Pseudospectra and stability radii of analytic matrix functions with application to time-delay systems

AbstractDefinitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated

Laser microscopy of tunneling magnetoresistance in manganite grain-boundary junctions

Using low-temperature scanning laser microscopy we directly image electric transport in a magnetoresistive element, a manganite thin film intersected by a grain boundary (GB). Imaging at variable temperature allows reconstruction and comparison of the local resistance vs temperature for both, the manganite film and the GB. Imaging at low temperature also shows that the GB switches between different resistive states due to the formation and growth of magnetic domains along the GB. We observe different types of domain wall growth; in most cases a domain wall nucleates at one edge of the bridge and then proceeds towards the other edge.Comment: 5 pages, 4 figures; submitted to Phys. Rev. Let

Isolas of 2-Pulse Solutions in Homoclinic Snaking Scenarios

Homoclinic snaking refers to the bifurcation structure of symmetric localised roll patterns that are often found to lie on two sinusoidal “snaking” bifurcation curves, which are connected by an infinite number of “rung” segments along which asymmetric localised rolls of various widths exist. The envelopes of all these structures have a unique maximum and we refer to them as symmetric or asymmetric 1-pulses. In this paper, the existence of stationary 1D patterns of symmetric 2-pulses that consist of two well-separated 1-pulses is established. Corroborating earlier numerical evidence, it is shown that symmetric 2-pulses exist along isolas in parameter space that are formed by parts of the snaking curves and the rungs mentioned above

Andreev bound states at a cuprate grain boundary junction: A lower bound for the upper critical field

We investigate in-plane quasiparticle tunneling across thin film grain boundary junctions (GBJs) of the electron-doped cuprate La$_{2-x}$Ce$_{x}$CuO$_4$ in magnetic fields up to $B=16$T, perpendicular to the CuO$_2$ layers. The differential conductance in the superconducting state shows a zero bias conductance peak (ZBCP) due to zero energy surface Andreev bound states. With increasing temperature $T$, the ZBCP vanishes at the critical temperature $T_c\approx29$K if B=0, and at $T=12$K for B=16 T. As the ZBCP is related to the macroscopic phase coherence of the superconducting state, we argue that the disappearance of the ZBCP at a field $B_{ZBCP}(T)$ must occur below the upper critical field $B_{c2}(T)$ of the superconductor. We find $B_{ZBCP}(0) \approx 25$T which is at least a factor of 2.5 higher than previous estimates of $B_{c2}(0)$.Comment: 4 pages, 4 figure

Design, Development and Testing of the Miniature Autonomous Extravehicular Robotic Camera (Mini AERCam) Guidance, Navigation and Control System

Engineers at NASA Johnson Space Center have designed, developed, and tested a nanosatellite-class free-flyer intended for future external inspection and remote viewing of human spaceflight activities. The technology demonstration system, known as the Miniature Autonomous Extravehicular Robotic Camera (Mini AERCam), has been integrated into the approximate form and function of a flight system. The primary focus has been to develop a system capable of providing external views of the International Space Station. The Mini AERCam system is spherical-shaped and less than eight inches in diameter. It has a full suite of guidance, navigation, and control hardware and software, and is equipped with two digital video cameras and a high resolution still image camera. The vehicle is designed for either remotely piloted operations or supervised autonomous operations. Tests have been performed in both a six degree-of-freedom closed-loop orbital simulation and on an air-bearing table. The Mini AERCam system can also be used as a test platform for evaluating algorithms and relative navigation for autonomous proximity operations and docking around the Space Shuttle Orbiter or the ISS