10,716 research outputs found
A new multidimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics
We present the new code ALCAR developed to model multidimensional, multi
energy-group neutrino transport in the context of supernovae and neutron-star
mergers. The algorithm solves the evolution equations of the 0th- and 1st-order
angular moments of the specific intensity, supplemented by an algebraic
relation for the 2nd-moment tensor to close the system. The scheme takes into
account frame-dependent effects of order O(v/c) as well as the most important
types of neutrino interactions. The transport scheme is significantly more
efficient than a multidimensional solver of the Boltzmann equation, while it is
more accurate and consistent than the flux-limited diffusion method. The
finite-volume discretization of the essentially hyperbolic system of moment
equations employs methods well-known from hydrodynamics. For the time
integration of the potentially stiff moment equations we employ a scheme in
which only the local source terms are treated implicitly, while the advection
terms are kept explicit, thereby allowing for an efficient computational
parallelization of the algorithm. We investigate various problem setups in one
and two dimensions to verify the implementation and to test the quality of the
algebraic closure scheme. In our most detailed test, we compare a fully
dynamic, one-dimensional core-collapse simulation with two published
calculations performed with well-known Boltzmann-type neutrino-hydrodynamics
codes and we find very satisfactory agreement.Comment: 30 pages, 12 figures. Revised version: several additional comments
and explanations, results remain unchanged. Accepted for publication in MNRA
Maximum information photoelectron metrology
Photoelectron interferograms, manifested in photoelectron angular
distributions (PADs), are a high-information, coherent observable. In order to
obtain the maximum information from angle-resolved photoionization experiments
it is desirable to record the full, 3D, photoelectron momentum distribution.
Here we apply tomographic reconstruction techniques to obtain such 3D
distributions from multiphoton ionization of potassium atoms, and fully analyse
the energy and angular content of the 3D data. The PADs obtained as a function
of energy indicate good agreement with previous 2D data and detailed analysis
[Hockett et. al., Phys. Rev. Lett. 112, 223001 (2014)] over the main spectral
features, but also indicate unexpected symmetry-breaking in certain regions of
momentum space, thus revealing additional continuum interferences which cannot
otherwise be observed. These observations reflect the presence of additional
ionization pathways and, most generally, illustrate the power of maximum
information measurements of this coherent observable
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests
We present a new numerical implementation of the general-relativistic
resistive magnetohydrodynamics (MHD) equations within the Whisky code. The
numerical method adopted exploits the properties of implicit-explicit
Runge-Kutta numerical schemes to treat the stiff terms that appear in the
equations for large electrical conductivities. Using tests in one, two, and
three dimensions, we show that our implementation is robust and recovers the
ideal-MHD limit in regimes of very high conductivity. Moreover, the results
illustrate that the code is capable of describing scenarios in a very wide
range of conductivities. In addition to tests in flat spacetime, we report
simulations of magnetized nonrotating relativistic stars, both in the Cowling
approximation and in dynamical spacetimes. Finally, because of its
astrophysical relevance and because it provides a severe testbed for
general-relativistic codes with dynamical electromagnetic fields, we study the
collapse of a nonrotating star to a black hole. We show that also in this case
our results on the quasinormal mode frequencies of the excited electromagnetic
fields in the Schwarzschild background agree with the perturbative studies
within 0.7% and 5.6% for the real and the imaginary part of the l=1 mode
eigenfrequency, respectively. Finally we provide an estimate of the
electromagnetic efficiency of this process.Comment: 22 pages, 19 figure
A discrete geometric approach for simulating the dynamics of thin viscous threads
We present a numerical model for the dynamics of thin viscous threads based
on a discrete, Lagrangian formulation of the smooth equations. The model makes
use of a condensed set of coordinates, called the centerline/spin
representation: the kinematical constraints linking the centerline's tangent to
the orientation of the material frame is used to eliminate two out of three
degrees of freedom associated with rotations. Based on a description of twist
inspired from discrete differential geometry and from variational principles,
we build a full-fledged discrete viscous thread model, which includes in
particular a discrete representation of the internal viscous stress.
Consistency of the discrete model with the classical, smooth equations is
established formally in the limit of a vanishing discretization length. The
discrete models lends itself naturally to numerical implementation. Our
numerical method is validated against reference solutions for steady coiling.
The method makes it possible to simulate the unsteady behavior of thin viscous
jets in a robust and efficient way, including the combined effects of inertia,
stretching, bending, twisting, large rotations and surface tension
Shape-from-shading using the heat equation
This paper offers two new directions to shape-from-shading, namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low-dimensional embedding. Turning our attention to the first of these contributions, we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that Lambert's law is satisfied. We perform our analysis on a plane perpendicular to the light source direction, where the z component of the surface normal is equal to the normalized image brightness. The x - y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation. We solve the heat equation for the scalar potential and, hence, recover the azimuthal component of the surface normal from the average image brightness, making use of a simple finite difference method. The second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals. We experiment with the resulting method on a variety of real-world image data, where it produces qualitatively good reconstructed surfaces
Probing the dynamical state of galaxy clusters
We show how hydrostatic equilibrium in galaxy clusters can be quantitatively
probed combining X-ray, SZ, and gravitational-lensing data. Our previously
published method for recovering three-dimensional cluster gas distributions
avoids the assumption of hydrostatic equilibrium. Independent reconstructions
of cumulative total-mass profiles can then be obtained from the gas
distribution, assuming hydrostatic equilibrium, and from gravitational lensing,
neglecting it. Hydrostatic equilibrium can then be quantified comparing the
two. We describe this procedure in detail and show that it performs well on
progressively realistic synthetic data. An application to a cluster merger
demonstrates how hydrostatic equilibrium is violated and restored as the merger
proceeds.Comment: 10 pages, 6 figures, submitted to A&
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