On a P\'olya functional for rhombi, isosceles triangles, and thinning convex sets

Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product of $\Vert v_{\Omega}\Vert_{L^{\infty}(\Omega)}\lambda(\Omega)$, where $\lambda(\Omega)$ is the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Omega)$. The upper bound is sharp in the limit of a thinning sequence of convex sets. For planar rhombi and isosceles triangles with area $1$, it is shown that $\Vert v_{\Omega}\Vert_{L^{1}(\Omega)}\lambda(\Omega)\ge \frac{\pi^2}{24}$, 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.