6,404 research outputs found

    Projective modules over non-commutative tori: classification of modules with constant curvature connection

    Full text link
    We study finitely generated projective modules over noncommutative tori. We prove that for every module EE with constant curvature connection the corresponding element [E][E] of the K-group is a generalized quadratic exponent and, conversely, for every positive generalized quadratic exponent μ\mu in the K-group one can find such a module EE with constant curvature connection that [E]=μ[E] = \mu . In physical words we give necessary and sufficient conditions for existence of 1/2 BPS states in terms of topological numbers.Comment: Latex. Misprints correcte

    Inhomogeneity-induced variance of cosmological parameters

    Full text link
    Modern cosmology relies on the assumption of large-scale isotropy and homogeneity of the Universe. However, locally the Universe is inhomogeneous and anisotropic. So, how can local measurements (at the 100 Mpc scale) be used to determine global cosmological parameters (defined at the 10 Gpc scale)? We use Buchert's averaging formalism and determine a set of locally averaged cosmological parameters in the context of the flat Lambda cold dark matter model. We calculate their ensemble means (i.e. their global values) and variances (i.e. their cosmic variances). We apply our results to typical survey geometries and focus on the study of the effects of local fluctuations of the curvature parameter. By this means we show, that in the linear regime cosmological backreaction and averaging can be reformulated as the issue of cosmic variance. The cosmic variance is found largest for the curvature parameter and discuss some of its consequences. We further propose to use the observed variance of cosmological parameters to measure the growth factor. [abbreviated]Comment: 12 pages, 10 figures, references added, estimate of lightcone effects added, matches version published in A&

    Rich Contacts: Corpus-Based Convolution of Audio Contact Gestures for Enhanced Musical Expression

    Get PDF
    We propose ways of enriching the timbral potential of gestural sonic material captured via piezo or contact microphones, through latency-free convolution of the microphone signal with grains from a sound corpus. This creates a new way to combine the sonic richness of large sound corpora, easily accessible via navigation through a timbral descriptor space, with the intuitive gestural interaction with a surface, captured by any contact microphone. We use convolution to excite the grains from the corpus via the microphone input, capturing the contact interaction sounds, which allows articulation of the corpus by hitting, scratching, or strumming a surface with various parts of the hands or objects. We also show how changes of grains have to be carefully handled, how one can smoothly interpolate between neighbouring grains, and finally evaluate the system against previous attempts

    Few-cycle phase-stable infrared OPCPA

    Get PDF
    Few-cycle laser pulses are an important tool for investigating laser-matter interactions. Apart from the mere resolution used in time-resolved processes, owing to this approach table-top sources nowadays can reach the limits of the perturbative regime and therewith enable extreme nonlinear optics. In the visible domain, femtosecond technology over the last decades has quickly developed, in recent years leading to the routine generation of carrier-envelope phase (CEP) stable few-cycle laser pulses at high energies, using ubiquitous Ti:Sapphire amplifiers. Near to mid-infrared few-cycle pulses in contrast can be employed for investigating interactions in the tunneling regime. The ponderomotive potential of the infrared light field allows quivered charged particles to acquire large energies, leading to applications like the generation of isolated attosecond pulses in the water window. In this wavelength regime however, the required sources are yet to be demonstrated or at least matured. The best candidate for few-cycle pulses in this domain is optical parametric amplification. This work describes the development of an optical parametric chirped pulse amplifier (OPCPA), used to create CEP-stable few-cycle pulses in the near infrared (NIR). It covers all essential parts of the system. First the signal pulses are generated from ultrashort lasers using spectral broadening techniques in chapter 2. After compression of these white light continua, intra-pulse broadband difference frequency generation yields CEP stable infrared pulses spanning over more than one octave. A thin-disk-based pump laser provides ample pump energy (20 mJ) at pulse durations around 1.5 ps. Its characterization and optimization for OPCPA is performed in chapter 3. The high peak energy of this pump laser leads to the buildup of optical nonlinearities and consequently shows distinct influence on the OPCPA system performance. The synchronization of the OPCPA pump and seed laser system is the topic of chapter 4. This chapter is not limited to NIR systems, but demonstrates enhanced (actively stabilized) synchronization of the jitter between pump and seed pulses to σ = 24 fs, which later results in improved output stability. The NIR OPCPA centered at 2.1 μm is described in chapter 5. This combines the efforts of the previous chapters and describes the generation and characterization of 100 μJ sub-two-cycle CEP-stable pulses, the shortest published to date at this energy level. As a first prototype (cutting edge) experiment, CEP dependent sub-fs currents in a dielectric are generated in chapter 6 using the developed light source. The results compared well to visible few-cycle laser sources and demonstrate the usability of the OPCPA system (beyond the charac- terizations of chapter 5) for investigating sub-cycle carrier dynamics in dielectrics. For the same purpose, to generate the currently most broadband NIR continua at kHz repetition rates and mJ-level pulse energies, the OPCPA system is further boosted and efficiently broadened to three optical octaves using a hollow core fiber setup (described in chapter 7). The spectral phase is characterized and demonstrates self-compression in the NIR around 1.3 μm. The process provides CEP-stable sub-2-cycle pulses in this regime directly, the shortest and most powerful reported to date. Furthermore, the spectral broadening in the infrared shows enhanced low-order harmonic gen- eration and cross-phase-modulation as the dominant mechanism. Experimentally the limited influence on the driver bandwidth is investigated. It is found that the processes allow using more efficient many-cycle infrared sources to generate several-octave spanning, compressible continua in the future. Even partial compression of these would then provide NIR transients for high-field experiments.Die Femtosekunden-Technologie hat sich in den letzten Jahrzehnten schnell fortentwickelt, vor allem im sichtbaren Wellenl ̈angen-Bereich. Speziell moderne Titanium-Saphir Verst ̈arker haben zuletzt zu (Träger-Einhüllenden-) phasenstabilen und hochenergetischen Laserpulsen geführt, die nur noch aus einzelnen optischen Zyklen bestehen. Diese erlauben die Investigation extrem nichtlinearer optischer Prozesse im Regime der Multiphotonenionisation. Um weiter im Infraroten Prozesse im Regime der Tunnelionisation zu untersuchen, fehlt es jedoch nach wie vor an Lichtquellen mit ähnlichen Characteristiken für Anwendungen wie die Generation von isolierten Attosekunden-Pulsen im Wasser-Transmissions-Fenster. Hier bietet die optische parametrische Verstärkung bisher die größten Perspektiven. Diese Arbeit beschäftigt sich mit der Entwicklung eines optischen parametrischen Verstärkers mit gestreckten Pulsen (engl.: optical parametric chirped pulse amplifier, OPCPA), der TE- phasen-stabile Pulse mit wenigen optischen Zyklen im nahen Infraroten erzeugt. Alle wesentlichen Teile des Systems werden beschrieben. Zuerst wird der Saat-Puls durch die spektrale Verbreiterung eines Titanium-Saphir Verstärkers gewonnen. Nach der Kompression des generierten Weißlichts führt die breitbandige Differenz-Frequenz-Generation (DFG) des Pulses mit sich selbst zu TE-phasen-stabilen Infrarot-Pulsen, deren Spektrum mehr als eine optische Oktave aufspannt. Ein Scheiben-Laser liefert die Pumpenergie (20 mJ) bei einer Pulsdauer von ca. 1.5 ps. Seine Charakterisierung und Optimierung für die OPCPA erfolgt in Kapitel 3. Die hohen Spitzeninten- sit ̈aten dieses Pumplasers führen zum Akkumulieren optischer Nichtlinearit ̈aten und beeinflussen die OPCPA im Folgenden negativ. Die Synchronisation von OPCPA Pump- und Saat-Lasern ist das Thema von Kapitel 4. Es demonstriert eine aktive Stabilisierung des zeitlichen Überlapps beider Pulse, der den gesamten Prozess im Folgenden stabilisiert, und ist nicht auf den Einsatz im Infraroten beschränkt, sondern für die meisten OPCPA Systeme anwendbar. Die in Kapitel 5 beschriebene infrarote OPCPA hat ihre Zentralwellenlänge bei 2.1 μm und baut auf den vorherigen Kapiteln auf. Die Erzeugung und Charakterisierung von Pulsen mit weniger als zwei optischen Zyklen, den bisher kürzesten in diesem Wellenlängen-Bereich und einer En- ergie von 100 μJ, werden beschrieben. Ferner erweist sich die TE-Phase der verstärkten Pulse als außerordentlich kurz- und langzeitstabil. Kapitel 6 demonstriert dann die Möglichkeiten des neuen Systems mit einem technisch anspruchsvollen Experiment. TE-phasen-abhängige Ströme mit einer Lebenszeit auf der Skala von Attosekunden werden in einem Dielektrikum erzeugt und gemessen. Die Resultate stimmen gut mit den bere- its gemessenen Werten im sichtbaren Bereich u ̈ berein und demonstrieren die Möglichkeiten und Einsetzbarkeit des Systems. Für ähnliche Anwendungen, allerdings bei noch höheren Intensitäten, wird in Kapitel 7 das OPCPA-System weiter verstärkt. Die spektrale Verbreiterung in einer gas-gefüllten Hohlfaser erzeugt ein Kontinuum über drei optische Oktaven. Dessen spektrale Phase wird im Folgen- den charakterisiert und zeigt Selbstkompression bei einer Wellenlänge von 1.3 μm. Der Prozess erzeugt TE-phasen-stabile Pulse kürzer also zwei optische Zyklen, welche die kürzesten und intensivsten darstellen, die in diesem Bereich bislang erzeugt wurden. Weiterhin zeigt die spektrale Verbreiterung im Infraroten besondere Merkmale. Speziell die Gen- eration von ungeraden Harmonischen niedriger Ordnung und deren Kreuz-Phasen-Modulation zeigen sich als dominante Prozesse, welche den Einfluss der Eingangsbandbreite minimieren. Eine experimentelle Untersuchung demonstriert dann, dass auch potentiell effizientere infrarote OPCPA Systeme mit deutlich längeren Pulsen ähnliche spektrale Bandbreiten erzeugen können. Die Komprimierung dieser sollte in der nahen Zukunft zu Hochfeld-Anwendungen mit infraroten Feldtransienten und synthetisierten elektrischen Feldern mit Sub-Zyklus Merkmalen führen

    Social networks, optimal contract design, and present bias

    Get PDF

    Error estimation of closed-form solution for annual rate of structural collapse

    Get PDF
    With the increasing emphasis of performance-based earthquake engineering (PBEE) in the engineering community, several investigations have been presented outlining simplified approaches suitable for performance-based seismic design (PBSD). Central to most of these PBSD approaches is the use of closed-form analytical solutions to the probabilistic integral equations representing the rate of exceedance of key performance measures. Situations where such closed-form solutions are not appropriate primarily relate to the problem of extrapolation outside of the region in which parameters of the closed-form solution are fit. This study presents a critical review of the closed form solution for the annual rate of structural collapse. The closed form solution requires the assumptions of lognormality of the collapse fragility and power model form of the ground motion hazard, of which the latter is more significant regarding the error of the closed-form solution. Via a parametric study, the key variables contributing to the error between the closed-form solution and solution via numerical integration are illustrated. As these key variables can not be easily measured it casts doubt on the use of such closed-form solutions in future PBSD, especially considering the simple and efficient nature of using direct numerical integration to obtain the solution
    corecore