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Fluid Dynamics
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The Theory of Quantum Torus Knots: Volume II
A detailed mathematical derivation of space curves is presented that links the diverse fields of superfluids, quantum mechanics, Navier-Stokes hydrodynamics, and Maxwell electromagnetism by a common foundation. The basic mathematical building block is called the theory of quantum torus knots (QTK).
The General Theory of Homogenization
Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.
An Introduction to Navier-Stokes Equation and Oceanography
This text corresponds to a graduate mathematics course taught at Carnegie Mellon University in the spring of 1999. Included are comments added to the lecture notes, a bibliography containing 23 items, and brief biographical information for all scientists mentioned in the text, thus showing that the creation of scientific knowledge is an international enterprise.
Nonsmooth Mechanics and Analysis
This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification. Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics. Audience This book is intended for researchers in mathematics and mechanics.
Transactions of the International Astronomical Union
IAU Transactions XXIIB summarizes the work of the XXIInd General Assembly. The discourses given during the Inaugural and Closing Ceremonies are reproduced in Chapters I and III, respectively. The proceedings of the two sessions of the General Assembly will be found in Chapter II, which includes the Resolutions and the report of the Finance Committee. The Statutes, Bye-Laws and a few working rules of the Union are published in Chapter IV. The Accounts and other aspects of the administration of the Union are recorded in Chapter V, together with the report of the Executive Committee for this last triennium, and provide the permanent record for the Union in the period 1991-1994. This volume also contains the Commission reports from The Hague compiled by the Presidents of the Commissions (Chapter VI). Finally, Chapter VII contains the list of countries adhering to the Union and the alphabetical, geographical and commission membership lists of about 8000 individual members. The IAU still appears to be unique among the scientific Unions in maintaining this category of individual membership which contributes in a crucial way to the spirit and the aims of the Union.
Metals and the Royal Society
In this book two distinguished metallurgists have traced the role of metallurgical technology in the creation of the scientific revolution and the formation of the Royal Society.
IUTAM Symposium on Developments in Geophysical Turbulence
This symposium continues a long tradition for IUGGjIUTAM symposia going back to "Fundamental Problems in Thrbulence and their Relation to Geophysics" Marseille, 1961. The five topics that were emphasized were: turbulence modeling, statistics of small scales and coherent structures, con vective turbulence, stratified turbulence, and historical developments. The objective was to consider the ubiquitous nature of turbulence in a variety of geophysical problems and related flows. Some history of the contribu tions of NCAR and its alumni were discussed, including those of Jackson R Herring, who has been a central figure at NCAR since 1972. To the original topics we added rotation, which appeared ...
