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第133行：
第133行： − − | first1= Leif − − 1 = Leif − − |author1-link= Leif Arkeryd − − 1-link = Leif Arkeryd − | title= On the Boltzmann equation part II: The full initial value problem | journal= Arch. Rational Mech. Anal. | volume= 45 | issue= 1 + − − 第二部分: 完整的初始值问题 | 日志 = 玻尔兹曼方程。Rational Mech.肛交。45 | issue = 1 − − − − | pages= 17–34 | year= 1972 | doi = 10.1007/BF00253393 | bibcode = 1972ArRMA..45...17A | s2cid= 119481100 − − 17-34 | year = 1972 | doi = 10.1007/BF00253393 | bibcode = 1972ArRMA. 45... 17A | s2cid = 119481100 第175行：
第159行： − − Category:Statistical mechanics − − 类别: 统计力学 第274行：
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→The collision term (Stosszahlansatz) and molecular chaos
==The collision term (Stosszahlansatz) and molecular chaos==
==The collision term (Stosszahlansatz) and molecular chaos==
===Two-body collision term ===
===Two-body collision term ===
A key insight applied by [[Ludwig Boltzmann|Boltzmann]] was to determine the collision term resulting solely from two-body collisions between particles that are assumed to be uncorrelated prior to the collision. This assumption was referred to by Boltzmann as the "''Stosszahlansatz'' " and is also known as the "[[molecular chaos]] assumption". Under this assumption the collision term can be written as a momentum-space integral over the product of one-particle distribution functions:<ref name="Encyclopaediaof" />
A key insight applied by [[Ludwig Boltzmann|Boltzmann]] was to determine the collision term resulting solely from two-body collisions between particles that are assumed to be uncorrelated prior to the collision. This assumption was referred to by Boltzmann as the "{{lang|de|Stosszahlansatz}}" and is also known as the "[[molecular chaos]] assumption". Under this assumption the collision term can be written as a momentum-space integral over the product of one-particle distribution functions:<ref name="Encyclopaediaof" />
:<math>
:<math>
is the magnitude of the relative momenta (see [[relative velocity]] for more on this concept), and ''I''(''g'', Ω) is the [[differential cross section]] of the collision, in which the relative momenta of the colliding particles turns through an angle θ into the element of the [[solid angle]] ''d''Ω, due to the collision.
is the magnitude of the relative momenta (see [[relative velocity]] for more on this concept), and ''I''(''g'', Ω) is the [[differential cross section]] of the collision, in which the relative momenta of the colliding particles turns through an angle θ into the element of the [[solid angle]] ''d''Ω, due to the collision.
===Simplifications to the collision term===
===Simplifications to the collision term===
| last1= Arkeryd
| last1= Arkeryd
| last1= Arkeryd
| last1= Arkeryd
1 = Leif
|author1-link= Leif Arkeryd
1-link = Leif Arkeryd
| title= On the Boltzmann equation part II: The full initial value problem | journal= Arch. Rational Mech. Anal. | volume= 45 | issue= 1
| pages= 17–34 | year= 1972 | doi = 10.1007/BF00253393 | bibcode = 1972ArRMA..45...17A | s2cid= 119481100
[[分类:偏微分方程]]
[[分类:偏微分方程]]
[[分类:统计力学]]
[[分类:统计力学]]