Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical modelling of phase separation on dynamic surfaces   The paper presents a model of lateral phase separation in a two component
material surface. The resulting fourth order nonlinear PDE can be seen as a
Cahn-Hilliard equation posed on a time-dependent surface. Only elementary
tangential calculus and the embedding of the surface in $\mathbb{R}^3$ are used
to formulate the model, thereby facilitating the development of a fully
Eulerian discretization method to solve the problem numerically. A hybrid
method, finite difference in time and trace finite element in space, is
introduced and stability of its semi-discrete version is proved. The method
avoids any triangulation of the surface and uses a surface-independent
background mesh to discretize the equation. Thus, the method is capable of
solving the Cahn-Hilliard equation numerically on implicitly defined surfaces
and surfaces undergoing strong deformations and topological transitions. We
assess the approach on a set of test problems and apply it to model spinodal
decomposition and pattern formation on colliding surfaces. Finally, we consider
the phase separation on a sphere splitting into two droplets.

26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph