8,064 research outputs found
Isospectral Graph Reductions and Improved Estimates of Matrices' Spectra
Via the process of isospectral graph reduction the adjacency matrix of a
graph can be reduced to a smaller matrix while its spectrum is preserved up to
some known set. It is then possible to estimate the spectrum of the original
matrix by considering Gershgorin-type estimates associated with the reduced
matrix. The main result of this paper is that eigenvalue estimates associated
with Gershgorin, Brauer, Brualdi, and Varga improve as the matrix size is
reduced. Moreover, given that such estimates improve with each successive
reduction, it is also possible to estimate the eigenvalues of a matrix with
increasing accuracy by repeated use of this process.Comment: 32 page
Restrictions and Stability of Time-Delayed Dynamical Networks
This paper deals with the global stability of time-delayed dynamical
networks. We show that for a time-delayed dynamical network with
non-distributed delays the network and the corresponding non-delayed network
are both either globally stable or unstable. We demonstrate that this may not
be the case if the network's delays are distributed. The main tool in our
analysis is a new procedure of dynamical network restrictions. This procedure
is useful in that it allows for improved estimates of a dynamical network's
global stability. Moreover, it is a computationally simpler and much more
effective means of analyzing the stability of dynamical networks than the
procedure of isospectral network expansions introduced in [Isospectral graph
transformations, spectral equivalence, and global stability of dynamical
networks. Nonlinearity, 25 (2012) 211-254]. The effectiveness of our approach
is illustrated by applications to various classes of Cohen-Grossberg neural
networks.Comment: 32 pages, 9 figure
Spatial field correlation, the building block of mesoscopic fluctuations
The absence of self averaging in mesoscopic systems is a consequence of
long-range intensity correlation. Microwave measurements suggest and
diagrammatic calculations confirm that the correlation function of the
normalized intensity with displacement of the source and detector,
and , respectively, can be expressed as the sum of three terms, with
distinctive spatial dependences. Each term involves only the sum or the product
of the square of the field correlation function, . The
leading-order term is the product, the next term is proportional to the sum.
The third term is proportional to .Comment: Submitted to PR
Electron dephasing near zero temperature: an experimental review
The behavior of the electron dephasing time near zero temperature,
, has recently attracted vigorous attention. This renewed interest
is primarily concerned with whether should reach a finite or an
infinite value as 0. While it is accepted that should
diverge if there exists only electron-electron (electron-phonon) scattering,
several recent measurements have found that depends only very
weakly on temperature, if at all, when is sufficiently low. This article
discusses the current experimental status of "the saturation problem", and
concludes that the origin(s) for this widely observed saturation are still
unresolved
Field and intensity correlations in random media
Measurements of the microwave field transmitted through a random medium
allows direct access to the field correlation function, whose complex square is
the short range or C1 contribution to the intensity correlation function C. The
frequency and spatial correlation function are compared to their Fourier pairs,
the time of flight distribution and the specific intensity, respectively. The
longer range contribution to intensity correlation is obtained directly by
subtracting C1 from C and is in good agreement with theory.Comment: 9 pages, 5 figures, submitted to Phys.Rev.
Optical Monitoring of PKS 1510-089: A Binary Black Hole System?
Three deep flux minima were observed with nearly the same time-scales and
intervals for the blazar PKS 1510-089 in the past few years. A binary black
hole system was proposed to be at the nucleus of this object, and a new minimum
was predicted to occur in 2002 March. We monitored this source with a 60/90 cm
Schmidt telescope from 2002 February to April. In combination with the data
obtained by Xie et al. (2004) in the same period, we presented for the 2002
minimum a nearly symmetric light curve, which would be required by an eclipsing
model of a binary black hole system. We also constrained the time-scale of the
minimum to be 35 min, which is more consistent with the time-scales ~42 min of
the three previous minima than the 89 min time-scale given by the same authors.
The wiggling miniarcsecond radio jet observed in this object is taken as a
further evidence for the binary black hole system. The `coupling' of the
periodicity in light curve and the helicity in radio jet is discussed in the
framework of a binary black hole system.Comment: 5 pages, 4 figures, accepted by MNRA
Non-Fermi liquid behavior of SrRuO_3 -- evidence from infrared conductivity
The reflectivity of the itinerant ferromagnet SrRuO_3 has been measured
between 50 and 25,000 cm-1 at temperatures ranging from 40 to 300 K, and used
to obtain conductivity, scattering rate, and effective mass as a function of
frequency and temperature. We find that at low temperatures the conductivity
falls unusually slowly as a function of frequency (proportional to
\omega^{-1/2}), and at high temperatures it even appears to increase as a
function of frequency in the far-infrared limit. The data suggest that the
charge dynamics of SrRuO_3 are substantially different from those of
Fermi-liquid metals.Comment: 4 pages, 3 postscript figure
- …