Heat-Diffusion-1D
This is a software providing a solution to the heat diffusion in a 1D structure.
We consider:
- Piecewise homogeneous materials
- Electron system heating with a Gaussian like source
- Two temperature model: electron & lattice temperature
The equation under consideration is:
where C = specific heat, k = conductivity, G is the coupling constant between the two systems (Electron and Lattice)
and 
are the respective temperatures of the electron and the lattice system with respect to space x and time t. The super letters L and E indicate wether a parameter belongs to the electron or lattice system and the sub index i denotes to which layer the parameter belongs.
Our approach is to use a combination of finite elements (B-Splines) to approximate the derivation in space and Explicit Euler to approximate the evolution in time. To stay within the stability region of the Explicit Euler algorithm, a well suited time step is automatically computed.
Example:
In this case the Material under consideration is one layer of Strontium Ruthenium Oxide and one layer of Strontium Titanium Oxide behind it.
| Temperature evolution of electron- lattice system | Gaussian laser pulse S(x,t) hitting sample |
|---|---|
 |
 |
Here we consider a laser source S(x,t) = lambda * exp(-lambda * (x-x0)) * G(t-t0) hitting a material from the left. I.e. Gaussian shape in time and exponentially decaying in space, according to Lambert-Beer’s law.
We can see the following effects in the animation:
- The electron system immediately gets heated up.
- Diffusion of the electron heating along the x-axis
- Heat gets transported to the lattice system
Documentation
Documentation and example sessions can be found in the Wiki
With:
This is a project from the Ultrafast Condensed Matter physics groupe in Stockholm. The main contributors are:
Dependencies:
How to contribute :
Fork from the Developer- branch and pull request to merge back into the original Developer- branch.
Working updates and improvements will then be merged into the Master branch, which will always contain the latest working version.