Download or read book Efficient Numerical Methods For Chemotaxis and Plasma Modulation Instability Studies written by Truong B. Nguyen and published by . This book was released on 2019 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we develop efficient numerical solvers for nonlinear systems of partial differential equations (PDEs). These systems of PDEs concern two different sets of physical problems. The first set includes chemotaxis models such as Keller-Segel models and cancer cell invasion models. Solutions of these models are observed to experience the blow-up phenomenon or the development of sharp and spiky features. Therefore, efficient and accurate numerical techniques must be employed in order to capture the solutions' behaviors. For this research, we design efficient solvers for these systems in the one and two spatial dimensions. In particular, we plan to apply adaptive moving mesh methods in which the mesh points are continuously redistributed by a coordinate transformation from the computational domain to the physical domain so that the grid nodes are concentrated in regions of large solution variations in the physical domain. The second system is the system of nonlinear PDEs that govern the plasma modulation instability of wave collapse. It is known that the nonlinear interaction of lower-hybrid wave with a much lower frequency plasma perturbation leads to the development of modulation instability which causes oscillations of electric field and formations of cavitons. Cavitons, which are regions where plasma's density is observed to be decreased, collapse in finite time and during this period, the trapped energy of electric field oscillations is dissipated and electrons are heated up. Direct experiment observations of collapse phenomenon of cavitons can be difficult. Therefore, numerical simulations are desired. To overcome the above challenges and achieve the thesis' goals, we first study the basic mechanisms of the adaptive moving mesh methods by implementing adaptive grid methods using finite difference and finite element discretization. We then apply them for well known toy problems e.g., Burgers' equations. On the other hand, we re-implement the pseudo-spectral method and we also apply the method to compute solutions to simple problems e.g., solving Poisson problems with periodic boundary conditions. Once the methods are tested with toy examples, we are ready to apply them to obtain numerical solutions to the nonlinear diffusion-reaction-chemotaxis models (cancer invasion models and Keller-Segel models) and the system of nonlinear equations that govern the modulation instability. In particular, we apply adaptive moving mesh methods for nonlinear diffusion-reaction-chemotaxis models. These model equations are discretized using finite difference (FD) and/or finite element (FE) methods. Positivity preserving schemes are used for the spatial discretization of these chemotaxis models to ensure that the physical solutions remain positive at all time levels. Numerical experiments are performed to demonstrate the performance of the adaptive mesh methods. Our numerical results show that the proposed moving mesh methods reduce the computational cost while improving the accuracy of the computed solutions when comparing to uniform grid methods. Meanwhile, we follow Shapiro's approach in his 1993 paper to further test our pseudo-spectral solver for solving the governing system of plasma modulation instability in two and three spatial dimensions. The pseudo-spectral method utilizes the computation of the fast Fourier transform (FFT) which is done by using FFTW library. High order time integration techniques are applied to calculate solutions at the a time. We further extend the pseudo-spectral method to a highly scalable solver by implementing it in parallel using Message Passing Interface (MPI). Our MPI code allows us to speed up the computations especially in the three dimensional problem. Next, we use our solvers to numerically study the effect of plasma's shear velocity on the wave collapse phenomenon. Finally, we implement a solver that uses adaptive moving mesh finite difference method for the system of PDEs that govern the modulation instability phenomenon in the two dimensional case.
Download or read book Hypocoercivity written by Cdric Villani and published by American Mathematical Soc.. This book was released on 2009-10-08 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, taking the general form ${\frac{\partial f}{\partial t}}+ L f =0$. The question is whether and how one can overcome the degeneracy by exploiting commutators.
Download or read book Nonlinear Equations written by and published by . This book was released on 1993 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solves systems of nonlinear equations having as many equations as unknowns.
Download or read book Mathematics of Wave Phenomena written by Willy Dörfler and published by Springer Nature. This book was released on 2020-10-01 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.
Download or read book Emergent Nonlinear Phenomena in Bose Einstein Condensates written by Panayotis G. Kevrekidis and published by Springer Science & Business Media. This book was released on 2007-12-29 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by experts in the fields of atomic physics and nonlinear science, covers the important developments in a special aspect of Bose-Einstein condensation, namely nonlinear phenomena in condensates. Topics covered include bright, dark, gap and multidimensional solitons; vortices; vortex lattices; optical lattices; multicomponent condensates; mathematical methods/rigorous results; and the beyond-the-mean-field approach.
Download or read book Human Health and Performance Risks of Space Exploration Missions written by Jancy C. McPhee and published by U. S. National Aeronautics & Space Administration. This book was released on 2009 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Feedback Control in Systems Biology written by Carlo Cosentino and published by CRC Press. This book was released on 2011-10-17 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like engineering systems, biological systems must also operate effectively in the presence of internal and external uncertainty—such as genetic mutations or temperature changes, for example. It is not surprising, then, that evolution has resulted in the widespread use of feedback, and research in systems biology over the past decade has shown that feedback control systems are widely found in biology. As an increasing number of researchers in the life sciences become interested in control-theoretic ideas such as feedback, stability, noise and disturbance attenuation, and robustness, there is a need for a text that explains feedback control as it applies to biological systems. Written by established researchers in both control engineering and systems biology, Feedback Control in Systems Biology explains how feedback control concepts can be applied to systems biology. Filling the need for a text on control theory for systems biologists, it provides an overview of relevant ideas and methods from control engineering and illustrates their application to the analysis of biological systems with case studies in cellular and molecular biology. Control Theory for Systems Biologists The book focuses on the fundamental concepts used to analyze the effects of feedback in biological control systems, rather than the control system design methods that form the core of most control textbooks. In addition, the authors do not assume that readers are familiar with control theory. They focus on "control applications" such as metabolic and gene-regulatory networks rather than aircraft, robots, or engines, and on mathematical models derived from classical reaction kinetics rather than classical mechanics. Another significant feature of the book is that it discusses nonlinear systems, an understanding of which is crucial for systems biologists because of the highly nonlinear nature of biological systems. The authors cover tools and techniques for the analysis of linear and nonlinear systems; negative and positive feedback; robustness analysis methods; techniques for the reverse-engineering of biological interaction networks; and the analysis of stochastic biological control systems. They also identify new research directions for control theory inspired by the dynamic characteristics of biological systems. A valuable reference for researchers, this text offers a sound starting point for scientists entering this fascinating and rapidly developing field.
Download or read book Dietary Reference Intakes for Vitamin C Vitamin E Selenium and Carotenoids written by Institute of Medicine and published by National Academies Press. This book was released on 2000-08-27 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the newest release in the authoritative series of quantitative estimates of nutrient intakes to be used for planning and assessing diets for healthy people. Dietary Reference Intakes (DRIs) is the newest framework for an expanded approach developed by U.S. and Canadian scientists. This book discusses in detail the role of vitamin C, vitamin E, selenium, and the carotenoids in human physiology and health. For each nutrient the committee presents what is known about how it functions in the human body, which factors may affect how it works, and how the nutrient may be related to chronic disease. Dietary Reference Intakes provides reference intakes, such as Recommended Dietary Allowances (RDAs), for use in planning nutritionally adequate diets for different groups based on age and gender, along with a new reference intake, the Tolerable Upper Intake Level (UL), designed to assist an individual in knowing how much is "too much" of a nutrient.
Download or read book Schr dinger Equations in Nonlinear Systems written by Wu-Ming Liu and published by Springer. This book was released on 2019-03-20 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schrödinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose–Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schrödinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose–Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.
Download or read book Bone Tissue Engineering written by Jeffrey O. Hollinger and published by CRC Press. This book was released on 2004-10-14 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on bone biology, Bone Tissue Engineering integrates basic sciences with tissue engineering. It includes contributions from world-renowned researchers and clinicians who discuss key topics such as different models and approaches to bone tissue engineering, as well as exciting clinical applications for patients. Divided into four sections, t
Download or read book Handbook of Brain Microcircuits written by Gordon M. Shepherd and published by Oxford University Press. This book was released on 2018 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to focus on principles, each chapter in this work is brief, organized around 1-3 wiring diagrams of the key circuits, with several pages of text that distil the functional significance of each microcircuit
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1986 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Control Theory and Systems Biology written by Pablo A. Iglesias and published by MIT Press. This book was released on 2010 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of how engineering techniques from control and systems theory can be used to help biologists understand the behavior of cellular systems.
Download or read book Comparative Oncology written by Alecsandru Ioan Baba and published by . This book was released on 2007 with total page 787 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Plasma Physics Volume 1 Physical Kinetics of Turbulent Plasmas written by Patrick H. Diamond and published by Cambridge University Press. This book was released on 2014-07-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-volume series presents the ideas, models and approaches essential to understanding plasma dynamics and self-organization for researchers and graduate students in plasma physics, controlled fusion and related fields such as plasma astrophysics. Volume I develops the physical kinetics of plasma turbulence through a focus on quasi-particle models and dynamics. It discusses the essential physics concepts and theoretical methods for describing weak and strong fluid and phase space turbulence in plasma systems far from equilibrium. The book connects the traditionally 'plasma' topic of weak or wave turbulence theory to more familiar fluid turbulence theory, and extends both to the realm of collisionless phase space turbulence. This gives readers a deeper understanding of these related fields, and builds a foundation for future applications to multi-scale processes of self-organization in tokamaks and other confined plasmas. This book emphasizes the conceptual foundations and physical intuition underpinnings of plasma turbulence theory.
Download or read book Root Ecology written by Hans de Kroon and published by Springer Science & Business Media. This book was released on 2003-05-21 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the course of evolution, a great variety of root systems have learned to overcome the many physical, biochemical and biological problems brought about by soil. This development has made them a fascinating object of scientific study. This volume gives an overview of how roots have adapted to the soil environment and which roles they play in the soil ecosystem. The text describes the form and function of roots, their temporal and spatial distribution, and their turnover rate in various ecosystems. Subsequently, a physiological background is provided for basic functions, such as carbon acquisition, water and solute movement, and for their responses to three major abiotic stresses, i.e. hard soil structure, drought and flooding. The volume concludes with the interactions of roots with other organisms of the complex soil ecosystem, including symbiosis, competition, and the function of roots as a food source.
Download or read book Wound Care written by Carrie Sussman and published by Lippincott Williams & Wilkins. This book was released on 2007 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for health care professionals in multiple disciplines and clinical settings, this comprehensive, evidence-based wound care text provides basic and advanced information on wound healing and therapies and emphasizes clinical decision-making. The text integrates the latest scientific findings with principles of good wound care and provides a complete set of current, evidence-based practices. This edition features a new chapter on wound pain management and a chapter showing how to use negative pressure therapy on many types of hard-to-heal wounds. Technological advances covered include ultrasound for wound debridement, laser treatments, and a single-patient-use disposable device for delivering pulsed radio frequency.
