 |
| Titel |
Laplacian trees - fingered growth in channel geometry |
| VerfasserIn |
P. Szymczak, T. Gubiec |
| Konferenz |
EGU General Assembly 2009
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250030657
|
|
|
|
|
|
| Zusammenfassung |
| A variety of natural growth processes, including viscous fingering, electrodeposition, or
solidification can be modeled in terms of Laplacian growth. Laplacian growth patterns are
formed when the boundary of a domain moves with a velocity proportional to the
gradient of a field Ψ, which satisfies the Laplace equation, -2Ψ = 0, outside the
domain.
A simple model of Laplacian growth is considered, in which the growth takes place only at
the tips of long, thin fingers [1]. The evolution of the fingers is studied by conformal mapping
techniques. Analytical and numerical solutions are obtained for different domains and
boundary conditions. In particular, a screening process is analyzed, when longer fingers
suppress growth of the shorter ones. Possible geophysical applications of the model are
discussed, including formation and evolution of the channels in a dissolving rock
fracture.
[1] T. Gubiec, P. Szymczak, Fingered growth in channel geometry: A Loewner equation
approach , Phys. Rev. E, 77 , 041602, 2008 |
|
|
|
|
|
|