Matematisk modellering

This book mathematically analyzes the basic problems of biology, decision making and psychology within the framework of the theory of open quantum systems.In recent years there has been an explosion of interest in applications of quantum theory in fields beyond physics. The main areas include psychology, decision-making, economics, finance, social science as well as genetics and molecular biology. The corresponding models are referred to as quantum-like; they don¿t concern any genuine physical processes in the human brain.Quantum-like models reflect the special features of information processing in biological, cognitive, and social systems which match well with the quantum formalism. This formalism gives rise to the quantum probability model (QP) which differs essentially from Kolmogorov's classical probability model. QP also serves as the basis for quantum information theory.Recently QP has been widely applied to the resolution of the basic paradoxes ofdecision making theory and to modeling experimental data stemming from cognition, psychology, economics, and finance thereby shedding light on probability fallacies and irrational behavior.In this book, the theory of quantum instruments and the quantum master equation are applied to the modeling of biological and cognitive processes, in particular, to the stability of complex biological and social systems interacting with their environment. An essential part of the book is devoted to the theory of the social laser and the Fröhlich condensate.

A broad range of phenomena in science and technology can be described by non-linear partial differential equations characterized by systems of conservation laws with source terms. Well known examples are hyperbolic systems with source terms, kinetic equations, and convection-reaction-diffusion equations. This book collects research advances in numerical methods for hyperbolic balance laws and kinetic equations together with related modelling aspects. All the contributions are based on the talks of the speakers of the Young Researchers¿ Conference ¿Numerical Aspects of Hyperbolic Balance Laws and Related Problems¿, hosted at the University of Verona, Italy, in December 2021.

This book provides an overview on the current progresses in artificial intelligence and neural nets in data science. The book is reporting on intelligent algorithms and applications modeling, prediction, and recognition tasks and many other application areas supporting complex multimodal systems to enhance and improve human-machine or human-human interactions. This field is broadly addressed by the scientific communities and has a strong commercial impact since investigates on the theoretical frameworks supporting the implementation of sophisticated computational intelligence tools. Such tools will support multidisciplinary aspects of data mining and data processing characterizing appropriate system reactions to human-machine interactional exchanges in interactive scenarios. The emotional issue has recently gained increasing attention for such complex systems due to its relevance in helping in the most common human tasks (like cognitive processes, perception, learning, communication, and even "rational" decision-making) and therefore improving the quality of life of the end users.

The book presents recent applications and developments in the field of control of industrial systems, covering a wide range of modeling and feedback control using various robust approaches such as fuzzy systems, sliding mode control, and H-infinity. This book provides insights into theory, applications, and perspectives relevant to the field of robotic systems, exoskeletons, power systems, photovoltaic systems, etc., as well as general methodologies and paradigms around them. Each chapter provides an enriched understanding of a research topic along with a balanced treatment of the relevant theories, methods, or applications. It reports on the latest advances in the field. This book is a good reference for graduate students, researchers, educators, engineers, and scientists and contains a total of 15 chapters divided into five parts as follows. The first part of this book focuses on the application of fuzzy control to robotic systems and consists of threechapters. The second part of this book proposes the control of lower and upper limb exoskeletons and includes two chapters. The third part is dedicated to the control of power systems and comprises three chapters. The fourth part deals with various approaches to the modeling and control of industrial processes and comprises four chapters. The fifth and final part describes observers and fault-tolerant control systems and comprises five chapters.

This book presents experimental as well as simulation methodologies for analysis and development of nanostructures for introducing the desirable effects through modifications in the basic structure of select nanomaterials. The initial chapters in this book focus on exploring the basic aspects of nanomaterials, e.g., distinguishing features, synthesis, processing, characterization, simulation and application dimensions, or nanostructures that enable novel/enhanced properties or functions. The chapters also cover the size-dependent electronic, optical, and magnetic properties of nanomaterials in exposing the specific properties essential for applications in nanophotonics, nanoplasmonics, nanosystems (e.g., biological, medical, chemical, catalytic, energy, and environmental applications), and nanodevices (e.g., electronic, photonic, magnetic, imaging, diagnostic, and sensor applications). This book is a useful resource for students, researchers, and technologists in gathering recent knowledge on novel nanostructures and their use in different application areas.

This book covers advanced reliability and maintainability knowledge as applied to recent engineering problems. It highlights research in the fields of reliability measures of binary and complex engineering systems, cost analysis, simulations, optimizations, risk factors, and sensitivity analysis. The book scrutinizes various advanced tools and techniques, methodology, and concepts to solve the various engineering problems related to reliability and maintainability of the industrial system at minimum cost and maximum profit. It consists of 15 chapters and offers a platform to researchers, academicians, professionals and scientists to enhance their knowledge and understanding the concept of reliability in engineering.

This book includes contributions about mathematics, physics, philosophy of science, economics and finance and resulted from the Summer School "e;Complexity and Emergence: Ideas, Methods, with a Special Attention to Economics and Finance"e; held in Lake Como School of Advanced Studies, on 22-27 July 2018.The aim of the book is to provide useful instruments from the theory of complex systems, both on the theoretical level and the methodological ones, profiting from knowledge and insights from leading experts of different communities. It moves from the volume editors' conviction that to achieve progress in understanding socio-economical as well as ecological problems of our complex word such preparation is needed, together with a critical reconsideration of our basic scientific and economical approach.The potential readers are primarily master and doctorate students of mathematics, information sciences, theoretical physics and economics, as well as research workers in those areas, who want to enlarge their spectrum of knowledge towards the area of complexity and emergence. Since ideas and methods of the theory of complex systems also apply to other areas (from engineering and architecture to biology and medicine, e.g.), students and research workers from those areas will also profit from this book.

This book presents insights into the thermal performance of solar thermal collectors using both computational and experimental modeling. It consists of various computational and experimental case studies conducted by the authors on the solar thermal collector system. The authors begin by developing thermal modeling using a case study that shows the effect of different governing parameters. A few more experimental cases studies follow that highlight the energy, exergy, and environmental performance of the solar thermal collector system and to examine the performance of a modified solar collector system, illustrating performance improvement techniques.Finally, application of different evolutionary optimization techniques such as soft computing and evolutionary methods, like fuzzy techniques, MCDM methods like fuzzy logic based expert system (FLDS), Artificial Neural Network (ANN), Grey relational analysis (GRA), Entropy-Jaya algorithm, Entropy-VIKOR etc. are employed.

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.

sinusoidal run rhythm entsteht durch die Addition phasengleicher Cosinusfunktionen in ganzzahligen Verhältnissen. Sie sind in ihren Maxima gegenüber entsprechenden notierten Rhythmen zeitlich und dynamisch verschoben und weisen eine Körperlichkeit auf, die in diskret gesteuerten Rhythmen nicht vorhanden ist. sinusoidal run rhythm definiert Rhythmus also als Welle und hebt sich so deutlich von der herkömmlichen Rhythmustheorie einer europäischen Musiktradition ab. Es eröffnet sich eine unerschöpfliche Vielfalt an betörend körperlicher Musik.Der Band bildet diese ästhetische Diversität in zahlreichen Illustrationen der sinusoidal run rhythm ab. Er bietet zum einen die Möglichkeit, in die Ausformungen eines erweiterten Rhythmusbegriffs einzutauchen und sich in die Schönheit einzelner Exemplare zu verlieren - dem Vorbild von Büchern zur Bestimmung von Käfern oder Schmetterlingen folgend. Andererseits regt die Theorie dazu an, die Grenzen zwischen Vorstellung und Aufführung, Partitur und Interpretation, Mensch und Maschine zu aufzuweichen und nach Anwendungen im Musikmachen, in der Musikanalyse, der Psychoakustik oder der Philosophie zu suchen.

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 reconsiders key issues, such as description and explanation, which affect data analytics. For starters: the soul does not exist. Once released from this cumbersome roommate, we are left with complex biological systems: namely, ourselves, who must configure their environment in terms of worlds that are compatible with what they sense. Far from supplying yet another cosmogony, the book provides the cultivated reader with computational tools for describing and understanding data arising from his surroundings, such as climate parameters or stock market trends, even the win/defeat story of his son football team. Besides the superposition of the very many universes considered by quantum mechanics, we aim to manage families of worlds that may have generated those data through the key feature of their compatibility. Starting from a sharp engineering of ourselves in term of pairs consisting of genome plus a neuron ensemble, we toss this feature in different cognitive frameworks within a span of exploitations ranging from probability distributions to the latest implementations of machine learning. From the perspective of human society as an ensemble of the above pairs, the book also provides scientific tools for analyzing the benefits and drawbacks of the modern paradigm of the world as a service.

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.

This Handbook offers the first comprehensive reference guide to the interdisciplinary field of abductive cognition, providing readers with extensive information on the process of reasoning to hypotheses in humans, animals, and in computational machines. It highlights the role of abduction in both theory practice: in generating and testing hypotheses and explanatory functions for various purposes and as an educational device. It merges logical, cognitive, epistemological and philosophical perspectives with more practical needs relating to the application of abduction across various disciplines and practices, such as in diagnosis, creative reasoning, scientific discovery, diagrammatic and ignorance-based cognition, and adversarial strategies. It also discusses the inferential role of models in hypothetical reasoning, abduction and creativity, including the process of development, implementation and manipulation for different scientific and technological purposes. Written by a group ofinternationally renowned experts in philosophy, logic, general epistemology, mathematics, cognitive, and computer science, as well as life sciences, engineering, architecture, and economics, the Handbook of Abductive Cognition offers a unique reference guide for readers approaching the process of reasoning to hypotheses from different perspectives and for various theoretical and practical purposes. Numerous diagrams, schemes and other visual representations are included to promote a better understanding of the relevant concepts and to make concepts highly accessible to an audience of scholars and students with different scientific backgrounds.

The fields of Artificial Intelligence and Machine Learning have grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This book represents a key reference for anybody interested in the intersection between Mathematics and AI/ML and provides an overview of the current research streams.

In this book, innovative research using artificial neural networks (ANNs) is conducted to automate the sizing task of RF IC design, which is used in two different steps of the automatic design process. The advances in telecommunications, such as the 5th generation broadband or 5G for short, open doors to advances in areas such as health care, education, resource management, transportation, agriculture and many other areas. Consequently, there is high pressure in today¿s market for significant communication rates, extensive bandwidths and ultralow-power consumption. This is where radiofrequency (RF) integrated circuits (ICs) come in hand, playing a crucial role. This demand stresses out the problem which resides in the remarkable difficulty of RF IC design in deep nanometric integration technologies due to their high complexity and stringent performances. Given the economic pressure for high quality yet cheap electronics and challenging time-to-market constraints, there is an urgent need for electronic design automation (EDA) tools to increase the RF designers¿ productivity and improve the quality of resulting ICs. In the last years, the automatic sizing of RF IC blocks in deep nanometer technologies has moved toward process, voltage and temperature (PVT)-inclusive optimizations to ensure their robustness. Each sizing solution is exhaustively simulated in a set of PVT corners, thus pushing modern workstations¿ capabilities to their limits.Standard ANNs applications usually exploit the model¿s capability of describing a complex, harder to describe, relation between input and target data. For that purpose, ANNs are a mechanism to bypass the process of describing the complex underlying relations between data by feeding it a significant number of previously acquired input/output data pairs that the model attempts to copy. Here, and firstly, the ANNs disrupt from the most recent trials of replacing the simulator in the simulation-based sizing with a machine/deep learning model, by proposing two different ANNs, the first classifies the convergence of the circuit for nominal and PVT corners, and the second predicts the oscillating frequencies for each case. The convergence classifier (CCANN) and frequency guess predictor (FGPANN) are seamlessly integrated into the simulation-based sizing loop, accelerating the overall optimization process. Secondly, a PVT regressor that inputs the circuit¿s sizing and the nominal performances to estimate the PVT corner performances via multiple parallel artificial neural networks is proposed. Two control phases prevent the optimization process from being misled by inaccurate performance estimates. As such, this book details the optimal description of the input/output data relation that should be fulfilled. The developed description is mainly reflected in two of the system¿s characteristics, the shape of the input data and its incorporation in the sizing optimization loop. An optimal description of thesecomponents should be such that the model should produce output data that fulfills the desired relation for the given training data once fully trained. Additionally, the model should be capable of efficiently generalizing the acquired knowledge in newer examples, i.e., never-seen input circuit topologies.

This monograph provides a comprehensive and self-contained treatment of continuum physics, illustrating a systematic approach to the constitutive equations for wide-ranging classes of materials. Derivations of results are detailed through careful proofs, and the contents have been developed to ensure a self-contained and consistent presentation.Part I reviews the kinematics of continuous bodies and illustrates the general setting of balance laws. Essential preliminaries to continuum physics ¿ such as reference and current configurations, transport relations, singular surfaces, objectivity, and objective time derivatives ¿ are covered in detail. A chapter on balance equations then develops the balance laws of mass, linear momentum, angular momentum, energy, and entropy, as well as the balance laws in electromagnetism.Part II is devoted to the general requirements on constitutive models, emphasizing the application of objectivity and consistency with the second law of thermodynamics. Common models of simple materials are then reviewed, and in this framework, detailed descriptions are given of solids (thermoelastic, elastic, and dissipative) and fluids (elastic, thermoelastic, viscous, and Newtonian).A wide of variety of constitutive models are investigated in Part III, which consists of separate chapters focused on several types of non-simple materials: materials with memory, aging and higher-order grade materials, mixtures, micropolar media, and porous materials. The interaction of the electromagnetic field with deformation is also examined within electroelasticity, magnetoelasticity, and plasma theory.Hysteretic effects and phase transitions are considered in Part IV. A new approach is established by treating entropy production as a constitutive function in itself, as is the case for entropy and entropy flux. This proves to be conceptually and practically advantageous in the modelling of nonlinear phenomena, such as those occurring in hysteretic continua (e.g., plasticity, electromagnetism, and the physics of shape memory alloys).Mathematical Modelling of Continuum Physics will be an important reference for mathematicians, engineers, physicists, and other scientists interested in research or applications of continuum mechanics.

This edited volume, with contributions from the Computer Aided Engineering for Batteries (CAEBAT) program, provides firsthand insights into nuances of implementing battery models in actual geometries. It discusses practical examples and gaps in our understanding, while reviewing in depth the theoretical background and algorithms. Over the last ten years, several world-class academics, automotive original equipment manufacturers (OEMs), battery cell manufacturers and software developers worked together under an effort initiated by the U.S. Department of Energy to develop mature, validated modeling tools to simulate design, performance, safety and life of automotive batteries. Until recently, battery modeling was a niche focus area with a relatively small number of experts. This book opens up the research topic for a broader audience from industry and academia alike. It is a valuable resource for anyone who works on battery engineering but has limited hands-on experience with coding.

This book develops and details a rigorous, canonical modeling approach for analyzing spatio-temporal brain wave dynamics. The nonlinear, nonstationary behavior of brain wave measures and general uncertainty associated with the brain makes it difficult to apply modern system identification techniques to such systems. While there is a substantial amount of literature on the use of stationary analyses for brain waves, relatively less work has considered real-time estimation and imaging of brain waves from noninvasive measurements. This book addresses the issue of modeling and imaging brain waves and biomarkers generally, treating the nonlinear and nonstationary dynamics in near real-time. Using a modal state-space formulation leads to intuitive, physically significant models which are used for analysis and diagnosis.A Modal Approach to the Space-Time Dynamics of Cognitive Biomarkers provides a much-needed reference for practicing researchers in biomarker modeling leveraging the lens of engineering dynamics.

The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician.Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader¿s intuition.By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation.Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.

This book contains the papers presented at the XXXI International Congress INGEGRAF ¿Graphic Expression: reunion, reflection, representation,¿ held on June 29¿30 and July 1, 2021, in Málaga, Spain. It reports on cutting-edge topics in product design and manufacturing, such as industrial methods for integrated product and process design, innovative design and computer-aided design. Further topics covered include virtual simulation and reverse engineering, additive manufacturing, product manufacturing,engineering methods in medicine and education, representation techniques and nautical, engineering and construction, aeronautics and aerospace design and modeling. The book is divided into six main sections, reflecting the focus and primary themes of the conference. The contributions presented here provide researchers, engineers and experts in a range of industrial engineering subfields with extensive information to support their daily work; but also they are intended to stimulate new research directions, advanced applications of the methods discussed and future interdisciplinary collaborations.