique resource and an exposition of the essential principles, mathematical structures, assumptions, and observational data on which the models and theories are based. It avoids discussion of many non-essential variations and technical details of the models.

## 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.