Experimental analysis of the Strato-rotational Instability in a cylindrical Couette flow

This study is devoted to the experimental analysis of the Strato-rotational Instability (SRI). This instability affects the classical cylindrical Couette flow when the fluid is stably stratified in the axial direction. In agreement with recent theoretical and numerical analyses, we describe for the first time in detail the destabilization of the stratified flow below the Rayleigh line (i.e. the stability threshold without stratification). We confirm that the unstable modes of the SRI are non axisymmetric, oscillatory, and take place as soon as the azimuthal linear velocity decreases along the radial direction. This new instability is relevant for accretion disks.Comment: 4 pages, 4 figures. PRL in press 200

Preference-Informed Fairness

We study notions of fairness in decision-making systems when individuals have diverse preferences over the possible outcomes of the decisions. Our starting point is the seminal work of Dwork et al. which introduced a notion of individual fairness (IF): given a task-specific similarity metric, every pair of individuals who are similarly qualified according to the metric should receive similar outcomes. We show that when individuals have diverse preferences over outcomes, requiring IF may unintentionally lead to less-preferred outcomes for the very individuals that IF aims to protect. A natural alternative to IF is the classic notion of fair division, envy-freeness (EF): no individual should prefer another individual's outcome over their own. Although EF allows for solutions where all individuals receive a highly-preferred outcome, EF may also be overly-restrictive. For instance, if many individuals agree on the best outcome, then if any individual receives this outcome, they all must receive it, regardless of each individual's underlying qualifications for the outcome. We introduce and study a new notion of preference-informed individual fairness (PIIF) that is a relaxation of both individual fairness and envy-freeness. At a high-level, PIIF requires that outcomes satisfy IF-style constraints, but allows for deviations provided they are in line with individuals' preferences. We show that PIIF can permit outcomes that are more favorable to individuals than any IF solution, while providing considerably more flexibility to the decision-maker than EF. In addition, we show how to efficiently optimize any convex objective over the outcomes subject to PIIF for a rich class of individual preferences. Finally, we demonstrate the broad applicability of the PIIF framework by extending our definitions and algorithms to the multiple-task targeted advertising setting introduced by Dwork and Ilvento

Water quality assessment, trophic classification and water resources management

Quantification of water quality (WQ) is an integral part of scientifically based water resources management. The main objective of this study was comparative analysis of two approaches applied for quantitative assessment of WQ: the trophic level index (TLI) and the Delphi method (DM). We analyzed the following features of these conceptually different approaches: A. similarity of estimates of lake WQ; B. sensitivity to indicating disturbances in the aquatic ecosystem structure and functioning; C. capacity to reflect the impact of major management measures on the quality of water resources. We compared the DM and TLI based on results from a series of lakes covering varying productivity levels, mixing regimes and climatic zones. We assumed that the conservation of aquatic ecosystem in some predefined, “reference”, state is a major objective of sustainable water resources management in the study lakes. The comparison between the two approaches was quantified as a relationship between the DM ranks and respective TLI values. We show that being a classification system, the TLI does not account for specific characteristics of aquatic ecosystems and the array of different potential uses of the water resource. It indirectly assumes that oligotrophication is identical to WQ improvement, and reduction of economic activity within the lake catchment area is the most effective way to improve WQ. WQ assessed with the TLI is more suitable for needs of natural water resources management if eutrophication is a major threat. The DM allows accounting for several water resource uses and therefore it may serve as a more robust and comprehensive tool for WQ quantification and thus for sustainable water resources management

Effects of wall compliance on the laminar–turbulent transition of torsional Couette flow

Torsional Couette flow between a rotating disk and a stationary wall is studied experimentally. The surface of the disk is either rigid or covered with a compliant coating. The influence of wall compliance on characteristic flow instabilities and on the laminar–turbulent flow transition is investigated. Data obtained from analysing flow visualizations are discussed. It is found that wall compliance favours two of the three characteristic wave patterns associated with the transition process and broadens the parameter regime in which these patterns are observed. The results for the effects of wall compliance on the third pattern are inconclusive. However, the experiments indicate that the third pattern is not a primary constituent of the laminar–turbulent transition process of torsional Couette flow

WISeREP - An Interactive Supernova Data Repository

We have entered an era of massive data sets in astronomy. In particular, the number of supernova (SN) discoveries and classifications has substantially increased over the years from few tens to thousands per year. It is no longer the case that observations of a few prototypical events encapsulate most spectroscopic information about SNe, motivating the development of modern tools to collect, archive, organize and distribute spectra in general, and SN spectra in particular. For this reason we have developed the Weizmann Interactive Supernova data REPository - WISeREP - an SQL-based database (DB) with an interactive web-based graphical interface. The system serves as an archive of high quality SN spectra, including both historical (legacy) data as well as data that is accumulated by ongoing modern programs. The archive provides information about objects, their spectra, and related meta-data. Utilizing interactive plots, we provide a graphical interface to visualize data, perform line identification of the major relevant species, determine object redshifts, classify SNe and measure expansion velocities. Guest users may view and download spectra or other data that have been placed in the public domain. Registered users may also view and download data that are proprietary to specific programs with which they are associated. The DB currently holds >8000 spectra, of which >5000 are public; the latter include published spectra from the Palomar Transient Factory, all of the SUSPECT archive, the Caltech-Core-Collapse Program, the CfA SN spectra archive and published spectra from the UC Berkeley SNDB repository. It offers an efficient and convenient way to archive data and share it with colleagues, and we expect that data stored in this way will be easy to access, increasing its visibility, usefulness and scientific impact.Comment: To be published in PASP. WISeREP: http://www.weizmann.ac.il/astrophysics/wiserep

Quantitative estimates of convergence in nonlinear operator extensions of Korovkin's theorems

This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of continuous real functions. Several examples illustrating the theory are included.Comment: 10 page

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

SN2007ax : An Extremely Faint Type Ia Supernova

We present multi-band photometric and optical spectroscopic observations of SN2007ax, the faintest and reddest Type Ia supernova (SNIa) yet observed. With M_B = -15.9 and (B-V)max = 1.2, this SN is over half a magnitude fainter at maximum light than any other SNIa. Similar to subluminous SN2005ke, SN2007ax also appears to show excess in UV emission at late time. Traditionally, Delta-m_15(B) has been used to parameterize the decline rate for SNeIa. However, the B-band transition from fast to slow decline occurs sooner than 15 days for faint SNeIa. Therefore we suggest that a more physically motivated parameter, the time of intersection of the two slopes, be used instead. Only by explaining the faintest (and the brightest) supernovae, we can thoroughly understand the physics of thermonuclear explosions. We suggest that future surveys should carefully design their cadence, depth, pointings and follow-up to find an unbiased sample of extremely faint members of this subclass of faint SNeIa.Comment: Accepted for publication in ApJ