Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolic and Elliptic Transport Barriers in Three-Dimensional Unsteady
  Flows   We develop a general theory of transport barriers for three-dimensional
unsteady flows with arbitrary time-dependence. The barriers are obtained as
two-dimensional Lagrangian Coherent Structures (LCSs) that create locally
maximal deformation. Along hyperbolic LCSs, this deformation is induced by
locally maximal normal repulsion or attraction. Along shear LCSs, the
deformation is created by locally maximal tangential shear. Hyperbolic LCSs,
therefore, play the role of generalized stable and unstable manifolds, while
closed shear LCSs (elliptic LCSs) act as generalized KAM tori or KAM-type
cylinders. All these barriers can be computed from our theory as explicitly
parametrized surfaces. We illustrate our results by visualizing two-dimensional
hyperbolic and elliptic barriers in steady and unsteady versions of the ABC
flow.

36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn