Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exploring families of energy-dissipation landscapes via tilting -- three
  types of EDP convergence   We introduce two new concepts of convergence of gradient systems $(\mathbf Q,
\mathcal E_\varepsilon,\mathcal R_\varepsilon)$ to a limiting gradient system
$(\mathbf Q, \mathcal E_0,\mathcal R_0)$. These new concepts are called `EDP
convergence with tilting' and `contact--EDP convergence with tilting'. Both are
based on the Energy-Dissipation-Principle (EDP) formulation of solutions of
gradient systems, and can be seen as refinements of the Gamma-convergence for
gradient flows first introduced by Sandier and Serfaty. The two new concepts
are constructed in order to avoid the `unnatural' limiting gradient structures
that sometimes arise as limits in EDP-convergence. EDP-convergence with tilting
is a strengthening of EDP-convergence by requiring EDP-convergence for a full
family of `tilted' copies of $(\mathbf Q, \mathcal E_\varepsilon,\mathcal
R_\varepsilon)$. It avoids unnatural limiting gradient structures, but many
interesting systems are non-convergent according to this concept. Contact--EDP
convergence with tilting is a relaxation of EDP convergence with tilting, and
still avoids unnatural limits but applies to a broader class of sequences
$(\mathbf Q, \mathcal E_\varepsilon,\mathcal R_\varepsilon)$. In this paper we
define these concepts, study their properties, and connect them with classical
EDP convergence. We illustrate the different concepts on a number of test
problems.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex