Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric variational approach to the dynamics of porous media filled
  with incompressible fluid   We derive the equations of motion for the dynamics of a porous media filled
with an incompressible fluid. We use a variational approach with a Lagrangian
written as the sum of terms representing the kinetic and potential energy of
the elastic matrix, and the kinetic energy of the fluid, coupled through the
constraint of incompressibility. As an illustration of the method, the
equations of motion for both the elastic matrix and the fluid are derived in
the spatial (Eulerian) frame. Such an approach is of relevance e.g. for
biological problems, such as sponges in water, where the elastic porous media
is highly flexible and the motion of the fluid has a 'primary' role in the
motion of the whole system. We then analyze the linearized equations of motion
describing the propagation of waves through the media. In particular, we derive
the propagation of S-waves and P-waves in an isotropic media. We also analyze
the stability criteria for the wave equations and show that they are equivalent
to the physicality conditions of the elastic matrix. Finally, we show that the
celebrated Biot's equations for waves in porous media are obtained for certain
values of parameters in our models.

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The categories of this paper are: comp-gas
19
The categories of this paper are: eess
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The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph