The large core limit of spiral waves in excitable media: A numerical approach

We modify the freezing method introduced by Beyn & Thuemmler, 2004, for analyzing rigidly rotating spiral waves in excitable media. The proposed method is designed to stably determine the rotation frequency and the core radius of rotating spirals, as well as the approximate shape of spiral waves in unbounded domains. In particular, we introduce spiral wave boundary conditions based on geometric approximations of spiral wave solutions by Archimedean spirals and by involutes of circles. We further propose a simple implementation of boundary conditions for the case when the inhibitor is non-diffusive, a case which had previously caused spurious oscillations. We then utilize the method to numerically analyze the large core limit. The proposed method allows us to investigate the case close to criticality where spiral waves acquire infinite core radius and zero rotation frequency, before they begin to develop into retracting fingers. We confirm the linear scaling regime of a drift bifurcation for the rotation frequency and the core radius of spiral wave solutions close to criticality. This regime is unattainable with conventional numerical methods.Comment: 32 pages, 17 figures, as accepted by SIAM Journal on Applied Dynamical Systems on 20/03/1

An efficient new route to dihydropyranobenzimidazole inhibitors of HCV replication.

A class of dihydropyranobenzimidazole inhibitors was recently discovered that acts against the hepatitis C virus (HCV) in a new way, binding to the IRES-IIa subdomain of the highly conserved 5' untranslated region of the viral RNA and thus preventing the ribosome from initiating translation. However, the reported synthesis of these compounds is lengthy and low-yielding, the intermediates are troublesome to purify, and the route is poorly structured for the creation of libraries. We report a streamlined route to this class of inhibitors in which yields are far higher and most intermediates are crystalline. In addition, a key variable side chain is introduced late in the synthesis, allowing analogs to be easily synthesized for optimization of antiviral activity

Pattern Selection in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing

We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe or hexagon patterns are linearly stable, whereas square patterns and patterns involving more than three modes are unstable. In the case of hexagon patterns up- and down-hexagons can be simultaneously stable. The third-order, weakly nonlinear analysis predicts stable square patterns and super-hexagons for larger amplitudes. Direct simulations show, however, that in this regime the third-order weakly nonlinear analysis is insufficient, and these patterns are, in fact unstable

Noise diffraction patterns eliminated in coherent optical systems

Lens rotation technique of noise diffraction pattern elimination spreads diffracted energy, normally concentrated over small area of image, over much larger annular area. Technique advantages include simplified lens selecting process, reduced clean room requirements, and low cost equipment requirements

Spatial rogue waves in photorefractive SBN crystals

We report on the excitation of large-amplitude waves, with a probability of around 1% of total peaks, on a photorefractive SBN crystal by using a simple experimental setup at room temperature. We excite the system using a narrow Gaussian beam and observe different dynamical regimes tailored by the value and time rate of an applied voltage. We identify two main dynamical regimes: a caustic one for energy spreading and a speckling one for peak emergence. Our observations are well described by a two-dimensional Schr\"odinger model with saturable local nonlinearity.Comment: 4 pages, 4 figure

Elimination of coherent noise in a coherent light imaging system

Optical imaging systems using coherent light introduce objectionable noise into the output image plane. Dust and bubbles on and in lenses cause most of the noise in the output image. This noise usually appears as bull's-eye diffraction patterns in the image. By rotating the lens about the optical axis these diffraction patterns can be essentially eliminated. The technique does not destroy the spatial coherence of the light and permits spatial filtering of the input plane

Easy implementable algorithm for the geometric measure of entanglement

We present an easy implementable algorithm for approximating the geometric measure of entanglement from above. The algorithm can be applied to any multipartite mixed state. It involves only the solution of an eigenproblem and finding a singular value decomposition, no further numerical techniques are needed. To provide examples, the algorithm was applied to the isotropic states of 3 qubits and the 3-qubit XX model with external magnetic field.Comment: 9 pages, 3 figure

Noise in Electron Devices

Contains research objectives and reports on two research projects.Lincoln Laboratory (Purchase Order DDL-B187)Department of the ArmyDepartment of the NavyDepartment of the Air Force under Contract AF19(122)-45

Coulomb Blockade of Tunneling between Disordered Conductors

We determine the zero-bias anomaly of the conductance of tunnel junctions by an approach unifying the conventional Coulomb blockade theory for ultrasmall junctions with the diffusive anomalies in disordered conductors. Both, electron-electron interactions within the electrodes and electron-hole interactions between the electrodes are taken into account nonperturbatively. Explicit results are given for one- and two-dimensional junctions, and the crossover to ultrasmall junctions is discussed.Comment: 4 pages, 1 figure. Final version published in Phys. Rev. Let

Tunneling Density of States of the Interacting Two-Dimensional Electron Gas

We investigate the influence of electron--electron interactions on the density of states of a ballistic two--dimensional electron gas. The density of states is determined nonperturbatively by means of path integral techniques allowing for reliable results near the Fermi surface, where perturbation theory breaks down. We find that the density of states is suppressed at the Fermi level to a finite value. This suppression factor grows with decreasing electron density and is weakened by the presence of gates.Comment: 4 pages, 2 figures; slightly shortened version published in PR