Cross-shaped and Degenerate Singularities in an Unstable Elliptic Free Boundary Problem

We investigate singular and degenerate behavior of solutions of the unstable free boundary problem $$\Delta u = -\chi_{\{u>0\}} .$$ First, we construct a solution that is not of class $C^{1,1}$ and whose free boundary consists of four arcs meeting in a {\em cross}-shaped singularity. This solution is completely unstable/repulsive from above and below which would make it hard to get by the usual methods, and even numerics is non-trivial. We also show existence of a degenerate solution. This answers two of the open questions in a recent paper by R. Monneau-G.S. Weiss

Backlund transformation and special solutions for Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations

Using the Weiss method of truncated singular expansions, we construct an explicit Backlund transformation of the Drinfeld-Sokolov-Satsuma-Hirota system into itself. Then we find all the special solutions generated by this transformation from the trivial zero solution of this system.Comment: LaTeX, 5 page

On integrability of the differential constraints arising from the singularity analysis

Integrability of the differential constraints arising from the singularity analysis of two (1+1)-dimensional second-order evolution equations is studied. Two nonlinear ordinary differential equations are obtained in this way, which are integrable by quadratures in spite of very complicated branching of their solutions.Comment: arxiv version is already offcia

Optical Properties of Quantum-Dot-Doped Liquid Scintillators

Semiconductor nanoparticles (quantum dots) were studied in the context of liquid scintillator development for upcoming neutrino experiments. The unique optical and chemical properties of quantum dots are particularly promising for the use in neutrinoless double beta decay experiments. Liquid scintillators for large scale neutrino detectors have to meet specific requirements which are reviewed, highlighting the peculiarities of quantum-dot-doping. In this paper, we report results on laboratory-scale measurements of the attenuation length and the fluorescence properties of three commercial quantum dot samples. The results include absorbance and emission stability measurements, improvement in transparency due to filtering of the quantum dot samples, precipitation tests to isolate the quantum dots from solution and energy transfer studies with quantum dots and the fluorophore PPO.Comment: version 2, minor text update

A Conceptual Framework for Studying the Sources of Variation in Program Effects

Evaluations of public programs in many fields reveal that (1) different types of programs (or different versions of the same program) vary in their effectiveness, (2) a program that is effective for one group of people might not be effective for other groups of people, and (3) a program that is effective in one set of circumstances may not be effective in other circumstances. This paper presents a conceptual framework for research on such variation in program effects and the sources of this variation. The framework is intended to help researchers -- both those who focus mainly on studying program implementation and those who focus mainly on estimating program effects -- see how their respective pieces fit together in a way that helps to identify factors that explain variation in program effects and thereby support more systematic data collection on these factors. The ultimate goal of the framework is to enable researchers to offer better guidance to policymakers and program operators on the conditions and practices that are associated with larger and more positive effects

Weak Localization and Transport Gap in Graphene Antidot Lattices

We fabricated and measured antidot lattices in single layer graphene with lattice periods down to 90 nm. In large-period lattices, a well-defined quantum Hall effect is observed. Going to smaller antidot spacings the quantum Hall effect gradually disappears, following a geometric size effect. Lattices with narrow constrictions between the antidots behave as networks of nanoribbons, showing a high-resistance state and a transport gap of a few mV around the Dirac point. We observe pronounced weak localization in the magnetoresistance, indicating strong intervalley scattering at the antidot edges. The area of phase-coherent paths is bounded by the unit cell size at low temperatures, so each unit cell of the lattice acts as a ballistic cavity.Comment: some revisions, to appear in New Journal of Physics, Special Issue Graphen