02676cam a22003615i 450000100090000000300040000900500170001300800410003001000170007102000420008802000390013003500240016904000710019304200140026407200130027807200130029108200190030410000340032324501330035730000450049049000440053550400710057952012660065065000220191665000370193865000430197565000280201865301220204670000350216870000310220371000350223483000450226918345704OSt20150123110422.0141023t20132013sz a f b 001 0 eng d a 2014430327 a9783037191293 (pbk. : acidfree paper) a3037191295 (pbk. : acidfree paper) a(OCoLC)ocn876427669 aCStbengcSTFerdadOCLCOdIPLdCUSdYDXCPdOCLCAdOCLCFdOHXdDLC alccopycat 7aQA2lcco 7aQC2lcco04a515.33 GAL2231 aGallagher, Isabelle,eauthor.10aFrom Newton to Boltzmann :bhard spheres and short-range potentials /cIsabelle Gallagher, Laure Saint-Raymond, Benjamin Texier. axi, 135 pages :billustrations ;c24 cm.1 aZurich lectures in advanced mathematics aIncludes bibliographical references (pages [130]-132) and indexes. a"The question addressed in this monograph is the relationship between the time-reversible Newton dynamics for a system of particles interacting via elastic collisions, and the irreversible Boltzmann dynamics which gives a statistical description of the collision mechanism. Two types of elastic collisions are considered: hard spheres, and compactly supported potentials. Following the steps suggested by Lanford in 1974, we describe the transition from Newton to Boltzmann by proving a rigorous convergence result in short time, as the number of particles tends to infinity and their size simultaneously goes to zero, in the Boltzmann-Grad scaling. Boltzmann's kinetic theory rests on the assumption that particle independence is propagated by the dynamics. This assumption is central to the issue of appearance of irreversibility. For finite numbers of particles, correlations are generated by collisions. The convergence proof establishes that for initially independent configurations, independence is statistically recovered in the limit. This book is intended for mathematicians working in the fields of partial differential equations and mathematical physics, and is accessible to graduate students with a background in analysis"--Publisher's description. 0aTransport theory. 0aDifferential equations, Partial. 7aDifferential equations, Partial.2fast 7aTransport theory.2fast aAtomic physicsaMatter constitution, propertiesaStatistical physical phenomenaaTransport theoryaEarly 21st century1 aSaint-Raymond, Laure,eauthor.1 aTexier, Benjamin,eauthor.2 aEuropean Mathematical Society. 0aZurich lectures in advanced mathematics.