196 research outputs found

    Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws.

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    We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fractional differentiability of order one-third in the interior of the domain, and if the normal component of the corresponding fluxes tend to zero as one approaches the boundary. This extends various recent results of the authors

    Weak solutions for Euler systems with non-local interactions

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    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

    Generalized Wasserstein distance and its application to transport equations with source

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    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

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

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    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

    Bayesian evidence synthesis to estimate HIV prevalence in men who have sex with men in Poland at the end of 2009.

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    HIV spread in men who have sex with men (MSM) is an increasing problem in Poland. Despite the existence of a surveillance system, there is no direct evidence to allow estimation of HIV prevalence and the proportion undiagnosed in MSM. We extracted data on HIV and the MSM population in Poland, including case-based surveillance data, diagnostic testing prevalence data and behavioural data relating to self-reported prior diagnosis, stratified by age (⩽35, >35 years) and region (Mazowieckie including the capital city of Warsaw; other regions). They were integrated into one model based on a Bayesian evidence synthesis approach. The posterior distributions for HIV prevalence and the undiagnosed fraction were estimated by Markov Chain Monte Carlo methods. To improve the model fit we repeated the analysis, introducing bias parameters to account for potential lack of representativeness in data. By placing additional constraints on bias parameters we obtained precisely identified estimates. This family of models indicates a high undiagnosed fraction [68·3%, 95% credibility interval (CrI) 53·9-76·1] and overall low prevalence (2·3%, 95% CrI 1·4-4·1) of HIV in MSM. Additional data are necessary in order to produce more robust epidemiological estimates. More effort is urgently needed to ensure timely diagnosis of HIV in Poland

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

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    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
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