Skip to content
GitLab
Projects
Groups
Snippets
/
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Sign in
Toggle navigation
Menu
Open sidebar
KiT-RT
KiT-RT
Commits
b5b4ac61
Commit
b5b4ac61
authored
Jan 23, 2021
by
Tianbai Xiao
Browse files
Update physics.rst
parent
b038b0f0
Changes
1
Hide whitespace changes
Inline
Side-by-side
doc/physics.rst
View file @
b5b4ac61
================
Transport
Theory
Kinetic
Theory
================
The kinetic theory is dedicated to describe the dynamical behavior of a many-particle system through ensemble averaging.
...
...
@@ -27,13 +27,13 @@ characteristic scales. Consider the molecular motion of gases as an
example. Down to the finest scale of a many-particle system, the
Newton’s second law depicts particle motions via
..
code::
math
.. math
::
\mathbf{F} = m \mathbf{a}
As a first order system it reads
..
code::
math
.. math
::
\frac{d \mathbf x}{dt} = \mathbf v, \ \frac{d \mathbf v}{dt} = \frac{\mathbf F}{m}
...
...
@@ -57,7 +57,7 @@ during most of time with mild intermolecular collisions. Such dynamics
can be described with an operator splitting approach, i.e. the kinetic
transport equation
..
code::
math
.. math
::
\frac{\partial f}{\partial t}+ \mathbf v \cdot \nabla_\mathbf x f + \mathbf a \cdot \nabla_\mathbf v f = Q(f)
...
...
@@ -66,7 +66,7 @@ collisions correspondingly. Different collision models can be inserted
into such equation. If the particles only collide with a background
material one obtains linear Boltzmann collision operator
..
code::
math
.. math
::
Q(f)=\int_{\mathbb R^3} \mathcal B(\mathbf v_*, \mathbf v) \left[ f(\mathbf v_*)-f(\mathbf v)\right] d\mathbf v_*
...
...
@@ -75,7 +75,7 @@ collisions at different velocities. If the interactions among particles
are considered, the collision operator becomes nonlinear. For example,
the two-body collision results in nonlinear Boltzmann equation
..
code::
math
.. math
::
Q(f)=\int_{\mathbb R^3} \int_{\mathcal S^2} \mathcal B(\cos \beta, |\mathbf{v}-\mathbf{v_*}|) \left[ f(\mathbf v')f(\mathbf v_*')-f(\mathbf v)f(\mathbf v_*)\right] d\mathbf \Omega d\mathbf v_*
jannick.wolters
@jm2154
mentioned in commit
9ea6982b
·
Apr 30, 2021
mentioned in commit
9ea6982b
mentioned in commit 9ea6982b4e4d05a7442e313076574a2b414ef02f
Toggle commit list
Write
Preview
Supports
Markdown
0%
Try again
or
attach a new file
.
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment