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Electrofluidodynamic Technologies (EFDTs) for Biomaterials and
Medical Devices: Principles and Advances focuses on the
fundamentals of EFDTs - namely electrospinning, electrospraying and
electrodynamic atomization - to develop active platforms made of
synthetic or natural polymers for use in tissue engineering,
restoration and therapeutic treatments. The first part of this book
deals with main technological aspects of EFDTs, such as basic
technologies and the role of process parameters. The second part
addresses applications of EFDTs in biomedical fields, with chapters
on their application in tissue engineering, molecular delivery and
implantable devices. This book is a valuable resource for materials
scientists, biomedical engineers and clinicians alike.
The book contains a selection of 43 scientific papers by the great
mathematician Ennio De Giorgi (1928-1996), which display the broad
range of his achievements and his entire intellectual career as a
problem solver and as a proponent of deep and ambitious
mathematical theories. All papers are written in English and 17 of
them appear also in their original Italian version in order to give
an impression of De Giorgi's original style. The editors also
provide a short biography of Ennio De Giorgi and a detailed account
of his scientific achievements, ranging from his seminal paper on
the solution of Hilbert's 19th problem to the theory of perimeter
and minimal surfaces, the theory of G-convergence and the
foundations of mathematics.
The book is devoted to the theory of gradient flows in the
general framework of metric spaces, and in the more specific
setting of the space of probability measures, which provide a
surprising link between optimal transportation theory and many
evolutionary PDE's related to (non)linear diffusion. Particular
emphasis is given to the convergence of the implicit time
discretization method and to the error estimates for this
discretization, extending the well established theory in Hilbert
spaces. The book is split in two main parts that can be read
independently of each other.
The theory of nonlinear hyperbolic equations in several space
dimensions has recently obtained remarkable achievements. This
volume provides an up-to-date overview of the status and
perspectives of two areas of research in PDEs, related to
hyperbolic conservation laws. The captivating volume contains
surveys of recent deep results and provides an overview of further
developments and related open problems. Readers should have basic
knowledge of PDE and measure theory.
This volume provides the texts of lectures given by L. Ambrosio,
L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer
course held in Cetraro (Italy) in 2005. These are introductory
reports on current research by world leaders in the fields of
calculus of variations and partial differential equations. The
topics discussed are transport equations for nonsmooth vector
fields, homogenization, viscosity methods for the infinite
Laplacian, weak KAM theory and geometrical aspects of
symmetrization. A historical overview of all CIME courses on the
calculus of variations and partial differential equations is
contributed by Elvira Mascolo.
Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampčre and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.
Interfaces are geometrical objects modelling free or moving boundaries and arise in a wide range of phase change problems in physical and biological sciences, particularly in material technology and in dynamics of patterns. Especially in the end of last century, the study of evolving interfaces in a number of applied fields becomes increasingly important, so that the possibility of describing their dynamics through suitable mathematical models became one of the most challenging and interdisciplinary problems in applied mathematics. The 2000 Madeira school reported on mathematical advances in some theoretical, modelling and numerical issues concerned with dynamics of interfaces and free boundaries. Specifically, the five courses dealt with an assessment of recent results on the optimal transportation problem, the numerical approximation of moving fronts evolving by mean curvature, the dynamics of patterns and interfaces in some reaction-diffusion systems with chemical-biological applications, evolutionary free boundary problems of parabolic type or for Navier-Stokes equations, and a variational approach to evolution problems for the Ginzburg-Landau functional.
This book presents the main mathematical prerequisites for analysis
in metric spaces. It covers abstract measure theory, Hausdorff
measures, Lipschitz functions, covering theorums, lower
semicontinuity of the one-dimensional Hausdorff measure, Sobolev
spaces of maps between metric spaces, and Gromov-Hausdorff theory,
all developed ina general metric setting. The existence of
geodesics (and more generally of minimal Steiner connections) is
discussed on general metric spaces and as an application of the
Gromov-Hausdorff theory, even in some cases when the ambient space
is not locally compact. A brief and very general description of the
theory of integration with respect to non-decreasing set functions
is presented following the Di Giorgi method of using the
'cavalieri' formula as the definition of the integral. Based on
lecture notes from Scuola Normale, this book presents the main
mathematical prerequisites for analysis in metric spaces.
Supplemented with exercises of varying difficulty it is ideal for a
graduate-level short course for applied mathematicians and
engineers.
Biomedical Composites, Second Edition, provides revised, expanded,
and updated content suitable for those active in the biomaterials
and bioengineering field. Three new chapters cover modeling of
biocomposites, 3D printing of customized scaffolds, and constructs
and regulatory issues. Chapters from the first edition have been
revised in order to provide up-to-date, comprehensive coverage of
developments in the field. Part One discusses the fundamentals of
biocomposites, with Part Two detailing a wide range of applications
of biocomposites. Chapters in Part Three discuss the
biocompatibility, mechanical behavior, and failure of
biocomposites, while the final section looks at the future for
biocomposites. Professor Luigi Ambrosio is the Director of the
Institute for Composite and Biomedical Materials, Italy. He is a
renowned scientist with expertise in biomedical composites and has
published over 150 papers in international scientific journals and
books, 16 patents, and over 250 presentations at international and
national conferences.
There have been important developments in materials and therapies
for the treatment of spinal conditions. Biomaterials for spinal
surgery summarises this research and how it is being applied for
the benefit of patients.
After an introduction to the subject, part one reviews fundamental
issues such as spinal conditions and their pathologies, spinal
loads, modelling and osteobiologic agents in spinal surgery. Part
two discusses the use of bone substitutes and artificial
intervertebral discs whilst part three covers topics such as the
use of injectable biomaterials like calcium phosphate for
vertebroplasty and kyphoplasty as well as scoliosis implants. The
final part of the book summarises developments in regenerative
therapies such as the use of stem cells for intervertebral disc
regeneration.
With its distinguished editors and international team of
contributors, Biomaterials for spinal surgery is a standard
reference for both those developing new biomaterials and therapies
for spinal surgery and those using them in clinical practice.
Summarises recent developments in materials and therapies for the
treatment of spinal conditions and examines how it is being applied
for the benefit of patientsReviews fundamental issues such as
spinal conditions and their pathologies, spinal loads, modelling
and osteobiologic agents in spinal surgeryDiscusses the use of bone
substitutes and artificial intervertebral discs and covers topics
such as the use of injectable biomaterials like calcium phosphate
for vertebroplasty and kyphoplasty
This book includes four courses on geometric measure theory, the
calculus of variations, partial differential equations, and
differential geometry. Authored by leading experts in their fields,
the lectures present different approaches to research topics with
the common background of a relevant underlying, usually
non-Riemannian, geometric structure. In particular, the topics
covered concern differentiation and functions of bounded variation
in metric spaces, Sobolev spaces, and differential geometry in the
so-called Carnot-Caratheodory spaces. The text is based on lectures
presented at the 10th School on "Analysis and Geometry in Metric
Spaces" held in Levico Terme (TN), Italy, in collaboration with the
University of Trento, Fondazione Bruno Kessler and CIME, Italy. The
book is addressed to both graduate students and researchers.
In recent years flows in networks have attracted the interest of
many researchers from different areas, e.g. applied mathematicians,
engineers, physicists, economists. The main reason for this
ubiquity is the wide and diverse range of applications, such as
vehicular traffic, supply chains, blood flow, irrigation channels,
data networks and others. This book presents an extensive set of
notes by world leaders on the main mathematical techniques used to
address such problems, together with investigations into specific
applications. The main focus is on partial differential equations
in networks, but ordinary differential equations and optimal
transport are also included. Moreover, the modeling is completed by
analysis, numerics, control and optimization of flows in networks.
The book will be a valuable resource for every researcher or
student interested in the subject.
At the summer school in Pisa in September 1996, Luigi Ambrosio and
Norman Dancer each gave a course on the geometric problem of
evolution of a surface by mean curvature, and degree theory with
applications to PDEs respectively. This self-contained presentation
accessible to PhD students bridged the gap between standard courses
and advanced research on these topics. The resulting book is
divided accordingly into 2 parts, and neatly illustrates the 2-way
interaction of problems and methods. Each of the courses is
augmented and complemented by additional short chapters by other
authors describing current research problems and results.
In 2008, a school on the theory of optimal transportation and its
applications took place in Pisa, with lectures by F. Barthe, W.
Gangbo, F. Maggi and R. McCann. In this book, the notes of the
first three lecturers are collected. They provide a deep insight on
concentration inequalities, evolution PDEs of Hamiltonian type,
geometric and functional inequalities.
This textbook is addressed to PhD or senior undergraduate students
in mathematics, with interests in analysis, calculus of variations,
probability and optimal transport. It originated from the teaching
experience of the first author in the Scuola Normale Superiore,
where a course on optimal transport and its applications has been
given many times during the last 20 years. The topics and the tools
were chosen at a sufficiently general and advanced level so that
the student or scholar interested in a more specific theme would
gain from the book the necessary background to explore it. After a
large and detailed introduction to classical theory, more specific
attention is devoted to applications to geometric and functional
inequalities and to partial differential equations.
This book deals with a class of mathematical problems which involve the minimization of the sum of a volume and a surface energy and have lately been refered to as 'free discontinuity problems'. Examples of such problems come from fracture mechanics, image analysis, or the theory of phase transitions. A systematic introduction to this field, this book is highly suitable for graduate students, bridging the gap between research level texts and elementary textbooks on measure theory and calculus of variation. The first half of the book contains a comprehensive and updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory, that is Abstract Measure Theory and Geometric Measure Theory.
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