45 research outputs found
Cascades infiniment divisibles voilées : au-delà des lois de puissance
Nous présentons les définitions et synthèses de processus stochastiques respectant des lois d'échelles voilées, qui
s'écartent de façon contrôlée d'un comportement en loi de puissance. Nous définissons des bruit, mouvement et
marche aléatoire issus de cascades infiniment divisibles (IDC) voilées. Nous étudions analytiquement le comportement
des moments des accroissements de ces processus à travers les échelles. Ces résultats théoriques sont illustrés sur
l'exemple d'une cascade log-Normale voilée. Les algorithmes de synthèse et les fonctions Matlab utilisés sont
disponibles sur nos pages web.We address the definitions and synthesis of stochastic processes which possess warped scaling laws that
depart from power law behaviors in a controlled manner. We define warped infinitely divisible cascading
(IDC) noise, motion and random walk. We provide a theoretical derivation of the scaling behavior of the
moments of their increments. We provide numerical simulations of a warped log-Normal cascade to illustrate
these results. Algorithms for synthesis and Matlab functions are available from our web pages
Probabilistic analysis of the upwind scheme for transport
We provide a probabilistic analysis of the upwind scheme for
multi-dimensional transport equations. We associate a Markov chain with the
numerical scheme and then obtain a backward representation formula of
Kolmogorov type for the numerical solution. We then understand that the error
induced by the scheme is governed by the fluctuations of the Markov chain
around the characteristics of the flow. We show, in various situations, that
the fluctuations are of diffusive type. As a by-product, we prove that the
scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all
a>0, for a Lipschitz continuous initial datum. Our analysis provides a new
interpretation of the numerical diffusion phenomenon
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Uncertainty quantification for kinetic models in socio-economic and life sciences
Kinetic equations play a major rule in modeling large systems of interacting
particles. Recently the legacy of classical kinetic theory found novel
applications in socio-economic and life sciences, where processes characterized
by large groups of agents exhibit spontaneous emergence of social structures.
Well-known examples are the formation of clusters in opinion dynamics, the
appearance of inequalities in wealth distributions, flocking and milling
behaviors in swarming models, synchronization phenomena in biological systems
and lane formation in pedestrian traffic. The construction of kinetic models
describing the above processes, however, has to face the difficulty of the lack
of fundamental principles since physical forces are replaced by empirical
social forces. These empirical forces are typically constructed with the aim to
reproduce qualitatively the observed system behaviors, like the emergence of
social structures, and are at best known in terms of statistical information of
the modeling parameters. For this reason the presence of random inputs
characterizing the parameters uncertainty should be considered as an essential
feature in the modeling process. In this survey we introduce several examples
of such kinetic models, that are mathematically described by nonlinear Vlasov
and Fokker--Planck equations, and present different numerical approaches for
uncertainty quantification which preserve the main features of the kinetic
solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic
Equations
HCN emission from translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of Orion B GMC: Revisiting its role as tracer of the dense gas reservoir for star formation
We present 5 deg^2 (~250 pc^2) HCN, HNC, HCO+, and CO J=1-0 maps of the Orion
B GMC, complemented with existing wide-field [CI] 492 GHz maps, as well as new
pointed observations of rotationally excited HCN, HNC, H13CN, and HN13C lines.
We detect anomalous HCN J=1-0 hyperfine structure line emission almost
everywhere in the cloud. About 70% of the total HCN J=1-0 luminosity arises
from gas at A_V < 8 mag. The HCN/CO J=1-0 line intensity ratio shows a bimodal
behavior with an inflection point at A_V < 3 mag typical of translucent gas and
UV-illuminated cloud edges. We find that most of the HCN J=1-0 emission arises
from extended gas with n(H2) < 10^4 cm^-3, even lower density gas if the
ionization fraction is > 10^-5 and electron excitation dominates. This result
explains the low-A_V branch of the HCN/CO J=1-0 intensity ratio distribution.
Indeed, the highest HCN/CO ratios (~0.1) at A_V < 3 mag correspond to regions
of high [CI] 492 GHz/CO J=1-0 intensity ratios (>1) characteristic of
low-density PDRs. Enhanced FUV radiation favors the formation and excitation of
HCN on large scales, not only in dense star-forming clumps. The low surface
brightness HCN and HCO+ J=1-0 emission scale with I_FIR (a proxy of the stellar
FUV radiation field) in a similar way. Together with CO J=1-0, these lines
respond to increasing I_FIR up to G0~20. On the other hand, the bright HCN
J=1-0 emission from dense gas in star-forming clumps weakly responds to I_FIR
once the FUV radiation field becomes too intense (G0>1500). The different power
law scalings (produced by different chemistries, densities, and line excitation
regimes) in a single but spatially resolved GMC resemble the variety of
Kennicutt-Schmidt law indexes found in galaxy averages. As a corollary for
extragalactic studies, we conclude that high HCN/CO J=1-0 line intensity ratios
do not always imply the presence of dense gas.Comment: accepted for publication in A&A. 24 pages, 18 figures, plus Appendix.
Abridged Abstract. English language not edite
Gas kinematics around filamentary structures in the Orion B cloud
Context. Understanding the initial properties of star-forming material and how they affect the star formation process is key. From an observational point of view, the feedback from young high-mass stars on future star formation properties is still poorly constrained. Aims. In the framework of the IRAM 30m ORION-B large program, we obtained observations of the translucent (2 ≤ AV < 6 mag) and moderately dense gas (6 ≤ AV < 15 mag), which we used to analyze the kinematics over a field of 5 deg2 around the filamentary structures. Methods. We used the Regularized Optimization for Hyper-Spectral Analysis (ROHSA) algorithm to decompose and de-noise the C 18 O(1−0) and 13CO(1−0) signals by taking the spatial coherence of the emission into account. We produced gas column density and mean velocity maps to estimate the relative orientation of their spatial gradients. Results. We identified three cloud velocity layers at different systemic velocities and extracted the filaments in each velocity layer. The filaments are preferentially located in regions of low centroid velocity gradients. By comparing the relative orientation between the column density and velocity gradients of each layer from the ORION-B observations and synthetic observations from 3D kinematic toy models, we distinguish two types of behavior in the dynamics around filaments: (i) radial flows perpendicular to the filament axis that can be either inflows (increasing the filament mass) or outflows and (ii) longitudinal flows along the filament axis. The former case is seen in the Orion B data, while the latter is not identified. We have also identified asymmetrical flow patterns, usually associated with filaments located at the edge of an H II region. Conclusions. This is the first observational study to highlight feedback from H II regions on filament formation and, thus, on star formation in the Orion B cloud. This simple statistical method can be used for any molecular cloud to obtain coherent information on the kinematics
Numerical schemes for semiconductors energy- transport models
International audienceWe introduce some finite volume schemes for unipolar energy-transportmodels. Using a reformulation in dual entropy variables, we can show the decay ofa discrete entropy with control of the discrete entropy dissipation
HCN emission from translucent gas and UV-illuminated cloud edges revealed by wide-field IRAM 30m maps of Orion B GMC: Revisiting its role as tracer of the dense gas reservoir for star formation
35 pags., 28 figs., 14 tabs.We present 5 deg^2 (~250 pc^2) HCN, HNC, HCO+, and CO J=1-0 maps of the Orion
B GMC, complemented with existing wide-field [CI] 492 GHz maps, as well as new
pointed observations of rotationally excited HCN, HNC, H13CN, and HN13C lines.
We detect anomalous HCN J=1-0 hyperfine structure line emission almost
everywhere in the cloud. About 70% of the total HCN J=1-0 luminosity arises
from gas at A_V < 8 mag. The HCN/CO J=1-0 line intensity ratio shows a bimodal
behavior with an inflection point at A_V < 3 mag typical of translucent gas and
UV-illuminated cloud edges. We find that most of the HCN J=1-0 emission arises
from extended gas with n(H2) ~< 10^4 cm^-3, even lower density gas if the
ionization fraction is > 10^-5 and electron excitation dominates. This result
explains the low-A_V branch of the HCN/CO J=1-0 intensity ratio distribution.
Indeed, the highest HCN/CO ratios (~0.1) at A_V < 3 mag correspond to regions
of high [CI] 492 GHz/CO J=1-0 intensity ratios (>1) characteristic of
low-density PDRs. Enhanced FUV radiation favors the formation and excitation of
HCN on large scales, not only in dense star-forming clumps. The low surface
brightness HCN and HCO+ J=1-0 emission scale with I_FIR (a proxy of the stellar
FUV radiation field) in a similar way. Together with CO J=1-0, these lines
respond to increasing I_FIR up to G0~20. On the other hand, the bright HCN
J=1-0 emission from dense gas in star-forming clumps weakly responds to I_FIR
once the FUV radiation field becomes too intense (G0>1500). The different power
law scalings (produced by different chemistries, densities, and line excitation
regimes) in a single but spatially resolved GMC resemble the variety of
Kennicutt-Schmidt law indexes found in galaxy averages. As a corollary for
extragalactic studies, we conclude that high HCN/CO J=1-0 line intensity ratios
do not always imply the presence of dense gas.M.G.S.M. and J.R.G. thank the Spanish MICINN for funding support under grant PID2019-106110GB-I00. This work was supported by the French Agence Nationale de la Recherche through the DAOISM grant ANR-21-CE31–0010, and by the Programme National “Physique et Chimie du Milieu Interstellaire”
(PCMI) of CNRS/INSU with INC/INP, co-funded by CEA and CNES. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute
of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004).Peer reviewe
Multidimensional infinitely divisible cascades
The framework of infinitely divisible scaling was first developed to analyse the statistical intermittency of turbulence in fluid dynamics. It also reveals a powerful tool to describe and model various situations including Internet traffic, financial time series, textures ... A series of recent works introduced the infinitely divisible cascades in 1 dimension, a family of multifractal processes that can be easily synthesized numerically. This work extends the definition of infinitely divisible cascades from 1 dimension to d dimensions in the scalar case. Thus, a class of models is proposed both for data analysis and for numerical simulation in dimension d≥1. In this article, we give the definitions and main properties of infinitely divisible cascades in d dimensions. Then we focus on the modelling of statistical intermittency in turbulent flows. Several other applications are considered. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200602.50.Ey Stochastic processes, 05.45.Df Fractals, 47.53.+n Fractals in fluid dynamics, 47.27.E- Turbulence simulation and modelling ,