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Continuum Mechanics
This book presents an introduction into the entire science of Continuum Mechanics in three parts. PART I: Continuum Mechanics introduces into the Foundations using tensors in Cartesian coordinate systems, classical theory of elasticity, and fluid mechanics. PART II: Mechanics of Materials has chapters on viscoelasticity, plasticity, principles of constitutive modelling, and thermodynamics. PART III presents Tensor Analysis and fundamental equations of Continuum Mechanics in curvilinear coordinates.
Continuous-Time Systems
The book systematically covers major foundations of the systems theory. First, the quantitative and qualitative methods of systems description are presented along with the stability analysis. The representation of linear time-invariant systems in the time domain is provided using the convolution, ordinarily differential equations (ODEs), and state space. In the frequency domain, these systems are analyzed using the Fourier and Laplace transforms. The linear time-varying systems are represented using the general convolution, ODEs, and state space. The nonlinear time-invariant systems are described employing the Taylor and Volterra series expansions, ODEs, state space, and approximate methods such as averaging, equivalent linearization, and describing function. Finally, the representation of nonlinear time-varying systems is given using the Taylor and Volterra series, ODEs, modulation functions method, and state space modelling.
Continuous System Simulation
Continuous System Simulation describes systematically and methodically how mathematical models of dynamic systems, usually described by sets of either ordinary or partial differential equations possibly coupled with algebraic equations, can be simulated on a digital computer.
Continuous Semigroups of Holomorphic Self-maps of the Unit Disc
The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Carathéodory prime ends topology and Gromov hyperbolicity theory.
Construction of Global Lyapunov Functions : Using Radial Basis Functions
In this volume, the basin of attraction of an equilibrium of an ordinary differential equation can be determined using a Lyapunov function. A new method to construct such a Lyapunov function using radial basis functions is presented.
Congruency, Expectations and Consumer Behavior in Digital Environments
A progress in technologies, the increasing expansion and use of digital environments lead to remarkable shifts of business activities. These transformations not only impact business but also affect consumers’ attitudes, beliefs, and practices. Thus, Frederic Nimmermann sheds light on consumer behavior in central subareas in digital environments such as advertising.
Computing the Electrical Activity in the Heart
This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. The book gives an introduction to the most important models of the field, followed by a detailed description of numerical techniques for the models. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers.
Computing in Algebraic Geometry : A Quick Start using SINGULAR
Algebraic geometry generally studies the properties of solution sets of systems of polynomial equations without direct reference to the actual polynomials used in these systems. … This is especially desirable for classwork where the development of the abstract machinery generally outlasts the patience of the students, except possibly the most motivated ones.
Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models
Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented.
Computer science logic ; Vol. 4207 ; 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL, Szeged, Hungary, September 25-29, 2006, Proceedings
Coverage includes automated deduction and interactive theorem proving, constructive mathematics and type theory, equational logic and term rewriting, automata and formal logics, modal and temporal logic, model checking, finite model theory, and more.
Computer Algebra Recipes for Mathematical Physics
Over two hundred novel and innovative computer algebra worksheets or ""recipes"" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn.
Computer algebra in scientific computing ; 23rd International Workshop, CASC 2021, Sochi, Russia, September 13–17, 2021, Proceedings
This book constitutes the proceedings of the 23rd International Workshop on Computer Algebra in Scientific Computing, CASC 2021, held in Sochi, Russia, in September 2021. The 24 full papers presented together with 1 invited talk were carefully reviewed and selected from 40 submissions. The papers cover theoretical computer algebra and its applications in scientific computing.
Computer algebra in scientific computing ; 22nd International Workshop, CASC 2020, Linz, Austria, September 14–18, 2020, Proceedings
This book constitutes the refereed proceedings of the 22nd International Workshop on Computer Algebra in Scientific Computing, CASC 2020, held in Linz, Austria, in September 2020. The conference was held virtually due to the COVID-19 pandemic. The 34 full papers presented together with 2 invited talks were carefully reviewed and selected from 41 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CAS in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.
Computer Algebra in Scientific Computing ; 10th International Workshop, CASC 2007, Bonn, Germany, September 16-20, 2007, Proceedings
The book covers not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms. Topics addressed are studies in polynomial and matrix algebra, quantifier elimination, and Gröbner bases, as well as stability investigation of both differential equations and difference methods for them. Several papers are devoted to the application of computer algebra methods and algorithms to the derivation of new mathematical models in biology and in mathematical physics.
Computational Turbulent Incompressible Flow: Applied Mathematics : Body and Soul 4
This is Volume 4 of the book series of the Body & Soul mathematics education reform program, and presents a unified new approach to computational simulation of turbulent.
Computational Textile
This edited book collects a number of representative applications of computational techniques in textile and garment industry. These applications cover the following issues: Textile quality assessment by image analysis, Modeling and simulation of textile structures, Computer aided garment design, Computerized textile management and textile Supply Chain, Textile quality subjective and objective evaluation; Computational thermal bioengineering of textiles and clothing; Computational biomechanical engineering of textiles and clothing.
Computational Techniques for Voltage Stability Assessment and Control
The key concepts of both saddle node and Hopf bifurcation are covered. These are illustrated with the differential-algebraic equation (DAE) model of the system. The model is complex enough to include Load Tap-Changing transformers as well as HVDC models. The dynamic model of the generating unit includes the exciter since it plays a crucial role in voltage stability. A promising decoupled dynamic simulation technique is introduced for time domain analysis. Computational Techniques for Voltage Stability Assessment and Control provides the computational tools and algorithms needed for development of on-line voltage security assessment
Computational Noncommutative Algebra and Applications
The fusion of algebra, analysis and geometry, and their application to real world problems, have been dominant themes underlying mathematics for over the years. This book features topics such as: signal and image processing in remote sensing, computer vision, medical image processing, biological signal processing, geometric algebras, and more.
Computational Methods in Transport : Verification and Validation
The focus of this book deals with a cross cutting issue affecting all particle transport algorithms and applications; verification and validation (V&V). In other words, are the equations being solved correctly and are the correct equations being solved? Verification and validation assures a scientist, engineer or mathematician that a simulation code is a mirror of reality and not just an expensive computer game. In this book, we will learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to benchmark and ascertain the accuracy of their transport simulations.
Computational Fluid Dynamics for Wind Engineering
Covers topics such as: Fluid mechanics, turbulence in fluid mechanics, turbulence modelling, and mathematical modelling of wind engineering problems The finite difference method for CFD, solutions to the incompressible Navier-Stokes equations, visualization, and animation in CFD, and the application of CFD to building and bridge aerodynamics How to compare CFD analysis with wind tunnel measurements, field measurements, and the ASCE-7 pressure coefficients Wind effects and strain on large structures
