Gravitational Lensing by Power-Law Mass Distributions: A Fast and Exact Series Approach

We present an analytical formulation of gravitational lensing using familiar triaxial power-law mass distributions, where the 3-dimensional mass density is given by $\rho(X,Y,Z) = \rho_0 [1 + (\frac{X}{a})^2 + (\frac{Y}{b})^2 + (\frac{Z}{c})^2]^{-\nu/2}$. The deflection angle and magnification factor are obtained analytically as Fourier series. We give the exact expressions for the deflection angle and magnification factor. The formulae for the deflection angle and magnification factor given in this paper will be useful for numerical studies of observed lens systems. An application of our results to the Einstein Cross can be found in Chae, Turnshek, & Khersonsky (1998). Our series approach can be viewed as a user-friendly and efficient method to calculate lensing properties that is better than the more conventional approaches, e.g., numerical integrations, multipole expansions.Comment: 24 pages, 3 Postscript figures, ApJ in press (October 10th

A study of radiometric surface temperatures: Their fluctuations, distribution and meaning

A consecutive night and day flight and measurements on the ground, were made in the region of Voves, south of Chartres. The statistical analysis of the thermal scanner data permitted the establishment of criteria for the homogeneity of surfaces. These criteria were used in defining the surface temperature values which are most representative for use in an energy balance approach to evapotranspiration (day) and heat balance (night). For a number of maize fields that airborne thermal scanner data permitted a detailed energy analysis of different fields of a same crop to be carried out. Such a detailed analysis was not necessary for a calculation of crop evapotranspiration which could be evaluated from the mean temperature of the crop surface. A differential analysis day night is of interest for enhancing the contrast between types of surfaces, as well as for a better definition of the daily energy balance. It should be stressed that, for a homogeneous region, a study such as the present one, could be carried out on a relatively small part of the total surface, as the results for a surface of 2.5 x 2 sq km were not significantly different from those obtained from a surface three times larger

Imaging stress and magnetism at high pressures using a nanoscale quantum sensor

Pressure alters the physical, chemical and electronic properties of matter. The development of the diamond anvil cell (DAC) enables tabletop experiments to investigate a diverse landscape of high-pressure phenomena ranging from the properties of planetary interiors to transitions between quantum mechanical phases. In this work, we introduce and utilize a novel nanoscale sensing platform, which integrates nitrogen-vacancy (NV) color centers directly into the culet (tip) of diamond anvils. We demonstrate the versatility of this platform by performing diffraction-limited imaging (~600 nm) of both stress fields and magnetism, up to pressures ~30 GPa and for temperatures ranging from 25-340 K. For the former, we quantify all six (normal and shear) stress components with accuracy $<0.01$ GPa, offering unique new capabilities for characterizing the strength and effective viscosity of solids and fluids under pressure. For the latter, we demonstrate vector magnetic field imaging with dipole accuracy $<10^{-11}$ emu, enabling us to measure the pressure-driven $\alpha\leftrightarrow\epsilon$ phase transition in iron as well as the complex pressure-temperature phase diagram of gadolinium. In addition to DC vector magnetometry, we highlight a complementary NV-sensing modality using T1 noise spectroscopy; crucially, this demonstrates our ability to characterize phase transitions even in the absence of static magnetic signatures. By integrating an atomic-scale sensor directly into DACs, our platform enables the in situ imaging of elastic, electric and magnetic phenomena at high pressures.Comment: 18 + 50 pages, 4 + 19 figure

Energy Gap Induced by Impurity Scattering: New Phase Transition in Anisotropic Superconductors

It is shown that layered superconductors are subjected to a phase transition at zero temperature provided the order parameter (OP) reverses its sign on the Fermi-surface but its angular average is finite. The transition is regulated by an elastic impurity scattering rate $1/\tau$. The excitation energy spectrum, being gapless at the low level of scattering, develops a gap as soon as the scattering rate exceeds some critical value of $1/\tau_\star$.Comment: Revtex, 11 page

Modeling Genomes to Phenomes to Populations in a Changing Climate: The Need for Collaborative Networks

Condensed Abstract Climate is changing globally and its impacts can arise at different levels of biological organization; yet, cross-level consequences of climate change are still poorly understood. Designing effective environmental management and adaptation plans requires implementation of mechanistic models that span the biological hierarchy. Because biological systems are inherently complex and dynamic in nature, dealing with complexities efficiently necessitates simplification of systems or approximation of relevant processes, but there is little consensus on mathematical approaches to scale from genes to populations. Here we present an effort that aims to bring together groups that often do not interact, but that are essential to illuminating the complexities of life: empirical scientists and mathematical modelers, spanning levels of biological organization from genomes to organisms to populations. Through interplay between theory, models, and data, we aim to facilitate the generation of a new synthesis and a conceptual framework for biology across levels

Ground State Properties of Anderson Impurity in a Gapless Host

Using the Bethe ansatz method, we study the ground state properties of a $U\to\infty$ Anderson impurity in a ``gapless'' host, where a density of band states vanishes at the Fermi level $\epsilon_F$ as $|\epsilon-\epsilon_F|$. As in metals, the impurity spin is proven to be screened at arbitrary parameters of the system. However, the impurity occupancy as a function of the bare impurity energy is shown to acquire novel qualitative features which demonstrate a nonuniversal behavior of the system. The latter explains why the Kondo screening is absent (or exists only at quite a large electron-impurity coupling) in earlier studies based on scaling arguments.Comment: 5 pages, no figure, RevTe

The low-frequency response in the surface superconducting state of ZrB12_{12} single crystal}

The large nonlinear response of a single crystal ZrB$_{12}$ to an ac field (frequency 40 - 2500 Hz) for $H_0>H_{c2}$ has been observed. Direct measurements of the ac wave form and the exact numerical solution of the Ginzburg-Landau equations, as well as phenomenological relaxation equation, permit the study of the surface superconducting states dynamics. It is shown, that the low frequency response is defined by transitions between the metastable superconducting states under the action of an ac field. The relaxation rate which determines such transitions dynamics, is found.Comment: 7 pages, 11 figure