21,022 research outputs found
Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction
Extinction of an epidemic or a species is a rare event that occurs due to a
large, rare stochastic fluctuation. Although the extinction process is
dynamically unstable, it follows an optimal path that maximizes the probability
of extinction. We show that the optimal path is also directly related to the
finite-time Lyapunov exponents of the underlying dynamical system in that the
optimal path displays maximum sensitivity to initial conditions. We consider
several stochastic epidemic models, and examine the extinction process in a
dynamical systems framework. Using the dynamics of the finite-time Lyapunov
exponents as a constructive tool, we demonstrate that the dynamical systems
viewpoint of extinction evolves naturally toward the optimal path.Comment: 21 pages, 5 figures, Final revision to appear in Bulletin of
Mathematical Biolog
Dust Emissivity in the Far-Infrared
We have derived the dust emissivity in the Far-Infrared (FIR) using data
available in the literature. We use two wavelength dependences derived from
spectra of Galactic FIR emission (Reach et al. 1995). A value for the
emissivity, normalised to the extinction efficiency in the V band, has been
retrieved from maps of Galactic FIR emission, dust temperature and extinction
(Schlegel et al. 1998).
Our results are similar to other measurements in the Galaxy but only
marginally consistent with the widely quoted values of Hildebrand (1983)
derived on one reflection nebula. The discrepancy with measurements on other
reflection nebulae (Casey 1991) is higher and suggests a different grain
composition in these environments with respect to the diffuse interstellar
medium.
We measure dust masses for a sample of six spiral galaxies with FIR
observations and obtain gas-to-dust ratios close to the Galactic value.Comment: 5 pages, 1 ps file, A&A letter accepte
ISO observations of spirals: modelling the FIR emission
ISO observations at 200 micron have modified our view of the dust component
in spiral galaxies. For a sample of seven resolved spirals we have retrieved a
mean temperature of 20K, about 10K lower than previous estimates based on IRAS
data at shorter wavelengths. Because of the steep dependence of far-infrared
emission on the dust temperature, the dust masses inferred from ISO fluxes are
a factor of 10 higher than those derived from IRAS data only, leading to
gas-to-dust ratios close to the value observed in the Galaxy. The scale-length
of the 200 micron emission is larger than for the IRAS 100 micron emission,
with colder dust at larger distances from the galactic centre, as expected if
the interstellar radiation field is the main source of dust heating. The 200
micron scale-length is also larger than the optical, for all the galaxies in
the sample. This suggests that the dust distribution is more extended than that
of the stars.A model of the dust heating is needed to derive the parameters of
the dust distribution from the FIR emission. Therefore, we have adapted an
existing radiative transfer code to deal with dust emission. Simulated maps of
the temperature distribution within the dust disk and of the dust emission at
any wavelength can be produced. The stellar spectral energy distribution is
derived from observations in the ultraviolet, optical and near infrared. The
parameters of the dust distribution (scale-lengths and optical depth) are
chosen to reproduce the observed characteristics of the FIR emission, i.e. the
shape of the spectrum, the flux and the spatial distribution. We describe the
application of the model to one of the galaxies in the sample, NGC 6946.Comment: 6 pages, 5 figures. Contribution to the proceedings of the workshop
"ISO Beyond Point Sources" held at VILSPA 14-17 September 199
Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections
This work focuses on the iterative solution of sequences of KKT linear
systems arising in interior point methods applied to large convex quadratic
programming problems. This task is the computational core of the interior point
procedure and an efficient preconditioning strategy is crucial for the
efficiency of the overall method. Constraint preconditioners are very effective
in this context; nevertheless, their computation may be very expensive for
large-scale problems, and resorting to approximations of them may be
convenient. Here we propose a procedure for building inexact constraint
preconditioners by updating a "seed" constraint preconditioner computed for a
KKT matrix at a previous interior point iteration. These updates are obtained
through low-rank corrections of the Schur complement of the (1,1) block of the
seed preconditioner. The updated preconditioners are analyzed both
theoretically and computationally. The results obtained show that our updating
procedure, coupled with an adaptive strategy for determining whether to
reinitialize or update the preconditioner, can enhance the performance of
interior point methods on large problems.Comment: 22 page
Competing Glauber and Kawasaki Dynamics
Using a quantum formulation of the master equation we study a kinetic Ising
model with competing stochastic processes: the Glauber dynamics with
probability and the Kawasaki dynamics with probability . Introducing
explicitely the coupling to a heat bath and the mutual static interaction of
the spins the model can be traced back exactly to a Ginzburg Landau functional
when the interaction is of long range order. The dependence of the correlation
length on the temperature and on the probability is calculated. In case
that the spins are subject to flip processes the correlation length disappears
for each finite temperature. In the exchange dominated case the system is
strongly correlated for each temperature.Comment: 9 pages, Revte
Dualism between Physical Frames and Time in Quantum Gravity
In this work we present a discussion of the existing links between the
procedures of endowing the quantum gravity with a real time and of including in
the theory a physical reference frame. More precisely, as first step, we
develop the canonical quantum dynamics, starting from the Einstein equations in
presence of a dust fluid and arrive to a Schroedinger evolution. Then, by
fixing the lapse function in the path integral of gravity, we get a
Schroedinger quantum dynamics, of which eigenvalues problem provides the
appearance of a dust fluid in the classical limit. The main issue of our
analysis is to claim that a theory, in which the time displacement invariance,
on a quantum level, is broken, is indistinguishable from a theory for which
this symmetry holds, but a real reference fluid is included.Comment: 9 pages, submitted to Mod. Phys. Lett. A, major replacements in
section 3 and
Latest evidence for a late time vacuum -- geodesic CDM interaction
We perform a reconstruction of the coupling function between vacuum energy
and geodesic cold dark matter using the latest observational data. We bin the
interaction in seventeen redshift bins but use a correlation prior to prevent
rapid, unphysical oscillations in the coupling function. This prior also serves
to eliminate any dependence of the reconstruction on the binning method. We use
two different forms of the correlation prior, finding that both give similar
results for the reconstruction of the dark matter -- dark energy interaction.
Calculating the Bayes factor for each case, we find no meaningful evidence for
deviation from the null interacting case, i.e. CDM, in our
reconstruction.Comment: 14 pages, 7 figures. Version 2 matches published version in Physics
of the Dark Universe (Figure 2 updated to better show H0 and sigma 8
tensions, additional discussion of results added in section 4.1
Disorder-Induced Stabilization of the Pseudogap in Strongly Correlated Systems
The interplay of strong interaction and strong disorder, as contained in the
Anderson-Hubbard model, is addressed using two non-perturbative numerical
methods: the Lanczos algorithm in the grand canonical ensemble at zero
temperature and Quantum Monte Carlo. We find distinctive evidence for a
zero-energy anomaly which is robust upon variation of doping, disorder and
interaction strength. Its similarities to, and differences from, pseudogap
formation in other contexts, including perturbative treatments of interactions
and disorder, classical theories of localized charges, and in the clean Hubbard
model, are discussed.Comment: 4.2 pages, 4 figure
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