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Mathematical Modelling of Complex Patterns Through Fractals and Dynamical Systems (Studies in Infrastructure and Control)

This book offers a wide range of interesting correlations beyond the domains of dynamical systems, complex systems, and fractal geometry. Exploring complex systems and their properties using the fractal approaches, this book provides initial solutions for new areas where fractal theory has yet to verify itsexpertise. Further, the book focusses on the latest scientific interest and illustrates general fractal theory in multidisciplinary areas such as computer science, electronics engineering, electrical engineering, bioengineering, biomedical, quantum physics and fluid dynamics research. This edited book is designed for professionals in the field of mathematics, computer science and physics, and even for non-specialists to help understand the concepts of fractals in nonlinear dynamical systems and complex systems while offering applications for researchers in the pure as well as in the applied background of science andengineering.

Mathematical Modelling of Fluid Dynamics and Nanofluids

Mathematical Modelling of Fluid Dynamics and Nanofluids serves as a comprehensive resource for various aspects of fluid dynamics simulations, nanofluid preparation, and numerical techniques.The book examines the practical implications and real-world applications of various concepts, including nanofluids, magnetohydrodynamics, heat and mass transfer, and radiation. By encompassing these diverse domains, it offers readers a broad perspective on the interconnectedness of these fields.The primary audience for this book includes researchers and graduate students who possess a keen interest in interdisciplinary studies within the realms of fluid dynamics, nanofluids, and biofluids. Its content caters to those who wish to deepen their knowledge and tackle complex problems at the intersection of these disciplines.

Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics

Beginning with an introduction to kidney function, renal replacement therapies, and an overview of clinical problems associated with haemodialysis, this book explores the principles of the short-term baroreflex regulation of the cardiovascular system and the mechanisms of water and solute transport across the human body from a mathematical model perspective. It synthesizes theoretical physiological concepts and practical aspects of mathematical modelling needed for simulation and quantitative analysis of the haemodynamic response to dialysis therapy.Including an up-to-date review of the literature concerning the modelled physiological mechanisms and processes, the book serves both as an overview of transport and regulatory mechanisms related to the cardiovascular system and body fluids and as a useful reference for the study and development of mathematical models of dynamic physiological processes.Mathematical Modelling of Haemodialysis: Cardiovascular Response, Body Fluid Shifts, and Solute Kinetics is intended for researchers and graduate students in biomedical engineering, physiology, or medicine interested in mathematical modelling of cardiovascular dynamics and fluid and solute transport across the human body, both under physiological conditions and during haemodialysis therapy.

Mathematical Modelling of Heat Transfer Performance of Heat Exchanger using Nanofluids

The book presents a detailed discussion of nanomaterials, nanofluids and application of nanofluids as a coolant to reduce heat transfer. It presents a detailed approach to the formulation of mathematical modelling applicable to any type of case study with a validation approach and sensitivity and optimization. Covers the aspects of formulation of mathematical modelling with optimization and sensitivity analysis. Presents a case study based on heat transfer improvement and performs operations using nanofluids. Examines the analysis of experimental data by the formulation of a mathematical model and correlation between input data and output data. Illustrates heat transfer improvement of heat exchangers using nanofluids through the mathematical modelling approach. Discusses applications of nanofluids in cooling systems. This book discusses the aspect of formulation of mathematical modelling with optimization and sensitivity analysis. It further presents a case study based on the heat transfer improvement and performing operations using nanofluids. The text covers sensitivity analysis and analysis from the indices of the model. It also discusses important concepts such as nanomaterials, applications of nanomaterials, and nanofluids. It will serve as an ideal reference text for senior undergraduate, and graduate students in fields including mechanical engineering, chemical engineering, aerospace engineering, industrial engineering, and manufacturing engineering.

Mathematical Modelling of Meteoroid Streams (SpringerBriefs in Astronomy)

Modern computer power and high-precision observational data have greatly improved the reliability of meteoroid stream models. At present, scientific research calls for two kinds of models: precise ones for individual streams, and statistically averaged ones for Solar System dust distribution models. Thus, there is a wide field of study open to stream modellers. This brief describes step-by-step computer simulations of meteoroid stream formation and evolution. Detailed derivations of relevant formulae are given, along with plenty of helpful, digestible figures explaining the subtleties of the method. Each theoretical section ends with examples aimed to help readers practice and master the material. Most of the examples are based on the Geminid meteoroid stream model, which has been developed by the author in the last 30 years. The book is intended for researchers interested in meteor astronomy and mathematical modelling, and it is also accessible to physics and astrophysics students.

Mathematical Modelling of Physical Systems

Mathematical Modelling of System Resilience

Almost all the systems in our world, including technical, social, economic, and environmental systems, are becoming interconnected and increasingly complex, and as such they are vulnerable to various risks. Due to this trend, resilience creation is becoming more important to system managers and decision makers, this to ensure sustained performance. In order to be able to ensure an acceptable sustained performance under such interconnectedness and complexity, resilience creation with a system approach is a requirement. Mathematical modeling based approaches are the most common approach for system resilience creation.Mathematical Modelling of System Resilience covers resilience creation for various system aspects including a functional system of the supply chain, overall supply chain systems; various methodologies for modeling system resilience; satellite-based approach for addressing climate related risks, repair-based approach for sustainable performance of an engineering system, and modeling measures of the reliability for a vertical take-off and landing system. Each of the chapters contributes state of the art research for the relevant resilience related topic covered in the chapter. Technical topics covered in the book include:1. Supply chain risk, vulnerability and disruptions 2. System resilience for containing failures and disruptions3. Resiliency considering frequency and intensities of disasters4. Resilience performance index5. Resiliency of electric Traction system6. Degree of resilience7. Satellite observation and hydrological risk8. Latitude of Resilience9. On-line repair for resilience10. Reliability design for Vertical Takeoff and landing Prototype

Mathematical Modelling of Waves in Multi-Scale Structured Media (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.

Mathematical Modelling of Weld Phenomena: No. 4

Contains the papers presented at the fourth International Seminar "Numerical Analysis of Weldability" held in September 1997 at Schloss Seggau near Graz, Austria.

Mathematical Modelling of Weld Phenomena: No. 5

Contains the papers presented at the fourth International Seminar "Numerical Analysis of Weldability" held in September 1997 at Schloss Seggau near Graz, Austria.

Mathematical Modelling of Zombies

In this terrible new COVID-19 world, the University of Ottawa is doing its part by offering a 50% discount on this very important book. We decided not to rewrite the witty book description, though we realize it is tone-deaf at the present moment, as we wanted to give readers a sense of the tone of this title. But don’t be deceived: while a fun read, this book will help you better understand how epidemiologists, governments and health care planners use mathematical models to figure out how quickly epidemics and pandemics spread, in order to plan appropriately. Reading has perhaps never been as important, and this book should be at the top of your reading list. You’re outnumbered, in fear for your life, surrounded by flesheating zombies. What can save you now? Mathematics, of course.Mathematical Modelling of Zombies engages the imagination to illustrate the power of mathematical modelling. Using zombies as a “hook,” you’ll learn how mathematics can predict the unpredictable. In order to be prepared for the apocalypse, you’ll need mathematical models, differential equations, statistical estimations, discretetime models, and adaptive strategies for zombie attacks—as well as baseball bats and Dire Straits records (latter two items not included).In Mathematical Modelling of Zombies, Robert Smith? brings together a highly skilled team of contributors to fend off a zombie uprising. You’ll also learn how modelling can advise government policy, how theoretical results can be communicated to a nonmathematical audience and how models can be formulated with only limited information. A forward by Andrew Cartmel—former script editor of Doctor Who, author, zombie fan and all-round famous person in science-fiction circles—even provides a genealogy of the undead. By understanding how to combat zombies, readers will be introduced to a wide variety of modelling techniques that are applicable to other real-world issues (biology, epidemiology, medicine, public health, etc.).So if the zombies turn up, reach for this book. The future of the human race may depend on it.

Mathematical Modelling of the Cell Cycle Stress Response

The cell cycle is a sequence of biochemical events that are controlled by complex but robust molecular machinery. This enables cells to achieve accurate self-reproduction under a broad range of conditions. Environmental changes are transmitted by molecular signaling networks, which coordinate their actions with the cell cycle. This work presents the first description of two complementary computational models describing the influence of osmotic stress on the entire cell cycle of S. cerevisiae. Our models condense a vast amount of experimental evidence on the interaction of the cell cycle network components with the osmotic stress pathway. Importantly, it is only by considering the entire cell cycle that we are able to make a series of novel predictions which emerge from the coupling between the molecular components of different cell cycle phases. The model-based predictions are supported by experiments in S. cerevisiae and, moreover, have recently been observed in other eukaryotes. Furthermore our models reveal the mechanisms that emerge as a result of the interaction between the cell cycle and stress response networks.

Mathematical Modelling, Nonlinear Control and Performance Evaluation of a Ground Based Mobile Air Defence System (Mechanisms and Machine Science #76)

In this book, the author deals with the mathematical modelling, nonlinear control and performance evaluation of a conceptual anti-aircraft gun based mobile air defence system engaging an attacking three-dimensional aerial target.This book is of interest to academic faculty, graduate students and industry professionals working in the fields of mathematical modelling and control, ground vehicles, mobile air defence systems and other related topics.

Mathematical Modelling, Optimization, Analytic and Numerical Solutions (Industrial and Applied Mathematics)

This book discusses a variety of topics related to industrial and applied mathematics, focusing on wavelet theory, sampling theorems, inverse problems and their applications, partial differential equations as a model of real-world problems, computational linguistics, mathematical models and methods for meteorology, earth systems, environmental and medical science, and the oil industry. It features papers presented at the International Conference in Conjunction with 14th Biennial Conference of ISIAM, held at Guru Nanak Dev University, Amritsar, India, on 2–4 February 2018. The conference has emerged as an influential forum, bringing together prominent academic scientists, experts from industry, and researchers. The topics discussed include Schrodinger operators, quantum kinetic equations and their application, extensions of fractional integral transforms, electrical impedance tomography, diffuse optical tomography, Galerkin method by using wavelets, a Cauchy problem associated with Korteweg–de Vries equation, and entropy solution for scalar conservation laws. This book motivates and inspires young researchers in the fields of industrial and applied mathematics.

Mathematical Models and Environmental Change: Case Studies in Long Term Management (Routledge Focus on Environment and Sustainability)

This book demonstrates how mathematical models constructed in system dynamics modelling platforms, such as Vensim, can be used for long-term management of environmental change. It is divided into two sections, with the first dedicated to theory, where the theory of co-evolutionary modelling and its use in the system dynamics model platform is developed. The book takes readers through the steps in the modelling process, different validation tools applicable to these types of models and different growth specification, as well as how to curve fit using numerical methods in Vensim. Section 2 comprises of a collection of applied case studies, including fisheries, game theory and wildlife management. The book concludes with lessons from the use of co-evolutionary models for long-term natural resource management. The book will be of great interest to students and scholars of environmental economics, natural resource management, system dynamics, ecological modelling and bioeconomics.

Mathematical Models and Methods for Plasma Physics, Volume 1

This monograph is dedicated to the derivation and analysis of fluid models occurring in plasma physics. It focuses on models involving quasi-neutrality approximation, problems related to laser propagation in a plasma, and coupling plasma waves and electromagnetic waves. Applied mathematicians will find a stimulating introduction to the world of plasma physics and a few open problems that are mathematically rich. Physicists who may be overwhelmed by the abundance of models and uncertain of their underlying assumptions will find basic mathematical properties of the related systems of partial differential equations. A planned second volume will be devoted to kinetic models. First and foremost, this book mathematically derives certain common fluid models from more general models. Although some of these derivations may be well known to physicists, it is important to highlight the assumptions underlying the derivations and to realize that some seemingly simple approximations turn out to be more complicated than they look. Such approximations are justified using asymptotic analysis wherever possible. Furthermore, efficient simulations of multi-dimensional models require precise statements of the related systems of partial differential equations along with appropriate boundary conditions. Some mathematical properties of these systems are presented which offer hints to those using numerical methods, although numerics is not the primary focus of the book.

Mathematical Models and Numerical Simulation in Electromagnetism

The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations that should be solved in order to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory based on ordinary differential equations. The book is mainly oriented to electric engineering applications, going from the general to the specific, namely, from the full Maxwell's equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standard exercises related to analytical calculus, the book includes some others oriented to real-life applications solved with MaxFEM free simulation software.

Mathematical Models for Dental Materials Research

This book presents a mechanistic approach—mathematical modeling—for carrying out dental materials research. This approach allows researchers to go beyond the null hypothesis and obtain a solution that is more general and therefore predictive for conditions other than those considered in a study. Hence it can be used either on its own or to complement the commonly used statistical approach. Through a series of practical problems with wide-ranging application, the reader will be guided on:How to construct a mathematical model for the behavior of dental materials by making informed assumptions of the physical, chemical, or mechanical situationHow to simplify the model by making suitable simplificationsHow to calibrate the model by calculating the values of key parameters using experimental resultsHow to refine the model when there are discrepancies between predictions and experimentsOnly elementary calculus is required to follow the examples and all the problems can be solved by using MS Excel© spreadsheets.This is an ideal book for dental materials researchers without a strong mathematical background who are interested in applying a more mechanistic approach to their research to give deeper insight into the problem at hand. Advance praise for Mathematical Models for Dental Materials Research:“This is a nice addition for research students on how to conduct their work and how to manage data analysis. It brings together a number of important aspects of dental materials investigations which has been missing in the literature. The practical examples make it much easier to understand.” – Michael F. Burrow, Clinical Professor in Prosthodontics, The University of Hong Kong“The great strengths of this volume are the real world examples of dental materials research in the successive chapters. In turn, this is an outcome of the outstanding expertise of both authors. I warmly recommend this book to the dental biomaterials community worldwide.” – David C. Watts, Professor of Biomaterials Science, University of Manchester, UK

Mathematical Models for Eddy Currents and Magnetostatics

This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i. e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problems are given. Related issues such as convergence of the approximations and error estimates are discussed. The second part of the monograph presents various coupled problems that involve eddy current or magnetostatic problems, in particular magneto-hydrodynamic problems and magnetic shaping problems concerning the melt flow of electrically conducting metals, induction heating processes, inductively coupled plasmas and ferromagnetic screening modeling. The presentation of each model comes with numerical illustration from industrial applications.

Mathematical Models in Biology

This book presents an exciting collection of contributions based on the workshop "Bringing Maths to Life" held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content useful as it addresses existing challenges in identifying the gaps between mathematical modeling and biological research. The shared solutions will aid and promote further collaboration between life sciences and mathematics.

Mathematical Models in Biology an Introduction

This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.

Mathematical Models in the Biosciences I

An award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences This is the first of a two-part series exploring essential concepts of calculus in the context of biological systems. Michael Frame covers essential ideas and theories of basic calculus and probability while providing examples of how they apply to subjects like chemotherapy and tumor growth, chemical diffusion, allometric scaling, predator-prey relations, and nerve impulses. Based on the author’s calculus class at Yale University, the book makes concepts of calculus more relatable for science majors and premedical students.

Mathematical Models in the Biosciences II

Volume Two of an award-winning professor&’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences This is the second of a two-part series exploring essential concepts of calculus in the context of biological systems. Building on the essential ideas and theories of basic calculus taught in Mathematical Models in the Biosciences I, this book focuses on epidemiological models, mathematical foundations of virus and antiviral dynamics, ion channel models and cardiac arrhythmias, vector calculus and applications, and evolutionary models of disease. It also develops differential equations and stochastic models of many biomedical processes, as well as virus dynamics, the Clancy-Rudy model to determine the genetic basis of cardiac arrhythmias, and a sketch of some systems biology. Based on the author&’s calculus class at Yale, the book makes concepts of calculus less abstract and more relatable for science majors and premedical students.

Mathematical Models of Cancer and Different Therapies: Unified Framework (Series in BioEngineering)

This book provides a unified framework for various currently available mathematical models that are used to analyze progression and regression in cancer development, and to predict its dynamics with respect to therapeutic interventions. Accurate and reliable model representations of cancer dynamics are milestones in the field of cancer research. Mathematical modeling approaches are becoming increasingly common in cancer research, as these quantitative approaches can help to validate hypotheses concerning cancer dynamics and thus elucidate the complexly interlaced mechanisms involved. Even though the related conceptual and technical information is growing at an exponential rate, the application of said information and realization of useful healthcare devices are lagging behind.In order to remedy this discrepancy, more interdisciplinary research works and course curricula need to be introduced in academic, industrial, and clinical organizations alike. To that end, this book reformulates most of the existing mathematical models as special cases of a general model, allowing readers to easily get an overall idea of cancer dynamics and its modeling. Moreover, the book will help bridge the gap between biologists and engineers, as it brings together cancer dynamics, the main steps involved in mathematical modeling, and control strategies developed for cancer management. This also allows readers in both medical and engineering fields to compare and contrast all the therapy-based models developed to date using a single source, and to identify unexplored research directions.

Mathematical Models of Cell-Based Morphogenesis: Passive and Active Remodeling (Theoretical Biology)

This book describes the shape formation of living organisms using mathematical models. Genes are deeply related to the shape of living organisms, and elucidation of a pathway of shape formation from genes is one of the fundamental problems in biology. Mathematical cell models are indispensable tools to elucidate this problem. The book introduces two mathematical cell models, the cell center model and the vertex model, with their applications. The cell center model is applied to elucidate the formation of neat cell arrangements in epidermis, cell patterns consisting of heterogeneous-sized cells, capillary networks, and the branching patterns of blood vessels. The vertex model is applied to elucidate the wound healing mechanisms of the epithelium and ordered pattern formation involving apoptosis. Pattern formation with differential cell adhesion is also described. The vertex model is then extended from a two-dimensional (2D) to a three-dimensional (3D) model. A cell aggregate involving a large cavity is described to explain the development of the mammalian blastocyst or the formation of an epithelial vesicle. Epithelial tissues and the polarity formation process of the epithelium are also explained. The vertex model also recapitulates active remodeling of tissues and describes the twisting of tissue that contributes to understanding the cardiac loop formation of the embryonic tube. The book showcases that mathematical cell models are indispensable tools to understand the shape formation of living organisms. Successful contribution of the mathematical cell models means that the remodeling of collective cells is self-construction. Examining the successive iterations of self-constructions leads to understanding the remarkable and mysterious morphogenesis that occurs during the development of living organisms. The intended readers of this book are not only theoretical or mathematical biologists, but also experimental and general biologists, including undergraduate and postgraduate students who are interested in the relationship between genes and morphogenesis.