Fan-extensions in fragile matroids

If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on understanding classes of fragile matroids. In certain cases, when F is a minor-closed class of S-fragile matroids, and N is in F, the only members of F that contain N as a minor are obtained from N by increasing the length of fans. We prove that if this is the case, then we can certify it with a finite case-analysis. The analysis involves examining matroids that are at most two elements larger than N.Comment: Small revisions and correction

Breakdown of the lattice polaron picture in La0.7Ca0.3MnO3 single crystals

When heated through the magnetic transition at Tc, La0.7Ca0.3MnO3 changes from a band metal to a polaronic insulator. The Hall constant R_H, through its activated behavior and sign anomaly, provides key evidence for polaronic behavior. We use R_H and the Hall mobility to demonstrate the breakdown of the polaron phase. Above 1.4Tc, the polaron picture holds in detail, while below, the activation energies of both R_H and the mobility deviate strongly from their polaronic values. These changes reflect the presence of metallic, ferromagnetic fluctuations, in the volume of which the Hall effect develops additional contributions tied to quantal phases.Comment: 11 pages, 3 figures, final version to appear in Phys. Rev. B Rapi

An order (n) algorithm for the dynamics simulation of robotic systems

The formulation of an Order (n) algorithm for DISCOS (Dynamics Interaction Simulation of Controls and Structures), which is an industry-standard software package for simulation and analysis of flexible multibody systems is presented. For systems involving many bodies, the new Order (n) version of DISCOS is much faster than the current version. Results of the experimental validation of the dynamics software are also presented. The experiment is carried out on a seven-joint robot arm at NASA's Goddard Space Flight Center. The algorithm used in the current version of DISCOS requires the inverse of a matrix whose dimension is equal to the number of constraints in the system. Generally, the number of constraints in a system is roughly proportional to the number of bodies in the system, and matrix inversion requires O(p exp 3) operations, where p is the dimension of the matrix. The current version of DISCOS is therefore considered an Order (n exp 3) algorithm. In contrast, the Order (n) algorithm requires inversion of matrices which are small, and the number of matrices to be inverted increases only linearly with the number of bodies. The newly-developed Order (n) DISCOS is currently capable of handling chain and tree topologies as well as multiple closed loops. Continuing development will extend the capability of the software to deal with typical robotics applications such as put-and-place, multi-arm hand-off and surface sliding

Control and structural optimization for maneuvering large spacecraft

Presented here are the results of an advanced control design as well as a discussion of the requirements for automating both the structures and control design efforts for maneuvering a large spacecraft. The advanced control application addresses a general three dimensional slewing problem, and is applied to a large geostationary platform. The platform consists of two flexible antennas attached to the ends of a flexible truss. The control strategy involves an open-loop rigid body control profile which is derived from a nonlinear optimal control problem and provides the main control effort. A perturbation feedback control reduces the response due to the flexibility of the structure. Results are shown which demonstrate the usefulness of the approach. Software issues are considered for developing an integrated structures and control design environment

Berry's phase contribution to the anomalous Hall effect of gadolinium

When conduction electrons are forced to follow the local spin texture, the resulting Berry phase can induce an anomalous Hall effect (AHE). In gadolinium, as in double-exchange magnets, the exchange interaction is mediated by the conduction electrons and the AHE may therefore resemble that of chromium dioxide and other metallic double-exchange ferromagnets. The Hall resistivity, magnetoresistance, and magnetization of single crystal gadolinium were measured in fields up to 30 T. Measurements between 2 K and 400 K are consistent with previously reported data. A scaling analysis for the Hall resistivity as a function of the magnetization suggests the presence of a Berry's-phase contribution to the anomalous Hall effect.Comment: 6 pages, 7 figures, submitted to Phys. Rev.

Reentrant spin glass behavior in a layered manganite La1.2Sr1.8Mn2O7 single crystals

We report here a detailed study of AC/DC magnetization and longitudinal/transverse transport properties of La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ single crystals below $T_{c}$ = 121 K. We find that the resistivity upturn below 40 K is related to the reentrant spin glass phase at the same temperature, accompanied by additional anomalous Hall effects. The carrier concentration from the ordinary Hall effects remains constant during the transition and is close to the nominal doping level (0.4 holes/Mn). The spin glass behavior comes from the competition between ferromagnetic double exchange and antiferromagnetic superexchange interactions, which leads to phase separation, i.e. a mixture of ferromagnetic and antiferromagnetic clusters, representing the canted antiferromagnetic state.Comment: 5 pages, 5 figures, submitted to Phys. Rev.