10,368 research outputs found
Asymptotic behavior for a viscous Hamilton-Jacobi equation with critical exponent
The large time behavior of non-negative solutions to the viscous
Hamilton-Jacobi equation in the whole space
is investigated for the critical exponent . Convergence
towards a rescaled self-similar solution of the linear heat equation is shown,
the rescaling factor being . The proof relies on the
construction of a one-dimensional invariant manifold for a suitable truncation
of the equation written in self-similar variables.Comment: 17 pages, no figur
Thermal convection in Earth's inner core with phase change at its boundary
Inner core translation, with solidification on one hemisphere and melting on
the other, provides a promising basis for understanding the hemispherical
dichotomy of the inner core, as well as the anomalous stable layer observed at
the base of the outer core - the F-layer - which might be sustained by
continuous melting of inner core material. In this paper, we study in details
the dynamics of inner core thermal convection when dynamically induced melting
and freezing of the inner core boundary (ICB) are taken into account. If the
inner core is unstably stratified, linear stability analysis and numerical
simulations consistently show that the translation mode dominates only if the
viscosity is large enough, with a critical viscosity value, of order Pas, depending on the ability of outer core convection to supply or
remove the latent heat of melting or solidification. If is smaller, the
dynamical effect of melting and freezing is small. Convection takes a more
classical form, with a one-cell axisymmetric mode at the onset and chaotic
plume convection at large Rayleigh number. [...] Thermal convection requires
that a superadiabatic temperature profile is maintained in the inner core,
which depends on a competition between extraction of the inner core internal
heat by conduction and cooling at the ICB. Inner core thermal convection
appears very likely with the low thermal conductivity value proposed by Stacey
& Davis (2007), but nearly impossible with the much higher thermal conductivity
recently put forward. We argue however that the formation of an iron-rich layer
above the ICB may have a positive feedback on inner core convection: it implies
that the inner core crystallized from an increasingly iron-rich liquid,
resulting in an unstable compositional stratification which could drive inner
core convection, perhaps even if the inner core is subadiabatic.Comment: 25 pages, 12 figure
Gaplessness of the Gaffnian
We study the Gaffnian trial wavefunction proposed to describe fractional
quantum Hall correlations at Bose filling factor and Fermi filling
. A family of Hamiltonians interpolating between a hard-core
interaction for which the physics is known and a projector whose ground state
is the Gaffnian is studied in detail. We give evidence for the absence of a gap
by using large-scale exact diagonalizations in the spherical geometry. This is
in agreement with recent arguments based on the fact that this wavefunction is
constructed from a non-unitary conformal field theory. By using the cylinder
geometry, we discuss in detail the nature of the underlying minimal model and
we show the appearance of heterotic conformal towers in the edge energy
spectrum where left and right movers are generated by distinct primary
operators.Comment: 11 pages, 5 figure
Nonclassical radiation from diamond nanocrystals
The quantum properties of the fluorescence light emitted by diamond
nanocrystals containing a single nitrogen-vacancy (NV) colored center is
investigated. We have observed photon antibunching with very low background
light. This system is therefore a very good candidate for the production of
single photon on demand. In addition, we have measured larger NV center
lifetime in nanocrystals than in the bulk, in good agreement with a simple
quantum electrodynamical model.Comment: 8 pages, 5 figures, revised version, to appear in PR
A Constraint Programming Approach for Mining Sequential Patterns in a Sequence Database
Constraint-based pattern discovery is at the core of numerous data mining
tasks. Patterns are extracted with respect to a given set of constraints
(frequency, closedness, size, etc). In the context of sequential pattern
mining, a large number of devoted techniques have been developed for solving
particular classes of constraints. The aim of this paper is to investigate the
use of Constraint Programming (CP) to model and mine sequential patterns in a
sequence database. Our CP approach offers a natural way to simultaneously
combine in a same framework a large set of constraints coming from various
origins. Experiments show the feasibility and the interest of our approach
Multi-Level Modeling of Quotation Families Morphogenesis
This paper investigates cultural dynamics in social media by examining the
proliferation and diversification of clearly-cut pieces of content: quoted
texts. In line with the pioneering work of Leskovec et al. and Simmons et al.
on memes dynamics we investigate in deep the transformations that quotations
published online undergo during their diffusion. We deliberately put aside the
structure of the social network as well as the dynamical patterns pertaining to
the diffusion process to focus on the way quotations are changed, how often
they are modified and how these changes shape more or less diverse families and
sub-families of quotations. Following a biological metaphor, we try to
understand in which way mutations can transform quotations at different scales
and how mutation rates depend on various properties of the quotations.Comment: Published in the Proceedings of the ASE/IEEE 4th Intl. Conf. on
Social Computing "SocialCom 2012", Sep. 3-5, 2012, Amsterdam, N
Civil Wars and International Trade.
This paper analyzes empirically the relationship between civil wars and international trade. We first show that trade destruction due to civil wars is very large and persistent and increases with the severity of the conflict. We then identify two effects that trade can have on the risk of civil conflicts: it may act as a deterrent if trade gains are put at risk during civil wars but it may also act as an insurance if international trade provides a substitute to internal trade during civil wars. We find support for the presence of these two mechanisms and conclude that trade openness may deter the most severe civil wars (those that destroy the largest amount of trade) but may increase the risk of lower scale conflicts.
Experimental study of parametric subharmonic instability for internal waves
Internal waves are believed to be of primary importance as they affect ocean
mixing and energy transport. Several processes can lead to the breaking of
internal waves and they usually involve non linear interactions between waves.
In this work, we study experimentally the parametric subharmonic instability
(PSI), which provides an efficient mechanism to transfer energy from large to
smaller scales. It corresponds to the destabilization of a primary plane wave
and the spontaneous emission of two secondary waves, of lower frequencies and
different wave vectors. Using a time-frequency analysis, we observe the time
evolution of the secondary waves, thus measuring the growth rate of the
instability. In addition, a Hilbert transform method allows the measurement of
the different wave vectors. We compare these measurements with theoretical
predictions, and study the dependence of the instability with primary wave
frequency and amplitude, revealing a possible effect of the confinement due to
the finite size of the beam, on the selection of the unstable mode
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