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Three Region Markov Process JS Model
written by Kostas Papamichalis
This simulation models a Markov process that distributes particles between three three regions A, B, and C.  In every time-intervals of the form:  Ik=[tk, tk+1), tk =kDt  k=0,1,...kmax, each particle performs just one jump to one of the neighboring regions with a given transition-probability, or it remains in the region it was at time  tk. The evolution of the system from its initial state to the final state of equilibrium, is described by a master equation. 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 the time-moments tk=kDt, k=0,1,... the program of the simulation counts the real number of particles in every sector. 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 sector-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 tk, the value of H is uniquely determined by the numbers of the particles that exist in each sector at tk. The corresponding graph is designed 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
Mathematical Tools
- Probability
Thermo & Stat Mech
- Ensembles
= Partition Function
- Kinetic and Diffusive Processes
= Approach to Equilibrium
- Probability
= Random Walks
- Statistical Physics
- Upper Undergraduate
- Graduate/Professional
- Instructional Material
= Interactive Simulation
Intended Users Formats Ratings
- Educators
- text/html
- application/javascript
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Access Rights:
Free access
This material is released under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 license.
Rights Holder:
Kostas Papamichalis
Record Creator:
Metadata instance created January 3, 2023 by kostas papamichalis
Record Updated:
January 4, 2023 by Wolfgang Christian
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K. Papamichalis, (2023), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669).
K. Papamichalis, Three Region Markov Process JS Model (2023), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669>.
APA Format
Papamichalis, K. (2023). Three Region Markov Process JS Model. Retrieved June 23, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669
Chicago Format
Papamichalis, Kostas. Three Region Markov Process JS Model. 2023. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669 (accessed 23 June 2024).
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Papamichalis, Kostas. Three Region Markov Process JS Model. 2023. 23 June 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669>.
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@misc{ Author = "Kostas Papamichalis", Title = {Three Region Markov Process JS Model}, Volume = {2024}, Number = {23 June 2024}, Year = {2023} }
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%A Kostas Papamichalis %T Three Region Markov Process JS Model %D 2023 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669 %O text/html

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%0 Electronic Source %A Papamichalis, Kostas %D 2023 %T Three Region Markov Process JS Model %V 2024 %N 23 June 2024 %9 text/html %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669

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Three Region Markov Process JS Model:

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relation by Wolfgang Christian

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