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Author: Arpan Ghosh
Publisher: Linköping University Electronic Press
ISBN: 9176850730
Category :
Languages : en
Pages : 16
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Book Description
The problem of mathematical modelling of incompressible flows with low velocities through narrow curvilinear pipes is addressed in this thesis. The main motivation for this modelling task is to eventually model the human circulatory system in a simple way that can facilitate the medical practitioners to efficiently diagnose any abnormality in the system. The thesis comprises of four articles. In the first article, a two-dimensional model describing the elastic behaviour of the wall of a thin, curved, exible pipe is presented. The wall is assumed to have a laminate structure consisting of several anisotropic layers of varying thickness. The width of the channel is allowed to vary along the pipe. The two-dimensional model takes the interactions of the wall with any surrounding material and the fluid flow into account and is obtained through a dimension reduction procedure. Examples of canonical shapes of pipes and their walls are provided with explicit systems of differential equations at the end. In the second article, a one-dimensional model describing the blood flow through a moderately curved, elastic blood vessel is presented. The two-dimensional model presented in the first paper is used to model the vessel wall while linearized Navier-Stokes equations are used to model the flow through the channel. Surrounding muscle tissues and presence of external forces other than gravity are taken into account. The model is again obtained via a dimension reduction procedure based on the assumption of thinness of the vessel relative to its length. Results of numerical simulations are presented to highlight the influence of different factors on the blood flow. The one-dimensional model described in the second paper is used to derive a simplified one-dimensional model of a false aneurysm which forms the subject of the third article. A false aneurysm is an accumulation of blood outside a blood vessel but confined by the surrounding muscle tissue. Numerical simulations are presented which demonstrate different characteristics associated with a false aneurysm. In the final article, a modified Reynolds equation, along with its derivation from Stokes equations through asymptotic methods, is presented. The equation governs the steady flow of a fluid with low Reynolds number through a narrow, curvilinear tube. The channel considered may have large curvature and torsion. Approximations of the velocity and the pressure of the fluid inside the channel are constructed. These approximations satisfy a modified Poiseuille equation. A justification for the approximations is provided along with a comparison with a simpler case.
Author: Arpan Ghosh
Publisher: Linköping University Electronic Press
ISBN: 9176850730
Category :
Languages : en
Pages : 16
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Book Description
The problem of mathematical modelling of incompressible flows with low velocities through narrow curvilinear pipes is addressed in this thesis. The main motivation for this modelling task is to eventually model the human circulatory system in a simple way that can facilitate the medical practitioners to efficiently diagnose any abnormality in the system. The thesis comprises of four articles. In the first article, a two-dimensional model describing the elastic behaviour of the wall of a thin, curved, exible pipe is presented. The wall is assumed to have a laminate structure consisting of several anisotropic layers of varying thickness. The width of the channel is allowed to vary along the pipe. The two-dimensional model takes the interactions of the wall with any surrounding material and the fluid flow into account and is obtained through a dimension reduction procedure. Examples of canonical shapes of pipes and their walls are provided with explicit systems of differential equations at the end. In the second article, a one-dimensional model describing the blood flow through a moderately curved, elastic blood vessel is presented. The two-dimensional model presented in the first paper is used to model the vessel wall while linearized Navier-Stokes equations are used to model the flow through the channel. Surrounding muscle tissues and presence of external forces other than gravity are taken into account. The model is again obtained via a dimension reduction procedure based on the assumption of thinness of the vessel relative to its length. Results of numerical simulations are presented to highlight the influence of different factors on the blood flow. The one-dimensional model described in the second paper is used to derive a simplified one-dimensional model of a false aneurysm which forms the subject of the third article. A false aneurysm is an accumulation of blood outside a blood vessel but confined by the surrounding muscle tissue. Numerical simulations are presented which demonstrate different characteristics associated with a false aneurysm. In the final article, a modified Reynolds equation, along with its derivation from Stokes equations through asymptotic methods, is presented. The equation governs the steady flow of a fluid with low Reynolds number through a narrow, curvilinear tube. The channel considered may have large curvature and torsion. Approximations of the velocity and the pressure of the fluid inside the channel are constructed. These approximations satisfy a modified Poiseuille equation. A justification for the approximations is provided along with a comparison with a simpler case.
Author: Zlatko Drmac
Publisher: Springer Science & Business Media
ISBN: 147574532X
Category : Computers
Languages : en
Pages : 346
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Book Description
Proceedings of the second conference on Applied Mathematics and Scientific Computing, held June 4-9, 2001 in Dubrovnik, Croatia. The main idea of the conference was to bring together applied mathematicians both from outside academia, as well as experts from other areas (engineering, applied sciences) whose work involves advanced mathematical techniques. During the meeting there were one complete mini-course, invited presentations, contributed talks and software presentations. A mini-course Schwarz Methods for Partial Differential Equations was given by Prof Marcus Sarkis (Worcester Polytechnic Institute, USA), and invited presentations were given by active researchers from the fields of numerical linear algebra, computational fluid dynamics , matrix theory and mathematical physics (fluid mechanics and elasticity). This volume contains the mini-course and review papers by invited speakers (Part I), as well as selected contributed presentations from the field of analysis, numerical mathematics, and engineering applications.
Author: Yuri Bazilevs
Publisher: Birkhäuser
ISBN: 3319408275
Category : Mathematics
Languages : en
Pages : 487
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Book Description
This contributed volume celebrates the work of Tayfun E. Tezduyar on the occasion of his 60th birthday. The articles it contains were born out of the Advances in Computational Fluid-Structure Interaction and Flow Simulation (AFSI 2014) conference, also dedicated to Prof. Tezduyar and held at Waseda University in Tokyo, Japan on March 19-21, 2014. The contributing authors represent a group of international experts in the field who discuss recent trends and new directions in computational fluid dynamics (CFD) and fluid-structure interaction (FSI). Organized into seven distinct parts arranged by thematic topics, the papers included cover basic methods and applications of CFD, flows with moving boundaries and interfaces, phase-field modeling, computer science and high-performance computing (HPC) aspects of flow simulation, mathematical methods, biomedical applications, and FSI. Researchers, practitioners, and advanced graduate students working on CFD, FSI, and related topics will find this collection to be a definitive and valuable resource.
Author: Luca Formaggia
Publisher: Springer Science & Business Media
ISBN: 8847011523
Category : Mathematics
Languages : en
Pages : 528
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Book Description
Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes. This book offers a mathematically sound and up-to-date foundation to the training of researchers and serves as a useful reference for the development of mathematical models and numerical simulation codes.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 348
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Book Description
Author: Johnny T. Ottesen
Publisher: SIAM
ISBN: 9780898718287
Category : Medical
Languages : en
Pages : 311
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Book Description
This book introduces mathematicians to real applications from physiology. Using mathematics to analyze physiological systems, the authors focus on models reflecting current research in cardiovascular and pulmonary physiology. In particular, they present models describing blood flow in the heart and the cardiovascular system, as well as the transport of oxygen and carbon dioxide through the respiratory system and a model for baroreceptor regulation.
Author: Chetan Trivedy
Publisher: CRC Press
ISBN: 0340985011
Category : Medical
Languages : en
Pages : 771
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Book Description
This book is a dedicated resource for those sitting the Part A of the MCEM (Membership of the College of Emergency Medicine) examination. It forms an essential revision guide for emergency trainees who need to acquire a broad understanding of the basic sciences, which underpin their approach to clinical problems in the emergency department. Common clinical scenarios are used to highlight the essential underlying basic science principles, providing a link between clinical management and a knowledge of the underlying anatomical, physiological, pathological and biochemical processes. Multiple choice questions with reasoned answers are used to confirm the candidates understanding and for self testing. Unlike other recent revision books which provide MCQ questions with extended answers, this book uses clinical cases linked to the most recent basic science aspects of the CEM syllabus to provide a book that not only serves as a useful revision resource for the Part A component of the MCEM examination, but also a unique way of understanding the processes underlying common clinical cases seen every day in the emergency department. This book is essential for trainees sitting the Part A of the MCEM exam and for clinicians and medical students who need to refresh their knowledge of basic sciences relevant to the management of clinical emergencies.
Author: Peter Lanzer
Publisher: Springer
ISBN: 9783642370779
Category : Medical
Languages : en
Pages : 5004
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Book Description
Vascular management and care has become a truly multidisciplinary enterprise as the number of specialists involved in the treatment of patients with vascular diseases has steadily increased. While in the past, treatments were delivered by individual specialists, in the twenty-first century a team approach is without doubt the most effective strategy. In order to promote professional excellence in this dynamic and rapidly evolving field, a shared knowledge base and interdisciplinary standards need to be established. Pan Vascular Medicine, 2nd edition has been designed to offer such an interdisciplinary platform, providing vascular specialists with state-of-the art descriptive and procedural knowledge. Basic science, diagnostics, and therapy are all comprehensively covered. In a series of succinct, clearly written chapters, renowned specialists introduce and comment on the current international guidelines and present up-to-date reviews of all aspects of vascular care.
Author: Gianni Pedrizzetti
Publisher: Springer
ISBN: 3709125421
Category : Technology & Engineering
Languages : en
Pages : 277
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Book Description
The book presents the state of the art in the interdisciplinary field of fluid mechanics applied to cardiovascular modelling. It is neither a monograph nor a collection of research papers, rather an extended review in the field. It is arranged in 4 scientific chapters each presenting thoroughly the approach of a leading research team; two additional chapters prepared by biomedical scientists present the topic by the applied perspective. A unique feature is a substantial (approx. one fourth of the book) medical introductory part, written by clinical researchers for scientific readers, that would require a large effort to be collected otherwise.
Author: I. E. Idelchik
Publisher:
ISBN: 9788179921180
Category : Fluid dynamics
Languages : en
Pages : 0
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Book Description
The handbook has been composed on the basis of processing, systematization and classification of the results of a great number of investigations published at different time. The essential part of the book is the outcome of investigations carried out by the author. The present edition of this handbook should assist in increasing the quality and efficiency of the design and usage of indutrial power engineering and other constructions and also of the devices and apparatus through which liquids and gases move.
