Acoustic characterization of Hofstadter butterfly with resonant scatterers

We are interested in the experimental characterization of the Hofstadter butterfly by means of acoustical waves. The transmission of an acoustic pulse through an array of 60 variable and resonant scatterers periodically distribued along a waveguide is studied. An arbitrary scattering arrangement is realized by using the variable length of each resonator cavity. For a periodic modulation, the structures of forbidden bands of the transmission reproduce the Hofstadter butterfly. We compare experimental, analytical, and computational realizations of the Hofstadter butterfly and we show the influence of the resonances of the scatterers on the structure of the butterfly

Optimisation of on-line principal component analysis

Different techniques, used to optimise on-line principal component analysis, are investigated by methods of statistical mechanics. These include local and global optimisation of node-dependent learning-rates which are shown to be very efficient in speeding up the learning process. They are investigated further for gaining insight into the learning rates' time-dependence, which is then employed for devising simple practical methods to improve training performance. Simulations demonstrate the benefit gained from using the new methods.Comment: 10 pages, 5 figure

Sheared bioconvection in a horizontal tube

The recent interest in using microorganisms for biofuels is motivation enough to study bioconvection and cell dispersion in tubes subject to imposed flow. To optimize light and nutrient uptake, many microorganisms swim in directions biased by environmental cues (e.g. phototaxis in algae and chemotaxis in bacteria). Such taxes inevitably lead to accumulations of cells, which, as many microorganisms have a density different to the fluid, can induce hydrodynamic instabilites. The large-scale fluid flow and spectacular patterns that arise are termed bioconvection. However, the extent to which bioconvection is affected or suppressed by an imposed fluid flow, and how bioconvection influences the mean flow profile and cell transport are open questions. This experimental study is the first to address these issues by quantifying the patterns due to suspensions of the gravitactic and gyrotactic green biflagellate alga Chlamydomonas in horizontal tubes subject to an imposed flow. With no flow, the dependence of the dominant pattern wavelength at pattern onset on cell concentration is established for three different tube diameters. For small imposed flows, the vertical plumes of cells are observed merely to bow in the direction of flow. For sufficiently high flow rates, the plumes progressively fragment into piecewise linear diagonal plumes, unexpectedly inclined at constant angles and translating at fixed speeds. The pattern wavelength generally grows with flow rate, with transitions at critical rates that depend on concentration. Even at high imposed flow rates, bioconvection is not wholly suppressed and perturbs the flow field.Comment: 19 pages, 9 figures, published version available at http://iopscience.iop.org/1478-3975/7/4/04600

Ultra-stable implanted 83Rb/83mKr electron sources for the energy scale monitoring in the KATRIN experiment

The KATRIN experiment aims at the direct model-independent determination of the average electron neutrino mass via the measurement of the endpoint region of the tritium beta decay spectrum. The electron spectrometer of the MAC-E filter type is used, requiring very high stability of the electric filtering potential. This work proves the feasibility of implanted 83Rb/83mKr calibration electron sources which will be utilised in the additional monitor spectrometer sharing the high voltage with the main spectrometer of KATRIN. The source employs conversion electrons of 83mKr which is continuously generated by 83Rb. The K-32 conversion line (kinetic energy of 17.8 keV, natural line width of 2.7 eV) is shown to fulfill the KATRIN requirement of the relative energy stability of +/-1.6 ppm/month. The sources will serve as a standard tool for continuous monitoring of KATRIN's energy scale stability with sub-ppm precision. They may also be used in other applications where the precise conversion lines can be separated from the low energy spectrum caused by the electron inelastic scattering in the substrate.Comment: 30 pages, 10 figures, 1 table, minor revision of the preprint, accepted by JINST on 5.2.201

A pulsed, mono-energetic and angular-selective UV photo-electron source for the commissioning of the KATRIN experiment

The KATRIN experiment aims to determine the neutrino mass scale with a sensitivity of 200 meV/c^2 (90% C.L.) by a precision measurement of the shape of the tritium $\beta$-spectrum in the endpoint region. The energy analysis of the decay electrons is achieved by a MAC-E filter spectrometer. To determine the transmission properties of the KATRIN main spectrometer, a mono-energetic and angular-selective electron source has been developed. In preparation for the second commissioning phase of the main spectrometer, a measurement phase was carried out at the KATRIN monitor spectrometer where the device was operated in a MAC-E filter setup for testing. The results of these measurements are compared with simulations using the particle-tracking software "Kassiopeia", which was developed in the KATRIN collaboration over recent years.Comment: 19 pages, 16 figures, submitted to European Physical Journal

Monitoring of tritium purity during long-term circulation in the KATRIN test experiment LOOPINO using laser Raman spectroscopy

The gas circulation loop LOOPINO has been set up and commissioned at Tritium Laboratory Karlsruhe (TLK) to perform Raman measurements of circulating tritium mixtures under conditions similar to the inner loop system of the neutrino-mass experiment KATRIN, which is currently under construction. A custom-made interface is used to connect the tritium containing measurement cell, located inside a glove box, with the Raman setup standing on the outside. A tritium sample (purity > 95%, 20 kPa total pressure) was circulated in LOOPINO for more than three weeks with a total throughput of 770 g of tritium. Compositional changes in the sample and the formation of tritiated and deuterated methanes CT_(4-n)X_n (X=H,D; n=0,1) were observed. Both effects are caused by hydrogen isotope exchange reactions and gas-wall interactions, due to tritium {\beta} decay. A precision of 0.1% was achieved for the monitoring of the T_2 Q_1-branch, which fulfills the requirements for the KATRIN experiment and demonstrates the feasibility of high-precision Raman measurements with tritium inside a glove box

Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?

We find that a 2D periodic potential with different modulation amplitudes in x- and y-direction and a perpendicular magnetic field may lead to a transition to electron transport along the direction of stronger modulation and to localization in the direction of weaker modulation. In the experimentally accessible regime we relate this new quantum transport phenomenon to avoided band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea

Magnetization in short-period mesoscopic electron systems

We calculate the magnetization of the two-dimensional electron gas in a short-period lateral superlattice, with the Coulomb interaction included in Hartree and Hartree-Fock approximations. We compare the results for a finite, mesoscopic system modulated by a periodic potential, with the results for the infinite periodic system. In addition to the expected strong exchange effects, the size of the system, the type and the strength of the lateral modulation leave their fingerprints on the magnetization.Comment: RevTeX4, 10 pages with 14 included postscript figures To be published in PRB. Replaced to repair figure

Duality Relation among Periodic Potential Problems in the Lowest Landau Level

Using a momentum representation of a magnetic von Neumann lattice, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic short-range potential problems in the lowest Landau level.We find that the energy spectra satisfy a duality relation between a period of the potential and a magnetic length. The energy spectra consist of the Hofstadter-type bands and flat bands. We also study the connection between a periodic short-range potential problem and a tight-binding model.Comment: 6 pages, 3 figures, final version to appear in PR

Hall conductance of Bloch electrons in a magnetic field

We study the energy spectrum and the quantized Hall conductance of electrons in a two-dimensional periodic potential with perpendicular magnetic field WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak Landau band coupling significant changes in the Hall conductance compared to the one-band approximation of Hofstadter's butterfly are found. The principal deviations are the rearrangement of subbands and unexpected subband contributions to the Hall conductance.Comment: to appear in PRB; Revtex, 9 pages, 5 postscript figures; figures with better resolution may be obtained from http://www.chaos.gwdg.d