6,614 research outputs found
Nonlinear Energy Response of Glass Forming Materials
A theory for the nonlinear energy response of a system subjected to a heat
bath is developed when the temperature of the heat bath is modulated
sinusoidally. The theory is applied to a model glass forming system, where the
landscape is assumed to have 20 basins and transition rates between basins obey
a power law distribution. It is shown that the statistics of eigenvalues of the
transition rate matrix, the glass transition temperature , the
Vogel-Fulcher temperature and the crossover temperature can be
determined from the 1st- and 2nd-order ac specific heats, which are defined as
coefficients of the 1st- and 2nd-order energy responses. The imaginary part of
the 1st-order ac specific heat has a broad peak corresponding to the
distribution of the eigenvalues. When the temperature is decreased below ,
the frequency of the peak decreases and the width increases. Furthermore, the
statistics of eigenvalues can be obtained from the frequency dependence of the
1st-order ac specific heat. The 2nd-order ac specific heat shows extrema as a
function of the frequency. The extrema diverge at the Vogel-Fulcher temperature
. The temperature dependence of the extrema changes significantly near
and some extrema vanish near .Comment: 20 pages, 10 figure
A q-analogue of Catalan Hankel determinants
In this paper we shall survey the various methods of evaluating Hankel
determinants and as an illustration we evaluate some Hankel determinants of a
q-analogue of Catalan numbers. Here we consider
as a q-analogue of Catalan numbers
, which is known as the moments of the little
q-Jacobi polynomials. We also give several proofs of this q-analogue, in which
we use lattice paths, the orthogonal polynomials, or the basic hypergeometric
series. We also consider a q-analogue of Schr\"oder Hankel determinants, and
give a new proof of Moztkin Hankel determinants using an addition formula for
.Comment: 17 page
Distributed Agreement on Activity Driven Networks
In this paper, we investigate asymptotic properties of a consensus protocol
taking place in a class of temporal (i.e., time-varying) networks called the
activity driven network. We first show that a standard methodology provides us
with an estimate of the convergence rate toward the consensus, in terms of the
eigenvalues of a matrix whose computational cost grows exponentially fast in
the number of nodes in the network. To overcome this difficulty, we then derive
alternative bounds involving the eigenvalues of a matrix that is easy to
compute. Our analysis covers the regimes of 1) sparse networks and 2)
fast-switching networks. We numerically confirm our theoretical results by
numerical simulations
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