Iutam Symposium On Discretization Methods For Evolving Discontinuities

In recent years, discretization methods have been proposed which are more flexible and which have the potential of capturing (moving) discontinuities in a robust and efficient manner. This monograph assembles contributions of leading experts with the most recent developments in this rapidly evolving field. It provides the most comprehensive coverage of state-of-the art numerical methods for treating discontinuities in mechanics.

The Symposium brought together many of the world’s experts in fluid mechanics, microfabrication and control theory to discover the synergy that can lead to real advances and perhaps find ways in which collaborative projects may proceed. The high profile meeting was attended by keynote speakers who are leaders in their fields. A key driver was the improvement in flow efficiency to reduce drag, and thereby emissions arising from transport. About 65 papers were presented.

This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.

This volume contains the proceedings of the IUTAM Symposium on Computational Physics and New Perspectives in Turbulence, held at Nagoya University, Nagoya, Japan, in September 2006. With special emphasis given to fundamental aspects of the physics of turbulence, coverage includes experimental approaches to fundamental problems in turbulence, turbulence modeling and numerical methods, and geophysical and astrophysical turbulence.

The book examines innovative numerical methods for computational solid and fluid mechanics that can be used to model complex problems in engineering. It also presents innovative and promising simulation methods, including the fundamentals of these methods, as well as advanced topics and complex applications. Further, the book explores how numerical simulations can significantly reduce the number of time-consuming and expensive experiments required, and can support engineering decisions by providing data that would be very difficult, if not impossible, to obtain experimentally. It also includes chapters covering topics such as particle methods addressing particle-based materials and numerical methods that are based on discrete element formulations; fictitious domain methods; phase field models; computational fluid dynamics based on modern finite volume schemes; hybridizable discontinuous Galerkin methods; and non-intrusive coupling methods for structural models.

The aim of this thesis is the simulation of progressive damage in brittle materials due to cracking. With this aim, the mathematical crack model will be solved using the eXtended Finite Element Method for the spatial discretization and time integration schemes for the numerical integration in the time domain. The time integration schemes considered are the Generalized-? method, the continuous GALERKIN method and the discontinuous GALERKIN method.

This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.

This book covers methods of Mathematical Morphology to model and simulate random sets and functions (scalar and multivariate). The introduced models concern many physical situations in heterogeneous media, where a probabilistic approach is required, like fracture statistics of materials, scaling up of permeability in porous media, electron microscopy images (including multispectral images), rough surfaces, multi-component composites, biological tissues, textures for image coding and synthesis. The common feature of these random structures is their domain of definition in n dimensions, requiring more general models than standard Stochastic Processes.The main topics of the book cover an introduction to the theory of random sets, random space tessellations, Boolean random sets and functions, space-time random sets and functions (Dead Leaves, Sequential Alternate models, Reaction-Diffusion), prediction of effective properties of random media, and probabilistic fracture theories.