42 research outputs found
Fluctuating hydrodynamics and turbulence in a rotating fluid: Universal properties
We analyze the statistical properties of three-dimensional () turbulence
in a rotating fluid. To this end we introduce a generating functional to study
the statistical properties of the velocity field . We obtain the master
equation from the Navier-Stokes equation in a rotating frame and thence a set
of exact hierarchical equations for the velocity structure functions for
arbitrary angular velocity . In particular we obtain the {\em
differential forms} for the analogs of the well-known von Karman-Howarth
relation for fluid turbulence. We examine their behavior in the limit of
large rotation. Our results clearly suggest dissimilar statistical behavior and
scaling along directions parallel and perpendicular to . The
hierarchical relations yield strong evidence that the nature of the flows for
large rotation is not identical to pure two-dimensional flows. To complement
these results, by using an effective model in the small- limit, within
a one-loop approximation, we show that the equal-time correlation of the
velocity components parallel to displays Kolmogorov scaling
, where as for all other components, the equal-time correlators scale
as in the inertial range where is a wavevector in . Our
results are generally testable in experiments and/or direct numerical
simulations of the Navier-Stokes equation in a rotating frame.Comment: 24 pages in preprint format; accepted for publication in Phys. Rev. E
(2011
On the Hausdorff dimension of regular points of inviscid Burgers equation with stable initial data
Consider an inviscid Burgers equation whose initial data is a Levy a-stable
process Z with a > 1. We show that when Z has positive jumps, the Hausdorff
dimension of the set of Lagrangian regular points associated with the equation
is strictly smaller than 1/a, as soon as a is close to 1. This gives a negative
answer to a conjecture of Janicki and Woyczynski. Along the way, we contradict
a recent conjecture of Z. Shi about the lower tails of integrated stable
processes
Girls\u27 Education Roadmap: 2021 Report Summary
While insufficient to meet the vast needs, billions of dollars are being invested in girls’ education advocacy, program, and policy solutions around the world. At the same time, hundreds of millions are invested in research about what works in education. And yet, the policies and approaches that are pursued often don’t line up with what researchers find is effective. The result is that governments, international organizations, and NGOs are too often investing scarce resources in policies or interventions without knowing whether they work. As noted in this report summary, the Girls’ Education Roadmap shares insights derived from data in the Evidence for Gender and Education Resource (EGER). The report reviews thousands of studies and assesses hundreds of organizations to figure out who’s doing what, what’s working where, and what are the biggest needs facing girls. The goals were to make sure governments, NGOs, and donors are investing in what works and to make sure researchers are focusing on answering the most urgent questions for the field
Girls\u27 Education Roadmap: 2021 Report
While insufficient to meet the vast needs, billions of dollars are being invested in girls’ education advocacy, program, and policy solutions around the world. At the same time, hundreds of millions are invested in research about what works in education. And yet, the policies and approaches that are pursued often don’t line up with what researchers find is effective. The result is that governments, international organizations, and NGOs are too often investing scarce resources in policies or interventions without knowing whether they work. In partnership with Echidna Giving, the GIRL Center at the Population Council developed the Evidence for Gender and Education Resource (EGER), an interactive online database that practitioners, researchers, donors, and decisionmakers can use to drive better results for girls, boys, and communities around the world. EGER addresses how to ensure that limited resources are invested in the most effective solutions to achieve gender equality in education. The resulting data provide valuable insights into gaps and opportunities for the global girls’ education field, and this report shares those insights
Levy stable distributions via associated integral transform
We present a method of generation of exact and explicit forms of one-sided,
heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x <
\infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a
distribution g_{\alpha}(x) suffices to obtain exactly g_{\alpha^{p}}(x), p=2,
3,... Similarly, from known g_{\alpha}(x) and g_{\beta}(x), 0 < \alpha, \beta <
1, we obtain g_{\alpha \beta}(x). The method is based on the construction of
the integral operator, called Levy transform, which implements the above
operations. For \alpha rational, \alpha = l/k with l < k, we reproduce in this
manner many of the recently obtained exact results for g_{l/k}(x). This
approach can be also recast as an application of the Efros theorem for
generalized Laplace convolutions. It relies solely on efficient definite
integration.Comment: 12 pages, typos removed, references adde
Statistical properties of driven Magnetohydrodynamic turbulence in three dimensions: Novel universality
We analyse the universal properties of nonequilibrium steady states of driven
Magnetohydrodynamic (MHD) turbulence in three dimensions (3d). We elucidate the
dependence of various phenomenologically important dimensionless constants on
the symmetries of the two-point correlation functions. We, for the first time,
also suggest the intriguing possibility of multiscaling universality class
varying continuously with certain dimensionless parameters. The experimental
and theoretical implications of our results are discussed.Comment: To appear in Europhys. Lett. (2004
The global picture of self-similar and not self-similar decay in Burgers Turbulence
This paper continue earlier investigations on the decay of Burgers turbulence
in one dimension from Gaussian random initial conditions of the power-law
spectral type . Depending on the power , different
characteristic regions are distinguished. The main focus of this paper is to
delineate the regions in wave-number and time in which self-similarity
can (and cannot) be observed, taking into account small- and large-
cutoffs. The evolution of the spectrum can be inferred using physical arguments
describing the competition between the initial spectrum and the new frequencies
generated by the dynamics. For large wavenumbers, we always have
region, associated to the shocks. When is less than one, the large-scale
part of the spectrum is preserved in time and the global evolution is
self-similar, so that scaling arguments perfectly predict the behavior in time
of the energy and of the integral scale. If is larger than two, the
spectrum tends for long times to a universal scaling form independent of the
initial conditions, with universal behavior at small wavenumbers. In the
interval the leading behaviour is self-similar, independent of and
with universal behavior at small wavenumber. When , the spectrum
has three scaling regions : first, a region at very small \ms1 with
a time-independent constant, second, a region at intermediate
wavenumbers, finally, the usual region. In the remaining interval,
the small- cutoff dominates, and also plays no role. We find also
(numerically) the subleading term in the evolution of the spectrum
in the interval . High-resolution numerical simulations have been
performed confirming both scaling predictions and analytical asymptotic theory.Comment: 14 pages, 19 figure
Merging and fragmentation in the Burgers dynamics
We explore the noiseless Burgers dynamics in the inviscid limit, the
so-called ``adhesion model'' in cosmology, in a regime where (almost) all the
fluid particles are embedded within point-like massive halos. Following
previous works, we focus our investigations on a ``geometrical'' model, where
the matter evolution within the shock manifold is defined from a geometrical
construction. This hypothesis is at variance with the assumption that the usual
continuity equation holds but, in the inviscid limit, both models agree in the
regular regions. Taking advantage of the formulation of the dynamics of this
``geometrical model'' in terms of Legendre transforms and convex hulls, we
study the evolution with time of the distribution of matter and the associated
partitions of the Lagrangian and Eulerian spaces. We describe how the halo mass
distribution derives from a triangulation in Lagrangian space, while the dual
Voronoi-like tessellation in Eulerian space gives the boundaries of empty
regions with shock nodes at their vertices. We then emphasize that this
dynamics actually leads to halo fragmentations for space dimensions greater or
equal to 2 (for the inviscid limit studied in this article). This is most
easily seen from the properties of the Lagrangian-space triangulation and we
illustrate this process in the two-dimensional (2D) case. In particular, we
explain how point-like halos only merge through three-body collisions while
two-body collisions always give rise to two new massive shock nodes (in 2D).
This generalizes to higher dimensions and we briefly illustrate the
three-dimensional (3D) case. This leads to a specific picture for the
continuous formation of massive halos through successive halo fragmentations
and mergings.Comment: 21 pages, final version published in Phys.Rev.
The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension
We extend the previously developed weak noise scheme, applied to the noisy
Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing
interface in arbitrary dimensions. By means of the Cole-Hopf transformation we
show that the growth morphology can be interpreted in terms of dynamically
evolving textures of localized growth modes with superimposed diffusive modes.
In the Cole-Hopf representation the growth modes are static solutions to the
diffusion equation and the nonlinear Schroedinger equation, subsequently
boosted to finite velocity by a Galilei transformation. We discuss the dynamics
of the pattern formation and, briefly, the superimposed linear modes.
Implementing the stochastic interpretation we discuss kinetic transitions and
in particular the properties in the pair mode or dipole sector. We find the
Hurst exponent H=(3-d)/(4-d) for the random walk of growth modes in the dipole
sector. Finally, applying Derrick's theorem based on constrained minimization
we show that the upper critical dimension is d=4 in the sense that growth modes
cease to exist above this dimension.Comment: 27 pages, 19 eps figs, revte
Weighted ergodic theorems for Banach-Kantorovich lattice
In the present paper we prove weighted ergodic theorems and multiparameter
weighted ergodic theorems for positive contractions acting on
. Our main tool is the use of methods of
measurable bundles of Banach-Kantorovich lattices.Comment: 11 page