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written by Kostas Papamichalis
A collection of N cells placed at the vertices of a 2d lattice, is considered. Each individual cell can contain no more than one particle. Every particle can emerge from an infinite reservoir of particles or get eliminated into it.  At any given moment t, every cell is possible to exist in one of two distinct states A (unoccupied ) or B (occupied). If at time t a cell is in A, the probability of transitioning to B within the infinitesimal interval [t,t+Dt) equals wABDt. Conversely, if at time t it is in B, then the probability of transitioning back to state A equals wBADt.

In this work, the following topics are studied:
1) A master equation that describes the evolution of each cell is derived and the limiting behaviour of its solution is obtained.
2) A Lyapunov function that corresponds to the master equation is constructed.

It is demonstrated and confirmed experimentally that, regardless of its initial state, the system converges towards its equilibrium state. It is confirmed that the stationary state of the system is described by a Poisson distribution.
Subjects Levels Resource Types
Mathematical Tools
- Statistics
Thermo & Stat Mech
- Probability
= Poisson Distribution
- Upper Undergraduate
- Graduate/Professional
- Instructional Material
= Interactive Simulation
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This material is released under a Creative Commons Attribution-Share Alike 4.0 license.
Rights Holder:
Kostas Papamichalis
Record Creator:
Metadata instance created June 7, 2024 by kostas papamichalis
Record Updated:
June 13, 2024 by Lyle Barbato
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K. Papamichalis, (2024), WWW Document, (http://users.sch.gr/kostaspapamichalis/webejs_birthDecayModel_kpm/index.html).
AJP/PRST-PER
K. Papamichalis, Birth-Decay Process Model (2024), <http://users.sch.gr/kostaspapamichalis/webejs_birthDecayModel_kpm/index.html>.
APA Format
Papamichalis, K. (2024). Birth-Decay Process Model. Retrieved July 17, 2024, from http://users.sch.gr/kostaspapamichalis/webejs_birthDecayModel_kpm/index.html
Chicago Format
Papamichalis, Kostas. Birth-Decay Process Model. 2024. http://users.sch.gr/kostaspapamichalis/webejs_birthDecayModel_kpm/index.html (accessed 17 July 2024).
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Papamichalis, Kostas. Birth-Decay Process Model. 2024. 17 July 2024 <http://users.sch.gr/kostaspapamichalis/webejs_birthDecayModel_kpm/index.html>.
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@misc{ Author = "Kostas Papamichalis", Title = {Birth-Decay Process Model}, Volume = {2024}, Number = {17 July 2024}, Year = {2024} }
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%A Kostas Papamichalis %T Birth-Decay Process Model %D 2024 %U http://users.sch.gr/kostaspapamichalis/webejs_birthDecayModel_kpm/index.html %O text/html

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%0 Electronic Source %A Papamichalis, Kostas %D 2024 %T Birth-Decay Process Model %V 2024 %N 17 July 2024 %9 text/html %U http://users.sch.gr/kostaspapamichalis/webejs_birthDecayModel_kpm/index.html


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