Towards Analytical Chaotic Evolutions in Brusselators PDF Download
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Author: Albert C.J. Luo
Publisher: Morgan & Claypool Publishers
ISBN: 1681738252
Category : Technology & Engineering
Languages : en
Pages : 110
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Book Description
The Brusselator is a mathematical model for autocatalytic reaction, which was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. The dynamics of the Brusselator gives an oscillating reaction mechanism for an autocatalytic, oscillating chemical reaction. The Brusselator is a slow-fast oscillating chemical reaction system. The traditional analytical methods cannot provide analytical solutions of such slow-fast oscillating reaction, and numerical simulations cannot provide a full picture of periodic evolutions in the Brusselator. In this book, the generalized harmonic balance methods are employed for analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion. The bifurcation tree of period-1 motion to chaos of the Brusselator is presented through frequency-amplitude characteristics, which be measured in frequency domains. Two main results presented in this book are: • analytical routes of periodical evolutions to chaos and • independent period-(2l + 1) evolution to chaos. This book gives a better understanding of periodic evolutions to chaos in the slow-fast varying Brusselator system, and the bifurcation tree of period-1 evolution to chaos is clearly demonstrated, which can help one understand routes of periodic evolutions to chaos in chemical reaction oscillators. The slow-fast varying systems extensively exist in biological systems and disease dynamical systems. The methodology presented in this book can be used to investigate the slow-fast varying oscillating motions in biological systems and disease dynamical systems for a better understanding of how infectious diseases spread.
Author: Albert C.J. Luo
Publisher: Morgan & Claypool Publishers
ISBN: 1681738252
Category : Technology & Engineering
Languages : en
Pages : 110
Get Book
Book Description
The Brusselator is a mathematical model for autocatalytic reaction, which was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. The dynamics of the Brusselator gives an oscillating reaction mechanism for an autocatalytic, oscillating chemical reaction. The Brusselator is a slow-fast oscillating chemical reaction system. The traditional analytical methods cannot provide analytical solutions of such slow-fast oscillating reaction, and numerical simulations cannot provide a full picture of periodic evolutions in the Brusselator. In this book, the generalized harmonic balance methods are employed for analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion. The bifurcation tree of period-1 motion to chaos of the Brusselator is presented through frequency-amplitude characteristics, which be measured in frequency domains. Two main results presented in this book are: • analytical routes of periodical evolutions to chaos and • independent period-(2l + 1) evolution to chaos. This book gives a better understanding of periodic evolutions to chaos in the slow-fast varying Brusselator system, and the bifurcation tree of period-1 evolution to chaos is clearly demonstrated, which can help one understand routes of periodic evolutions to chaos in chemical reaction oscillators. The slow-fast varying systems extensively exist in biological systems and disease dynamical systems. The methodology presented in this book can be used to investigate the slow-fast varying oscillating motions in biological systems and disease dynamical systems for a better understanding of how infectious diseases spread.
Author: Albert C.J. Luo
Publisher: Springer Nature
ISBN: 3031796616
Category : Technology & Engineering
Languages : en
Pages : 94
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Book Description
The Brusselator is a mathematical model for autocatalytic reaction, which was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. The dynamics of the Brusselator gives an oscillating reaction mechanism for an autocatalytic, oscillating chemical reaction. The Brusselator is a slow-fast oscillating chemical reaction system. The traditional analytical methods cannot provide analytical solutions of such slow-fast oscillating reaction, and numerical simulations cannot provide a full picture of periodic evolutions in the Brusselator. In this book, the generalized harmonic balance methods are employed for analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion. The bifurcation tree of period-1 motion to chaos of the Brusselator is presented through frequency-amplitude characteristics, which be measured in frequency domains. Two main results presented in this book are: • analytical routes of periodical evolutions to chaos and • independent period-(2𝑙 + 1) evolution to chaos. This book gives a better understanding of periodic evolutions to chaos in the slow-fast varying Brusselator system, and the bifurcation tree of period-1 evolution to chaos is clearly demonstrated, which can help one understand routes of periodic evolutions to chaos in chemical reaction oscillators. The slow-fast varying systems extensively exist in biological systems and disease dynamical systems. The methodology presented in this book can be used to investigate the slow-fast varying oscillating motions in biological systems and disease dynamical systems for a better understanding of how infectious diseases spread.
Author: Siyuan Xing
Publisher: Springer Nature
ISBN: 3031796691
Category : Technology & Engineering
Languages : en
Pages : 73
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Book Description
In this book, the global sequential scenario of bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is presented for a better understanding of global behaviors and motion transitions for one periodic motion to another one. A 1-dimensional (1-D), time-delayed, nonlinear dynamical system is considered as an example to show how to determine the global sequential scenarios of the bifurcation trees of periodic motions to chaos. All stable and unstable periodic motions on the bifurcation trees can be determined. Especially, the unstable periodic motions on the bifurcation trees cannot be achieved from the traditional analytical methods, and such unstable periodic motions and chaos can be obtained through a specific control strategy. The sequential periodic motions in such a 1-D time-delayed system are achieved semi-analytically, and the corresponding stability and bifurcations are determined by eigenvalue analysis. Each bifurcation tree of a specific periodic motion to chaos are presented in detail. The bifurcation tree appearance and vanishing are determined by the saddle-node bifurcation, and the cascaded period-doubled periodic solutions are determined by the period-doubling bifurcation. From finite Fourier series, harmonic amplitude and harmonic phases for periodic motions on the global bifurcation tree are obtained for frequency analysis. Numerical illustrations of periodic motions are given for complex periodic motions in global bifurcation trees. The rich dynamics of the 1-D, delayed, nonlinear dynamical system is presented. Such global sequential periodic motions to chaos exist in nonlinear dynamical systems. The frequency-amplitude analysis can be used for re-construction of analytical expression of periodic motions, which can be used for motion control in dynamical systems.
Author: Shung Sung
Publisher: Springer Nature
ISBN: 3031796896
Category : Technology & Engineering
Languages : en
Pages : 110
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Book Description
This book describes the Asymptotic Modal Analysis (AMA) method to predict the high-frequency vibroacoustic response of structural and acoustical systems. The AMA method is based on taking the asymptotic limit of Classical Modal Analysis (CMA) as the number of modes in the structural system or acoustical system becomes large in a certain frequency bandwidth. While CMA requires both the computation of individual modes and a modal summation, AMA evaluates the averaged modal response only at a center frequency of the bandwidth and does not sum the individual contributions from each mode to obtain a final result. It is similar to Statistical Energy Analysis (SEA) in this respect. However, while SEA is limited to obtaining spatial averages or mean values (as it is a statistical method), AMA is derived systematically from CMA and can provide spatial information as well as estimates of the accuracy of the solution for a particular number of modes. A principal goal is to present the state-of-the-art of AMA and suggest where further developments may be possible. A short review of the CMA method as applied to structural and acoustical systems subjected to random excitation is first presented. Then the development of AMA is presented for an individual structural system and an individual acoustic cavity system, as well as a combined structural-acoustic system. The extension of AMA for treating coupled or multi-component systems is then described, followed by its application to nonlinear systems. Finally, the AMA method is summarized and potential further developments are discussed.
Author: John Gardner
Publisher: Springer Nature
ISBN: 3031797051
Category : Technology & Engineering
Languages : en
Pages : 95
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Book Description
The vapor compression cycle (VCC) underpins the vast majority of refrigeration systems throughout the world. Most undergraduate thermodynamics courses cover the VCC, albeit in a cursory fashion. This book is designed to offer an in-depth look at the analysis, design and operation of large-scale industrial ammonia-based refrigeration systems. An important feature of this work is a treatment of computer-aided analysis using CoolProp, an open source resource for evaluating thermodynamic properties. CoolProp can be incorporated into a large number of common computational platforms including Microsfot Excel, Python, and Matlab, all of which are covered in this book.
Author: John Gardner
Publisher: Morgan & Claypool Publishers
ISBN: 1636391931
Category : Technology & Engineering
Languages : en
Pages : 113
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Book Description
The vapor compression cycle (VCC) underpins the vast majority of refrigeration systems throughout the world. Most undergraduate thermodynamics courses cover the VCC, albeit in a cursory fashion. This book is designed to offer an in-depth look at the analysis, design and operation of large-scale industrial ammonia-based refrigeration systems. An important feature of this work is a treatment of computer-aided analysis using CoolProp, an open source resource for evaluating thermodynamic properties. CoolProp can be incorporated into a large number of common computational platforms including Microsfot Excel, Python, and Matlab, all of which are covered in this book.
Author: Anthony D'Angelo Jr.
Publisher: Springer Nature
ISBN: 3031796853
Category : Technology & Engineering
Languages : en
Pages : 113
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Book Description
This book is intended for students taking a Machine Design course leading to a Mechanical Engineering Technology degree. It can be adapted to a Machine Design course for Mechanical Engineering students or used as a reference for adopting systems engineering into a design course. The book introduces the fundamentals of systems engineering, the concept of synthesis, and the basics of trade-off studies. It covers the use of a functional flow block diagram to transform design requirements into the design space to identify all success modes. The book discusses fundamental stress analysis for structures under axial, torsional, or bending loads. In addition, the book discusses the development of analyzing shafts under combined loads by using Mohr’s circle and failure mode criterion. Chapter 3 provides an overview of fatigue and the process to develop the shaft-sizing equations under dynamic loading conditions. Chapter 4 discusses power equations and the nomenclature and stress analysis for spur and straight bevel gears and equations for analyzing gear trains. Other machine component topics include derivation of the disc clutch and its relationship to compression springs, derivation of the flat belt equations, roller and ball bearing life equations, roller chains, and keyways. Chapter 5 introduces the area of computational machine design and provides codes for developing simple and powerful computational methods to solve: cross product required to calculate the torques and bending moments on shafts, 1D stress analysis, reaction loads on support bearings, Mohr’s circle, shaft sizing under dynamic loading, and cone clutch. The final chapter shows how to integrate Systems Engineering into machine design for a capstone project as a project-based collaborative design methodology. The chapter shows how each design requirement is transformed through the design space to identify the proper engineering equations.
Author: Ramana Pidaparti
Publisher: Springer Nature
ISBN: 3031796934
Category : Technology & Engineering
Languages : en
Pages : 81
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Book Description
Capstone Design: Project Process and Reviews (Student Engineering Design Workbook) provides a brief overview of the design process as well as templates, tools, and student design notes. The goal of this workbook is to provide students in multiple disciplines with a systematic iterative process to follow in their Capstone Design projects and get feedback through design reviews. Students should treat this workbook as a working document and document individual/team decisions, make sketches of their concepts, and add additional design documentation. This workbook also assists in documenting student responsibility and accountability for individual contributions to the project. Freshman- and sophomore-level students may also find this workbook helpful for design projects. Finally, this workbook will also serve as an evaluation and assessment tool for the faculty mentor/advisor.
Author: Sayavur Bakhtiyarov
Publisher: Springer Nature
ISBN: 3031796977
Category : Technology & Engineering
Languages : en
Pages : 77
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Book Description
Fluid Mechanics is the study of liquid or gas behavior in motion or at rest. It is one of the fundamental branches of Engineering Mechanics, which is important to educate professional engineers of any major. Many of the engineering disciplines apply Fluid Mechanics principles and concepts. In order to absorb the materials of Fluid Mechanics, it is not enough just to consume theoretical laws and theorems. A student also must develop an ability to solve practical problems. Therefore, it is necessary to solve many problems independently. This book is a supplement to the Fluid Mechanics course in learning and applying the principles required to solve practical engineering problems in the following branches of Fluid Mechanics: Hydrostatics, Fluid Kinematics, Fluid Dynamics, Turbulent Flow and Gas Dynamics (Compressible Fluid Flow). This book contains practical problems in Fluid Mechanics, which are a complement to Fluid Mechanics textbooks. The book is the product of material covered in many classes over a period of four decades at several universities. It consists of 18 sets of problems where students are introduced to various topics of the Fluid Mechanics. Each set involves 30 problems, which can be assigned as individual homework as well as test/exam problems. The solution of a similar problem for each set is provided. The sequence of the topics and some of the problems were adopted from Fluid Mechanics by R. C. Hibbeler, 2nd edition, 2018, Pearson.
Author: Tariq M. Arif
Publisher: Springer Nature
ISBN: 3031796659
Category : Technology & Engineering
Languages : en
Pages : 93
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Book Description
This book provides a short introduction and easy-to-follow implementation steps of deep learning using Google Cloud Platform. It also includes a practical case study that highlights the utilization of Python and related libraries for running a pre-trained deep learning model. In recent years, deep learning-based modeling approaches have been used in a wide variety of engineering domains, such as autonomous cars, intelligent robotics, computer vision, natural language processing, and bioinformatics. Also, numerous real-world engineering applications utilize an existing pre-trained deep learning model that has already been developed and optimized for a related task. However, incorporating a deep learning model in a research project is quite challenging, especially for someone who doesn't have related machine learning and cloud computing knowledge. Keeping that in mind, this book is intended to be a short introduction of deep learning basics through the example of a practical implementation case. The audience of this short book is undergraduate engineering students who wish to explore deep learning models in their class project or senior design project without having a full journey through the machine learning theories. The case study part at the end also provides a cost-effective and step-by-step approach that can be replicated by others easily.
