Magnification relations of quad lenses and applications on Einstein crosses

In this work, we mainly study the magnification relations of quad lens models for cusp, fold and cross configurations. By dividing and ray-tracing in different image regions, we numerically derive the positions and magnifications of the four images for a point source lying inside of the astroid caustic. Then, based on the magnifications, we calculate the signed cusp and fold relations for the singular isothermal elliptical lenses. The signed fold relation map has positive and negative regions, and the positive region is usually larger than the negative region as has been confirmed before. It can also explain that for many observed fold image pairs, the fluxes of the Fermat minimum images are apt to be larger than those of the saddle images. We define a new quantity cross relation which describes the magnification discrepancy between two minimum images and two saddle images. Distance ratio is also defined as the ratio of the distance of two saddle images to that of two minimum images. We calculate the cross relations and distance ratios for nine observed Einstein crosses. In theory, for most of the quad lens models, the cross relations decrease as the distance ratios increase. In observation, the cross relations of the nine samples do not agree with the quad lens models very well, nevertheless, the cross relations of the nine samples do not give obvious evidence for anomalous flux ratio as the cusp and fold types do. Then, we discuss several reasons for the disagreement, and expect good consistencies for more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA

Removal of spacecraft-surface particulate contaminants by simulated micrometeoroid impacts

A series of hypervelocity impacts has been conducted in an exploding lithium-wire accelerator to examine with a far-field holographic system the removal of particulate contaminants from external spacecraft surfaces subjected to micrometeoroid bombardment. The impacting projectiles used to simulate the micrometeoroids were glass spheres nominally 37 microns in diameter, having velocities between 4 and 17 km/sec. The particulates were glass spheres nominally 25, 50, and 75 microns in diameter which were placed on aluminum targets. For these test, particulates detached had velocities that were log-normally distributed. The significance of the log-normal behavior of the ejected-particulate velocity distribution is that the geometric mean velocity and the geometric standard deviation are the only two parameters needed to model completely the process of particles removed or ejected from a spacecraft surface by a micrometeoroid impact

Critical thickness and orbital ordering in ultrathin La0.7Sr0.3MnO3 films

Detailed analysis of transport, magnetism and x-ray absorption spectroscopy measurements on ultrathin La0.7Sr0.3MnO3 films with thicknesses from 3 to 70 unit cells resulted in the identification of a lower critical thickness for a non-metallic, non-ferromagnetic layer at the interface with the SrTiO3 (001) substrate of only 3 unit cells (~12 Angstrom). Furthermore, linear dichroism measurements demonstrate the presence of a preferred (x2-y2) in-plane orbital ordering for all layer thicknesses without any orbital reconstruction at the interface. A crucial requirement for the accurate study of these ultrathin films is a controlled growth process, offering the coexistence of layer-by-layer growth and bulk-like magnetic/transport properties.Comment: 22 pages, 6 figures, accepted for publication in Physical Review

Time Dependent Floquet Theory and Absence of an Adiabatic Limit

Quantum systems subject to time periodic fields of finite amplitude, lambda, have conventionally been handled either by low order perturbation theory, for lambda not too large, or by exact diagonalization within a finite basis of N states. An adiabatic limit, as lambda is switched on arbitrarily slowly, has been assumed. But the validity of these procedures seems questionable in view of the fact that, as N goes to infinity, the quasienergy spectrum becomes dense, and numerical calculations show an increasing number of weakly avoided crossings (related in perturbation theory to high order resonances). This paper deals with the highly non-trivial behavior of the solutions in this limit. The Floquet states, and the associated quasienergies, become highly irregular functions of the amplitude, lambda. The mathematical radii of convergence of perturbation theory in lambda approach zero. There is no adiabatic limit of the wave functions when lambda is turned on arbitrarily slowly. However, the quasienergy becomes independent of time in this limit. We introduce a modification of the adiabatic theorem. We explain why, in spite of the pervasive pathologies of the Floquet states in the limit N goes to infinity, the conventional approaches are appropriate in almost all physically interesting situations.Comment: 13 pages, Latex, plus 2 Postscript figure

Observation of ferromagnetic resonance in strontium ruthenate (SrRuO3)

We report the observation of ferromagnetic resonance (FMR) in SrRuO3 using the time-resolved magneto-optical Kerr effect. The FMR oscillations in the time-domain appear in response to a sudden, optically induced change in the direction of easy-axis anistropy. The high FMR frequency, 250 GHz, and large Gilbert damping parameter, alpha ~ 1, are consistent with strong spin-orbit coupling. We find that the parameters associated with the magnetization dynamics, including alpha, have a non-monotonic temperature dependence, suggestive of a link to the anomalous Hall effect.Comment: submitted to Phys. Rev. Let

Explicit Integration of the Full Symmetric Toda Hierarchy and the Sorting Property

We give an explicit formula for the solution to the initial value problem of the full symmetric Toda hierarchy. The formula is obtained by the orthogonalization procedure of Szeg\"{o}, and is also interpreted as a consequence of the QR factorization method of Symes \cite{symes}. The sorting property of the dynamics is also proved for the case of a generic symmetric matrix in the sense described in the text, and generalizations of tridiagonal formulae are given for the case of matrices with $2M+1$ nonzero diagonals.Comment: 13 pages, Latex

Fermions on spontaneously generated spherical extra dimensions

We include fermions to the model proposed in hep-th/0606021, and obtain a renormalizable 4-dimensional SU(N) gauge theory which spontaneously generates fuzzy extra dimensions and behaves like Yang-Mills theory on M^4 \times S^2. We find a truncated tower of fermionic Kaluza-Klein states transforming under the low-energy gauge group, which is found to be either SU(n), or SU(n_1) x SU(n_2) x U(1). The latter case implies a nontrivial U(1) flux on S^2, leading to would-be zero modes for the bifundamental fermions. In the non-chiral case they may pair up to acquire a mass, and the emerging picture is that of mirror fermions. We discuss the possible implementation of a chirality constraint in 6 dimensions, which is nontrivial at the quantum level due to the fuzzy nature of the extra dimensions.Comment: 34 pages. V2: references added, minor corrections V3: discussion added, final versio