12 research outputs found
High-frequency dynamics of wave localisation
We study the effect of localisation on the propagation of a pulse through a
multi-mode disordered waveguide. The correlator of the
transmitted wave amplitude u at two frequencies differing by delta_omega has
for large delta_omega the stretched exponential tail ~exp(-sqrt{tau_D
delta_omega/2}). The time constant tau_D=L^2/D is given by the diffusion
coefficient D, even if the length L of the waveguide is much greater than the
localisation length xi. Localisation has the effect of multiplying the
correlator by a frequency-independent factor exp(-L/2xi), which disappears upon
breaking time-reversal symmetry.Comment: 3 pages, 1 figur
Clustering dynamics of Lagrangian tracers in free-surface flows
We study the formation of clusters of passive Lagrangian tracers in a
non-smooth turbulent flow in a flat free-slip surface as a model for particle
dynamics on free surfaces. Single particle and pair dispersion show different
behavior for short and large times: on short times particles cluster
exponentially rapidly until patches of the size of the divergence correlation
length are depleted; on larger times the pair dispersion is dominated by almost
ballistic hopping between clusters. We also find that the distribution of
particle density is close to algebraic and can trace this back to the
exponential distribution of the divergence field of the surface flow.Comment: 5 pages, 5 Postscript figure
The clustering instability of inertial particles spatial distribution in turbulent flows
A theory of clustering of inertial particles advected by a turbulent velocity
field caused by an instability of their spatial distribution is suggested. The
reason for the clustering instability is a combined effect of the particles
inertia and a finite correlation time of the velocity field. The crucial
parameter for the clustering instability is a size of the particles. The
critical size is estimated for a strong clustering (with a finite fraction of
particles in clusters) associated with the growth of the mean absolute value of
the particles number density and for a weak clustering associated with the
growth of the second and higher moments. A new concept of compressibility of
the turbulent diffusion tensor caused by a finite correlation time of an
incompressible velocity field is introduced. In this model of the velocity
field, the field of Lagrangian trajectories is not divergence-free. A mechanism
of saturation of the clustering instability associated with the particles
collisions in the clusters is suggested. Applications of the analyzed effects
to the dynamics of droplets in the turbulent atmosphere are discussed. An
estimated nonlinear level of the saturation of the droplets number density in
clouds exceeds by the orders of magnitude their mean number density. The
critical size of cloud droplets required for clusters formation is more than
m.Comment: REVTeX 4, 15 pages, 2 figures(included), PRE submitte
Fokker-Planck equations and density of states in disordered quantum wires
We propose a general scheme to construct scaling equations for the density of
states in disordered quantum wires for all ten pure Cartan symmetry classes.
The anomalous behavior of the density of states near the Fermi level for the
three chiral and four Bogoliubov-de Gennes universality classes is analysed in
detail by means of a mapping to a scaling equation for the reflection from a
quantum wire in the presence of an imaginary potential.Comment: 10 pages, 5 figures, revised versio
Bistability driven by white shot noise
We consider mean-first-passage times and transition rates in bistable systems driven by white shot noise. We obtain closed analytical expressions, asymptotic approximations, and numerical simulations in two cases of interest: (i) jumps sizes exponentially distributed and (ii) jumps of the same size