APS Excellence in Physics Education Award
November 2019

Education Prize Logo
Science SPORE Prize
November 2011

NSF Logo
The Open Source Physics Project is supported by NSF DUE-0442581.

Website Detail Page

Item Picture
Diffusion of particles along an 1-d lattice
written by Kostas Papamichalis
This simulation uses a Markov chain to simulate the diffusion of N particles along an one dimension, finite lattice, toward the state of equilibrium. The particles are distributed along the 1D lattice cells. In a time interval of length Dt, each particle can perform just one jump between neighboring cells with a certain transition probability. The evolution of the system from its initial state to the final state of equilibrium, is described by a master equation. The initial state of the system and the transition probabilities are selected by the user. The main objective of the simulation is the confirmation of the theoretical proposition that "irrespectively of the form of the initial distribution, the system converges to a certain equilibrium state which is determined by the transition probabilities".  

In a sequence of time-moments the program of the simulation counts the real number of particles in every cell. The intermediate states of the system between the initial state and the final state of equilibrium are depicted by a varying histogram and a sequence of changing cell-colors. On the other hand, the distribution of the particles at the equilibrium state has been determined according to the theoretical model and it is depicted in the same graphs. The user compares the real-time data with the theoretical predictions.

Finally, a Lyapunov functional H is determined for the system. Each time-moment, the value of H is uniquely determined by the corresponding distribution of the particles in the cells of the lattice. The variation of H with time is depicted in real time. By using this graph, the user can estimate the relaxation time of the process toward the equilibrium-state.
1 supplemental document is available
1 source code document is available
Subjects Levels Resource Types
Thermo & Stat Mech
- Kinetic and Diffusive Processes
= Diffusion
- Upper Undergraduate
- Graduate/Professional
- Instructional Material
= Curriculum
= Interactive Simulation
Intended Users Formats Ratings
- Learners
- Educators
- text/html
- application/pdf
- application/javascript
  • Currently 0.0/5

Want to rate this material?
Login here!

Access Rights:
Free access
This material is released under a Creative Commons Attribution-Share Alike 4.0 license.
Rights Holder:
Kostas Papamichalis
Record Creator:
Metadata instance created November 2, 2022 by kostas papamichalis
Record Updated:
November 9, 2022 by Wolfgang Christian
ComPADRE is beta testing Citation Styles!

Record Link
AIP Format
K. Papamichalis, (2022), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16356&DocID=5664).
K. Papamichalis, Diffusion of particles along an 1-d lattice (2022), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16356&DocID=5664>.
APA Format
Papamichalis, K. (2022). Diffusion of particles along an 1-d lattice. Retrieved May 30, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16356&DocID=5664
Chicago Format
Papamichalis, Kostas. Diffusion of particles along an 1-d lattice. 2022. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16356&DocID=5664 (accessed 30 May 2024).
MLA Format
Papamichalis, Kostas. Diffusion of particles along an 1-d lattice. 2022. 30 May 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16356&DocID=5664>.
BibTeX Export Format
@misc{ Author = "Kostas Papamichalis", Title = {Diffusion of particles along an 1-d lattice}, Volume = {2024}, Number = {30 May 2024}, Year = {2022} }
Refer Export Format

%A Kostas Papamichalis %T Diffusion of particles along an 1-d lattice %D 2022 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16356&DocID=5664 %O text/html

EndNote Export Format

%0 Electronic Source %A Papamichalis, Kostas %D 2022 %T Diffusion of particles along an 1-d lattice %V 2024 %N 30 May 2024 %9 text/html %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16356&DocID=5664

Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.

Citation Source Information

The AIP Style presented is based on information from the AIP Style Manual.

The APA Style presented is based on information from APA Style.org: Electronic References.

The Chicago Style presented is based on information from Examples of Chicago-Style Documentation.

The MLA Style presented is based on information from the MLA FAQ.

Save to my folders


Similar Materials

OSP Projects:
Open Source Physics - EJS Modeling
Physlet Physics
Physlet Quantum Physics
STP Book