# Berlin 2012 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 22: Posters I

### DY 22.17: Poster

### Mittwoch, 28. März 2012, 17:00–19:00, Poster A

**Rigorous selection theory of free dendritic growth in a flow** — •Martin von Kurnatowski and Klaus Kassner — Otto-von-Guericke-University Magdeburg, Department of Theoretical Physics, Universitätsplatz 2, 39106 Magdeburg

The problem of a crystal growing freely in its undercooled melt is governed by heat transport. The two-phase boundary takes a nearly parabolic shape. This dendrite is stabilized by *anisotropic* surface tension which acts as a singular perturbation and selects the growth velocity and the length scale of the pattern. So far, the selection problem has usually been treated with the Kruskal-Segur-method [1], which is only applicable to linear field equations.

We extend this method with the asymptotic Zauderer decomposition scheme. This powerful combination is able to deal with many unsolved problems in crystal growth such as *nonlinear* convective effects. An equation determining the shape of the dendrite is derived from the diffusion-advection equation. Only at this point, a particular flow velocity field has to be inserted, which we approximate as a potential flow. Subsequently, a solution to this equation is constructed by asymptotic matching in the complex plane using WKB techniques. Shape and growth velocity are finally selected by numerical integration of a local equation close to the singular point of the problem.

*[1] M. Ben Amar, Phys. Rev. A 41, p. 2080 (1990)*