27,492 research outputs found
On a P\'olya functional for rhombi, isosceles triangles, and thinning convex sets
Let be an open convex set in with finite width, and
let be the torsion function for , i.e. the solution of
. An upper bound is obtained for the product
of , where
is the bottom of the spectrum of the Dirichlet Laplacian
acting in . The upper bound is sharp in the limit of a thinning
sequence of convex sets. For planar rhombi and isosceles triangles with area
, it is shown that , and that this bound is sharp.Comment: 12 pages, 4 figure
Stochastically perturbed flows: Delayed and interrupted evolution
We present analytical expressions for the time-dependent and stationary
probability distributions corresponding to a stochastically perturbed
one-dimensional flow with critical points, in two physically relevant
situations: delayed evolution, in which the flow alternates with a quiescent
state in which the variate remains frozen at its current value for random
intervals of time; and interrupted evolution, in which the variate is also
re-set in the quiescent state to a random value drawn from a fixed
distribution. In the former case, the effect of the delay upon the first
passage time statistics is analyzed. In the latter case, the conditions under
which an extended stationary distribution can exist as a consequence of the
competition between an attractor in the flow and the random re-setting are
examined. We elucidate the role of the normalization condition in eliminating
the singularities arising from the unstable critical points of the flow, and
present a number of representative examples. A simple formula is obtained for
the stationary distribution and interpreted physically. A similar
interpretation is also given for the known formula for the stationary
distribution in a full-fledged dichotomous flow.Comment: 27 pages; no figures. Submitted to Stochastics and Dynamic
Analytic calculation of energy transfer and heat flux in a one-dimensional system
In the context of the problem of heat conduction in one-dimensional systems,
we present an analytical calculation of the instantaneous energy transfer
across a tagged particle in a one-dimensional gas of equal-mass, hard-point
particles. From this, we obtain a formula for the steady-state energy flux, and
identify and separate the mechanical work and heat conduction contributions to
it. The nature of the Fourier law for the model, and the nonlinear dependence
of the rate of mechanical work on the stationary drift velocity of the tagged
particle, are analyzed and elucidated.Comment: 17 pages including title pag
Concentration, Spin and Shape of Dark Matter Haloes as a Function of the Cosmological Model: WMAP1, WMAP3 and WMAP5 results
We investigate the effects of changes in the cosmological parameters between
the WMAP 1st, 3rd, and 5th year results on the structure of dark matter haloes.
We use a set of simulations that cover 5 decades in halo mass ranging from the
scales of dwarf galaxies (V_c ~30 km/s) to clusters of galaxies (V_c ~ 1000
km/s). We find that the concentration mass relation is a power law in all three
cosmologies. However the slope is shallower and the zero point is lower moving
from WMAP1 to WMAP5 to WMAP3. For haloes of mass log(M_200/Msun) = 10, 12, and
14 the differences in the concentration parameter between WMAP1 and WMAP3 are a
factor of 1.55, 1.41, and 1.29, respectively. As we show, this brings the
central densities of dark matter haloes in good agreement with the central
densities of dwarf and low surface brightness galaxies inferred from their
rotation curves, for both the WMAP3 and WMAP5 cosmologies. We also show that
none of the existing toy models for the concentration-mass relation can
reproduce our simulation results over the entire range of masses probed. In
particular, the model of Bullock et al (B01) fails at the higher mass end (M >
1e13 Msun), while the NFW model of Navarro, Frenk & White (1997) fails
dramatically at the low mass end (M < 1e12 Msun). We present a new model, based
on a simple modification of that of B01, which reproduces the
concentration-mass relations in our simulations over the entire range of masses
probed (1e10 Msun < M < 1e15 Msun). Haloes in the WMAP3 cosmology (at a fixed
mass) are more flatted compared to the WMAP1 cosmology, with a medium to long
axis ration reduced by ~10 %. Finally, we show that the distribution of halo
spin parameters is the same for all three cosmologies.Comment: 16 pages, 16 figures, references updated, minor changes. Accepted for
publication on MNRAS. WMAP5 simulations available upon reques
Explaining UXOR variability with self-shadowed disks
In this Letter we propose a new view on UX Orionis type variability. The idea
is based on the earlier proposal by various authors that UXORs are
nearly-edge-on disks in which hydrodynamic fluctuations could cause clumps of
dust and gas to cross the line of sight. However, because the standard disk
models have a flaring geometry, it is mostly the outer regions of the disk that
obscure the star. The time scales for such obscuration events would be too long
to match the observed time scales of weeks to months. Recent 2-D
self-consistent models of Herbig Ae/Be protoplanetary disks (Dullemond et al.
2002,2003 henceforth D02/DD03), however, have indicated that for Herbig Ae/Be
star disks there exists, in addition to the usual flared disks, also a new
class of disks: those that are fully self-shadowed. Only their puffed-up inner
rim (at the dust evaporation radius) is directly irradiated by the star, while
the disk at larger radius resides in the shadow of the rim. For these disks
there exist inclinations at which the line of sight towards the star skims the
upper parts of the puffed-up inner rim, while passing high over the surface of
outer disk regions. Small hydrodynamic fluctuations in the puffed-up inner rim
could then be held responsible for the extinction events seen in UXORs. If this
idea is correct, it makes a prediction for the shape of the SEDs of these
stars. It was shown by D02/DD03 that flared disks have a strong far-IR excess
and can be classified as `group I' (in the classification of Meeus et al.
2001), while self-shadowed disks have a relatively weak far-IR excess and are
classified as `group II'. Our model therefore predicts that UXORs belong to the
`group II' sources. We show that this correlation is indeed found within a
sample of 86 Herbig Ae/Be stars.Comment: Accepted for publication in ApJ Letters (a few lines added to
original version to accommodate comments of referee
Instability statistics and mixing rates
We claim that looking at probability distributions of \emph{finite time}
largest Lyapunov exponents, and more precisely studying their large deviation
properties, yields an extremely powerful technique to get quantitative
estimates of polynomial decay rates of time correlations and Poincar\'e
recurrences in the -quite delicate- case of dynamical systems with weak chaotic
properties.Comment: 5 pages, 5 figure
Inflammatory Responses and Barrier Function of Endothelial Cells Derived from Human Induced Pluripotent Stem Cells
Several studies have reported endothelial cell (EC) derivation from human induced pluripotent stem cells (hiPSCs). However, few have explored their functional properties in depth with respect to line-to-line and batch-to-batch variability and how they relate to primary ECs. We therefore carried out accurate characterization of hiPSC-derived ECs (hiPSC-ECs) from multiple (non-integrating) hiPSC lines and compared them with primary ECs in various functional assays, which included barrier function using real-time impedance spectroscopy with an integrated assay of electric wound healing, endothelia-leukocyte interaction under physiological flow to mimic inflammation and angiogenic responses in in vitro and in vivo assays. Overall, we found many similarities but also some important differences between hiPSC-derived and primary ECs. Assessment of vasculogenic responses in vivo showed little difference between primary ECs and hiPSC-ECs with regard to functional blood vessel formation, which may be important in future regenerative medicine applications requiring vascularization. In this article, Orlova and colleagues show that hiPSC-ECs have similar features to primary ECs but also show some differences. hiPSC-ECs exhibited higher barrier function, lower expression of pro-inflammatory adhesive receptors, and more stringent stromal cell requirements. Importantly, healthy control CD31+ hiPSC-ECs showed high consistency between different batches and lines, forming a good basis for disease modeling applications
Macroscopic limit cycle via pure noise-induced phase transition
Bistability generated via a pure noise-induced phase transition is reexamined
from the view of bifurcations in macroscopic cumulant dynamics. It allows an
analytical study of the phase diagram in more general cases than previous
methods. In addition using this approach we investigate patially-extended
systems with two degrees of freedom per site. For this system, the analytic
solution of the stationary Fokker-Planck equation is not available and a
standard mean field approach cannot be used to find noise induced phase
transitions. A new approach based on cumulant dynamics predicts a noise-induced
phase transition through a Hopf bifurcation leading to a macroscopic limit
cycle motion, which is confirmed by numerical simulation.Comment: 8 pages, 8 figure
Mediated tunable coupling of flux qubits
It is sketched how a monostable rf- or dc-SQUID can mediate an inductive
coupling between two adjacent flux qubits. The nontrivial dependence of the
SQUID's susceptibility on external flux makes it possible to continuously tune
the induced coupling from antiferromagnetic (AF) to ferromagnetic (FM). In
particular, for suitable parameters, the induced FM coupling can be
sufficiently large to overcome any possible direct AF inductive coupling
between the qubits.
The main features follow from a classical analysis of the multi-qubit
potential. A fully quantum treatment yields similar results, but with a
modified expression for the SQUID susceptibility.
Since the latter is exact, it can also be used to evaluate the
susceptibility--or, equivalently, energy-level curvature--of an isolated
rf-SQUID for larger shielding and at degenerate flux bias, i.e., a (bistable)
qubit. The result is compared to the standard two-level (pseudospin) treatment
of the anticrossing, and the ensuing conclusions are verified numerically.Comment: REVTeX 4, 16 pp., 4 EPS figures. N.B.: "Alec" is my first, and
"Maassen van den Brink" my family name. v2: major expansion and rewriting,
new title and co-author; to appear in New Journal of Physics special issue
(R. Fazio, ed.
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