4,661 research outputs found
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
Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates
AbstractWe develop the symmetric interior penalty discontinuous Galerkin (DG) method for the time-dependent Maxwell equations in second-order form. We derive optimal a priori error estimates in the energy norm for smooth solutions. We also consider the case of low-regularity solutions that have singularities in space
- …