The Monge-Ampère-Kantorovich approach to reconstruction in cosmology Export

@misc{citeulike:2298784, abstract = {Motion of a continuous fluid can be decomposed into an "incompressible" rearrangement, which preserves the volume of each infinitesimal fluid element, and a gradient map that transfers fluid elements in a way unaffected by any pressure or elasticity (the polar decomposition of Y. Brenier). The Euler equation describes a system whose kinematics is dominated by the incompressible rearrangement. The opposite limit, in which the incompressible component is negligible, corresponds to the Zel'dovich approximation, a model of motion of self-gravitating fluid in cosmology. We present a method of approximate reconstruction of the large-scale proper motions of matter in the Universe from the present-day mass density field. The method is based on recovering the corresponding gradient transfer map. We discuss its algorithmics, tests of the method against mock cosmological catalogues, and its application to observational data, which result in tight constraints on the mean mass density Omega\_m and age of the Universe.}, archivePrefix = {arXiv}, author = {Mohayaee, Roya and Sobolevskii, Andrei}, citeulike-article-id = {2298784}, citeulike-linkout-0 = {http://arxiv.org/abs/0712.2561}, citeulike-linkout-1 = {http://arxiv.org/pdf/0712.2561}, day = {16}, eprint = {0712.2561}, keywords = {ansobolarxiv, cosmo, mak, optimization}, month = {Dec}, posted-at = {2008-01-28 18:44:46}, priority = {2}, title = {The Monge-Amp\`ere-Kantorovich approach to reconstruction in cosmology}, url = {http://arxiv.org/abs/0712.2561}, year = {2007} }

TY - ELEC ID - citeulike:2298784 L3 - citeulike-article-id:2298784 N2 - Motion of a continuous fluid can be decomposed into an "incompressible" rearrangement, which preserves the volume of each infinitesimal fluid element, and a gradient map that transfers fluid elements in a way unaffected by any pressure or elasticity (the polar decomposition of Y. Brenier). The Euler equation describes a system whose kinematics is dominated by the incompressible rearrangement. The opposite limit, in which the incompressible component is negligible, corresponds to the Zel'dovich approximation, a model of motion of self-gravitating fluid in cosmology. We present a method of approximate reconstruction of the large-scale proper motions of matter in the Universe from the present-day mass density field. The method is based on recovering the corresponding gradient transfer map. We discuss its algorithmics, tests of the method against mock cosmological catalogues, and its application to observational data, which result in tight constraints on the mean mass density Omega_m and age of the Universe. TI - The Monge-Amp\`ere-Kantorovich approach to reconstruction in cosmology KW - ansobolarxiv KW - cosmo KW - mak KW - optimization AU - Mohayaee, Roya AU - Sobolevskii, Andrei PY - 2007/Dec/16/ UR - http://arxiv.org/abs/0712.2561 ER -