Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

Rotating Hele-Shaw cells with ferrofluids

We investigate the flow of two immiscible, viscous fluids in a rotating Hele-Shaw cell, when one of the fluids is a ferrofluid and an external magnetic field is applied. The interplay between centrifugal and magnetic forces in determining the instability of the fluid-fluid interface is analyzed. The linear stability analysis of the problem shows that a non-uniform, azimuthal magnetic field, applied tangential to the cell, tends to stabilize the interface. We verify that maximum growth rate selection of initial patterns is influenced by the applied field, which tends to decrease the number of interface ripples. We contrast these results with the situation in which a uniform magnetic field is applied normally to the plane defined by the rotating Hele-Shaw cell.Comment: 12 pages, 3 ps figures, RevTe

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters

A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes

A Lagrangian numerical scheme for solving nonlinear degenerate Fokker{Planck equations in space dimensions d>2 is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies and given external potentials, e.g. the porous medium equation and the fast diffusion equation. The key ingredient in our approach is the gradient ow structure of the dynamics. For discretization of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. Thanks to that time discretisation, the fully discrete solution inherits energy estimates from the original gradient ow, and these lead to weak compactness of the trajectories in the continuous limit. Consistency is analyzed in the planar situation, d = 2. A variety of numerical experiments for the porous medium equation indicates that the scheme is well-adapted to track the growth of the solution's support

A cohomological formula for the Atiyah-Patodi-Singer index on manifolds with boundary

International audienceWe give a cohomological formula for the index of a fully elliptic pseudodifferential operator on a manifold with boundary. As in the classic case of Atiyah-Singer, we use an embedding into an euclidean space to express the index as the integral of a cohomology class depending in this case on a noncommutative symbol, the integral being over a $C^\infty$-manifold called the singular normal bundle associated to the embedding. The formula is based on a K-theoretical Atiyah-Patodi-Singer theorem for manifolds with boundary that is drawn from Connes' tangent groupoid approach

Mid-Infrared Diagnostics of LINERs

We report results from the first mid-infrared spectroscopic study of a comprehensive sample of 33 LINERs, observed with the Spitzer Space Telescope. We compare the properties of two different LINER populations: infrared-faint LINERs, with LINER emission arising mostly in compact nuclear regions, and infrared-luminous LINERs, which often show spatially extended (non-AGN) LINER emission. We show that these two populations can be easily distinguished by their mid-infrared spectra in three different ways: (i) their mid-IR spectral energy distributions (SEDs), (ii) the emission features of polycyclic aromatic hydrocarbons (PAHs), and (iii) various combinations of IR fine-structure line ratios. IR-luminous LINERs show mid-IR SEDs typical of starburst galaxies, while the mid-IR SEDs of IR-faint LINERs are much bluer. PAH flux ratios are significantly different in the two groups. Fine structure emission lines from highly excited gas, such as [O IV], are detected in both populations, suggesting the presence of an additional AGN also in a large fraction of IR-bright LINERs, which contributes little to the combined mid-IR light. The two LINER groups occupy different regions of mid-infrared emission-line excitation diagrams. The positions of the various LINER types in our diagnostic diagrams provide important clues regarding the power source of each LINER type. Most of these mid-infrared diagnostics can be applied at low spectral resolution, making AGN- and starburst-excited LINERs distinguishable also at high redshifts.Comment: 11 pages, including 2 eps figures, accepted for publication in ApJ

Inclusive One Jet Production With Multiple Interactions in the Regge Limit of pQCD

DIS on a two nucleon system in the regge limit is considered. In this framework a review is given of a pQCD approach for the computation of the corrections to the inclusive one jet production cross section at finite number of colors and discuss the general results.Comment: 4 pages, latex, aicproc format, Contribution to the proceedings of "Diffraction 2008", 9-14 Sep. 2008, La Londe-les-Maures, Franc

Effects of artificial day length on early sexual maturation, reproductive performance, and egg quality in female European sea bass Dicentrarchus labrax (Linnaeus, 1758)

Juvenile sea bass, Dicentrarchus labrax (Linnaeus, 1758), (4-5 months old) were kept during four (experiment I) or three (experiment II) consecutive years under artificial photoperiod conditions. Compared with the control group, in experiment I, during the first reproductive cycle, the EX and LO groups showed a statistically significant advance and delay of 53 and 58 days, respectively, in mean spawning time. In Experiment II, the SLmar and CO groups presented a significant advance in spawning time, of 1 and 2 months, respectively, compared with the controls. From these results, it can be concluded that long-term application of artificial photoperiods can advance or delay the time of first spawning in D. labrax, as well as altering their rates of relative fecundity, and the quality of eggs and larvae.Se estudió la influencia del fotoperiodo en juveniles de lubina Dicentrarchus labrax (Linnaeus, 1758), de 4-5 meses de edad, mantenidos en cautividad durante 4 y 3 años consecutivos (experimentos I y II, respectivamente). En el experimento I, durante el primer ciclo reproductor, se observó que los grupos EX (fotoperiodo expandido) y LO (fotoperiodo largo constante) adelantaron y retrasaron el periodo medio de puesta en 53 y 58 días, respectivamente, en comparación con el grupo control. En el siguiente ciclo reproductor, estos grupos retrasaron el periodo medio de puesta en 21 y 31 días, respectivamente, con respecto al control. En general, las fecundidades relativas y las tasas de viabilidad de huevos y larvas de los grupos experimentales fueron un 50 % más bajas que las observadas en el grupo control. En el experimento II, los grupos SLmar y CO adelantaron en 1 o 2 meses el periodo medio de puesta en comparación con el grupo control (NP). En conclusión, el fotoperiodo puede alterar la aparición de la primera madurez sexual en las hembras, el periodo de puesta, la fecundidad y las tasas de viabilidad de huevos y larvas.Instituto Español de Oceanografí

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