Modeling and Control in Vibrational and Structural Dynamics: A Differential Geometric Approach describes the control behavior of mechanical objects, such as wave equations, plates, and shells. It shows how the differential geometric approach is used when the coefficients of partial differential equations (PDEs) are variable in space (waves/plates), when the PDEs themselves are defined on curved surfaces (shells), and when the systems have quasilinear principal parts.
To make the book self-contained, the author starts with the necessary background on Riemannian geometry. He then describes differential geometric energy methods that are generalizations of the classical energy methods of the 1980s. He illustrates how a basic computational technique can enable multiplier schemes for controls and provide mathematical models for shells in the form of free coordinates. The author also examines the quasilinearity of models for nonlinear materials, the dependence of controllability/stabilization on variable coefficients and equilibria, and the use of curvature theory to check assumptions.
With numerous examples and exercises throughout, this book presents a complete and up-to-date account of many important advances in the modeling and control of vibrational and structural dynamics.
The Black Sea ecosystem is a unique marine environment. Its isolation from the ocean and large catchment basin, covering industrial and rural parts of the European and Asian continents, render the Black Sea ecosystem extremely vulnerable to the imposed environmental burdens Complex scientific problems related to the recent evolution of the Black Sea ecosystem were tackled in the framework of the NATO TU BLACK SEA project Ecosystem modelling as a management tool for the Black Sea', implemented between 1993 and 1997. The primary results and the products of the TU BLACK SEA project were presented to the scientific community at a dedicated symposium held on 15-19 June, 1997 at Zori Rossii on the Crimean coast of the Black Sea. The present two volumes contain 47 of the papers presented at the symposium, selected by peer review. Volume I contains 27 papers in all, two on the NATO TU Black SEA database and database management system, eight on the Black Sea biogeochemistry, and 17 on the biological structure of the basin. Of the 20 papers appearing in Volume II, nine are physical processes and 11 are on the modelling of the circulation and the ecosystems of the Black Sea.
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