Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space

Urban Public Works in Spatial Equilibrium: Experimental Evidence from Ethiopia

This paper evaluates a large urban public works program randomly rolled out across neighborhoods of Addis Ababa, Ethiopia. We find the program increased public employment and reduced private labor supply among beneficiaries and improved local amenities in treated locations. We then combine a spatial equilibrium model and unique commuting data to estimate the spillover effects of the program on private sector wages across neighborhoods: under full program rollout, wages increased by 18.6 percent. Using our model, we show that welfare gains to the poor are six times larger when we include the indirect effects on private wages and local amenities

Orbital and physical parameters of eclipsing binaries from the ASAS catalogue -- I. A sample of systems with components' masses between 1 and 2 M⊙_\odot

We derive the absolute physical and orbital parameters for a sample of 18 detached eclipsing binaries from the \emph{All Sky Automated Survey} (ASAS) database based on the available photometry and our own radial velocity measurements. The radial velocities (RVs) are computed using spectra we collected with the 3.9-m Anglo-Australian Telescope and its \emph{University College London Echelle Spectrograph} and the 1.9-m SAAO Radcliffe telescope and its \emph{Grating Instrument for Radiation Analysis with a Fibre Fed Echelle}. In order to obtain as precise RVs as possible, most of the systems were observed with an iodine cell available at the AAT/UCLES and/or analyzed using the two-dimensional cross-correlation technique (TODCOR). The RVs were measured with TODCOR using synthetic template spectra as references. However, for two objects we used our own approach to the tomographic disentangling of the binary spectra to provide observed template spectra for the RV measurements and to improve the RV precision even more. For one of these binaries, AI Phe, we were able to the obtain an orbital solution with an RV $rms$ of 62 and 24 m s$^{-1}$ for the primary and secondary respectively. For this system, the precision in $M \sin^3{i}$ is 0.08%. For the analysis, we used the photometry available in the ASAS database. We combined the RV and light curves using PHOEBE and JKTEBOP codes to obtain the absolute physical parameters of the systems. Having precise RVs we were able to reach $\sim$0.2 % precision (or better) in masses in several cases but in radii, due to the limited precision of the ASAS photometry, we were able to reach a precision of only 1% in one case and 3-5 % in a few more cases. For the majority of our objects, the orbital and physical analysis is presented for the first time.Comment: 16 pages, 2 figures, 6 tables in the main text, 1 table in appendix, to appear in MNRA

High Mass Triple Systems: The Classical Cepheid Y Car

We have obtained an HST STIS ultraviolet high dispersion Echelle mode spectrum the binary companion of the double mode classical Cepheid Y Car. The velocity measured for the hot companion from this spectrum is very different from reasonable predictions for binary motion, implying that the companion is itself a short period binary. The measured velocity changed by 7 km/ s during the 4 days between two segments of the observation confirming this interpretation. We summarize "binary" Cepheids which are in fact members of triple system and find at least 44% are triples. The summary of information on Cepheids with orbits makes it likely that the fraction is under-estimated.Comment: accepted by A

Geometric approach to nonvariational singular elliptic equations

In this work we develop a systematic geometric approach to study fully nonlinear elliptic equations with singular absorption terms as well as their related free boundary problems. The magnitude of the singularity is measured by a negative parameter $(\gamma -1)$, for $0 < \gamma < 1$, which reflects on lack of smoothness for an existing solution along the singular interface between its positive and zero phases. We establish existence as well sharp regularity properties of solutions. We further prove that minimal solutions are non-degenerate and obtain fine geometric-measure properties of the free boundary $\mathfrak{F} = \partial \{u > 0 \}$. In particular we show sharp Hausdorff estimates which imply local finiteness of the perimeter of the region $\{u > 0 \}$ and $\mathcal{H}^{n-1}$ a.e. weak differentiability property of $\mathfrak{F}$.Comment: Paper from D. Araujo's Ph.D. thesis, distinguished at the 2013 Carlos Gutierrez prize for best thesis, Archive for Rational Mechanics and Analysis 201

Homogenization and enhancement for the G-equation

We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally we also consider advection depending on position at the integral scale

V(RI)sub(c) Photometry of Cepheids in the Magellanic Clouds

We present V(RI)sub data for thirteen Cepheids in the Large Magellanic Cloud ans fifty-five in each wavelength band. The median uncertainty in the photometry iy Moffett, Gieren & Barnes (1998) which contained 1000 measures ($\pm 0.01$ mag) in each wavelength band on 22 variables with periods in the range 8--133 days.Comment: LaTeX file (9 pages), LaTeX table (1 page), 2 figures of 3 panels eacs PASP (July

The Search for Stellar Companions to Exoplanet Host Stars Using the CHARA Array

Most exoplanets have been discovered via radial velocity studies, which are inherently insensitive to orbital inclination. Interferometric observations will show evidence of a stellar companion if it sufficiently bright, regardless of the inclination. Using the CHARA Array, we observed 22 exoplanet host stars to search for stellar companions in low-inclination orbits that may be masquerading as planetary systems. While no definitive stellar companions were discovered, it was possible to rule out certain secondary spectral types for each exoplanet system observed by studying the errors in the diameter fit to calibrated visibilities and by searching for separated fringe packets.Comment: 26 pages, 5 tables, 8 figure

Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)