User:
Limit balance
Definition 
One of the simplified way of working with the LBM method is to assume that the distributions that are originally generated by the scattering that creates the particle return to thermodynamic equilibrium in a relaxation-like process. This can be considered for some processes such as interactions with the medium that only deposit energy and do not generate new particles. In the case of generation and absorption of particles it is however necessary to identify the process and consider it in the term collisions of the iteration.
ID:(9163, 0)
Photons case
Image
In the case of the photons we have that the distribution in equilibrium is the one of Bose Einstein reason why in the situation of balance the distribution will have to be of the form
| $\displaystyle\frac{1}{e^{\hbar\omega/kT}-1}$ |
Otherwise the possible scatterings correspond to
- Rayleigh
- Compton
- Photoelectric effect
- Peer formation
ID:(9164, 0)
Extending the Solution to Bosons and Fermions
Description
Variables
Calculations
to 
,
then, select the variable: 
to 
Calculations
Variable
Given
Calculate
Target :
Equation
To be used
Equations
Examples
One of the simplified way of working with the LBM method is to assume that the distributions that are originally generated by the scattering that creates the particle return to thermodynamic equilibrium in a relaxation-like process. This can be considered for some processes such as interactions with the medium that only deposit energy and do not generate new particles. In the case of generation and absorption of particles it is however necessary to identify the process and consider it in the term collisions of the iteration.
(ID 9163)
In the case of the photons we have that the distribution in equilibrium is the one of Bose Einstein reason why in the situation of balance the distribution will have to be of the form
| $\displaystyle\frac{1}{e^{\hbar\omega/kT}-1}$ |
Otherwise the possible scatterings correspond to
- Rayleigh
- Compton
- Photoelectric effect
- Peer formation
(ID 9164)
In the case of the electrons it is necessary that the distribution in equilibrium is the one of Fermi-Direc so in the situation of equilibrium the distribution will have to be of the form
| $f^{eq}_i=\displaystyle\frac{1}{e^{\beta (m_ev_i^2/2-\mu)}+1}$ |
Otherwise the possible scatterings correspond to
- Absorption
- Elastic collision
- Electron-electron collision
- Excitation and deexicitation
(ID 9165)
ID:(1150, 0)