2,173 research outputs found
Counting Hamilton cycles in sparse random directed graphs
Let D(n,p) be the random directed graph on n vertices where each of the
n(n-1) possible arcs is present independently with probability p. A celebrated
result of Frieze shows that if then D(n,p) typically
has a directed Hamilton cycle, and this is best possible. In this paper, we
obtain a strengthening of this result, showing that under the same condition,
the number of directed Hamilton cycles in D(n,p) is typically
. We also prove a hitting-time version of this statement,
showing that in the random directed graph process, as soon as every vertex has
in-/out-degrees at least 1, there are typically
directed Hamilton cycles
Astrometric Effects of a Stochastic Gravitational Wave Background
A stochastic gravitational wave background causes the apparent positions of
distant sources to fluctuate, with angular deflections of order the
characteristic strain amplitude of the gravitational waves. These fluctuations
may be detectable with high precision astrometry, as first suggested by
Braginsky et al. in 1990. Several researchers have made order of magnitude
estimates of the upper limits obtainable on the gravitational wave spectrum
\Omega_gw(f), at frequencies of order f ~ 1 yr^-1, both for the future
space-based optical interferometry missions GAIA and SIM, and for VLBI
interferometry in radio wavelengths with the SKA. For GAIA, tracking N ~ 10^6
quasars over a time of T ~ 1 yr with an angular accuracy of \Delta \theta ~ 10
\mu as would yield a sensitivity level of \Omega_gw ~ (\Delta \theta)^2/(N T^2
H_0^2) ~ 10^-6, which would be comparable with pulsar timing. In this paper we
take a first step toward firming up these estimates by computing in detail the
statistical properties of the angular deflections caused by a stochastic
background. We compute analytically the two point correlation function of the
deflections on the sphere, and the spectrum as a function of frequency and
angular scale. The fluctuations are concentrated at low frequencies (for a
scale invariant stochastic background), and at large angular scales, starting
with the quadrupole. The magnetic-type and electric-type pieces of the
fluctuations have equal amounts of power.Comment: 23 pages, 2 figures, references added and minor text correction
Program
Program for the 44th Annual Fay B. Kaigler Children\u27s Book Festiva
Program
Program for the 41st annual Fay B. Kaigler Children\u27s Book Festiva
Program
Program for the 40th annual Fay B. Kaigler Children\u27s Book Festiva
Program
Program for the 40th annual Fay B. Kaigler Children\u27s Book Festiva
Program
Program for the 43rd annual Fay B. Kaigler Children\u27s Book Festiva
Long-term Evolution of Protostellar and Protoplanetary Disks. I. Outbursts
As an initial investigation into the long-term evolution of protostellar
disks, we explore the conditions required to explain the large outbursts of
disk accretion seen in some young stellar objects. We use one-dimensional
time-dependent disk models with a phenomenological treatment of the
magnetorotational instability (MRI) and gravitational torques to follow disk
evolution over long timescales. Comparison with our previous two-dimensional
disk model calculations (Zhu et al. 2009b, Z2009b) indicates that the neglect
of radial effects and two-dimensional disk structure in the one-dimensional
case makes only modest differences in the results; this allows us to use the
simpler models to explore parameter space efficiently. We find that the mass
infall rates typically estimated for low-mass protostars generally result in
AU-scale disk accretion outbursts, as predicted by our previous analysis (Zhu
et al. 2009a,Z2009a). We also confirm quasi-steady accretion behavior for high
mass infall rates if the values of -parameter for the magnetorotational
instability is small, while at this high accretion rate convection from the
thermal instability may lead to some variations. We further constrain the
combinations of the -parameter and the MRI critical temperature, which
can reproduce observed outburst behavior. Our results suggest that dust
sublimation may be connected with full activation of the MRI. This is
consistent with the idea that small dust captures ions and electrons to
suppress the MRI. In a later paper we will explore both long-term outburst and
disk evolution with this model, allowing for infall from protostellar envelopes
with differing angular momenta.Comment: Accepted to publish in Ap
Experimental investigation of the fundamental modes of a collisionless plasma Final report, 10 Mar. 1964 - 31 Oct. 1967
Propagation of electron cyclotron waves and effects of low frequency noise in collisionless plasm
- …