Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial chaos based uncertainty quantification in Hamiltonian,
  multi-time scale, and chaotic systems   Polynomial chaos is a powerful technique for propagating uncertainty through
ordinary and partial differential equations. Random variables are expanded in
terms of orthogonal polynomials and differential equations are derived for the
expansion coefficients. Here we study the structure and dynamics of these
differential equations when the original system has Hamiltonian structure, has
multiple time scales, or displays chaotic dynamics. In particular, we prove
that the differential equations for the expansion coefficients in generalized
polynomial chaos expansions of Hamiltonian systems retain the Hamiltonian
structure relative to the ensemble average Hamiltonian. We connect this with
the volume-preserving property of Hamiltonian flows to show that, for an
oscillator with uncertain frequency, a finite expansion must fail at long
times, regardless of the order of the expansion. Also, using a two-time scale
forced nonlinear oscillator, we show that a polynomial chaos expansion of the
time-averaged equations captures uncertainty in the slow evolution of the
Poincar\'e section of the system and that, as the time scale separation
increases, the computational advantage of this procedure increases. Finally,
using the forced Duffing oscillator as an example, we demonstrate that when the
original dynamical system displays chaotic dynamics, the resulting dynamical
system from polynomial chaos also displays chaotic dynamics, limiting its
applicability.

22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an