Nonlinear Systems

The editors of this book have incorporated contributions from a diverse group of leading researchers in the field of nonlinear systems. To enrich the scope of the content, this book contains a valuable selection of works on fractional differential equations.The book aims to provide an overview of the current knowledge on nonlinear systems and some aspects of fractional calculus. The main subject areas are divided into two theoretical and applied sections. Nonlinear systems are useful for researchers in mathematics, applied mathematics, and physics, as well as graduate students who are studying these systems with reference to their theory and application. This book is also an ideal complement to the specific literature on engineering, biology, health science, and other applied science areas. The opportunity given by IntechOpen to offer this book under the open access system contributes to disseminating the field of nonlinear systems to a wide range of researchers

Hydrodynamics

The phenomena related to the flow of fluids are generally complex, and difficult to quantify. New approaches - considering points of view still not explored - may introduce useful tools in the study of Hydrodynamics and the related transport phenomena. The details of the flows and the properties of the fluids must be considered on a very small scale perspective. Consequently, new concepts and tools are generated to better describe the fluids and their properties. This volume presents conclusions about advanced topics of calculated and observed flows. It contains eighteen chapters, organized in five sections: 1) Mathematical Models in Fluid Mechanics, 2) Biological Applications and Biohydrodynamics, 3) Detailed Experimental Analyses of Fluids and Flows, 4) Radiation-, Electro-, Magnetohydrodynamics, and Magnetorheology, 5) Special Topics on Simulations and Experimental Data. These chapters present new points of view about methods and tools used in Hydrodynamics

Dynamics and mechanism studies of nonlinear chemical systems

The kinetics and mechanisms of oxidation of selected thiocarbamides (tetra-methylthiourea, trimethylthiourea, phenylthiourea, and 2-aminoethanethiolsulfuric acid) by chlorite in aqueous acidic media are investigated using UV/Vis, NMR, Stopped-flow techniques, and qualitative analysis. The reactions were extremely complex, with reaction dynamics strongly influenced by the pH of the reaction medium and formation of stable intermediates (sulfonic acids). Results revealed that oxidations of substituted thioureas do not always proceed via a stepwise oxidation of the sulfur center. Instead, reactions occurred in two stages: S-oxygenation of the sulfur center to yield the sulfinic acid, which then reacts in the second phase predominantly through an initial hydrolysis to produce a urea-type residue and the sulfoxylate anion. The sulfoxylate anion, a highly reducing species, is then rapidly oxidized to sulfate.;Experimental and numerical studies of local periodic forcing on an excitable Belousov-Zhabotinsky (BZ) medium in a thin gel layer are reported. Rather than the traditional suprathreshold perturbations giving rise to a local oscillatory state, waves were initiated in an excitable system via localized small amplitude variations in light intensity, without crossing into the oscillatory regime of the autonomous system. Initiation of waves in the initially quiescent medium was possible when the frequency of the sinusoidal perturbation was suitably tuned to that of the autonomous system. The region in phase space where wave initiation was possible depended on the parameter values of the perturbation, namely forcing frequency and forcing amplitude, and on the inherent properties of the autonomous system. Resonance patterns are found by relating the period between two waves to the period of the sinusoidal perturbation.;Experimental and theoretical studies of the peroxidase-oxidase (PO) reaction are reviewed. Numerical investigations into the initiation of trigger waves in an oscillatory one-dimensional PO reaction-diffusion system are presented. Trigger waves are initiated in the oscillatory system via localized perturbations in the concentration of one of the variables using the extended BFSO model. The chemical waves traveled with a sharp front and were not able to penetrate barriers to diffusion, which are properties characteristic of trigger waves

Integrative and theoretical research on the architecture of a biological system and its disorder

Uchida S., Asai Y., Kariya Y., et al. Integrative and theoretical research on the architecture of a biological system and its disorder. Journal of Physiological Sciences , (2019); https://doi.org/10.1007/s12576-019-00667-8.An organism stems from assemblies of a variety of cells and proteins. This complex system serves as a unit, and it exhibits highly sophisticated functions in response to exogenous stimuli that change over time. The complete sequencing of the entire human genome has allowed researchers to address the enigmas of life and disease at the gene- or molecular-based level. The consequence of such studies is the rapid accumulation of a multitude of data at multiple levels, ranging from molecules to the whole body, that has necessitated the development of entirely new concepts, tools, and methodologies to analyze and integrate these data. This necessity has given birth to systems biology, an advanced theoretical and practical research framework that has totally changed the directions of not only basic life science but also medicine. During the symposium of the 95th Annual Meeting of The Physiological Society of Japan 2018, five researchers reported on their respective studies on systems biology. The topics included reactions of drugs, ion-transport architecture in an epithelial system, multi-omics in renal disease, cardiac electrophysiological systems, and a software platform for computer simulation. In this review article these authors have summarized recent achievements in the field and discuss next-generation studies on health and disease

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included

Biochemical and Mechanical Processes in Synovial Fluids: Modeling, Analysis and Computational Simulations

Synovial fluid is a polymeric liquid which generally behaves as a viscoelastic fluid due to the presence of polysaccharide molecules called hyaluronan. In this thesis, we study the biological and biochemical properties of synovial fluid, its complex rheology and interaction with synovial membrane during filtration process. From the mathematical point of view, we model the synovial fluid as a viscous incompressible fluid for which we develop a novel generalized power-law fluid model wherein the power-law exponent depends on the concentration of the hyaluronan. Such a model is adequate to describe the flows of synovial fluid as long as it is not subjected to instantaneous stimuli. Moreover, we try to find a suitable linear viscoelastic model which can describe the viscoelastic responses of synovial fluid during small deformation experiments, as, again, a function of concentration. Then, we consider the governing equations, namely the constraint of incompressibility, the balance of linear momentum - generalized Navier-Stokes equations and the convection--diffusion equation for the concentration of hyaluronan. The part of mathematical analysis is focused on the formulation of the stationary problem in the weak sense and the proof of the existence of the corresponding weak solution, for the case of a generalized viscous problem with concentration dependent power-law exponent. For that, we use the method of monotone operators, where the essential role plays the proof of Hölder continuity of the concentration. In the numerical part of the thesis, we consider different numerical stabilization methods which ensure better numerical solvability of the system with dominant convection, as is typical for synovial fluid flow. By their implementation into already existing code, we numerically solve for the flow of the synovial fluid in a rectangular cavity, in order to gain some insight into the response of such a fluid so that we can solve in the future the flows in more realistic geometries. We also compare the solutions obtained with different models of generalized viscosities and different stabilization techniques. As last, we propose a mathematical model for flow and transport processes of diluted solutions, and afterwards of synovial fluid, in domains separated by a leaky semipermeable membrane. We formulate transmission conditions for the flow and the solute concentration across the membrane which take into account the property of the membrane to partly reject the solute, the accumulation of rejected solute at the membrane, and the influence of the solute concentration on the volume flow, known as the osmotic effect

Cardiac Arrhythmias

This book is useful for physicians taking care of patients with cardiac arrhythmias and includes six chapters written by experts in their field. Chapter 1 discusses basic mechanisms of cardiac arrhythmias. Chapter 2 discusses the chronobiological aspects of the impact of apnoic episodes on ventricular arrhythmias. Chapter 3 discusses navigation, detection, and tracking during cardiac ablation interventions. Chapter 4 discusses epidemiology and pathophysiology of ventricular arrhythmias in several noncardiac diseases, methods used to assess arrhythmia risk, and their association with long-term outcomes. Chapter 5 discusses the treatment of ventricular arrhythmias including indications for implantation of an AICD for primary and for secondary prevention in patients with and without congestive heart failure. Chapter 6 discusses surgical management of atrial fibrillation

Microgravity science and applications program tasks, 1991 revision

Presented here is a compilation of the active research tasks for FY 1991 sponsored by the Microgravity Science and Applications Division of the NASA Office of Space Science and Applications. The purpose is to provide an overview of the program scope for managers and scientists in industry, university, and government communities. Included is an introductory description of the program, the strategy and overall goal, identification of the organizational structures and the people involved, and a description of each. The tasks are grouped into several categories: electronic materials; solidification of metals, alloys, and composites; fluids, interfaces, and transport; biotechnology; combustion science; glasses and ceramics; experimental technology, instrumentation, and facilities; and Physical and Chemistry Experiments (PACE). The tasks cover both the ground based and flight programs