## Detail Page

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
- Instructional Material
= Interactive Simulation
Intended Users Formats Ratings
- Educators
- text/html
- application/javascript
• Currently 0.0/5

Want to rate this material?

Mirror:
http://users.sch.gr/kostaspapamic…
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
Other Collections:

ComPADRE is beta testing Citation Styles!

AIP Format
K. Papamichalis, (2023), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669).
AJP/PRST-PER
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 April 24, 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 24 April 2024).
MLA Format
Papamichalis, Kostas. Three Region Markov Process JS Model. 2023. 24 Apr. 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669>.
BibTeX Export Format
@misc{ Author = "Kostas Papamichalis", Title = {Three Region Markov Process JS Model}, Volume = {2024}, Number = {24 April 2024}, Year = {2023} }
Refer Export Format

%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

EndNote Export Format

%0 Electronic Source %A Papamichalis, Kostas %D 2023 %T Three Region Markov Process JS Model %V 2024 %N 24 April 2024 %9 text/html %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=16393&DocID=5669

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.

### Three Region Markov Process JS Model:

Is Based On Easy Java Simulations Modeling and Authoring Tool

Use the Easy Java Simulations Modeling and Authoring Tool to edit and to explore the source code for the Three Region Markov Process JS Model.

relation by Wolfgang Christian

Know of another related resource? Login to relate this resource to it.
Save to my folders