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Roustem N. Miftahof, Pohang University of Science and Technology, Republic of Korea,Hong Gil Nam, Pohang University of Science and Technology, Republic of Korea
Roustem N. Miftahof, Pohang University of Science and Technology, Republic of Korea,Hong Gil Nam, Pohang University of Science and Technology, Republic of Korea
Roustem N. Miftahof, Pohang University of Science and Technology, Republic of Korea,Hong Gil Nam, Pohang University of Science and Technology, Republic of Korea
Roustem N. Miftahof, Pohang University of Science and Technology, Republic of Korea,Hong Gil Nam, Pohang University of Science and Technology, Republic of Korea
Roustem N. Miftahof, Pohang University of Science and Technology, Republic of Korea,Hong Gil Nam, Pohang University of Science and Technology, Republic of Korea
A fundamental goal in constitutive modelling is to predict the mechanical behaviour of a material under various loading states. A biological tissue is a collection of cells, and extracellular matrices, that perform various specialized functions. There are four basic primary tissues types: muscular, nervous, epithelial and connective. Muscle tissue produces mechanical work through contraction–relaxation. For example, skeletal muscles are responsible for locomotion primarily through voluntary muscle contraction, cardiac muscles provide the active pumping of blood from the heart, and smooth muscles, which are part of the organs of the digestive tract, facilitate peristalsis, propulsion, microcirculation, etc.
Nervous tissue provides communication among organs and systems predominantly by electrical signals. Neurons are responsible for the production and propagation of the waves of depolarization in the myelinated and unmyelinated nerve fibres, smooth muscle syncytia and other cell aggregates. Neuroglial cells are a diverse group of morphoelements that play a supportive, mainly trophic, role.
Epithelial tissue covers the outer and inner surfaces of most of the organs. Various types of cells line the digestive, reproductive and urinary tracts, blood vessels, ducts, etc. They act as a protective barrier and are instrumental in selective regulation of the transport of specific agents and substrates.
Connective tissue includes a diverse set of cells surrounded by a large amount of extracellular matrix. Its main function is to provide a level of mechanical support to the organ.
Roustem N. Miftahof, Pohang University of Science and Technology, Republic of Korea,Hong Gil Nam, Pohang University of Science and Technology, Republic of Korea
Roustem N. Miftahof, Pohang University of Science and Technology, Republic of Korea,Hong Gil Nam, Pohang University of Science and Technology, Republic of Korea
The small intestine is a long cylindrical tube that extends from the stomach to the caecum of the colon. The absolute length of the small bowel generally makes up to 80% to 90% of the entire gut length. In the abdomen most of the intestine is loosely suspended by the mesentery and it is looped upon itself. The diameter of the intestine is not constant but gradually decreases from the proximal to the distal part. For example, the diameter of the duodenum is 25–35 mm, that of the jejunum is ∼30 mm and that of the ileum is 20–25 mm.
The intestinal wall is a biological composite formed of four layers: mucosa, submucosa, muscular and serosa. The mucosa is the innermost layer and its primary function is to digest and absorb nutrients.
The submucosa consists mainly of connective tissue and serves a purely mechanical function. Septa of connective-tissue fibres carrying nerves, blood and lymphatic vessels penetrate into the muscle layer and form a fibrillary three-dimensional network. It maintains a stable organization of the wall and allows the intestine to undergo reversible changes in length and diameter, offering remarkable properties of stiffness and elasticity.
The muscle coat is made of two smooth muscle layers – a thick (inner) layer of circumferentially oriented smooth muscle cells and a thin (outer) layer of longitudinally oriented muscle elements. The two layers are distinct and separate, although there are intermediate bundles that pass from one layer to the other.
Roustem N. Miftahof, Pohang University of Science and Technology, Republic of Korea,Hong Gil Nam, Pohang University of Science and Technology, Republic of Korea
In this note, we study deterministic and stochastic models for the spread of cholera. The deterministic model for the total number of cholera cases fits the observed total number of cholera cases in some recent outbreaks. The stochastic model for the total number of cholera cases leads to a binomial type distribution with a mean that agrees with the deterministic model.
This monograph deals with the structure, generation and stability of flames from a mathematical point of view. It uses a specific mathematical approach to provide a unified theoretical description of fundamental flame phenomena. Its importance stems from the fact that it provides the first clear evidence that combustion can be legitimately treated as a mathematical science as well as an empirical one. The book will be of interest to researchers in combustion, fluid mechanics and applied mathematics, as well as to graduate students taking advanced courses in these areas.
The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications.
Phyllotaxis, the study of the patterns exhibited by leaves and other organs of plants, raises some of the deepest questions of plant morphogenesis. What principles of biological organisation produce these dynamical geometric systems? The constant occurrence of the Fibonacci sequence in such systems is a phenomenon that has fascinated botanists and mathematicians for centuries. In this book, first published in 1994, the many facets of phyllotaxis are dealt with in an integrated manner for the first time. The author describes a unified concept of phyllotaxis based on experimental, anatomical, cellular, physiological and paleontological observations. The book provides a framework for formal analyses of botanical data and emphasises the relevance of the phyllotactic paradigm in the study of other structures, such as crystals and proteins. It is of interest to cystallographers and physicists as well as to botanists and mathematicians.