A beginner's introduction to Fukaya categories

The goal of these notes is to give a short introduction to Fukaya categories and some of their applications. The first half of the text is devoted to a brief review of Lagrangian Floer (co)homology and product structures. Then we introduce the Fukaya category (informally and without a lot of the necessary technical detail), and briefly discuss algebraic concepts such as exact triangles and generators. Finally, we mention wrapped Fukaya categories and outline a few applications to symplectic topology, mirror symmetry and low-dimensional topology. This text is based on a series of lectures given at a Summer School on Contact and Symplectic Topology at Universit\'e de Nantes in June 2011.Comment: 42 pages, 13 figure

A custom designed density estimation method for light transport

We present a new Monte Carlo method for solving the global illumination problem in environments with general geometry descriptions and light emission and scattering properties. Current Monte Carlo global illumination algorithms are based on generic density estimation techniques that do not take into account any knowledge about the nature of the data points --- light and potential particle hit points --- from which a global illumination solution is to be reconstructed. We propose a novel estimator, especially designed for solving linear integral equations such as the rendering equation. The resulting single-pass global illumination algorithm promises to combine the flexibility and robustness of bi-directional path tracing with the efficiency of algorithms such as photon mapping

BaFe_{1.8}Co_{0.2}As_2 thin film hybrid Josephson junctions

Josephson junctions with iron pnictides open the way for fundamental experiments on superconductivity in these materials and their application in superconducting devices. Here, we present hybrid Josephson junctions with a BaFe_{1.8}Co_{0.2}As_2 thin film electrode, an Au barrier and a PbIn counter electrode. The junctions show RSJ-like current-voltage characteristics up to the critical temperature of the counter electrode of about 7.2K. The temperature dependence of the critical current, IC, does not show an Ambegaokar-Baratoff behavior. Well-pronounced Shapiro steps are observed at microwave frequencies of 10-18GHz. Assuming an excess current, I_ex, of 200 {\mu}A at 4.2K we get an effective I_C R_N product of 6 {\mu}V.Comment: submitted to Appl. Phys. Let

The Evolution of Distorted Rotating Black Holes II: Dynamics and Analysis

We have developed a numerical code to study the evolution of distorted, rotating black holes. This code is used to evolve a new family of black hole initial data sets corresponding to distorted ``Kerr'' holes with a wide range of rotation parameters, and distorted Schwarzschild black holes with odd-parity radiation. Rotating black holes with rotation parameters as high as $a/m=0.87$ are evolved and analyzed in this paper. The evolutions are generally carried out to about $t=100M$, where $M$ is the ADM mass. We have extracted both the even- and odd-parity gravitational waveforms, and find the quasinormal modes of the holes to be excited in all cases. We also track the apparent horizons of the black holes, and find them to be a useful tool for interpreting the numerical results. We are able to compute the masses of the black holes from the measurements of their apparent horizons, as well as the total energy radiated and find their sum to be in excellent agreement with the ADM mass.Comment: 26 pages, LaTeX with RevTeX 3.0 macros. 27 uuencoded gz-compressed postscript figures. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/ Submitted to Physical Review

Influence of the spreading resistance on the conductance spectrum of planar hybrid thin film SNS' junctions based on iron pnictides

To investigate the superconducting properties of iron pnictides we prepared planar hybrid SNS' junctions in thin film technology with a pnictide base electrode, a gold barrier layer and a lead counter electrode. Our design allows characterization of the electrodes and the junction independently in a 4-probe method. We show how both electrodes influence the measured spectra due to their spreading resistance. While the Pb electrode has a constant resistance above its $T_c$, the contribution of the pnictide electrode is clearly current-dependent and thus it needs a more advanced method to be corrected. We present an empirical method, which is simple to apply and allows to deal with the spreading resistance in our junctions to recalculate the actual conductance and voltage of one junction at given temperature

Sub 20 nm Short Channel Carbon Nanotube Transistors

Carbon nanotube field-effect transistors with sub 20 nm long channels and on/off current ratios of > 1000000 are demonstrated. Individual single-walled carbon nanotubes with diameters ranging from 0.7 nm to 1.1 nm grown from structured catalytic islands using chemical vapor deposition at 700 degree Celsius form the channels. Electron beam lithography and a combination of HSQ, calix[6]arene and PMMA e-beam resists were used to structure the short channels and source and drain regions. The nanotube transistors display on-currents in excess of 15 microA for drain-source biases of only 0.4 Volt.Comment: Nano Letters in pres

Influence of Josephson current second harmonic on stability of magnetic flux in long junctions

We study the long Josephson junction (LJJ) model which takes into account the second harmonic of the Fourier expansion of Josephson current. The dependence of the static magnetic flux distributions on parameters of the model are investigated numerically. Stability of the static solutions is checked by the sign of the smallest eigenvalue of the associated Sturm-Liouville problem. New solutions which do not exist in the traditional model, have been found. Investigation of the influence of second harmonic on the stability of magnetic flux distributions for main solutions is performed.Comment: 4 pages, 6 figures, to be published in Proc. of Dubna-Nano2010, July 5-10, 2010, Russi