1,454 research outputs found
Fractal clustering of inertial particles in random flows
It is shown that preferential concentrations of inertial (finite-size)
particle suspensions in turbulent flows follow from the dissipative nature of
their dynamics. In phase space, particle trajectories converge toward a
dynamical fractal attractor. Below a critical Stokes number (non-dimensional
viscous friction time), the projection on position space is a dynamical fractal
cluster; above this number, particles are space filling. Numerical simulations
and semi-heuristic theory illustrating such effects are presented for a simple
model of inertial particle dynamics.Comment: 4 pages, 4 figures, Physics of Fluids, in pres
Optimal Transport Filtering with Particle Reweighing in Finance
We show the application of an optimal transportation approach to estimate
stochastic volatility process by using the flow that optimally transports the
set of particles from the prior to a posterior distribution. We also show how
to direct the flow to a rarely visited areas of the state space by using a
particle method (a mutation and a reweighing mechanism). We demonstrate the
efficiency of our approach on a simple example of the European option price
under the Stein-Stein stochastic volatility model for which a closed form
formula is available. Both homotopy and reweighted homotopy methods show a
lower variance, root-mean squared errors and a bias compared to other filtering
schemes recently developed in the signal-processing literature, including
particle filter techniques
On the Super-Additivity and Estimation Biases of Quantile Contributions
Sample measures of top centile contributions to the total (concentration) are
downward biased, unstable estimators, extremely sensitive to sample size and
concave in accounting for large deviations. It makes them particularly unfit in
domains with power law tails, especially for low values of the exponent. These
estimators can vary over time and increase with the population size, as shown
in this article, thus providing the illusion of structural changes in
concentration. They are also inconsistent under aggregation and mixing
distributions, as the weighted average of concentration measures for A and B
will tend to be lower than that from A U B. In addition, it can be shown that
under such fat tails, increases in the total sum need to be accompanied by
increased sample size of the concentration measurement. We examine the
estimation superadditivity and bias under homogeneous and mixed distributions
Selection of dune shapes and velocities. Part 2: A two-dimensional modelling
We present in this paper a simplification of the dune model proposed by
Sauermann et al. which keeps the basic mechanisms but allows analytical and
parametric studies. Two kinds of purely propagative two dimensional solutions
are exhibited: dunes and domes, which, by contrast to the former, do not show
avalanche slip face. Their shape and velocity can be predicted as a function of
their size. We recover in particular that dune profiles are not scale invariant
(small dunes are flatter than the large ones), and that the inverse of the
velocity grows almost linearly with the dune size. We furthermore get the
existence of a critical mass below which no stable dune exists. However, the
linear stability analysis of a flat sand sheet shows that it is unstable at
large wavelengths and suggests a mechanism of dune initiation.Comment: submitted to Eur. Phys. J. B, 13 pages, 17 figure
Selection of dune shapes and velocities. Part 1: Dynamics of sand, wind and barchans
Almost fifty years of investigations of barchan dunes morphology and dynamics
is reviewed, with emphasis on the physical understanding of these objects. The
characteristics measured on the field (shape, size, velocity) and the physical
problems they rise are presented. Then, we review the dynamical mechanisms
explaining the formation and the propagation of dunes. In particular a complete
and original approach of the sand transport over a flat sand bed is proposed
and discussed. We conclude on open problems by outlining future research
directions.Comment: submitted to Eur. Phys. J. B, 20 pages, 20 figure
Properties of Random Complex Chemical Reaction Networks and Their Relevance to Biological Toy Models
We investigate the properties of large random conservative chemical reaction
networks composed of elementary reactions endowed with either mass-action or
saturating kinetics, assigning kinetic parameters in a
thermodynamically-consistent manner. We find that such complex networks exhibit
qualitatively similar behavior when fed with external nutrient flux. The
nutrient is preferentially transformed into one specific chemical that is an
intrinsic property of the network. We propose a self-consistent proto-cell toy
model in which the preferentially synthesized chemical is a precursor for the
cell membrane, and show that such proto-cells can exhibit sustainable
homeostatic growth when fed with any nutrient diffusing through the membrane,
provided that nutrient is metabolized at a sufficient rate
Steric Constraints as a Global Regulation of Growing Leaf Shape
Shape is one of the important characteristics for the structures observed in
living organisms. Whereas biologists have proposed models where the shape is
controlled on a molecular level [1], physicists, following Turing [2] and
d'Arcy Thomson [3], have developed theories where patterns arise spontaneously
[4]. Here, we propose a volume constraint that restricts the possible shapes of
leaves. Focusing on palmate leaves, the central observation is that developing
leaves first grow folded inside a bud, limited by the previous and subsequent
leaves. We show that growing folded in this small volume controls globally the
leaf development. This induces a direct relationship between the way it was
folded and the final unfolded shape of the leaf. These dependencies can be
approximated as simple geometrical relationships that we confirm on both folded
embryonic and unfolded mature leaves. We find that independently of their
position in the phylogenetic tree, these relationships work for folded species,
but do not work for non-folded species. This steric constraint is a simple way
to impose a global regulation for the leaf growth. Such steric regulation
should be more general and considered as a new simple means of global
regulation.Comment: 6 pages 4 figures, Supplementary materials (8 pages, 7 figures
Géométrie, graphiques, fonctions au collège
L'apprentissage des mathématiques s'inscrit sur le long terme et en général dans une structure institutionnelle : l'école. L'apprenant construit sa connaissance au fil des années, dans un rapport interactif avec ses enseignants, les autres élèves de sa classe et toutes les autres sources que la vie sociale met à sa disposition.Dans le texte ci-dessous, nous présentons un ensemble de problèmes dont l'enjeu mathématique est la notion d'approximation traitée à un moment de la scolarité : élèves de 12-15 ans, de façon contextualisée. Ce n'est qu'une approche, la question du calcul d'erreur n'est pas abordée. Nombres et mesures y sont impliqués dans différents cadres en interaction : numérique, géométrique, fonctionnel, graphique. Nous y expliquons nos choix didactiques et les raisons des choix de l'ingénierie proposée. La référence est la dialectique outil/objet et jeux de cadres. Elle nous offre une grille pour élaborer les séquences de classe et aussi pour repérer et analyser les relations entre l'enseignant et les élèves : qui est responsable de quoi, qui fait quoi. L'enseignant a des marges de manoeuvre pour organiser et conduire son enseignement, il a des attentes concernant les élèves. Nous y faisons référence
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