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Mathematical Modeling of Biological Processes
by Avner Friedman Chiu-Yen KaoThis book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.
Mathematical Modeling of Biosensors: An Introduction For Chemists And Mathematicians (Springer Series on Chemical Sensors and Biosensors #9)
by Romas Baronas Feliksas Ivanauskas Juozas KulysThis newly designed and enlarged edition offers an up-to-date presentation of biosensor development and modeling from both a chemical and a mathematical point of view. An entire new chapter in particular is dedicated to optimal design of biosensors. Two more new chapters discuss biosensors which utilize microbial cells and are based on carbon nanotubes respectively. All the other chapters have been revised and updated. The book contains unique modeling methods for amperometric, potentiometric and optical biosensors based mainly on biocatalysts . It examines processes that occur in the sensors' layers and at their interface, and it provides analytical and numerical methods to solve equations of conjugated enzymatic (chemical) and diffusion processes. The action of single enzyme as well as polyenzyme biosensors and biosensors based on chemically modified electrodes is studied. The modeling of biosensors that contain perforated membranes and multipart mass transport profiles is critically investigated. Furthermore, it is fully described how signals can be biochemically amplified, how cascades of enzymatic substrate conversion are triggered, and how signals are processed via a chemometric approach and artificial neuronal networks. The results of digital modeling are compared with both proximal analytical solutions and experimental data.
Mathematical Modeling of Biosensors
by Juozas Kulys Romas Baronas Feliksas IvanauskasThis book presents biosensor development and modeling from both a chemical and a mathematical point of view. It contains unique modeling methods for catalytical (amperometric, potentiometer and optical) biosensors. It examines processes that occur in the sensors' layers and at their interface, and it provides analytical and numerical methods to solve enzymatic kinetic and diffusion equations. The action of single enzyme as well as polyenzyme biosensors is studied, and the modeling of biosensors that contain perforated membranes and multipart mass transport profiles is critically investigated. Furthermore, it is fully described how signals can be biochemically amplified, how cascades of enzymatic substrate conversion are triggered, and how signals are processed via a chemometric approach and artificial neuronal networks. The results of digital modeling are compared with both proximal analytical solutions and experimental data.
Mathematical Modeling of Disperse Two-Phase Flows
by Christophe MorelThis book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas. Chapters clarify many difficult subjects, including modeling of the interfacial area concentration. Basic knowledge of the subjects treated in this book is essential to practitioners of Computational Fluid Dynamics for two-phase flows in a variety of industrial and environmental settings. The author provides a complete derivation of the basic equations, followed by more advanced subjects like turbulence equations for the two phases (continuous and disperse) and multi-size particulate flow modeling. As well as theoretical material, readers will discover chapters concerned with closure relations and numerical issues. Many physical models are presented, covering key subjects including heat and mass transfers between phases, interfacial forces and fluid particles coalescence and breakup, amongst others. This book is highly suitable for students in the subject area, but may also be a useful reference text for more advanced scientists and engineers.
Mathematical Modeling of Emission in Small-Size Cathode (Heat and Mass Transfer)
by Vladimir Danilov Roman Gaydukov Vadim KretovThis book deals with mathematical modeling, namely, it describes the mathematical model of heat transfer in a silicon cathode of small (nano) dimensions with the possibility of partial melting taken into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type free boundary problems. The approach used is not purely mathematical but is based on the understanding of the solution structure (construction and study of asymptotic solutions) and computer calculations. The book presents an algorithm for numerical solution of the equations of the mathematical model including its parallel implementation. The results of numerical simulation concludes the book. The book is intended for specialists in the field of heat transfer and field emission processes and can be useful for senior students and postgraduates.
Mathematical Modeling of Food Processing
by Mohammed M. FaridWritten by international experts from industry, research centers, and academia, Mathematical Modeling of Food Processing discusses the physical and mathematical analysis of transport phenomena associated with food processing. The models presented describe many of the important physical and biological transformations that occur in food during proces
Mathematical Modeling Of Melting And Freezing Processes
by V. AlexiadesThis reference book presents mathematical models of melting and solidification processes that are the key to the effective performance of latent heat thermal energy storage systems (LHTES), utilized in a wide range of heat transfer and industrial applications. This topic has spurred a growth in research into LHTES applications in energy conservation and utilization, space station power systems, and thermal protection of electronic equipment in hostile environments. Further, interest in mathematical modeling has increased with the speread of high powered computers used in most industrial and academic settings. In two sections, the book first describes modeling of phase change processes and then describes applications for LHTES. It is aimed at graduate students, researchers, and practicing engineers in heat transfer, materials processing, multiphase systems, energy conservation, metallurgy, microelectronics, and cryosurgery.
Mathematical Modeling of Mitochondrial Swelling
by Messoud EfendievThe mathematical models considered in this book can help to understand the swelling of mitochondria. For the first time, it presents new mathematical models of mitochondrial swelling that take into account, in particular, spatial effects. The results presented here could make it possible to predict properties of the underlying biological mechanisms. Taking into account that mitochondria could move within a cell, lead to a PDE-PDE model. The book discusses the well-posedness and long-term dynamics of solutions, depending on boundary conditions reflecting the in vitro and in vivo cases. These analytical and numerical results have inspired colleagues from the Institute of Pharmacology and Toxicology of the Helmholtz Center Munich to design new experiments justifying the theoretical and numerical results that are obtained. The book is intended for graduates students and researchers with a solid mathematical background and an interest in cell biology.
Mathematical Modeling of Pharmacokinetic Data
by DavidW.A. BourneA concise guide to mathematical modeling and analysis of pharmacokinetic data, this book contains valuable methods for maximizing the information obtained from given data. It is an ideal resource for scientists, scholars, and advanced students.
Mathematical Modeling of Protein Complexes (Biological and Medical Physics, Biomedical Engineering)
by Tatiana Koshlan Kirill KulikovThis book is devoted to the physical and mathematical modeling of the formation of complexes of protein molecules. The models developed show remarkable sensitivity to the amino acid sequences of proteins, which facilitates experimental studies and allows one to reduce the associated costs by reducing the number of measurements required according to the developed criteria. These models make it possible to reach a conclusion about the interactions between different amino acid chains and to identify more stable sites on proteins. The models also take the phosphorylation of amino acid residues into account. At the end of the book, the authors present possible directions of application of their physical and mathematical models in clinical medicine.
Mathematical Modeling of Shock-Wave Processes in Condensed Matter: From Statistical Thermodynamics to Control Theory (Shock Wave and High Pressure Phenomena)
by Tatiana Aleksandrovna KhantulevaThis book offers an interdisciplinary theoretical approach based on non-equilibrium statistical thermodynamics and control theory for mathematically modeling shock-induced out-of-equilibrium processes in condensed matter. The book comprises two parts. The first half of the book establishes the theoretical approach, reviewing fundamentals of non-equilibrium statistical thermodynamics and control theory of adaptive systems. The latter half applies the presented approach to a problem on shock-induced plane wave propagation in condensed matter. The result successfully reproduces the observed feature of waveform propagation in experiments, which conventional continuous mechanics cannot access. Further, the consequent stress–strain relationships derived with relaxation and inertia effect in elastic–plastic transition determines material properties in transient regimes.
Mathematical Modeling of Social Relationships: What Mathematics Can Tell Us About People (Computational Social Sciences)
by Urszula Strawinska-Zanko Larry S. LiebovitchThis edited volume presents examples of social science research projects that employ new methods of quantitative analysis and mathematical modeling of social processes. This book presents the fascinating areas of empirical and theoretical investigations that use formal mathematics in a way that is accessible for individuals lacking extensive expertise but still desiring to expand their scope of research methodology and add to their data analysis toolbox. Mathematical Modeling of Social Relationships professes how mathematical modeling can help us understand the fundamental, compelling, and yet sometimes complicated concepts that arise in the social sciences. This volume will appeal to upper-level students and researchers in a broad area of fields within the social sciences, as well as the disciplines of social psychology, complex systems, and applied mathematics.
Mathematical Modeling of Unsteady Inviscid Flows (Interdisciplinary Applied Mathematics #50)
by Jeff D. EldredgeThis book builds inviscid flow analysis from an undergraduate-level treatment of potential flow to the level required for research. The tools covered in this book allow the reader to develop physics-based mathematical models for a variety of flows, including attached and separated flows past wings, fins, and blades of various shapes undergoing arbitrary motions. The book covers all of the ingredients of these models: the solution of potential flows about arbitrary body shapes in two- and three-dimensional contexts, with a particular focus on conformal mapping in the plane; the decomposition of the flow into contributions from ambient vorticity and body motion; generalized edge conditions, of which the Kutta condition is a special case; and the calculation of force and moment, with extensive treatments of added mass and the influence of fluid vorticity. The book also contains an extensive primer with all of the necessary mathematical tools. The concepts are demonstrated on several example problems, both classical and modern.
Mathematical Modeling Through Topological Surgery and Applications (Springer Theses)
by Stathis AntoniouTopological surgery is a mathematical technique used for creating new manifolds out of known ones. In this book the authors observe that it also occurs in natural phenomena of all scales: 1-dimensional surgery happens during DNA recombination and when cosmic magnetic lines reconnect; 2-dimensional surgery happens during tornado formation and cell mitosis; and they conjecture that 3-dimensional surgery happens during the formation of black holes from cosmic strings, offering an explanation for the existence of a black hole’s singularity. Inspired by such phenomena, the authors present a new topological model that extends the formal definition to a continuous process caused by local forces. Lastly, they describe an intrinsic connection between topological surgery and a chaotic dynamical system exhibiting a “hole drilling” behavior. The authors’ model indicates where to look for the forces causing surgery and what deformations should be observed in the local submanifolds involved. These predictions are significant for the study of phenomena exhibiting surgery and they also open new research directions. This novel study enables readers to gain a better understanding of the topology and dynamics of various natural phenomena, as well as topological surgery itself and serves as a basis for many more insightful observations and new physical implications.
Mathematical Modelling in Health, Social and Applied Sciences (Forum for Interdisciplinary Mathematics)
by Hemen DuttaThis book discusses significant research findings in the field of mathematical modelling, with particular emphasis on important applied-sciences, health, and social issues. It includes topics such as model on viral immunology, stochastic models for the dynamics of influenza, model describing the transmission of dengue, model for human papillomavirus (HPV) infection, prostate cancer model, realization of economic growth by goal programming, modelling of grazing periodic solutions in discontinuous systems, modelling of predation system, fractional epidemiological model for computer viruses, and nonlinear ecological models. A unique addition in the proposed areas of research and education, this book is a valuable resource for graduate students, researchers and educators associated with the study of mathematical modelling of health, social and applied-sciences issues. Readers interested in applied mathematics should also find this book valuable.
Mathematical Modelling in Plant Biology
by Richard J. MorrisProgress in plant biology relies on the quantification, analysis and mathematical modeling of data over different time and length scales. This book describes common mathematical and computational approaches as well as some carefully chosen case studies that demonstrate the use of these techniques to solve problems at the forefront of plant biology. Each chapter is written by an expert in field with the goal of conveying concepts whilst at the same time providing sufficient background and links to available software for readers to rapidly build their own models and run their own simulations. This book is aimed at postgraduate students and researchers working the field of plant systems biology and synthetic biology, but will also be a useful reference for anyone wanting to get into quantitative plant biology.
Mathematical Modelling in Solid Mechanics
by Francesco Dell'Isola Mircea Sofonea David SteigmannThis book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling analysis of elasto-plastic structures engineering optimization and design, global optimization and related algorithms The book presents selected papers presented at ETAMM 2016. It includes new and original results written by internationally recognized specialists.
Mathematical Modelling, Nonlinear Control and Performance Evaluation of a Ground Based Mobile Air Defence System (Mechanisms and Machine Science #76)
by Constantinos FrangosIn 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 of Chromosome Replication and Replicative Stress
by Jens KarschauDNA replication is arguably the most crucial process at work in living cells. It is the mechanism by which organisms pass their genetic information from one generation to the next and life on Earth would be unthinkable without it. Despite the discovery of DNA structure in the 1950s, the mechanism of its replication remains rather elusive. This work makes important contributions to this line of research. In particular, it addresses two key questions in the area of DNA replication: which evolutionary forces drive the positioning of replication origins in the chromosome and how is the spatial organization of replication factories achieved inside the nucleus of a cell?. A cross-disciplinary approach uniting physics and biology is at the heart of this research. Along with experimental support, statistical physics theory produces optimal origin positions and provides a model for replication fork assembly in yeast. Advances made here can potentially further our understanding of disease mechanisms such as the abnormal replication in cancer.
Mathematical Modelling of Complex Patterns Through Fractals and Dynamical Systems (Studies in Infrastructure and Control)
by Gowrisankar Arulprakash Kishore Bingi Cristina SerpaThis 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
by Katta Ramesh Fateh Mebarek-Oudina Basma SouayehMathematical 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
by Leszek Pstras Jacek WaniewskiBeginning 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
by Prashant Maheshwary Chandrahas C. Handa Neetu Gyanchandani Pramod BelkhodeThe 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)
by Galina O. RyabovaModern 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.