1,782 research outputs found
On the boundary treatment in spectral methods for hyperbolic systems
Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions are clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100
Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas
We use the Bianchi-I spacetime to study the local dynamics of a magnetized
self-gravitating Fermi gas. The set of Einstein-Maxwell field equations for
this gas becomes a dynamical system in a 4-dimensional phase space. We consider
a qualitative study and examine numeric solutions for the degenerate zero
temperature case. All dynamic quantities exhibit similar qualitative behavior
in the 3-dimensional sections of the phase space, with all trajectories
reaching a stable attractor whenever the initial expansion scalar H_{0} is
negative. If H_{0} is positive, and depending on initial conditions, the
trajectories end up in a curvature singularity that could be isotropic(singular
"point") or anisotropic (singular "line"). In particular, for a sufficiently
large initial value of the magnetic field it is always possible to obtain an
anisotropic type of singularity in which the "line" points in the same
direction of the field.Comment: 6 pages, 3 figures (accepted in General Relativity and Gravitation
Preconditioned Minimal Residual Methods for Chebyshev Spectral Caluclations
The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a DuFort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method
Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability
In the present work fournontrivial stages of electrokinetic instability are
identified by direct numerical simulation (DNS) of the full
Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of
the initial conditions (milliseconds); ii) 1D self-similar evolution
(milliseconds-seconds); iii) The primary instability of the self-similar
solution (seconds); iv) The nonlinear stage with secondary instabilities. The
self-similar character of evolution at intermediately large times is confirmed.
Rubinstein and Zaltzman instability and noise-driven nonlinear evolution to
over-limiting regimes in ion-exchange membranes are numerically simulated and
compared with theoretical and experimental predictions. The primary instability
which happens during this stage is found to arrest self-similar growth of the
diffusion layer and specifies its characteristic length as was first
experimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). A
novel principle for the characteristic wave number selection from the
broadbanded initial noise is established.Comment: 13 pages, 8 figure
Pseudospectral versus finite-differences schemes in the numerical integration of stochastic models of surface growth
We present a comparison between finite differences schemes and a
pseudospectral method applied to the numerical integration of stochastic
partial differential equations that model surface growth. We have studied, in
1+1 dimensions, the Kardar, Parisi and Zhang model (KPZ) and the Lai, Das Sarma
and Villain model (LDV). The pseudospectral method appears to be the most
stable for a given time step for both models. This means that the time up to
which we can follow the temporal evolution of a given system is larger for the
pseudospectral method. Moreover, for the KPZ model, a pseudospectral scheme
gives results closer to the predictions of the continuum model than those
obtained through finite difference methods. On the other hand, some numerical
instabilities appearing with finite difference methods for the LDV model are
absent when a pseudospectral integration is performed. These numerical
instabilities give rise to an approximate multiscaling observed in the
numerical simulations. With the pseudospectral approach no multiscaling is seen
in agreement with the continuum model.Comment: 13 single column pages, RevTeX, 6 eps fig
Kardar-Parisi-Zhang asymptotics for the two-dimensional noisy Kuramoto-Sivashinsky equation
We study numerically the Kuramoto-Sivashinsky (KS) equation forced by
external white noise in two space dimensions, that is a generic model for e.g.
surface kinetic roughening in the presence of morphological instabilities.
Large scale simulations using a pseudospectral numerical scheme allow us to
retrieve Kardar-Parisi-Zhang (KPZ) scaling as the asymptotic state of the
system, as in the 1D case. However, this is only the case for sufficiently
large values of the coupling and/or system size, so that previous conclusions
on non-KPZ asymptotics are demonstrated as finite size effects. Crossover
effects are comparatively stronger for the 2D case than for the 1D system.Comment: 5 pages, 3 figures; supplemental material available at journal web
page and/or on reques
Effect of convective outer layers modeling on non-adiabatic seismic observables of delta Scuti stars
The identification of pulsation modes in delta Scuti stars is mandatory to
constrain the theoretical stellar models. The non-adiabatic observables used in
the photometric identification methods depend, however,on convection modeling
in the external layers. Our aim is to determine how the treatment of convection
in the atmospheric and sub-atmospheric layers affects the mode identification,
and what information about the thermal structure of the external layers can be
obtained from amplitude ratios and phase lags in Str\"omgren photometric bands.
We derive non-adiabatic parameters for delta Scuti stars by using, for the
first time, stellar models with the same treatment of convection in the
interior and in the atmosphere. We compute classical non-gray mixing length
models, and as well non-gray ``Full Spectrum of Turbulence'' models.
Furthermore, we compute the photometric amplitudes and phases of pulsation by
using the colors and the limb-darkening coefficents as derived from the same
atmosphere models used in the stellar modeling. We show that the non-adiabatic
phase-lag is mainly sensitive to the thermal gradients in the external layers,
(and hence to the treatment of convection), and that this sensitivity is also
clearly reflected in the multi-color photometric phase differences.Comment: 14 pag. 19 figs. accepted for publication in Astronomy and
Astrophysic
On statistically stationary homogeneous shear turbulence
A statistically stationary turbulence with a mean shear gradient is realized
in a flow driven by suitable body forces. The flow domain is periodic in
downstream and spanwise directions and bounded by stress free surfaces in the
normal direction. Except for small layers near the surfaces the flow is
homogeneous. The fluctuations in turbulent energy are less violent than in the
simulations using remeshing, but the anisotropy on small scales as measured by
the skewness of derivatives is similar and decays weakly with increasing
Reynolds number.Comment: 4 pages, 5 figures (Figs. 3 and 4 as external JPG-Files
A Comparison of Measured Crab and Vela Glitch Healing Parameters with Predictions of Neutron Star Models
There are currently two well-accepted models that explain how pulsars exhibit
glitches, sudden changes in their regular rotational spin-down. According to
the starquake model, the glitch healing parameter, Q, which is measurable in
some cases from pulsar timing, should be equal to the ratio of the moment of
inertia of the superfluid core of a neutron star (NS) to its total moment of
inertia. Measured values of the healing parameter from pulsar glitches can
therefore be used in combination with realistic NS structure models as one test
of the feasibility of the starquake model as a glitch mechanism. We have
constructed NS models using seven representative equations of state of
superdense matter to test whether starquakes can account for glitches observed
in the Crab and Vela pulsars, for which the most extensive and accurate glitch
data are available. We also present a compilation of all measured values of Q
for Crab and Vela glitches to date which have been separately published in the
literature. We have computed the fractional core moment of inertia for stellar
models covering a range of NS masses and find that for stable NSs in the
realistic mass range 1.4 +/- 0.2 solar masses, the fraction is greater than
0.55 in all cases. This range is not consistent with the observational
restriction Q < 0.2 for Vela if starquakes are the cause of its glitches. This
confirms results of previous studies of the Vela pulsar which have suggested
that starquakes are not a feasible mechanism for Vela glitches. The much larger
values of Q observed for Crab glitches (Q > 0.7) are consistent with the
starquake model predictions and support previous conclusions that starquakes
can be the cause of Crab glitches.Comment: 8 pages, including 3 figures and 1 table. Accepted for publication in
Ap
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