Matematik for ingeniører

This contributed volume presents recent developments in nonlinear dynamics applied to engineering. Specifically, the authors address stability and bifurcation in large-scale, complex rotor dynamic systems; periodic motions and their bifurcations in nonlinear circuit systems, fault diagnosis of complex engineering systems with nonlinear approaches, singularities in fluid-machinery and bifurcation analysis, nonlinear behaviors in rotor dynamic system with multi-mistuned blades, mode localization induced by mistuning in impellers with periodical and cyclic symmetry, and nonlinear behaviors in fluid-structure interaction and their control. These new results will maximize reader understand on the recent progress in nonlinear dynamics applied to large-scale, engineering systems in general and nonlinear rotors and impellers in particular.

Das Buch bietet eine umfassende und praxisorientierte Einfuhrung in die wesentlichen Grundlagen und Konzepte der Informatik. Es umfasst den Stoff, der typischerweise in den ersten Semestern eines Informatikstudiums vermittelt wird, vertieft Zusammenhange, die daruber hinausgehen und macht sie verstandlich. Die Themenauswahl orientiert sich an der langfristigen Relevanz fur die praktische Anwendung. Praxisnah und aktuell werden die Inhalte fur Studierende der Informatik und verwandter Studiengange sowie fur im Beruf stehende Praktiker vermittelt. Die vorliegende funfte Auflage wurde grundlegend uberarbeitet und aktualisiert.

This text describes a comprehensive adjoint sensitivity analysis methodology (nth-CASAM), developed by the author, which enablesthe efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The nth-CASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby overcoming the so-called ¿curse of dimensionality¿ in sensitivity and uncertainty analysis. The nth-CASAM is applicable to any model; the larger the number of model parameters, the more efficient the nth-CASAM becomes for computing arbitrarily high-order response sensitivities. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling.This Volume Two, the second of three, presents the large-scale application of the nth-CASAM to perform a representative fourth-order sensitivity analysis of the Polyethylene-Reflected Plutonium benchmark described in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This benchmark is modeled mathematically by the Boltzmann particle transport equation, involving 21,976 imprecisely-known parameters, the numerical solution of which requires representative large-scale computations. The sensitivity analysis presented in this volume is the most comprehensive ever performed in the field of reactor physics and the results presented in this book prove, perhaps counter-intuitively, that many of the 4th-order sensitivities are much larger than the corresponding 3rd-order ones, which are, in turn, much larger than the 2nd-order ones, all of which are much larger than the 1st-order sensitivities. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of exactly obtained expressions of arbitrarily-high-order response sensitivities.

Nonlinear Approaches in Engineering Applications: Design Engineering Problems examines the latest applications of nonlinear approaches in engineering and addresses a range of scientific problems. Chapters are authored by world-class scientists and researchers and focus on the application of nonlinear approaches in different disciplines of engineering and scientific applications, with a strong emphasis on application, physical meaning, and methodologies of the approaches. Topics covered are of high interest in engineering and physics, and an attempt has been made to expose engineers and researchers to a broad range of practical topics and approaches. This book is appropriate for researchers, students, and practicing engineers who are interested in the applications of engineering, physics, and mathematics in nonlinear approaches to solving engineering and science problems.    

The book is very useful for researchers, graduate students and educators associated with or interested in recent advances in different aspects of modelling, computational methods and techniques necessary for solving problems arising in the real-world problems. The book includes carefully peer-reviewed research articles presented in the ¿5th International Conference on Mathematical Modelling, Applied Analysis and Computation¿, held at JECRC University, Jaipur, during 4¿6 August 2022 concentrating on current advances in mathematical modelling and computation via tools and techniques from mathematics and allied areas. It is focused on papers dealing with necessary theory and methods in a balanced manner and contributes towards solving problems arising in engineering, control systems, networking system, environment science, health science, physical and biological systems, social issues of current interest, etc.

The book presents the proceedings of four conferences: The 26th International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA'20), The 18th International Conference on Scientific Computing (CSC'20); The 17th International Conference on Modeling, Simulation and Visualization Methods (MSV'20); and The 16th International Conference on Grid, Cloud, and Cluster Computing (GCC'20). The conferences took place in Las Vegas, NV, USA, July 27-30, 2020. The conferences are part of the larger 2020 World Congress in Computer Science, Computer Engineering, & Applied Computing (CSCE'20), which features 20 major tracks. Authors include academics, researchers, professionals, and students.Presents the proceedings of four conferences as part of the 2020 World Congress in Computer Science, Computer Engineering, & Applied Computing (CSCE'20);Includes the research tracks Parallel and Distributed Processing, Scientific Computing, Modeling, Simulation and Visualization, and Grid, Cloud, and Cluster Computing;Features papers from PDPTA'20, CSC'20, MSV'20, and GCC'20.

This text describes a comprehensive adjoint sensitivity analysis methodology (C-ASAM), developed by the author, enabling the efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The model¿s responses can be either scalar-valued functionals of the model¿s parameters and state variables (as customarily encountered, e.g., in optimization problems) or general function-valued responses, which are often of interest but are currently not amenable to efficient sensitivity analysis. The C-ASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby breaking the so-called ¿curse of dimensionality¿ in sensitivity and uncertainty analysis. The C-ASAM applies to any model; the larger the number of model parameters, the more efficient the C-ASAM becomes for computing arbitrarily high-order response sensitivities. The text includes illustrative paradigm problems which are fully worked-out to enable the thorough understanding of the C-ASAM¿s principles and their practical application. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling. It serves as a textbook or as supplementary reading for graduate course on these topics, in academic departments in the natural, biological, and physical sciences and engineering.This Volume Three, the third of three, covers systems that are nonlinear in the state variables, model parameters and associated responses. The selected illustrative paradigm problems share these general characteristics. A separate Volume One covers systems that are linear in the state variables.

This book provides an introduction to the fundamental theory, practical implementation, and core and emerging applications of the material point method (MPM) and its variants. The MPM combines the advantages of both finite element analysis (FEM) and meshless/meshfree methods (MMs) by representing the material by a set of particles overlaid on a background mesh that serves as a computational scratchpad.The book shows how MPM allows a robust, accurate, and efficient simulation of a wide variety of material behaviors without requiring overly complex implementations. MPM and its variants have been shown to be successful in simulating a large number of high deformation and complicated engineering problems such as densification of foam, sea ice dynamics, landslides, and energetic device explosions, to name a few, and have recently found applications in the movie industry. It is hoped that this comprehensive exposition on MPM variants and their applications will not only provide anopportunity to re-examine previous contributions, but also to re-organize them in a coherent fashion and in anticipation of new advances.Sample algorithms for the solutions of benchmark problems are provided online so that researchers and graduate students can modify these algorithms and develop their own solution algorithms for specific problems. The goal of this book is to provide students and researchers with a theoretical and practical knowledge of the material point method to analyze engineering problems, and it may help initiate and promote further in-depth studies on the subjects discussed.

This book presents the modeling and scaling of physical problems, which result in normalized perturbation equations. This is followed by solving perturbation problems and evaluating the results. The author refines perturbation methods into simple, understandable elements and avoids unnecessary theorems and proofs. In addition, the results are consolidated and interpreted, and the presented examples are succinct to illustrate the essential techniques. This book is ideal and beneficial for practicing scientists and engineers who need to understand and apply perturbation methods to difficult problems with applications in mathematics, engineering, and biology. Discussions on new perspectives, simpler presentations on convergence, and the expansion of integrals are included.

This is a book for a lab course meant to accompany, or follow, any standard course in electronic circuit analysis. It has been written for sophomore or junior electrical and computer engineering students, either concurrently with their electronic circuit analysis class or following that class. This book is appropriate for non-majors, such as students in other branches of engineering and in physics, for which electronic circuits is a required course or elective and for whom a working knowledge of electronic circuits is desirable. This book has the following objectives: 1. To support, verify, and supplement the theory; to show the relations and differences between theory and practice. 2. To teach measurement techniques. 3. To convince students that what they are taught in their lecture classes is real and useful. 4. To help make students tinkerers and make them used to asking ¿what if¿ questions.

The volume provides a comprehensive understanding of the macroscopic failure behavior of solids from the description of the microscopic failure processes and their coupling with the microstructure. Several fundamental questions were addressed: the relation between the microstructural features of materials and their fracture properties and crack trajectories; the role of damage mechanisms and non-linear deformations near the crack tip on the failure behavior of solids; and finally the role of dynamic inertial effects during fast fracture was more briefly evoked. The chapters provide a pedagogical overview of recently developed concepts and tools, that permit to perform the transition from small scales to large ones in fracture problems, thus introducing basic rules for the rational design of tough solids.

Dieses Buch hat sich als Basis fur den Einsatz von Visual Basic fur Studierende aller Fachbereiche und in der Praxis bestens bewahrt. Hier lernen Sie die grundlegenden Programmiertechniken anhand einfacher Beispiele in Verbindung mit Visual Basic kennen und einsetzen. Alle eingefuhrten Sprachelemente gelten fur die Versionen Visual Basic 6.0, VB .NET und Visual Basic for Application (VBA). Die vermittelten Kenntnisse dienen sowohl als Basis fur weiterfuhrende VB-Programme als auch fur die Einarbeitung in andere Sprachen. Schritte der Programmentwicklung, Algorithmen-Entwurfe, Unterprogrammtechniken und die Nutzung komplexer Datentypen werden vollstandig anhand von leicht nachvollziehbaren Beispielaufgaben erlautert. Inklusive Objekt-orientierter Programmierung - das Buch zeigt, wie es geht.

¿This book comprises selected papers of the 26th International Conference on Difference Equations and Applications, ICDEA 2021, held virtually at the University of Sarajevo, Bosnia and Herzegovina, in July 2021.The book includes the latest and significant research and achievements in difference equations, discrete dynamical systems, and their applications in various scientific disciplines.The book is interesting for Ph.D. students and researchers who want to keep up to date with the latest research, developments, and achievements in difference equations, discrete dynamical systems, and their applications, the real-world problems.

An original method of investigation of the conjugate conductive-convective problem of periodic heat transfer is developed. The novelty of the approach is that a particular conjugate problem is replaced by a general boundary-value problem for the heat conduction equation in the solid. Within the framework of the hyperbolic model of thermal conductivity, the effect of self-reinforcement of the degree of conjugation by increasing the period of oscillations is found. The processes of hydrodynamics and heat exchange with periodic internal structure are considered: periodic model of turbulent heat transfer, hydrodynamic instability, bubbles dynamics in liquid, and model of evaporating meniscus. The book is intended as a source and reference work for researchers and graduate students interested in the field of conjugate heat transfer.

This book is an attempt to develop a guide for the user who is interested in learning the method by doing. There is enough discussion of some of the basic theory so that the user can get a broad understanding of the process. And there are many examples with step-by-step instructions for the user to quickly develop some proficiency in using FEA. We have used Matlab and its PDE toolbox for the examples in this text. The syntax and the modeling process are easy to understand and a new user can become productive very quickly. The PDE toolbox, just like any other commercial software, can solve certain classes of problems well but is not capable of solving every type of problem. For example, it can solve linear problems but is not capable of handling non-linear problems. Being aware of the capabilities of any tool is an important lesson for the user and we have, with this book, tried to highlight that lesson as well.

This book illustrates why abstract mathematical entities are needed to represent some aspects of physical reality. It provides an overview of different types of numbers and functions along with their historical background and applications.

Exploring the concept of homotopy from topology, different homotopy-based methods have been proposed for analytically solving nonlinear differential equations, given by approximate series solutions. Homotopy-Based Methods in Water Engineering attempts to present the applicability of these methods to water engineering problems.