15 research outputs found
Elastic properties of a tungsten-silver composite by reconstruction and computation
We statistically reconstruct a three-dimensional model of a tungsten-silver
composite from an experimental two-dimensional image. The effective Young's
modulus () of the model is computed in the temperature range 25-1060^o C
using a finite element method. The results are in good agreement with
experimental data. As a test case, we have reconstructed the microstructure and
computed the moduli of the overlapping sphere model. The reconstructed and
overlapping sphere models are examples of bi-continuous (non-particulate)
media. The computed moduli of the models are not generally in good agreement
with the predictions of the self-consistent method. We have also evaluated
three-point variational bounds on the Young's moduli of the models using the
results of Beran, Molyneux, Milton and Phan-Thien. The measured data were close
to the upper bound if the properties of the two phases were similar ().Comment: 23 Pages, 12 Figure
Pion light-cone wave function and pion distribution amplitude in the Nambu-Jona-Lasinio model
We compute the pion light-cone wave function and the pion quark distribution
amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars
regularization method and as a result the distribution amplitude satisfies
proper normalization and crossing properties. In the chiral limit we obtain the
simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and
= -M / f_pi^2 for the second moment of the pion light-cone
wave function, where M is the constituent quark mass and f_pi is the pion decay
constant. After the QCD Gegenbauer evolution of the pion distribution amplitude
good end-point behavior is recovered, and a satisfactory agreement with the
analysis of the experimental data from CLEO is achieved. This allows us to
determine the momentum scale corresponding to our model calculation, which is
close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis
of the pion parton distribution function. The value of is, after the
QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear
integral relation between the pion distribution amplitude and the parton
distribution function of the pion, which holds at the leading-order QCD
evolution.Comment: mistake in Eq.(38) correcte
Mean first-passage time for random walks on undirected networks
In this paper, by using two different techniques we derive an explicit
formula for the mean first-passage time (MFPT) between any pair of nodes on a
general undirected network, which is expressed in terms of eigenvalues and
eigenvectors of an associated matrix similar to the transition matrix. We then
apply the formula to derive a lower bound for the MFPT to arrive at a given
node with the starting point chosen from the stationary distribution over the
set of nodes. We show that for a correlated scale-free network of size with
a degree distribution , the scaling of the lower bound is
. Also, we provide a simple derivation for an eigentime
identity. Our work leads to a comprehensive understanding of recent results
about random walks on complex networks, especially on scale-free networks.Comment: 7 pages, no figures; definitive version published in European
Physical Journal