23,036 research outputs found
Online approximations for wind-field models
We study online approximations to Gaussian process models for spatially distributed systems. We apply our method to the prediction of wind fields over the ocean surface from scatterometer data. Our approach combines a sequential update of a Gaussian approximation to the posterior with a sparse representation that allows to treat problems with a large number of observations
Nucleon self-energies for supernova equations of state
Nucleon self-energies and interaction potentials in supernova (SN) matter,
which are known to have an important effect on nucleosynthesis conditions in SN
ejecta are investigated. Corresponding weak charged-current interaction rates
with unbound nucleons that are consistent with existing SN equations of state
(EOSs) are specified. The nucleon self-energies are made available online as
electronic tables. The discussion is mostly restricted to relativistic
mean-field models.
In the first part of the article, the generic properties of this class of
models at finite temperature and asymmetry are studied. It is found that the
quadratic expansion of the EOS in terms of asymmetry works reasonably well at
finite temperatures and deviations originate mostly from the kinetic part. The
interaction part of the symmetry energy is found to be almost temperature
independent. At low densities, the account of realistic nucleon masses requires
the introduction of a linear term in the expansion. Finally, it is shown that
the important neutron-to-proton potential difference is given approximately by
the asymmetry of the system and the interaction part of the zero-temperature
symmetry energy. The results of different interactions are then compared with
constraints from nuclear experiments and thereby the possible range of the
potential difference is limited.
In the second part, for a certain class of SN EOS models, the formation of
nuclei is considered. Only moderate modifications are found for the
self-energies of unbound nucleons that enter the weak charged-current
interaction rates. This is because in the present approach the binding energies
of bound states do not contribute to the single-particle energies of unbound
nucleons.Comment: 25 pages, 12 figures, v3: editorial corrections, matches published
versio
Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents
There are two main strategies for improving the projection-based reduced
order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to
the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM
bases that yield more accurate ROMs. In this paper, we use the latter. We
propose new Lagrangian inner products that we use together with Eulerian and
Lagrangian data to construct new Lagrangian ROMs. We show that the new
Lagrangian ROMs are orders of magnitude more accurate than the standard
Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to
construct the ROM basis. Specifically, for the quasi-geostrophic equations, we
show that the new Lagrangian ROMs are more accurate than the standard Eulerian
ROMs in approximating not only Lagrangian fields (e.g., the finite time
Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction).
We emphasize that the new Lagrangian ROMs do not employ any closure modeling to
model the effect of discarded modes (which is standard procedure for
low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase
in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian
inner products used to build the Lagrangian ROM basis
Stationary field-aligned MHD flows at astropauses and in astrotails. Principles of a counterflow configuration between a stellar wind and its interstellar medium wind
A stellar wind passing through the reverse shock is deflected into the
astrospheric tail and leaves the stellar system either as a sub-Alfvenic or as
a super-Alfvenic tail flow. An example is our own heliosphere and its
heliotail. We present an analytical method of calculating stationary,
incompressible, and field-aligned plasma flows in the astrotail of a star. We
present a recipe for constructing an astrosphere with the help of only a few
parameters, like the inner Alfven Mach number and the outer Alfven Mach number,
the magnetic field strength within and outside the stellar wind cavity, and the
distribution of singular points of the magnetic field within these flows.
Within the framework of a one-fluid approximation, it is possible to obtain
solutions of the MHD equations for stationary flows from corresponding static
MHD equilibria, by using noncanonical mappings of the canonical variables. The
canonical variables are the Euler potentials of the magnetic field of
magnetohydrostatic equilibria. Thus we start from static equilibria determined
by the distribution of magnetic neutral points, and assume that the Alfven Mach
number for the corresponding stationary equilibria is finite. The topological
structure determines the geometrical structure of the interstellar gas -
stellar wind interface. Additional boundary conditions like the outer magnetic
field and the jump of the magnetic field across the astropause allow
determination of the noncanonical transformations. This delivers the strength
of the magnetic field at every point in the astrotail region beyond the reverse
shock. The mathematical technique for describing such a scenario is applied to
astrospheres in general, but is also relevant for the heliosphere. It shows the
restrictions of the outer and the inner magnetic field strength in comparison
with the corresponding Alfven Mach numbers in the case of subalfvenic flows.Comment: 19 pages, 17 figures, accepted for publication in A&
Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport. I. Numerical method and results for a 15 M_sun star
Supernova models with a full spectral treatment of the neutrino transport are
presented, employing the Prometheus/Vertex neutrino-hydrodynamics code with a
``ray-by-ray plus'' approximation for treating two- (or three-) dimensional
problems. The method is described in detail and critically assessed with
respect to its capabilities, limitations, and inaccuracies in the context of
supernova simulations. In this first paper of a series, 1D and 2D core-collapse
calculations for a (nonrotating) 15 M_sun star are discussed, uncertainties in
the treatment of the equation of state -- numerical and physical -- are tested,
Newtonian results are compared with simulations using a general relativistic
potential, bremsstrahlung and interactions of neutrinos of different flavors
are investigated, and the standard approximation in neutrino-nucleon
interactions with zero energy transfer is replaced by rates that include
corrections due to nucleon recoil, thermal motions, weak magnetism, and nucleon
correlations. Models with the full implementation of the ``ray-by-ray plus''
spectral transport were found not to explode, neither in spherical symmetry nor
in 2D with a 90 degree lateral wedge. The success of previous 2D simulations
with grey, flux-limited neutrino diffusion can therefore not be confirmed.
Omitting the radial velocity terms in the neutrino momentum equation leads to
``artificial'' explosions by increasing the neutrino energy density in the
convective gain layer by about 20--30% and thus the integral neutrino energy
deposition in this region by about a factor of two. (abbreviated)Comment: 46 pages plus 13 pages online material; 49 figures; referee's
comments included, version accepted by Astronomy & Astrophysic
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