# 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 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.

## British Technology Index

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1981 |

ISBN 10 | : |

ISBN 13 | : UOM:39015024228697 |

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

**British Technology Index Book Review:**

## 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.

## Scientific and Technical Aerospace Reports

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1969-11 |

ISBN 10 | : |

ISBN 13 | : NYPL:33433060143850 |

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

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

## 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.

## 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:**

## ERDA Energy Research Abstracts

Author | : United States. Energy Research and Development Administration |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1976-05 |

ISBN 10 | : |

ISBN 13 | : UOM:39015026174121 |

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

**ERDA Energy Research Abstracts Book Review:**

## Communications in Applied Analysis

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2008 |

ISBN 10 | : |

ISBN 13 | : UOM:39015081659537 |

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

**Communications in Applied 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.

## 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.

## 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.

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

Author | : Robert Martin,Cesare Frepoli |

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.Related Link(s)

## Neutron Physics

Author | : Karl-Heinrich Beckurts,Karl Wirtz |

Publsiher | : Springer Science & Business Media |

Total Pages | : 444 |

Release | : 2013-06-29 |

ISBN 10 | : 3642876145 |

ISBN 13 | : 9783642876141 |

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

**Neutron Physics Book Review:**

This book is based upon a series of lectures I have occasionally given at the University of Gottingen since 1951. They were meant to introduce the students of experimental physics to the work in a neutron physics laboratory dealing with the problem of measuring neutron flux, diffusion length, Fermi age, effective neutron temperature, absorption cross sections and similar problems. Moreover, these lectures were intended to prepare the students for a subsequent lecture covering the physics of nuclear reactors. The original character of this series of lectures has been retained in the book. It is intended for use by students as well as anyone desiring to work on neutron physics measurements. The first half mainly covers the theory of neutron fields, i. e. essentially diffusion and slowing down theory. The second half is largely concerned with measurements in neutron fields. The appendix contains information and data which, in our experience, are frequently required in a neutron laboratory. The field of nuclear physics proper is briefly touched upon in the first two chapters, but only to the extent necessary for the understanding of the following chapters. The multitude of applications of neutron radiation has not been covered. The conclusion of this manuscript coincided with the end of my long period of activity with the Max-Planck-Institut fur Physik at Gottingen. To Professor HEISENBERG lowe thanks for his advice and suggestions for many of the subjects treated here.

## The Algorithmic Beauty of Seaweeds Sponges and Corals

Author | : Jaap A. Kaandorp,Janet E. Kübler |

Publsiher | : Springer Science & Business Media |

Total Pages | : 193 |

Release | : 2013-04-17 |

ISBN 10 | : 3662043394 |

ISBN 13 | : 9783662043394 |

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

**The Algorithmic Beauty of Seaweeds Sponges and Corals Book Review:**

With contributions by E.Abraham, D.Barnes, R.Carpenter, L.Collado, P.Dodds, S.Dudgeon, D.Garbary, S.Gatti, B.Helmuth, M.R.Koehl, H.Lasker, R.Merks., W.Müller, S.Muko, B. Rinkevich, J.Sanchez, P.Sloot, M.Vermeij

## 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

## 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.