Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beyond Kinetic Relations   We introduce the concept of kinetic equations representing a natural
extension of the more conventional notion of a kinetic relation. Algebraic
kinetic relations, widely used to model dynamics of dislocations, cracks and
phase boundaries, link the instantaneous value of the velocity of a defect with
an instantaneous value of the driving force. The new approach generalizes
kinetic relations by implying a relation between the velocity and the driving
force which is nonlocal in time. To make this relations explicit one needs to
integrate the system of kinetic equations. We illustrate the difference between
kinetic relation and kinetic equations by working out in full detail a
prototypical model of an overdamped defect in a one-dimensional discrete
lattice. We show that the minimal nonlocal kinetic description containing now
an internal time scale is furnished by a system of two ordinary differential
equations coupling the spatial location of defect with another internal
parameter that describes configuration of the core region.

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The categories of this paper are: cs
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph