114,036 research outputs found
Motions in liquid-vapour interfaces by using a continuous mechanical model
By using a limit analysis for the motion equations of viscous fluid endowed
with internal capillarity, we are able to propose a dynamical expression for
the surface tension of moving liquid-vapour interfaces without any
phenomenological assumption. The proposed relation extends the static case,
yields the Laplace formula in cases of mass transfer across interfacial layers
and allows to take the second coefficient of viscosity of compressible fluids
into account. We generalize the Maxwell rule in dynamics and directly explain
the Marangoni effect.Comment: 15 page
Continuum mechanics at nanoscale. A tool to study trees' watering and recovery
The cohesion-tension theory expounds the crude sap ascent thanks to the
negative pressure generated by evaporation of water from leaves. Nevertheless,
trees pose multiple challenges and seem to live in unphysical conditions: the
negative pressure increases cavitation; it is possible to obtain a water
equilibrium between connected parts where one is at a positive pressure and the
other one is at negative pressure; no theory is able to satisfactorily account
for the refilling of vessels after embolism events. A theoretical form of our
paper in the Journal of Theoretical Biology is proposed together with new
results: a continuum mechanics model of the disjoining pressure concept refers
to the Derjaguin School of physical chemistry. A comparison between liquid
behaviour both in tight-filled microtubes and in liquid thin-films is offered
when the pressure is negative in liquid bulks and is positive in liquid
thin-films and vapour bulks. In embolized xylem microtubes, when the air-vapour
pocket pressure is greater than the air-vapour bulk pressure, a refilling flow
occurs between the air-vapour domains to empty the air-vapour pockets although
the liquid-bulk pressure remains negative. The model has a limit of validity
taking the maximal size of trees into account. These results drop inkling that
the disjoining pressure is an efficient tool to study biological liquids in
contact with substrates at a nanoscale range.Comment: The paper is a review and overlap of my different papers about the
watering of trees as a mathematical development of my paper in The Journal of
Theoretical Biology. These results are presented together with new
researches: transfer of liquid water and vapour between xylem microtubes, an
explanation of ultrasounds generated in the watering network considered as
sound pipes, numerical calculations of flows in thin liquid films and of
Poiseuille flows in xylem microtubes, an estimation of the velocity for the
ascent of crude sap and of the recovery time of trees during the spring
perio
Trimness of Closed Intervals in Cambrian Semilattices
In this article, we give a short algebraic proof that all closed intervals in
a -Cambrian semilattice are trim for any Coxeter
group and any Coxeter element . This means that if such an
interval has length , then there exists a maximal chain of length
consisting of left-modular elements, and there are precisely join- and
meet-irreducible elements in this interval. Consequently every graded interval
in is distributive. This problem was open for any
Coxeter group that is not a Weyl group.Comment: Final version. The contents of this paper were formerly part of my
now withdrawn submission arXiv:1312.4449. 12 pages, 3 figure
Electronic correlations, Jahn-Teller distortions and Mott transition to superconductivity in alkali-C60 compounds
The discovery in 1991 of high temperature superconductivity (SC) in A3C60
compounds, where A is an alkali ion, has been rapidly ascribed to a BCS
mechanism, in which the pairing is mediated by on ball optical phonon modes.
While this has lead to consider that electronic correlations were not important
in these compounds, further studies of various AnC60 with n=1, 2, 4 allowed to
evidence that their electronic properties cannot be explained by a simple
progressive band filling of the C60 six-fold degenerate t1u molecular level.
This could only be ascribed to the simultaneous influence of electron
correlations and Jahn-Teller Distortions (JTD) of the C60 ball, which
energetically favour evenly charged C60 molecules. This is underlined by the
recent discovery of two expanded fulleride Cs3C60 isomeric phases which are
Mott insulators at ambient pressure. Both phases undergo a pressure induced
first order Mott transition to SC with a (p, T) phase diagram displaying a dome
shaped SC, a common situation encountered nowadays in correlated electron
systems. NMR experiments allowed us to study the magnetic properties of the
Mott phases and to evidence clear deviations from BCS expectations near the
Mott transition. So, although SC involves an electron-phonon mechanism, the
incidence of electron correlations has an importance on the electronic
properties, as had been anticipated from DMFT calculations.Comment: Small review article 10 pages, 12 figures. Talk given at the 2011
Eurasia-Pacific Summer School and Conference on Correlated Electrons, in
Tutunc (Turkey
Representation of bi-parameter singular integrals by dyadic operators
We prove a dyadic representation theorem for bi-parameter singular integrals.
That is, we represent certain bi-parameter operators as rapidly decaying
averages of what we call bi-parameter shifts. A new version of the product
space T1 theorem is established as a consequence.Comment: 26 page
Existence and properties of p-tupling fixed points
We prove the existence of fixed points of p-tupling renormalization operators
for interval and circle mappings having a critical point of arbitrary real
degree r > 1. Some properties of the resulting maps are studied: analyticity,
univalence, behavior as tends to infinity.Comment: LaTeX 2
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