Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new paradigm for modulated phases in multi-stage structural
  transformations   For multi-stage, displacive structural transitions we present a general
framework that accounts for various intermediate modulated phases, elastic
constant, phonon and related thermodynamic anomalies. Based on the presence or
absence of modulated phases we classify these transformations in four
categories and apply this approach to four different representative materials:
Ni-Mn-Ga, NiTi(Fe),Ni-Al, Cu-Zn-Al and alpha-U. We suggest that the anomalous
increase in elastic constant(s) and phonon frequency observed when approaching
the martensitic transition from above is a signature of the conmensurate
modulated phase.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
19
The categories of this paper are: eess