Weak solutions for Euler systems with non-local interactions

We consider several modi cations of the Euler system of uid dynamics including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension N = 2 ; 3. These models arise in the study of self-organisation in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of in nitely many global-in-time weak solutions for any bounded initial data. Then we consider the class of dissipative solutions satisfying, in addition, the associated global energy balance (inequality). We identify a large set of initial data for which the problem admits in nitely many dissipative weak solutions. Finally, we establish a weak-strong uniqueness principle for the pressure driven Euler system with non-local interaction terms as well as for the pressureless system with Newtonian interaction

Optical determination and identification of organic shells around nanoparticles: application to silver nanoparticles

We present a simple method to prove the presence of an organic shell around silver nanoparticles. This method is based on the comparison between optical extinction measurements of isolated nanoparticles and Mie calculations predicting the expected wavelength of the Localized Surface Plasmon Resonance of the nanoparticles with and without the presence of an organic layer. This method was applied to silver nanoparticles which seemed to be well protected from oxidation. Further experimental characterization via Surface Enhanced Raman Spectroscopy (SERS) measurements allowed to identify this protective shell as ethylene glycol. Combining LSPR and SERS measurements could thus give proof of both presence and identification for other plasmonic nanoparticles surrounded by organic shells

Generalized Wasserstein distance and its application to transport equations with source

In this article, we generalize the Wasserstein distance to measures with different masses. We study the properties of such distance. In particular, we show that it metrizes weak convergence for tight sequences. We use this generalized Wasserstein distance to study a transport equation with source, in which both the vector field and the source depend on the measure itself. We prove existence and uniqueness of the solution to the Cauchy problem when the vector field and the source are Lipschitzian with respect to the generalized Wasserstein distance

Accommodation functions: co-dependency and relationship to refractive error

We assessed the extent to which different accommodative functions are correlated and whether accommodative functions predict the refractive error or the progression of myopia over a 12 month period in 64 young adults (30 myopes and 34 non-myopes). The functions were: amplitude of accommodation; monocular and binocular accommodative facility (6 m and 40 cm); monocular and binocular accommodative response to target distance; AC/A and CA/C ratios, tonic accommodation (dark focus and pinhole), accommodative hysteresis, and nearwork-induced transient myopia. Within groups of related accommodative functions (such as facility measures or open-loop measures) measurements on individuals were generally significantly correlated, however correlations between functions from different groups were generally not significant. Although accommodative amplitude and pinhole (open loop) accommodation were significantly different in myopes than in non-myopes, these functions were unrelated to myopia progression. Facility of accommodation and accommodative lag was independent predictors of myopia progression

Icebergs in the North Atlantic: Modelling circulation changes and glacio-marine deposition

In order to investigate meltwater events in the North Atlantic, a simple iceberg generation, drift, and melting routine was implemented in a high-resolution OGCM. Starting from the modelled last glacial state, every 25th day cylindrical model icebergs 300 meters high were released at 32 specific points along the coasts. Icebergs launched at the Barents Shelf margin spread a light meltwater lid over the Norwegian and Greenland Seas, shutting down the deep convection and the anti-clockwise circulation in this area. Due to the constraining ocean circulation, the icebergs produce a tongue of relatively cold and fresh water extending eastward from Hudson Strait that must develop at this location, regardless of iceberg origin. From the total amount of freshwater inferred by the icebergs, the thickness of the deposited IRD could be calculated in dependance of iceberg sediment concentration. In this way, typical extent and thickness of Heinrich layers could be reproduced, running the model for 250 years of steady state with constant iceberg meltwater inflow

Finite Minds and Open Minds

One of the most persistent complaints about Peter Klein’s infinitism involves the finite mind objection: given that we are finite, how can we ever handle an infinite series of reasons? Klein’s answer has been that we need not actually produce an infinite series; it is enough that such a series be available to us. In this paper a different reply is presented through the reconstruction of epistemic justification as a trade-off. In acting as responsible agents, we are striking a balance between the number of reasons that we can handle and the level of precision that we want our beliefs to have. If we are unable or unwilling to manage a large number of reasons, then we have to pay the price in terms of justificatory inexactitude and thereby of accepting relatively untrustworthy beliefs. As well as being intuitively attractive, this idea of a trade-off is warranted by the mathematics of epistemic justification, understood as involving probabilistic relations

Developmental changes in the balance of disparity, blur and looming/proximity cues to drive ocular alignment and focus

Accurate co-ordination of accommodation and convergence is necessary to view near objects and develop fine motor co-ordination. We used a remote haploscopic videorefraction paradigm to measure longitudinal changes in simultaneous ocular accommodation and vergence to targets at different depths, and to all combinations of blur, binocular disparity, and change-in-size (“proximity”) cues. Infants were followed longitudinally and compared to older children and young adults, with the prediction that sensitivity to different cues would change during development. Mean infant responses to the most naturalistic condition were similar to those of adults from 6-7 weeks (accommodation) and 8-9 weeks (vergence). Proximity cues influenced responses most in infants less than 14 weeks of age, but sensitivity declined thereafter. Between 12-28 weeks of age infants were equally responsive to all three cues, while in older children and adults manipulation of disparity resulted in the greatest changes in response. Despite rapid development of visual acuity (thus increasing availability of blur cues), responses to blur were stable throughout development. Our results suggest that during much of infancy, vergence and accommodation responses are not dependent on the development of specific depth cues, but make use of any cues available to drive appropriate changes in response