A renormalization approach for the 2D Anderson model at the band edge: Scaling of the localization volume

We study the localization volumes $V$ (participation ratio) of electronic wave functions in the 2d-Anderson model with diagonal disorder. Using a renormalization procedure, we show that at the band edges, i.e. for energies $E\approx \pm 4$, $V$ is inversely proportional to the variance \var of the site potentials. Using scaling arguments, we show that in the neighborhood of $E=\pm 4$, $V$ scales as V=\var^{-1}g((4-\ve E\ve)/\var) with the scaling function $g(x)$. Numerical simulations confirm this scaling ansatz

Pushbroom Stereo for High-Speed Navigation in Cluttered Environments

We present a novel stereo vision algorithm that is capable of obstacle detection on a mobile-CPU processor at 120 frames per second. Our system performs a subset of standard block-matching stereo processing, searching only for obstacles at a single depth. By using an onboard IMU and state-estimator, we can recover the position of obstacles at all other depths, building and updating a full depth-map at framerate. Here, we describe both the algorithm and our implementation on a high-speed, small UAV, flying at over 20 MPH (9 m/s) close to obstacles. The system requires no external sensing or computation and is, to the best of our knowledge, the first high-framerate stereo detection system running onboard a small UAV

Pore opening effects and transport diffusion in the Knudsen regime in comparison to self- (or tracer-) diffusion

We study molecular diffusion in linear nanopores with different types of roughness in the so-called Knudsen regime. Knudsen diffusion represents the limiting case of molecular diffusion in pores, where mutual encounters of the molecules within the free pore space may be neglected and the time of flight between subsequent collisions with the pore walls significantly exceeds the interaction time between the pore wall and the molecules. We present an extension of a commonly used procedure to calculate transport diffusion coefficients. Our results show that using this extension, the coefficients of self- and transport diffusion in the Knudsen regime are equal for all regarded systems, which improves previous literature data.Comment: 5 pages, 7 figure

Periodic orbit theory and spectral rigidity in pseudointegrable systems

We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers $g$ that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity $\Delta_3(L)$ using semiclassical quantum mechanics with $L$ reaching up to quite large values. We find that the diagonal approximation is applicable when averaging over a suitable energy interval. Comparing systems of various shapes we find that our results agree well with $\Delta_3$ calculated directly from the eigenvalues by spectral statistics. Therefore, additional terms as e.g. diffraction terms seem to be small in the case of the systems investigated in this work. By reducing the size of the corners, the spectral statistics of our pseudointegrable systems approaches the one of an integrable system, whereas very large differences between integrable and pseudointegrable systems occur, when the salient corners are large. Both types of behavior can be well understood by the properties of the periodic orbits in the system

Electron muon identification by atmospheric shower and electron beam in a new concept of an EAS detector

We present results demonstrating the time resolution and $\mu$/e separation capabilities with a new concept of an EAS detector capable for measurements of cosmic rays arriving with large zenith angles. This kind of detector has been designed to be a part of a large area (several square kilometers) surface array designed to measure Ultra High Energy (10-200 PeV) $\tau$ neutrinos using the Earth-skimming technique. A criteria to identify electron-gammas is also shown and the particle identification capability is tested by measurements in coincidence with the KASKADE-GRANDE experiment in Karlsruhe, Germany.Comment: accepted by Astrophysical Journal on January 12 2015, 16 pages 3 Figure