A Note on the Regularity of Inviscid Shell Model of Turbulence

In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade initiated in \cite{CLT05}. We prove the global existence of weak solutions of the inviscid sabra shell model, and show that these solutions are unique for some short interval of time. In addition, we prove that the solutions conserve the energy, provided that the components of the solution satisfy $|{u_n}| \le C k_n^{-1/3} (\sqrt{n} \log(n+1))^{-1}$, for some positive absolute constant $C$, which is the analogue of the Onsager's conjecture for the Euler's equations. Moreover, we give a Beal-Kato-Majda type criterion for the blow-up of solutions of the inviscid sabra shell model and show the global regularity of the solutions in the ``two-dimensional'' parameters regime

Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion

Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the well-posedness theory of these models. We prove local well-posedness on bounded domains for dimensions $d\geq 2$ and in all of space for $d\geq 3$, the uniqueness being a result previously not known for PKS with degenerate diffusion. We generalize the notion of criticality for PKS and show that subcritical problems are globally well-posed. For a fairly general class of problems, we prove the existence of a critical mass which sharply divides the possibility of finite time blow up and global existence. Moreover, we compute the critical mass for fully general problems and show that solutions with smaller mass exists globally. For a class of supercritical problems we prove finite time blow up is possible for initial data of arbitrary mass.Comment: 31 page

Interaction of vortices in viscous planar flows

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations of the vortices do not depend on the viscosity parameter \nu, and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex system is well-posed on the interval [0,T]. Under these assumptions, we prove that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a superposition of Lamb-Oseen vortices whose centers evolve according to a viscous regularization of the point vortex system. Convergence holds uniformly in time, in a strong topology which allows to give an accurate description of the asymptotic profile of each individual vortex. In particular, we compute to leading order the deformations of the vortices due to mutual interactions. This allows to estimate the self-interactions, which play an important role in the convergence proof.Comment: 39 pages, 1 figur

Mercury release and speciation in chemical looping combustion of coal

In the in situ Gasification Chemical Looping Combustion of coal (iG-CLC), the fuel is gasified in situ in the fuel reactor and gasification products are converted to CO2 and H2O by reaction with the oxygen carrier. This work is the first study on mercury release in Chemical Looping Combustion of coal. The fraction of the mercury in coal vaporized in the fuel reactor depended mainly on the fuel reactor temperature and the coal type. In the fuel reactor, mercury was mainly emitted as Hg0 in the gas phase and the amount increased with the temperature. In the air reactor, mercury was mostly emitted as Hg2+. In a real CLC system, mercury emissions to the atmosphere will decrease compared to conventional combustion as only mercury released in the air reactor will reach the atmosphere. However, measures should be taken to reduce Hg0 in the CO2 stream before the purification and compression steps in order to avoid operational problems.The authors thank the Government of Aragón and La Caixa (2012-GA-LC-076 project) and the Spanish Ministry for Science and Innovation (ENE2010-19550 project) for the financial support. P. Gayán thanks CSIC for the financial support of the project 201180E102. The authors also thank to Alcoa Europe-Alúmina Española S.A. for providing the Fe-enriched sand fraction used in this work. G. Galo is acknowledged for his contribution to the experimental results.Peer reviewe

Late pleistocene sedimentation history of the Shirshov Ridge, Bering Sea

The analysis of the lithology, grain-size distribution, clay minerals, and geochemistry of Upper Pleistocene sediments from the submarine Shirshov Ridge (Bering Sea) showed that the main source area was the Yukon–Tanana terrane of Central Alaska. The sedimentary materials were transported by the Yukon River through Beringia up to the shelf break, where they were entrained by a strong northwestward-flowing sea current. The lithological data revealed several pulses of ice-rafted debris deposition, roughly synchronous with Heinrich events, and periods of weaker bottom-current intensity. Based on the geochemical results, we distinguished intervals of an increase in paleoproductivity and extension of the oxygen minimum zone. The results suggest that there were three stages of deposition driven by glacioeustatic sea-level fluctuations and glacial cycles in Alaska