3,441 research outputs found
A flow-pattern map for phase separation using the Navier-Stokes Cahn-Hilliard model
We use the Navier-Stokes-Cahn-Hilliard model equations to simulate phase
separation with flow. We study coarsening - the growth of extended domains
wherein the binary mixture phase separates into its component parts. The
coarsening is characterized by two competing effects: flow, and the
Cahn-Hilliard diffusion term, which drives the phase separation. Based on
extensive two-dimensional direct numerical simulations, we construct a
flow-pattern map outlining the relative strength of these effects in different
parts of the parameter space. The map reveals large regions of parameter space
where a standard theory applies, and where the domains grow algebraically in
time. However, there are significant parts of the parameter space where the
standard theory does not apply. In one region, corresponding to low values of
viscosity and diffusion, the coarsening is accelerated compared to the standard
theory. Previous studies involving Stokes flow report on this phenomenon; we
complete the picture by demonstrating that this anomalous regime occurs not
only for Stokes flow, but also, for flows dominated by inertia. In a second
region, corresponding to arbitrary viscosities and high Cahn-Hilliard
diffusion, the diffusion overwhelms the hydrodynamics altogether, and the
latter can effectively be ignored, in contrast to the prediction of the
standard scaling theory. Based on further high-resolution simulations in three
dimensions, we find that broadly speaking, the above description holds there
also, although the formation of the anomalous domains in the
low-viscosity-low-diffusion part of the parameter space is delayed in three
dimensions compared to two.Comment: 17 pages, 13 figure
Introduction of longitudinal and transverse Lagrangian velocity increments in homogeneous and isotropic turbulence
Based on geometric considerations, longitudinal and transverse Lagrangian
velocity increments are introduced as components along, and perpendicular to,
the displacement of fluid particles during a time scale {\tau}. It is argued
that these two increments probe preferentially the stretching and spinning of
material fluid elements, respectively. This property is confirmed (in the limit
of vanishing {\tau}) by examining the variances of these increments conditioned
on the local topology of the flow. Interestingly, these longitudinal and
transverse Lagrangian increments are found to share some qualitative features
with their Eulerian counterparts. In particular, direct numerical simulations
at turbulent Reynolds number up to 300 show that the distributions of the
longitudinal increment are negatively skewed at all {\tau}, which is a
signature of time irreversibility of turbulence in the Lagrangian framework.
Transverse increments are found more intermittent than longitudinal increments,
as quantified by the comparison of their respective flatnesses and scaling
laws. Although different in nature, standard Lagrangian increments (projected
on fixed axis) exhibit scaling properties that are very close to transverse
Lagrangian increments
Small-scale anisotropy induced by spectral forcing and by rotation in non-helical and helical turbulence
We study the effect of large-scale spectral forcing on the scale-dependent
anisotropy of the velocity field in direct numerical simulations of homogeneous
incompressible turbulence. Two forcing methods are considered: the steady ABC
single wavenumber scheme and the unsteady non-helical or helical Euler scheme.
The results are also compared with high resolution data obtained with the
negative viscosity scheme. A fine-grained characterization of anisotropy,
consisting in measuring some quantities related to the two-point velocity
correlations, is used: we perform a modal decomposition of the spectral
velocity tensor into energy, helicity and polarization spectra. Moreover, we
include the explicit dependence of these three spectra on the wavevector
direction. The conditions that allow anisotropy to develop in the small scales
due to forcing alone are clearly identified. It is shown that, in turbulent
flows expected to be isotropic, the ABC forcing yields significant energy and
helicity directional anisotropy down to the smallest resolved scales, like the
helical Euler scheme when an unfavourable forcing scale is used. The
direction-and scale-dependent anisotropy is then studied in rotating
turbulence. It is first shown that, in the ABC-forced simulations the slope of
the energy spectrum is altered and the level of anisotropy is similar to that
obtained at lower Rossby number in Euler-forced runs, a result due both to the
nature of the forcing itself and to the fact that it allows an inverse cascade
to develop. Second, we show that, even at low rotation rate, the natural
anisotropy induced by the Coriolis force is visible at all scales. Finally, we
identify two different wavenumber ranges in which anisotropy behaves
differently, and show that if the Rossby number is not too low the
characteristic lenghscale separating them is the one at which rotation and
dissipation effects balance
Recent Fluid Deformation closure for velocity gradient tensor dynamics in turbulence: time-scale effects and expansions
In order to model pressure and viscous terms in the equation for the
Lagrangian dynamics of the velocity gradient tensor in turbulent flows,
Chevillard & Meneveau (Phys. Rev. Lett. 97, 174501, 2006) introduced the Recent
Fluid Deformation closure. Using matrix exponentials, the closure allows to
overcome the unphysical finite-time blow-up of the well-known Restricted Euler
model. However, it also requires the specification of a decorrelation time
scale of the velocity gradient along the Lagrangian evolution, and when the
latter is chosen too short (or, equivalently, the Reynolds number is too high),
the model leads to unphysical statistics. In the present paper, we explore the
limitations of this closure by means of numerical experiments and analytical
considerations. We also study the possible effects of using time-correlated
stochastic forcing instead of the previously employed white-noise forcing.
Numerical experiments show that reducing the correlation time scale specified
in the closure and in the forcing does not lead to a commensurate reduction of
the autocorrelation time scale of the predicted evolution of the velocity
gradient tensor. This observed inconsistency could explain the unrealistic
predictions at increasing Reynolds numbers.We perform a series expansion of the
matrix exponentials in powers of the decorrelation time scale, and we compare
the full original model with a linearized version. The latter is not able to
extend the limits of applicability of the former but allows the model to be
cast in terms of a damping term whose sign gives additional information about
the stability of the model as function of the second invariant of the velocity
gradient tensor.Comment: 11 pages, 14 figures, submitted to the special issue "Fluids and
Turbulence" of Physica
Flow-parametric regulation of shear-driven phase separation in two and three dimensions
The Cahn-Hilliard equation with an externally-prescribed chaotic shear flow
is studied in two and three dimensions. The main goal is to compare and
contrast the phase separation in two and three dimensions, using
high-resolution numerical simulation as the basis for the study. The model flow
is parametrized by its amplitudes (thereby admitting the possibility of
anisotropy), lengthscales, and multiple time scales, and the outcome of the
phase separation is investigated as a function of these parameters as well as
the dimensionality. In this way, a parameter regime is identified wherein the
phase separation and the associated coarsening phenomenon are not only arrested
but in fact the concentration variance decays, thereby opening up the
possibility of describing the dynamics of the concentration field using the
theories of advection diffusion. This parameter regime corresponds to long flow
correlation times, large flow amplitudes and small diffusivities. The onset of
this hyperdiffusive regime is interpreted by introducing Batchelor
lengthscales. A key result is that in the hyperdiffusive regime, the
distribution of concentration (in particular, the frequency of extreme values
of concentration) depends strongly on the dimensionality. Anisotropic scenarios
are also investigated: for scenarios wherein the variance saturates
(corresponding to coarsening arrest), the direction in which the domains align
depends on the flow correlation time. Thus, for correlation times comparable to
the inverse of the mean shear rate, the domains align in the direction of
maximum flow amplitude, while for short correlation times, the domains
initially align in the opposite direction. However, at very late times (after
the passage of thousands of correlation times), the fate of the domains is the
same regardless of correlation time, namely alignment in the direction of
maximum flow amplitude.Comment: 27 pages, 14 figure
Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states
A simplified thermodynamic approach of the incompressible 2D Euler equation
is considered based on the conservation of energy, circulation and microscopic
enstrophy. Statistical equilibrium states are obtained by maximizing the
Miller-Robert-Sommeria (MRS) entropy under these sole constraints. The
vorticity fluctuations are Gaussian while the mean flow is characterized by a
linear relationship. Furthermore, the maximization of
entropy at fixed energy, circulation and microscopic enstrophy is equivalent to
the minimization of macroscopic enstrophy at fixed energy and circulation. This
provides a justification of the minimum enstrophy principle from statistical
mechanics when only the microscopic enstrophy is conserved among the infinite
class of Casimir constraints. A new class of relaxation equations towards the
statistical equilibrium state is derived. These equations can provide an
effective description of the dynamics towards equilibrium or serve as numerical
algorithms to determine maximum entropy or minimum enstrophy states. We use
these relaxation equations to study geometry induced phase transitions in
rectangular domains. In particular, we illustrate with the relaxation equations
the transition between monopoles and dipoles predicted by Chavanis and Sommeria
[J. Fluid. Mech. 314, 267 (1996)]. We take into account stable as well as
metastable states and show that metastable states are robust and have negative
specific heats. This is the first evidence of negative specific heats in that
context. We also argue that saddle points of entropy can be long-lived and play
a role in the dynamics because the system may not spontaneously generate the
perturbations that destabilize them.Comment: 26 pages, 10 figure
The Origin of Tomb Painting in Etruria
Tomb paintings and other artistic categories such as stone sculpture had their origin in Etruria in the second quarter of the 7th century BC, when local elites received goods and customs from several regions of the Eastern Mediterranean. Near Eastern and Greek craftsmen migrated to Etruria from at least the end of 8th century BC and influenced the style of Etruscan art, which also developed from local Iron Age roots. The earliest paintings are concentrated in Veii and Caere in Southern Etruria, where they were used to emphasize architectural elements and to depict animals, perhaps with a symbolic meaning
Le mélanome et les polymorphismes associés au dysfonctionnement du système immunitaire
La recherche biomédicale profite de plus en plus au développement des techniques de séquençage et d'analyse de l'ADN. Les coûts du séquençage ont drastiquement baissés au cours de ces dernières années et les genomes-wides associations studies (GWAS) ont révolutionné l'approche de la recherche génétique en mettant en évidence associations et single-nucleotide-polymorphisms (SNPs) qui pourraient être importantes pour la susceptibilité à développer des maladies dites communes.
La majorité des cancers appartiennent à cette définition de maladie commune, ils sont généralement causés par une accumulation de lésions/mutations de l'ADN aboutissant à une perte de contrôle de la prolifération et du cycle cellulaire. Ces mutations peuvent être héréditaires, acquises ou une combinaison des deux. Dans la plupart des cancers communs (cancers qui n'ont pas une hérédité familiale importante) les mutations de l'ADN sont souvent amenées par des facteurs tels que inflammation chronique, tabac, virus, exposition aux radiations, aux agents chimiques. Ceci est le cas pour le mélanome également, un cancer de la peau qui est corrélé à l'exposition des rayons UV solaires ou artificiels.
Une hypothèse largement acceptée aujourd'hui est que les tumeurs, à travers leur accumulation progressive de mutations somatiques et d'anomalies chromosomiques, finissent par échapper au contrôle exercé par le système immunitaire. Il est par conséquence imaginable que des polymorphismes naturels puissent renforcer ou affaiblir la capacité du système immunitaire à freiner voir arrêter la progression tumorale
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