東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

From Newton to Boltzmann: Hard Spher...

Gallagher, Isabelle,

FindBook

Google Book

Amazon

博客來

From Newton to Boltzmann: Hard Spheres and Short-range Potentials

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	From Newton to Boltzmann: Hard Spheres and Short-range Potentials/ Isabelle Gallagher, Laure Saint-Raymond, Benjamin Texier
作者:	Gallagher, Isabelle,
其他作者:	Saint-Raymond, Laure,
出版者:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2014,
面頁冊數:	1 online resource (148 pages)
標題:	Differential equations -
電子資源:	https://doi.org/10.4171/129
電子資源:	https://www.ems-ph.org/img/books/gallagher_mini.gif
ISBN:	9783037196298

From Newton to Boltzmann: Hard Spheres and Short-range Potentials
Gallagher, Isabelle,

From Newton to Boltzmann: Hard Spheres and Short-range Potentials[electronic resource] /Isabelle Gallagher, Laure Saint-Raymond, Benjamin Texier - Zuerich, Switzerland :European Mathematical Society Publishing House,2014 - 1 online resource (148 pages) - Zurich Lectures in Advanced Mathematics (ZLAM).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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.

ISBN: 9783037196298

Standard No.: 10.4171/129doiSubjects--Topical Terms:

704075
Differential equations

From Newton to Boltzmann: Hard Spheres and Short-range Potentials
LDR:02319nmm a22003015a 4500 001 2233255
003 CH-001817-3
005 20140123234500.0
006 a fot ||| 0|
007 cr nn mmmmamaa
008 210928e20140118sz fot ||| 0|eng d
020 $a 9783037196298
024 7 0 $a 10.4171/129 $2 doi
035 $a 173-140123
040 $a ch0018173
072 7 $a PBKJ $2 bicssc
084 $a 35-xx $2 msc
100 1 $a Gallagher, Isabelle, $e author. $3 3481061
245 1 0 $a From Newton to Boltzmann: Hard Spheres and Short-range Potentials $h [electronic resource] / $c Isabelle Gallagher, Laure Saint-Raymond, Benjamin Texier
260 3 $a Zuerich, Switzerland : $b European Mathematical Society Publishing House, $c 2014
300 $a 1 online resource (148 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 0 $a Zurich Lectures in Advanced Mathematics (ZLAM)
506 1 $a Restricted to subscribers: $u https://www.ems-ph.org/ebooks.php
520 $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.
650 0 7 $a Differential equations $3 704075
650 0 7 $a Partial differential equations $2 msc. $3 1597893
700 1 $a Saint-Raymond, Laure, $e author. $3 3481062
700 1 $a Texier, Benjamin, $e author. $3 3481063
856 4 0 $u https://doi.org/10.4171/129
856 4 2 $3 cover image $u https://www.ems-ph.org/img/books/gallagher_mini.gif