Efficient PML for the wave equation

In the last decade, the perfectly matched layer (PML) approach has proved a flexible and accurate method for the simulation of waves in unbounded media. Most PML formulations, however, usually require wave equations stated in their standard second-order form to be reformulated as first-order systems, thereby introducing many additional unknowns. To circumvent this cumbersome and somewhat expensive step, we instead propose a simple PML formulation directly for the wave equation in its second-order form. Inside the absorbing layer, our formulation requires only two auxiliary variables in two space dimensions and four auxiliary variables in three space dimensions; hence it is cheap to implement. Since our formulation requires no higher derivatives, it is also easily coupled with standard finite difference or finite element methods. Strong stability is proved while numerical examples in two and three space dimensions illustrate the accuracy and long time stability of our PML formulation.Comment: 16 pages, 6 figure

Convergence analysis of energy conserving explicit local time-stepping methods for the wave equation

Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any explicit time-marching method. In [18] a leap-frog (LF) based explicit local time-stepping (LTS) method was proposed, which overcomes the severe bottleneck due to a few small elements by taking small time-steps in the locally refined region and larger steps elsewhere. Here a rigorous convergence proof is presented for the fully-discrete LTS-LF method when combined with a standard conforming finite element method (FEM) in space. Numerical results further illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of corner singularities

Outer planets probe testing

An atmospheric entry Probe is being developed by NASA Ames Research Center (ARC) to conduct in situ scientific investigations of the outer planets' atmospheres. A full scale engineering model of an MDAC-E Probe configuration, was fabricated by NASA ARC. Proof-of-concept test validation of the structural and thermal design is being obtained at NASA ARC. The model was successfully tested for shock and dynamic loading and is currently in thermal vacuum testing

Discrete nonlinear Schrödinger equations for periodic optical systems : pattern formation in \chi(3) coupled waveguide arrays

Discrete nonlinear Schrödinger equations have been used for many years to model the propagation of light in optical architectures whose refractive index profile is modulated periodically in the transverse direction. Typically, one considers a modal decomposition of the electric field where the complex amplitudes satisfy a coupled system that accommodates nearest neighbour linear interactions and a local intensity dependent term whose origin lies in the χ (3) contribution to the medium's dielectric response. In this presentation, two classic continuum configurations are discretized in ways that have received little attention in the literature: the ring cavity and counterpropagating waves. Both of these systems are defined by distinct types of boundary condition. Moreover, they are susceptible to spatial instabilities that are ultimately responsible for generating spontaneous patterns from arbitrarily small background disturbances. Good agreement between analytical predictions and simulations will be demonstrated

Would You Choose to be Happy? Tradeoffs Between Happiness and the Other Dimensions of Life in a Large Population Survey

A large literature documents the correlates and causes of subjective well-being, or happiness. But few studies have investigated whether people choose happiness. Is happiness all that people want from life, or are they willing to sacrifice it for other attributes, such as income and health? Tackling this question has largely been the preserve of philosophers. In this article, we find out just how much happiness matters to ordinary citizens. Our sample consists of nearly 13,000 members of the UK and US general populations. We ask them to choose between, and make judgments over, lives that are high (or low) in different types of happiness and low (or high) in income, physical health, family, career success, or education. We find that people by and large choose the life that is highest in happiness but health is by far the most important other concern, with considerable numbers of people choosing to be healthy rather than happy. We discuss some possible reasons for this preference

Modeling laser wakefield accelerators in a Lorentz boosted frame

Modeling of laser-plasma wakefield accelerators in an optimal frame of reference \cite{VayPRL07} is shown to produce orders of magnitude speed-up of calculations from first principles. Obtaining these speedups requires mitigation of a high-frequency instability that otherwise limits effectiveness in addition to solutions for handling data input and output in a relativistically boosted frame of reference. The observed high-frequency instability is mitigated using methods including an electromagnetic solver with tunable coefficients, its extension to accomodate Perfectly Matched Layers and Friedman's damping algorithms, as well as an efficient large bandwidth digital filter. It is shown that choosing the frame of the wake as the frame of reference allows for higher levels of filtering and damping than is possible in other frames for the same accuracy. Detailed testing also revealed serendipitously the existence of a singular time step at which the instability level is minimized, independently of numerical dispersion, thus indicating that the observed instability may not be due primarily to Numerical Cerenkov as has been conjectured. The techniques developed for Cerenkov mitigation prove nonetheless to be very efficient at controlling the instability. Using these techniques, agreement at the percentage level is demonstrated between simulations using different frames of reference, with speedups reaching two orders of magnitude for a 0.1 GeV class stages. The method then allows direct and efficient full-scale modeling of deeply depleted laser-plasma stages of 10 GeV-1 TeV for the first time, verifying the scaling of plasma accelerators to very high energies. Over 4, 5 and 6 orders of magnitude speedup is achieved for the modeling of 10 GeV, 100 GeV and 1 TeV class stages, respectively

First Long-Term Application of Squeezed States of Light in a Gravitational-Wave Observatory

We report on the first long-term application of squeezed vacuum states of light to improve the shot-noise-limited sensitivity of a gravitational-wave observatory. In particular, squeezed vacuum was applied to the German/British detector GEO600 during a period of three months from June to August 2011, when GEO600 was performing an observational run together with the French/Italian Virgo detector. In a second period squeezing application continued for about 11 months from November 2011 to October 2012. During this time, squeezed vacuum was applied for 90.2% (205.2 days total) of the time that science-quality data was acquired with GEO600. Sensitivity increase from squeezed vacuum application was observed broad-band above 400Hz. The time average of gain in sensitivity was 26% (2.0dB), determined in the frequency band from 3.7kHz to 4.0kHz. This corresponds to a factor of two increase in observed volume of the universe, for sources in the kHz region (e.g. supernovae, magnetars). We introduce three new techniques to enable stable long-term application of squeezed light, and show that the glitch-rate of the detector did not increase from squeezing application. Squeezed vacuum states of light have arrived as a permanent application, capable of increasing the astrophysical reach of gravitational-wave detectors.Comment: 4 pages, 4 figure

Speeding up simulations of relativistic systems using an optimal boosted frame

It can be computationally advantageous to perform computer simulations in a Lorentz boosted frame for a certain class of systems. However, even if the computer model relies on a covariant set of equations, it has been pointed out that algorithmic difficulties related to discretization errors may have to be overcome in order to take full advantage of the potential speedup. We summarize the findings, the difficulties and their solutions, and show that the technique enables simulations important to several areas of accelerator physics that are otherwise problematic, including self-consistent modeling in three-dimensions of laser wakefield accelerator stages at energies of 10 GeV and above.Comment: To be published in the proceedings of DPF-2009, Detroit, MI, July 2009, eConf C09072

The upgrade of GEO600

The German / British gravitational wave detector GEO 600 is in the process of being upgraded. The upgrading process of GEO 600, called GEO-HF, will concentrate on the improvement of the sensitivity for high frequency signals and the demonstration of advanced technologies. In the years 2009 to 2011 the detector will undergo a series of upgrade steps, which are described in this paper.Comment: 9 pages, Amaldi 8 conference contributio

"Das schnelle Date" - Internetgestützte Sexualkontakte und HIV-Infektionsrisiko: Ergebnisse einer 2006 durchgeführten Internetbefragung

Der seit Ende der 1990er Jahre diskutierten Frage, ob bei Sexualkontakten, die über Kontaktseiten im Internet hergestellt werden, in geringerem Umfang präventive Vorkehrungen in Hinblick auf HIV-Übertragungen erfolgen als bei andernorts angebahnten Kontakten, sollte in einer im Frühjahr 2006 durchgeführten Online-Umfrage nachgegangen werden. Die Umfrage erfolgte über vier Dating-Portale für heterosexuelle Frauen und Männer und über vier Portale für homound bisexuelle Männer. Von den berücksichtigten 5.050 Fragebögen entfielen 76 Prozent auf Männer, die ausschließlich gleichgeschlechtliche Sexualkontakte in den 12 Monaten vor der Befragung angaben, 11 Prozent der Männer wurden aufgrund ihrer Angaben als bisexuell und weitere 11 Prozent als heterosexuell definiert. Frauen stellten lediglich 2 Prozent der BefragungsteilnehmerInnen. Etwa drei Viertel aller Befragten schätzten an Kontaktseiten, das sie darüber Menschen mit gleichen Vorlieben kennenlernen können, dabei muss es sich nicht um sexuelle Vorlieben handeln: So haben etwa 22 Prozent der Frauen, 12 Prozent der homosexuellen, 9 Prozent der heterosexuellen und 6 Prozent der bisexuellen Männer überhaupt keine(n) Sexpartner(in) in den 12 Monaten vor der Befragung gesucht. Online gesucht aber keine(n) Partner(in) gefunden haben 18 Prozent der Frauen, 21 Prozent der homosexuellen, 24 Prozent der bisexuellen und 45 Prozent der heterosexuellen Männer. Etwa die Hälfte der homo- und bisexuellen Männer haben ihre SexualpartnerInnen mehrheitlich oder ausschließlich über das Internet kennengelernt, während dies nur auf 39 Prozent der heterosexuellen Männer zutrifft (zwei Drittel geben dies in der kleinen Gruppe der Frauen an). Dass heterosexuelle Männer die geringsten Erfolge beim Anbahnen von Sexualkontakten über das Internet haben, zeigen auch andere erhobene Daten. Unter den Befragungsteilnehmern erfolgte regelmäßiger Kondomgebrauch bei Vaginal- oder Analverkehr - je nach Gruppenzugehörigkeit - zu sehr unterschiedlichen Anteilen. 55 Prozent der homosexuellen und 47 Prozent der bisexuellen Männer benutzten grundsätzlich Kondome, 38 Prozent der heterosexuellen Männer und 34 Prozent der Frauen gaben dies an. Hinsichtlich des Risikos, sich mit HIV zu infizieren (ungeschützter Anal- oder Vaginalverkehr mit PartnerInnen mit unbekanntem oder diskordantem Serostatus - Expositionsrisiko), bestanden nur geringe Unterschiede zwischen homo- (27%), bi- (31%) und heterosexuellen Männern (26%) bzw. Frauen (27%). Ein Transmissionsrisiko konnte lediglich in der Teilgruppe der homosexuellen (8%) und bisexuellen (1%) Männer festgestellt werden, da in den anderen beiden Gruppen niemand HIV-positiv war. Es zeigt sich, dass bei der überwiegenden Mehrheit aller Befragten das HIV-bezogene sexuelle Risikoverhalten bei online- und offline-Dates gleich ist.Are people more likely to risk an HIV infection with sex partners they meet online as compared to those whom they meet offline? This question has been the subject of research since the late 1990s in several post-industrialized countries. This paper presents the results of a study conducted in Germany in 2006. A link to an anonymous, self-administered online questionnaire was posted on four dating websites for heterosexual men and women and on four dating websites for men who have sex with men. Of the 5,050 respondents included in the analysis, 76 per cent were men who reported sexual contacts in the previous twelve months exclusively with other men; 11 per cent could be classified as bisexual men (sexual contacts with men and women), and 11 per cent as heterosexual men (sexual contact with women only). Two per cent of all respondents were women; because of the small number of respondents this group was not further stratified in the analysis. Finding persons with similar interests was the most frequently expressed positive aspect of dating websites (78% among homosexual men, 80% among bisexual men, 74% among heterosexual men, and 73% among women). This did not necessarily mean similar sexual interests: 22 per cent of the women, 12 per cent of the homosexual men, 6 per cent of the bisexual men, and 9 per cent of the heterosexual men claimed they had not been looking for sex partners during their visits to the sites in the previous twelve months. Many respondents reported being unsuccessful in finding a sex partner online: 18 per cent of the women, 21 per cent of the homosexual men, 24 per cent of the bisexual men, and 45 per cent of the heterosexual men. While during the previous twelve months half of the homo- and bisexual men found most (if not all) of their sex partners on the Internet, the respective proportions were 39 per cent among heterosexual men, and 67% in the small group of female respondents. Taken together, heterosexual men were the least successful in finding sex partners on the Internet. Regular use of condoms for every anal or vaginal intercourse was reported by 55 per cent of the homosexual men, 47 per cent of the bisexual men, 38 of the heterosexual men, and 34 per cent of the women. However, regarding unprotected anal or vaginal intercourse with a sex partner of unknown or discordant HIV serostatus, the proportions among the different subgroups were very similar (homosexual men: 27%; bisexual men: 31%; heterosexual men: 26%; women: 27%). The risk of transmitting a known HIV infection to sex partners was only present among homosexual (8%) and bisexual (1%) men, primarily because only respondents from these two subgroups identified as HIV-positive. For the large majority (83-86%) of men, HIV risk behaviours are the same, regardless if sex partners are met online or offline