Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid
  raft formation in cell membranes   We propose and investigate a model for lipid raft formation and dynamics in
biological membranes. The model describes the lipid composition of the membrane
and an interaction with cholesterol. To account for cholesterol exchange
between cytosol and cell membrane we couple a bulk-diffusion to an evolution
equation on the membrane. The latter describes a relaxation dynamics for an
energy taking lipid-phase separation and lipid-cholesterol interaction energy
into account. It takes the form of an (extended) Cahn--Hilliard equation.
Different laws for the exchange term represent equilibrium and non-equilibrium
models. We present a thermodynamic justification, analyze the respective
qualitative behavior and derive asymptotic reductions of the model. In
particular we present a formal asymptotic expansion near the sharp interface
limit, where the membrane is separated into two pure phases of saturated and
unsaturated lipids, respectively. Finally we perform numerical simulations and
investigate the long-time behavior of the model and its parameter dependence.
Both the mathematical analysis and the numerical simulations show the emergence
of raft-like structures in the non-equilibrium case whereas in the equilibrium
case only macrodomains survive in the long-time evolution.

8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph