1,527 research outputs found
A cloudy Vlasov solution
We propose to integrate the Vlasov-Poisson equations giving the evolution of
a dynamical system in phase-space using a continuous set of local basis
functions. In practice, the method decomposes the density in phase-space into
small smooth units having compact support. We call these small units ``clouds''
and choose them to be Gaussians of elliptical support. Fortunately, the
evolution of these clouds in the local potential has an analytical solution,
that can be used to evolve the whole system during a significant fraction of
dynamical time. In the process, the clouds, initially round, change shape and
get elongated. At some point, the system needs to be remapped on round clouds
once again. This remapping can be performed optimally using a small number of
Lucy iterations. The remapped solution can be evolved again with the cloud
method, and the process can be iterated a large number of times without showing
significant diffusion. Our numerical experiments show that it is possible to
follow the 2 dimensional phase space distribution during a large number of
dynamical times with excellent accuracy. The main limitation to this accuracy
is the finite size of the clouds, which results in coarse graining the
structures smaller than the clouds and induces small aliasing effects at these
scales. However, it is shown in this paper that this method is consistent with
an adaptive refinement algorithm which allows one to track the evolution of the
finer structure in phase space. It is also shown that the generalization of the
cloud method to the 4 dimensional and the 6 dimensional phase space is quite
natural.Comment: 46 pages, 25 figures, submitted to MNRA
A "metric" semi-Lagrangian Vlasov-Poisson solver
We propose a new semi-Lagrangian Vlasov-Poisson solver. It employs elements
of metric to follow locally the flow and its deformation, allowing one to find
quickly and accurately the initial phase-space position of any test
particle , by expanding at second order the geometry of the motion in the
vicinity of the closest element. It is thus possible to reconstruct accurately
the phase-space distribution function at any time and position by
proper interpolation of initial conditions, following Liouville theorem. When
distorsion of the elements of metric becomes too large, it is necessary to
create new initial conditions along with isotropic elements and repeat the
procedure again until next resampling. To speed up the process, interpolation
of the phase-space distribution is performed at second order during the
transport phase, while third order splines are used at the moments of
remapping. We also show how to compute accurately the region of influence of
each element of metric with the proper percolation scheme. The algorithm is
tested here in the framework of one-dimensional gravitational dynamics but is
implemented in such a way that it can be extended easily to four or
six-dimensional phase-space. It can also be trivially generalised to plasmas.Comment: 32 pages, 14 figures, accepted for publication in Journal of Plasma
Physics, Special issue: The Vlasov equation, from space to laboratory plasma
Observational Constraints on Higher Order Clustering up to $z\simeq 1
Constraints on the validity of the hierarchical gravitational instability
theory and the evolution of biasing are presented based upon measurements of
higher order clustering statistics in the Deeprange Survey, a catalog of
galaxies with derived from a KPNO 4m CCD imaging
survey of a contiguous region. We compute the
3-point and 4-point angular correlation functions using a direct estimation for
the former and the counts-in-cells technique for both. The skewness
decreases by a factor of as galaxy magnitude increases over the
range (). This decrease is
consistent with a small {\it increase} of the bias with increasing redshift,
but not by more than a factor of 2 for the highest redshifts probed. Our
results are strongly inconsistent, at about the level, with
typical cosmic string models in which the initial perturbations follow a
non-Gaussian distribution - such models generally predict an opposite trend in
the degree of bias as a function of redshift. We also find that the scaling
relation between the 3-point and 4-point correlation functions remains
approximately invariant over the above magnitude range. The simplest model that
is consistent with these constraints is a universe in which an initially
Gaussian perturbation spectrum evolves under the influence of gravity combined
with a low level of bias between the matter and the galaxies that decreases
slightly from to the current epoch.Comment: 28 pages, 4 figures included, ApJ, accepted, minor change
Density functional theory study of Fe(II) adsorption and oxidation on goethite surfaces
We study the interactions between Fe(II) aqua complexes and surfaces of
goethite (alpha-FeOOH) by means of density functional theory calculations
including the so-called Hubbard U correction to the exchange-correlation
functional. Using a thermodynamic approach, we find that (110) and (021)
surfaces in contact with aqueous solutions are almost equally stable, despite
the evident needlelike shape of goethite crystals indicating substantially
different reactivity of the two faces. We thus suggest that crystal anisotropy
may result from different growth rates due to virtually barrierless adsorption
of hydrated ions on the (021) but not on the (110) surface. No clear evidence
is found for spontaneous electron transfer from an adsorbed Fe(II) hex-aqua
complex to a defect-free goethite substrate. Crystal defects are thus inferred
to play an important role in assisting such electron transfer processes
observed in a recent experimental study. Finally, goethite surfaces are
observed to enhance the partial oxidation of adsorbed aqueous Fe(II) upon
reaction with molecular oxygen. We propose that this catalytic oxidation effect
arises from donation of electronic charge from the bulk oxide to the oxidizing
agent through shared hydroxyl ligands anchoring the Fe(II) complexes on the
surface
The three dimensional skeleton: tracing the filamentary structure of the universe
The skeleton formalism aims at extracting and quantifying the filamentary
structure of the universe is generalized to 3D density fields; a numerical
method for computating a local approximation of the skeleton is presented and
validated here on Gaussian random fields. This method manages to trace well the
filamentary structure in 3D fields such as given by numerical simulations of
the dark matter distribution on large scales and is insensitive to monotonic
biasing. Two of its characteristics, namely its length and differential length,
are analyzed for Gaussian random fields. Its differential length per unit
normalized density contrast scales like the PDF of the underlying density
contrast times the total length times a quadratic Edgeworth correction
involving the square of the spectral parameter. The total length scales like
the inverse square smoothing length, with a scaling factor given by 0.21 (5.28+
n) where n is the power index of the underlying field. This dependency implies
that the total length can be used to constrain the shape of the underlying
power spectrum, hence the cosmology. Possible applications of the skeleton to
galaxy formation and cosmology are discussed. As an illustration, the
orientation of the spin of dark halos and the orientation of the flow near the
skeleton is computed for dark matter simulations. The flow is laminar along the
filaments, while spins of dark halos within 500 kpc of the skeleton are
preferentially orthogonal to the direction of the flow at a level of 25%.Comment: 17 pages, 11 figures, submitted to MNRA
Ethical Implications in AI-Powered Trend Research Platforms
The manuscript discusses the limitations of applying AI in trend research platforms for the fashion system. This analysis intends to take a position within the emergent research topic of AI. Considering its ethical implications, we explore the opportunities of implementing AI to support trend research from a design-oriented perspective, realising the relationship between fashion and trends, which is central in shaping the future. Examples of AI-powered trend platforms evidence how valuable their insights are for strategic innovation. The analysis focuses on platforms that provide tailored services using AI and expert interpretation. Virtue ethics of technology serves as a useful framework to examine this topic, proposing a new set of virtues that respond to technology’s shaping of behaviour and its disadvantages. The risks of applying AI are many-fold; the consequences perpetuate power imbalances and social inequality. Proposing guidelines for enabling a responsible practice explores how to forge ethics into AI, creating a pluralised practice
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