Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Implicit operators for networked mechanical and thermal systems with
  integer-order components   Complex systems are composed of a large number of simple components connected
to each other in the form of a network. It is shown that, for some network
configurations, the equivalent dynamic behavior of the system is governed by an
implicit integro-differential operator even though the individual components
themselves satisfy equations that use explicit operators of integer order. The
networks considered here are infinite trees and ladders, and each is composed
only of two types of integer-order components with potential-driven flows that
are repeated ad infinitum. In special cases the equivalent operator for the
system is a fractional-order derivative, but in general it is implicit and can
only be expressed as a solution of an operator equation. These implicit
operators, which are a generalization of fractional-order derivatives, play an
important role in the analysis and modeling of complex systems.

16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc