Ebook: A new perspective on relativity : an odyssey in non-Euclidean geometries

This volume documents the research carried out by visiting scientists attached to the Institute for Mathematical Sciences (IMS) at the National University of Singapore and the Institute of High Performance Computing (IHPC) under the program "Advances and Mathematical Issues in Large Scale Simulation." From 2002 to 2003, researchers from various countries gathered to initiate interesting and innovative work on various themes related to multiscale simulation and fast algorithms. Today, modeling and simulation are used extensively to solve complex problems and to reduce the use of experimentation during the design and analysis stage. It is important to know the various issues that have to be considered in the successful development of computational methodologies for such work. This volume is a compilation of the research by various visiting scientists in the area of modeling and multiscale simulation. Each article covers a major project and documents how computational methodology, mathematical modeling, high performance computing and simulation are combined in a multiscale scheme to solve a variety of complex problems. Some of these include the design, synthesis, processing, characterization and manufacture of nanomaterials and nanostructures, new algorithms for computational work, and grid computing. Through the included examples, readers can realize the vast potential of computational modeling and large scale simulation for the solution of problems in a variety of disciplines and applications 1. Introduction -- 2. Which geometry? -- 3. A brief history of light, electromagnetism and gravity -- 4. Electromagnetic radiation -- 5. The origins of mass -- 6. Thermodynamics of relativity -- 7. General relativity in a non-euclidean geometrical setting -- 8. Relativity of hyperbolic space -- 9. Nonequivalence of gravitation and acceleration -- 10. Aberration and radiation pressure in the Klein and PoincareМЃ models -- 11. The inertia of polarization