5,178 research outputs found
The Incompressible Euler Limit of the Boltzmann Equation with Accommodation Boundary Condition
The convergence of solutions of the incompressible Navier-Stokes equations
set in a domain with boundary to solutions of the Euler equations in the large
Reynolds number limit is a challenging open problem both in 2 and 3 space
dimensions. In particular it is distinct from the question of existence in the
large of a smooth solution of the initial-boundary value problem for the Euler
equations. The present paper proposes three results in that direction. First,
if the solutions of the Navier-Stokes equations satisfy a slip boundary
condition with vanishing slip coefficient in the large Reynolds number limit,
we show by an energy method that they converge to the classical solution of the
Euler equations on its time interval of existence. Next we show that the
incompressible Navier-Stokes limit of the Boltzmann equation with Maxwell's
accommodation condition at the boundary is governed by the Navier-Stokes
equations with slip boundary condition, and we express the slip coefficient at
the fluid level in terms of the accommodation parameter at the kinetic level.
This second result is formal, in the style of [Bardos-Golse-Levermore, J. Stat.
Phys. 63 (1991), 323-344]. Finally, we establish the incompressible Euler limit
of the Boltzmann equation set in a domain with boundary with Maxwell's
accommodation condition assuming that the accommodation parameter is small
enough in terms of the Knudsen number. Our proof uses the relative entropy
method following closely the analysis in [L. Saint-Raymond, Arch. Ration. Mech.
Anal. 166 (2003), 47-80] in the case of the 3-torus, except for the boundary
terms, which require special treatment.Comment: 40 page
Photoferroelectric oxides
Giant photovoltaic effect due to bulk photovoltaic effect observed in
multiferroic BiFeO3 thin films has triggered a renewed interest on
photoferroelectric materials for photovoltaic applications. Tremendous advance
has been done to improve power conversion efficiency (up to up to 8.1%) in
photoferroelectrics via absorption increase using narrow bandgap
ferroelectrics. Other strategies, as it is the more efficient use of
ferroelectric internal electric field, are ongoing. Moreover, as a by-product,
several progress have been also achieved on photostriction that is the
photo-induced deformation phenomenon. Here, we review ongoing and promising
routes to improve ferroelectrics photoresponse
Entropy production and multiple equilibria: the case of the ice-albedo feedback
Nonlinear feedbacks in the Earth System provide mechanisms that can prove
very useful in understanding complex dynamics with relatively simple concepts.
For example, the temperature and the ice cover of the planet are linked in a
positive feedback which gives birth to multiple equilibria for some values of
the solar constant: fully ice-covered Earth, ice-free Earth and an intermediate
unstable solution. In this study, we show an analogy between a classical
dynamical system approach to this problem and a Maximum Entropy Production
(MEP) principle view, and we suggest a glimpse on how to reconcile MEP with the
time evolution of a variable. It enables us in particular to resolve the
question of the stability of the entropy production maxima. We also compare the
surface heat flux obtained with MEP and with the bulk-aerodynamic formula.Comment: 29 pages, 12 figure
Statistical optimization for passive scalar transport: maximum entropy production vs maximum Kolmogorov-Sinay entropy
We derive rigorous results on the link between the principle of maximum
entropy production and the principle of maximum Kolmogorov-Sinai entropy using
a Markov model of the passive scalar diffusion called the Zero Range Process.
We show analytically that both the entropy production and the Kolmogorov-Sinai
entropy seen as functions of f admit a unique maximum denoted fmaxEP and
fmaxKS. The behavior of these two maxima is explored as a function of the
system disequilibrium and the system resolution N. The main result of this
article is that fmaxEP and fmaxKS have the same Taylor expansion at _rst order
in the deviation of equilibrium. We find that fmaxEP hardly depends on N
whereas fmaxKS depends strongly on N. In particular, for a fixed difference of
potential between the reservoirs, fmaxEP (N) tends towards a non-zero value,
while fmaxKS (N) tends to 0 when N goes to infinity. For values of N typical of
that adopted by Paltridge and climatologists we show that fmaxEP and fmaxKS
coincide even far from equilibrium. Finally, we show that one can find an
optimal resolution N_ such that fmaxEP and fmaxKS coincide, at least up to a
second order parameter proportional to the non-equilibrium uxes imposed to the
boundaries.Comment: Nonlinear Processes in Geophysics (2015
Phase transitions and marginal ensemble equivalence for freely evolving flows on a rotating sphere
The large-scale circulation of planetary atmospheres like that of the Earth
is traditionally thought of in a dynamical framework. Here, we apply the
statistical mechanics theory of turbulent flows to a simplified model of the
global atmosphere, the quasi-geostrophic model, leading to non-trivial
equilibria. Depending on a few global parameters, the structure of the flow may
be either a solid-body rotation (zonal flow) or a dipole. A second order phase
transition occurs between these two phases, with associated spontaneous
symmetry-breaking in the dipole phase. This model allows us to go beyond the
general theory of marginal ensemble equivalence through the notion of Goldstone
modes.Comment: 7 pages, 3 figures; accepted for publication in Physical Review
- …