Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice Model with Nearest-Neighbor and Next-Nearest-Neighbor
  Interactions for Gradient Elasticity   Lattice models for the second-order strain-gradient models of elasticity
theory are discussed. To combine the advantageous properties of two classes of
second-gradient models, we suggest a new lattice model that can be considered
as a discrete microstructural basis for gradient continuum models. It was
proved that two classes of the second-gradient models (with positive and
negative sign in front the gradient) can have a general lattice model as a
microstructural basis. To obtain the second-gradient continuum models we
consider a lattice model with the nearest-neighbor and next-nearest-neighbor
interactions with two different coupling constants. The suggested lattice model
gives unified description of the second-gradient models with positive and
negative signs of the strain gradient terms. The sign in front the gradient is
determined by the relation of the coupling constants of the nearest-neighbor
and next-nearest-neighbor interactions.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph