8 research outputs found
A fractional Brownian motion model for the turbulent refractive index in lightwave propagation
It is discussed the limitations of the widely used markovian approximation
applied to model the turbulent refractive index in lightwave propagation.
It is well-known the index is a passive scalar field. Thus, the actual
knowledge about these quantities is used to propose an alternative stochastic
process to the markovian approximation: the fractional Brownian motion. This
generalizes the former introducing memory; that is, there is correlation along
the propagation path.Comment: 11 pages, no figures. Submitted and revised for Optics Communication
Canonical quantization of the boundary Wess-Zumino-Witten model
We present an analysis of the canonical structure of the WZW theory with
untwisted conformal boundary conditions. The phase space of the boundary theory
on a strip is shown to coincide with the phase space of the Chern-Simons theory
on a solid cylinder (a disc times a line) with two Wilson lines. This reveals a
new aspect of the relation between two-dimensional boundary conformal field
theories and three-dimensional topological theories. A decomposition of the
Chern-Simons phase space on a punctured disc in terms of the one on a punctured
sphere and of coadjoint orbits of the loop group easily lends itself to
quantization, providing at the same time a quantization of the boundary WZW
model.Comment: 49 pages, latex, 5 figur
Active and passive fields face to face
The statistical properties of active and passive scalar fields transported by
the same turbulent flow are investigated. Four examples of active scalar have
been considered: temperature in thermal convection, magnetic potential in
two-dimensional magnetohydrodynamics, vorticity in two-dimensional Ekman
turbulence and potential temperature in surface flows. In the cases of
temperature and vorticity, it is found that the active scalar behavior is akin
to that of its co-evolving passive counterpart. The two other cases indicate
that this similarity is in fact not generic and differences between passive and
active fields can be striking: in two-dimensional magnetohydrodynamics the
magnetic potential performs an inverse cascade while the passive scalar
cascades toward the small-scales; in surface flows, albeit both perform a
direct cascade, the potential temperature and the passive scalar have different
scaling laws already at the level of low-order statistical objects. These
dramatic differences are rooted in the correlations between the active scalar
input and the particle trajectories. The role of such correlations in the issue
of universality in active scalar transport and the behavior of dissipative
anomalies is addressed.Comment: 36 pages, 20 eps figures, for the published version see
http://www.iop.org/EJ/abstract/1367-2630/6/1/07
Anisotropy in Turbulent Flows and in Turbulent Transport
We discuss the problem of anisotropy and intermittency in statistical theory
of high Reynolds-number turbulence (and turbulent transport). We present a
detailed description of the new tools that allow effective data analysis and
systematic theoretical studies such as to separate isotropic from anisotropic
aspects of turbulent statistical fluctuations. Employing the invariance of the
equations of fluid mechanics to all rotations, we show how to decompose the
(tensorial) statistical objects in terms of the irreducible representation of
the SO(3) symmetry group. For the case of turbulent advection of passive scalar
or vector fields, this decomposition allows rigorous statements to be made: (i)
the scaling exponents are universal, (ii) the isotropic scaling exponents are
always leading, (iii) the anisotropic scaling exponents form a discrete
spectrum which is strictly increasing as a function of the anisotropic degree.
Next we explain how to apply the SO(3) decomposition to the statistical
Navier-Stokes theory. We show how to extract information about the scaling
behavior in the isotropic sector. Doing so furnishes a systematic way to assess
the universality of the scaling exponents in this sector, clarifying the
anisotropic origin of the many measurements that claimed the opposite. A
systematic analysis of Direct Numerical Simulations and of experiments provides
a strong support to the proposition that also for the non-linear problem there
exists foliation of the statistical theory into sectors of the symmetry group.
The exponents appear universal in each sector, and again strictly increasing as
a function of the anisotropic degreee.Comment: 150 pages, 26 figures, submitted to Phys. Re
Quantum matrix algebra for the SU(n) WZNW model
The zero modes of the chiral SU(n) WZNW model give rise to an intertwining
quantum matrix algebra A generated by an n x n matrix a=(a^i_\alpha) (with
noncommuting entries) and by rational functions of n commuting elements
q^{p_i}. We study a generalization of the Fock space (F) representation of A
for generic q (q not a root of unity) and demonstrate that it gives rise to a
model of the quantum universal enveloping algebra U_q(sl_n), each irreducible
representation entering F with multiplicity 1. For an integer level k the
complex parameter q is an even root of unity, q^h=-1 (h=k+n) and the algebra A
has an ideal I_h such that the factor algebra A_h = A/I_h is finite
dimensional.Comment: 48 pages, LaTeX, uses amsfonts; final version to appear in J. Phys.