This innovative text emphasizes a "less-is-more" approach to modeling complicated systems such as heat transfer by treating them first as "1-node lumped models" that yield simple closed-form solutions. The author develops numerical techniques for students to obtain more detail, but also trains them to use the techniques only when simpler approaches fail. Covering all essential methods offered in traditional texts, but with a different order, Professor Sidebotham stresses inductive thinking and problem solving as well as a constructive understanding of modern, computer-based practice. Readers learn to develop their own code in the context of the material, rather than just how to use packaged software, offering a deeper, intrinsic grasp behind models of heat transfer. Developed from over twenty-five years of lecture notes to teach students of mechanical and chemical engineering at The Cooper Union for the Advancement of Science and Art, the book is ideal for students and practitionersacross engineering disciplines seeking a solid understanding of heat transfer.

Marshall's theories of economic and social advancement are explained with reference to the scientific and philosophical movements which influenced them: utilitarianism, evolutionism, mathematical marginalism and ethical idealism.

With the availability of high speed computers and advances in computational techniques, the application of mathematical modeling to biological systems is expanding. This comprehensive and richly illustrated volume provides up-to-date, wide-ranging material on the mathematical modeling of kidney physiology, including clinical data analysis and practice exercises. Basic concepts and modeling techniques introduced in this volume can be applied to other areas (or organs) of physiology.

Together, the volumes in this series present all of the data needed at various length scales for a multidisciplinary approach to modeling and simulation of flows in the cardiovascular and ventilatory systems, especially multiscale modeling and coupled simulations. The cardiovascular and respiratory systems are tightly coupled, as their primary function is to supply oxygen to, and remove carbon dioxide from, the body's cells. Because physiological conduits have deformable and reactive walls, macroscopic flow behavior and prediction must be coupled to nano- and microscopic events in a corrector scheme of regulated mechanism. Therefore, investigation of flows of blood and air in physiological conduits requires an understanding of the biology, chemistry, and physics of these systems, together with the mathematical tools to describe their functioning in quantitative terms. The present volume focuses on macroscopic aspects of the cardiovascular and respiratory systems in normal conditions, i.e., anatomy and physiology, as well as the acquisition and processing of medical images and physiological signals.

The theory of blood circulation is the oldest and most advanced branch of biomechanics, with roots extending back to Huangti and Aristotle, and with contributions from Galileo, Santori, Descartes, Borelli, Harvey, Euler, Hales, Poiseuille, Helmholtz, and many others. It represents a major part of humanity's concept of itself. This book presents selected topics of this great body of ideas from a historical perspective, binding important experiments together with mathematical threads. The objectives and scope of this book remain the same as in the first edition: to present a treatment of circulatory biomechanics from the stand­ points of engineering, physiology, and medical science, and to develop the subject through a sequence of problems and examples. The name is changed from Biodynamics: Circulation to Biomechanics: Circulation to unify the book with its sister volumes, Biomechanics: Mechanical Properties of Living Tissues, and Biomechanics: Motion, Flow, Stress, and Growth. The major changes made in the new edition are the following: When the first edition went to press in 1984, the question of residual stress in the heart was raised for the first time, and the lung was the only organ analyzed on the basis of solid morphologic data and constitutive equations. The detailed analysis of blood flow in the lung had been done, but the physiological validation experiments had not yet been completed.

Biomechanics aims to explain the mechanics oflife and living. From molecules to organisms, everything must obey the laws of mechanics. Clarification of mechanics clarifies many things. Biomechanics helps us to appreciate life. It sensitizes us to observe nature. It is a tool for design and invention of devices to improve the quality of life. It is a useful tool, a simple tool, a valuable tool, an unavoidable tool. It is a necessary part of biology and engineering. The method of biomechanics is the method of engineering, which consists of observation, experimentation, theorization, validation, and application. To understand any object, we must know its geometry and materials of construc­ tion, the mechanical properties of the materials involved, the governing natural laws, the mathematical formulation of specific problems and their solutions, and the results of validation. Once understood, one goes on to develop applications. In my plan to present an outline of biomechanics, I followedthe engineering approach and used three volumes. In the first volume, Biomechanics: Mechanical Properties of Living Tissues, the geometrical struc­ ture and the rheological properties of various materials, tissues, and organs are presented. In the second volume, Biodynamics: Circulation, the physiology of blood circulation is analyzed by the engineering method.

Differential equations with delay naturally arise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings. It presents explicit conditions for exponential, absolute and input-to-state stabilities. These stability conditions are mainly formulated in terms of the determinants and eigenvalues of auxiliary matrices dependent on a parameter; the suggested approach allows us to apply the well-known results of the theory of matrices. In addition, solution estimates for the considered equations are established which provide the bounds for regions of attraction of steady states.

This text is designed for a first course in biological mass transport, and the material in it is presented at a level that is appropriate to advanced undergraduates or early graduate level students. Its orientation is somewhat more physical and mathematical than a biology or standard physiology text, reflecting its origins in a transport course that I teach to undergraduate (and occasional graduate) biomedical engineering students in the Whiting School of Engineering at Johns Hopkins. The audience for my cours- and presumably for this text - also includes chemical engineering undergraduates concentrating in biotechnology, and graduate students in biophysics. The organization of this book differs from most texts that at­ tempt to present an engineering approach to biological transport. What distinguishes biological transport from other mass transfer processes is the fact that biological transport is biological. Thus, we do not start with the engineering principles of mass transport (which are well presented elsewhere) and then seek biological ap­ plications of these principles; rather, we begin with the biological processes themselves, and then develop the tools that are needed to describe them. As a result, more physiology is presented in this text than is often found in books dealing with engineering applica­ tions in the life sciences.

The use of digital signal processing is ubiquitous in the field of physiology and biomedical engineering. The application of such mathematical and computational tools requires a formal or explicit understanding of physiology. Formal models and analytical techniques are interlinked in physiology as in any other field. This book takes a unitary approach to physiological systems, beginning with signal measurement and acquisition, followed by signal processing, linear systems modelling, and computer simulations. The signal processing techniques range across filtering, spectral analysis and wavelet analysis. Emphasis is placed on fundamental understanding of the concepts as well as solving numerical problems. Graphs and analogies are used extensively to supplement the mathematics. Detailed models of nerve and muscle at the cellular and systemic levels provide examples for the mathematical methods and computer simulations. Several of the models are sufficiently sophisticated to be of value in understanding real world issues like neuromuscular disease. This second edition features expanded problem sets and a link to extra downloadable material.

The development of a proper description of the living world today stands as one of the most significant challenges to physics. A variety of new experimental techniques in molecular biology, microbiol­ ogy, physiology and other fields of biological research constantly expand our knowledge and enable us to make increasingly more detailed functional and structural descriptions. Over the past decades, the amount and complexity of available information have multiplied dramatically, while at the same time our basic understanding of the nature of regulation, behavior, morphogenesis and evolution in the living world has made only modest progress. A key obstacle is clearly the proper handling of the available data. This requires a stronger emphasis on mathematical modeling through which the consistency of the adopted explanations can be checked, and general princi­ ples may be extracted. As an even more serious problem, however, it appears that the proper physical concepts for the development of a theoretically oriented biology have not hitherto been available. Classical mechanics and equilibrium thermody­ namics, for instance, are inappropriate and useless in some of the most essen­ tial biological contexts. Fortunately, there is now convincing evidence that the concepts and methods of the newly developed fields of nonlinear dynam­ ics and complex systems theory, combined with irreversible thermodynamics and far-from-equilibrium statistical mechanics will enable us to move ahead with many of these problems.

Complex Social Networks is a newly emerging (hot) topic with applications in a variety of domains, such as communication networks, engineering networks, social networks, and biological networks. In the last decade, there has been an explosive growth of research on complex real-world networks, a theme that is becoming pervasive in many disciplines, ranging from mathematics and computer science to the social and biological sciences. Optimization of complex communication networks requires a deep understanding of the interplay between the dynamics of the physical network and the information dynamics within the network. Although there are a few books addressing social networks or complex networks, none of them has specially focused on the optimization perspective of studying these networks. This book provides the basic theory of complex networks with several new mathematical approaches and optimization techniques to design and analyze dynamic complex networks. A wide range of applications and optimization problems derived from research areas such as cellular and molecular chemistry, operations research, brain physiology, epidemiology, and ecology.

The sense of touch is fundamental during the interaction between humans and their environment; in virtual reality, objects are created by computer simulations and they can be experienced through haptic devices. In this context haptic textures are fundamental for a realistic haptic perception of virtual objects.

The challenge for the biosciences in the twenty-first century is to integrate genome sequencing information into a better understanding of biology, physiology, and human pathology. Such attempts at integration are moving the world toward a new generation of bioscience and bioengineering, where biological, physiological, and pathological information from humans and other living animals can be quantitatively described in silico across multiple scales of time and size and through diverse hierarchies of organization — from molecules to cells and organs, to individuals. To "harness" such complexity, international communities of integrative bioscientists and bioengineers aim to establish frameworks and information infrastructures for describing biological structures and physiological functions on multiple scales of time and space. This textbook includes a public platform to describe physiological functions using mathematical equations and guides the reader to perform mathematical modeling and computer simulations, to combine existing models as well as to create new models. Accessible to biologists, physiologists, and students of the sciences, with illustrative details provided when necessary, this book seeks to achieve a systematic way of harnessing biological complexity. Sharing the databases among communities worldwide will help to find comprehensive answers to all the important questions.

There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context.

In 1979, the Nobel Prize for Medicine and Physiology was awarded jointly to Allan McLeod Cormack and Godfrey Newbold Houns eld, the two pioneering scienti- engineers primarily responsible for the development, in the 1960s and early 1970s, of computerized axial tomography, popularly known as the CAT or CT scan. In his papers [13], Cormack, then a Professor at Tufts University, in Massachusetts, dev- oped certain mathematical algorithms that, he envisioned, could be used to create an image from X-ray data. Working completely independently of Cormack and at about the same time, Houns eld, a research scientist at EMI Central Research Laboratories in the United Kingdom, designed the rst operational CT scanner as well as the rst commercially available model. (See [22] and [23]. ) Since 1980, the number of CT scans performed each year in the United States has risen from about 3 million to over 67 million. What few people who have had CT scans probably realize is that the fundamental problem behind this procedure is essentially mathematical: If we know the values of the integral of a two- or three-dimensional fu- tion along all possible cross-sections, then how can we reconstruct the function itself? This particular example of what is known as an inverse problem was studied by Johann Radon, an Austrian mathematician, in the early part of the twentieth century.