90,888 research outputs found
Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations
We investigate mathematically a nonlinear approximation type approach
recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to
solve high dimensional partial differential equations. We show the link between
the approach and the greedy algorithms of approximation theory studied e.g. in
[R.A. DeVore and V.N. Temlyakov, Adv. Comput. Math., 1996]. On the prototypical
case of the Poisson equation, we show that a variational version of the
approach, based on minimization of energies, converges. On the other hand, we
show various theoretical and numerical difficulties arising with the non
variational version of the approach, consisting of simply solving the first
order optimality equations of the problem. Several unsolved issues are
indicated in order to motivate further research
A mathematical formalization of the parallel replica dynamics
The purpose of this article is to lay the mathematical foundations of a well
known numerical approach in computational statistical physics and molecular
dynamics, namely the parallel replica dynamics introduced by A.F. Voter. The
aim of the approach is to efficiently generate a coarse-grained evolution (in
terms of state-to-state dynamics) of a given stochastic process. The approach
formally consists in concurrently considering several realizations of the
stochastic process, and tracking among the realizations that which, the
soonest, undergoes an important transition. Using specific properties of the
dynamics generated, a computational speed-up is obtained. In the best cases,
this speed-up approaches the number of realizations considered. By drawing
connections with the theory of Markov processes and, in particular, exploiting
the notion of quasi-stationary distribution, we provide a mathematical setting
appropriate for assessing theoretically the performance of the approach, and
possibly improving it
Thermodynamic dislocation theory of high-temperature deformation in aluminum and steel
The statistical-thermodynamic dislocation theory developed in previous papers
is used here in an analysis of high-temperature deformation of aluminum and
steel. Using physics-based parameters that we expect theoretically to be
independent of strain rate and temperature, we are able to fit experimental
stress-strain curves for three different strain rates and three different
temperatures for each of these two materials. Our theoretical curves include
yielding transitions at zero strain in agreement with experiment. We find that
thermal softening effects are important even at the lowest temperatures and
smallest strain rates.Comment: 7 pages, 8 figure
On the filamentary environment of galaxies
The correlation between the large-scale distribution of galaxies and their
spectroscopic properties at z=1.5 is investigated using the Horizon MareNostrum
cosmological run.
We have extracted a large sample of 10^5 galaxies from this large
hydrodynamical simulation featuring standard galaxy formation physics. Spectral
synthesis is applied to these single stellar populations to generate spectra
and colours for all galaxies. We use the skeleton as a tracer of the cosmic web
and study how our galaxy catalogue depends on the distance to the skeleton. We
show that galaxies closer to the skeleton tend to be redder, but that the
effect is mostly due to the proximity of large haloes at the nodes of the
skeleton, rather than the filaments themselves.
This effects translate into a bimodality in the colour distribution of our
sample. The origin of this bimodality is investigated and seems to follow from
the ram pressure stripping of satellite galaxies within the more massive
clusters of the simulation.
The virtual catalogues (spectroscopical properties of the MareNostrum
galaxies at various redshifts) are available online at
http://www.iap.fr/users/pichon/MareNostrum/cataloguesComment: 18 pages, 27 figures, accepted for publication in MNRA
Initial POLAR MFE observation of substorm signatures in the polar magnetosphere
This paper studies substorm influences in the polar magnetosphere using data from the POLAR magnetic field experiment (MFE). The POLAR spacecraft remains in the high altitude polar magnetosphere for extended periods around apogee. There it can stay at nearly constant altitude through all phases of a substorm, which was not possible on previous missions. We report such an event on March 28, 1996. Ground magnetometers monitored substorm activity, while the POLAR spacecraft, directly over the pole at (−0.8, −0.6, 8.5) RE in GSM coordinates, observed a corresponding perturbation in the total magnetic field strength. The total magnetic field first increased, then recovered toward quiet levels, consistent with erosion of magnetic flux from the dayside magnetosphere, followed by transport of that flux to the magnetotail, and eventual onset of tail reconnection and the return of that magnetic flux to the dayside magnetosphere
Bose-enhanced chemistry: Amplification of selectivity in the dissociation of molecular Bose-Einstein condensates
We study the photodissociation chemistry of a quantum degenerate gas of
bosonic triatomic molecules, assuming two open rearrangement channels
( or ). The equations of motion are equivalent to those of a
parametric multimode laser, resulting in an exponential buildup of macroscopic
mode populations. By exponentially amplifying a small differential in the
single-particle rate-coefficients, Bose stimulation leads to a nearly complete
selectivity of the collective -body process, indicating a novel type of
ultra-selective quantum degenerate chemistry.Comment: 5 pages, 3 figure
An HI Imaging Survey of Asymptotic Giant Branch Stars
We present an imaging study of a sample of eight asymptotic giant branch
(AGB) stars in the HI 21-cm line. Using observations from the Very Large Array,
we have unambiguously detected HI emission associated with the extended
circumstellar envelopes of six of the targets. The detected HI masses range
from M_HI ~ 0.015-0.055 M_sun. The HI morphologies and kinematics are diverse,
but in all cases appear to be significantly influenced by the interaction
between the circumstellar envelope and the surrounding medium. Four stars (RX
Lep, Y UMa, Y CVn, and V1942 Sgr) are surrounded by detached HI shells ranging
from 0.36 to 0.76 pc across. We interpret these shells as resulting from
material entrained in a stellar outflow being abruptly slowed at a termination
shock where it meets the local medium. RX Lep and TX Psc, two stars with
moderately high space velocities (V_space>56 km/s), exhibit extended gaseous
wakes (~0.3 and 0.6 pc in the plane of the sky), trailing their motion through
space. The other detected star, R Peg, displays a peculiar "horseshoe-shaped"
HI morphology with emission extended on scales up to ~1.7 pc; in this case, the
circumstellar debris may have been distorted by transverse flows in the local
interstellar medium. We briefly discuss our new results in the context of the
entire sample of evolved stars that has been imaged in HI to date.Comment: Accepted to AJ. A version with full resolution figures is available
at http://www.haystack.mit.edu/hay/staff/lmatthew/matthews_HI_survey.pd
Quantifying the Effect of Non-Larmor Motion of Electrons on the Pressure Tensor
In space plasma, various effects of magnetic reconnection and turbulence
cause the electron motion to significantly deviate from their Larmor orbits.
Collectively these orbits affect the electron velocity distribution function
and lead to the appearance of the "non-gyrotropic" elements in the pressure
tensor. Quantification of this effect has important applications in space and
laboratory plasma, one of which is tracing the electron diffusion region (EDR)
of magnetic reconnection in space observations. Three different measures of
agyrotropy of pressure tensor have previously been proposed, namely,
, and . The multitude of contradictory measures has
caused confusion within the community. We revisit the problem by considering
the basic properties an agyrotropy measure should have. We show that
, and are all defined based on the sum of the
principle minors (i.e. the rotation invariant ) of the pressure tensor. We
discuss in detail the problems of -based measures and explain why they may
produce ambiguous and biased results. We introduce a new measure
constructed based on the determinant of the pressure tensor (i.e. the rotation
invariant ) which does not suffer from the problems of -based
measures. We compare with other measures in 2 and 3-dimension
particle-in-cell magnetic reconnection simulations, and show that can
effectively trace the EDR of reconnection in both Harris and force-free current
sheets. On the other hand, does not show prominent peaks in
the EDR and part of the separatrix in the force-free reconnection simulations,
demonstrating that does not measure all the non-gyrotropic
effects in this case, and is not suitable for studying magnetic reconnection in
more general situations other than Harris sheet reconnection.Comment: accepted by Phys. of Plasm
A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows
A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is demonstrated with the solution of the start-up Couette flow of the Hookean and FENE dumbbell model fluids
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