1,181 research outputs found
The predictability problem in systems with an uncertainty in the evolution law
The problem of error growth due to the incomplete knowledge of the evolution
law which rules the dynamics of a given physical system is addressed. Major
interest is devoted to the analysis of error amplification in systems with many
characteristic times and scales. The importance of a proper parameterization of
fast scales in systems with many strongly interacting degrees of freedom is
highlighted and its consequences for the modelization of geophysical systems
are discussed.Comment: 20 pages RevTeX, 6 eps figures (included
Non Asymptotic Properties of Transport and Mixing
We study relative dispersion of passive scalar in non-ideal cases, i.e. in
situations in which asymptotic techniques cannot be applied; typically when the
characteristic length scale of the Eulerian velocity field is not much smaller
than the domain size. Of course, in such a situation usual asymptotic
quantities (the diffusion coefficients) do not give any relevant information
about the transport mechanisms. On the other hand, we shall show that the
Finite Size Lyapunov Exponent, originally introduced for the predictability
problem, appears to be rather powerful in approaching the non-asymptotic
transport properties. This technique is applied in a series of numerical
experiments in simple flows with chaotic behaviors, in experimental data
analysis of drifter and to study relative dispersion in fully developed
turbulence.Comment: 19 RevTeX pages + 8 figures included, submitted on Chaos special
issue on Transport and Mixin
Scaling and universality in turbulent convection
Anomalous correlation functions of the temperature field in two-dimensional
turbulent convection are shown to be universal with respect to the choice of
external sources. Moreover, they are equal to the anomalous correlations of the
concentration field of a passive tracer advected by the convective flow itself.
The statistics of velocity differences is found to be universal, self-similar
and close to Gaussian. These results point to the conclusion that temperature
intermittency in two-dimensional turbulent convection may be traced back to the
existence of statistically preserved structures, as it is in passive scalar
turbulence.Comment: 4 pages, 6 figure
Monotonic Distributive Semilattices
In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; ArgentinaFil: Menchón, MarÃa Paula. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentin
Tumbling of polymers in semidilute solution under shear flow
The tumbling dynamics of individual polymers in semidilute solution is
studied by large-scale non-equilibrium mesoscale hydrodynamic simulations. We
find that the tumbling time is equal to the non-equilibrium relaxation time of
the polymer end-to-end distance along the flow direction and strongly depends
on concentration. In addition, the normalized tumbling frequency as well as the
widths of the alignment distribution functions for a given
concentration-dependent Weissenberg number exhibit a weak concentration
dependence in the cross-over regime from a dilute to a semidilute solution. For
semidilute solutions a universal behavior is obtained. This is a consequence of
screening of hydrodynamic interactions at polymer concentrations exceeding the
overlap concentration
Acceleration statistics of heavy particles in turbulence
We present the results of direct numerical simulations of heavy particle
transport in homogeneous, isotropic, fully developed turbulence, up to
resolution (). Following the trajectories of up
to 120 million particles with Stokes numbers, , in the range from 0.16 to
3.5 we are able to characterize in full detail the statistics of particle
acceleration. We show that: ({\it i}) The root-mean-squared acceleration
sharply falls off from the fluid tracer value already at quite
small Stokes numbers; ({\it ii}) At a given the normalised acceleration
increases with consistently
with the trend observed for fluid tracers; ({\it iii}) The tails of the
probability density function of the normalised acceleration
decrease with . Two concurrent mechanisms lead to the above results:
preferential concentration of particles, very effective at small , and
filtering induced by the particle response time, that takes over at larger
.Comment: 10 pages, 3 figs, 2 tables. A section with new results has been
added. Revised version accepted for pubblication on Journal of Fluid
Mechanic
Intermittency in two-dimensional Ekman-Navier-Stokes turbulence
We study the statistics of the vorticity field in two-dimensional
Navier-Stokes turbulence with a linear Ekman friction. We show that the
small-scale vorticity fluctuations are intermittent, as conjectured by Nam et
al. [Phys. Rev. Lett. vol.84 (2000) 5134]. The small-scale statistics of
vorticity fluctuations coincides with the one of a passive scalar with finite
lifetime transported by the velocity field itself.Comment: 4 pages, 7 figure
On the terminal velocity of sedimenting particles in a flowing fluid
The influence of an underlying carrier flow on the terminal velocity of
sedimenting particles is investigated both analytically and numerically. Our
theoretical framework works for a general class of (laminar or turbulent)
velocity fields and, by means of an ordinary perturbation expansion at small
Stokes number, leads to closed partial differential equations (PDE) whose
solutions contain all relevant information on the sedimentation process. The
set of PDE's are solved by means of direct numerical simulations for a class of
2D cellular flows (static and time dependent) and the resulting phenomenology
is analysed and discussed.Comment: 13 pages, 2 figures, submitted to JP
Nonlinear dynamics of the viscoelastic Kolmogorov flow
The weakly nonlinear regime of a viscoelastic Navier--Stokes fluid is
investigated. For the purely hydrodynamic case, it is known that large-scale
perturbations tend to the minima of a Ginzburg-Landau free-energy functional
with a double-well (fourth-order) potential. The dynamics of the relaxation
process is ruled by a one-dimensional Cahn--Hilliard equation that dictates the
hyperbolic tangent profiles of kink-antikink structures and their mutual
interactions. For the viscoelastic case, we found that the dynamics still
admits a formulation in terms of a Ginzburg--Landau free-energy functional. For
sufficiently small elasticities, the phenomenology is very similar to the
purely hydrodynamic case: the free-energy functional is still a fourth-order
potential and slightly perturbed kink-antikink structures hold. For
sufficiently large elasticities, a critical point sets in: the fourth-order
term changes sign and the next-order nonlinearity must be taken into account.
Despite the double-well structure of the potential, the one-dimensional nature
of the problem makes the dynamics sensitive to the details of the potential. We
analysed the interactions among these generalized kink-antikink structures,
demonstrating their role in a new, elastic instability. Finally, consequences
for the problem of polymer drag reduction are presented.Comment: 26 pages, 17 figures, submitted to The Journal of Fluid Mechanic
Statistical geometry in scalar turbulence
A general link between geometry and intermittency in passive scalar
turbulence is established. Intermittency is qualitatively traced back to events
where tracer particles stay for anomalousy long times in degenerate geometries
characterized by strong clustering. The quantitative counterpart is the
existence of special functions of particle configurations which are
statistically invariant under the flow. These are the statistical integrals of
motion controlling the scalar statistics at small scales and responsible for
the breaking of scale invariance associated to intermittency.Comment: 4 pages, 5 figure
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