# A Discrete Model For Pattern Formation In Volatile Thin Films

Mathematical Modelling of Natural Phenomena (2012)

- Volume: 7, Issue: 4, page 39-52
- ISSN: 0973-5348

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topMalik-Garbi, M., and Agam, O.. "A Discrete Model For Pattern Formation In Volatile Thin Films." Mathematical Modelling of Natural Phenomena 7.4 (2012): 39-52. <http://eudml.org/doc/222442>.

@article{Malik2012,

abstract = {We introduce a model, similar to diffusion limited aggregation (DLA), which serves as a
discrete analog of the continuous dynamics of evaporation of thin liquid films. Within
mean field approximation the dynamics of this model, averaged over many realizations of
the growing cluster, reduces to that of the idealized evaporation model in which surface
tension is neglected. However fluctuations beyond the mean field level play an important
role, and we study their effect on the conserved quantities of the idealized evaporation
model. Assuming the cluster to be a fractal, a heuristic approach is developed in order to
explain the distinctive increase of the fractal dimension with the cluster size.},

author = {Malik-Garbi, M., Agam, O.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {viscous fingering; diffusion limited aggregation; reaction-diffusion},

language = {eng},

month = {7},

number = {4},

pages = {39-52},

publisher = {EDP Sciences},

title = {A Discrete Model For Pattern Formation In Volatile Thin Films},

url = {http://eudml.org/doc/222442},

volume = {7},

year = {2012},

}

TY - JOUR

AU - Malik-Garbi, M.

AU - Agam, O.

TI - A Discrete Model For Pattern Formation In Volatile Thin Films

JO - Mathematical Modelling of Natural Phenomena

DA - 2012/7//

PB - EDP Sciences

VL - 7

IS - 4

SP - 39

EP - 52

AB - We introduce a model, similar to diffusion limited aggregation (DLA), which serves as a
discrete analog of the continuous dynamics of evaporation of thin liquid films. Within
mean field approximation the dynamics of this model, averaged over many realizations of
the growing cluster, reduces to that of the idealized evaporation model in which surface
tension is neglected. However fluctuations beyond the mean field level play an important
role, and we study their effect on the conserved quantities of the idealized evaporation
model. Assuming the cluster to be a fractal, a heuristic approach is developed in order to
explain the distinctive increase of the fractal dimension with the cluster size.

LA - eng

KW - viscous fingering; diffusion limited aggregation; reaction-diffusion

UR - http://eudml.org/doc/222442

ER -

## References

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- Here the Hamiltonian which defines the evolution does not account for the constraint that A particle cannot be born on a site ocuupied by B particle. This constraint can be taken into account by replcing the term with , where Θ(x) is the haviside function and ϵ is a positive infintesimal number.

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