1,184 research outputs found
Warm turbulence in the Boltzmann equation
We study the single-particle distributions of three-dimensional hard sphere
gas described by the Boltzmann equation. We focus on the steady homogeneous
isotropic solutions in thermodynamically open conditions, i.e. in the presence
of forcing and dissipation. We observe nonequilibrium steady state solution
characterized by a warm turbulence, that is an energy and particle cascade
superimposed on the Maxwell-Boltzmann distribution. We use a dimensional
analysis approach to relate the thermodynamic quantities of the steady state
with the characteristics of the forcing and dissipation terms. In particular,
we present an analytical prediction for the temperature of the system which we
show to be dependent only on the forcing and dissipative scales. Numerical
simulations of the Boltzmann equation support our analytical predictions.Comment: 4 pages, 5 figure
Modulational instability, wave breaking and formation of large scale dipoles in the atmosphere
In the present Letter we use the Direct Numerical Simulation (DNS) of the
Navier-Stokes equation for a two-phase flow (water and air) to study the
dynamics of the modulational instability of free surface waves and its
contribution to the interaction between ocean and atmosphere. If the steepness
of the initial wave is large enough, we observe a wave breaking and the
formation of large scale dipole structures in the air. Because of the multiple
steepening and breaking of the waves under unstable wave packets, a train of
dipoles is released and propagate in the atmosphere at a height comparable with
the wave length. The amount of energy dissipated by the breaker in water and
air is considered and, contrary to expectations, we observe that the energy
dissipation in air is larger than the one in the water. Possible consequences
on the wave modelling and on the exchange of aerosols and gases between air and
water are discussed
Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations
The rogue wave solutions (rational multi-breathers) of the nonlinear
Schrodinger equation (NLS) are tested in numerical simulations of weakly
nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order
solutions from 1 to 5 are considered. A higher accuracy of wave propagation in
space is reached using the modified NLS equation (MNLS) also known as the
Dysthe equation. This numerical modelling allowed us to directly compare
simulations with recent results of laboratory measurements in
\cite{Chabchoub2012c}. In order to achieve even higher physical accuracy, we
employed fully nonlinear simulations of potential Euler equations. These
simulations provided us with basic characteristics of long time evolution of
rational solutions of the NLS equation in the case of near breaking conditions.
The analytic NLS solutions are found to describe the actual wave dynamics of
steep waves reasonably well.Comment: under revision in Physical Review
Electronic screening and correlated superconductivity in carbon nanotubes
A theoretical analysis of the superconductivity observed recently in Carbon
nanotubes is proposed. We argue that ultra-small (diameter )
single wall carbon nanotubes (with transition temperature )
and entirely end-bonded multi-walled ones () can superconduct
by an electronic mechanism, basically the same in both cases. By a Luttinger
liquid -like approach, one finds enhanced superconducting correlations due to
the strong screening of the long-range part of the Coulomb repulsion. Based on
this finding, we perform a detailed analysis on the resulting
Hubbard-like model, and calculate transition temperatures of the same order
of magnitude as the measured ones.Comment: 6 pages, 1 figure, PACS: 71.10.Pm,74.50.+r,71.20.Tx, to appear in
Phys. Rev.
Modulational instability and wave amplification in finite water depth
The modulational instability of a uniform wave train to side band
perturbations is one of the most plausible mechanisms for the generation of
rogue waves in deep water. In a condition of finite water depth, however, the
interaction with the sea floor generates a wave-induced current that
subtracts energy from the wave field and consequently attenuates the
instability mechanism. As a result, a plane wave remains stable under the
influence of collinear side bands for relative depths <i>kh</i> ≤ 1.36 (where <i>k</i>
is the wavenumber of the plane wave and <i>h</i> is the water depth), but it can
still destabilise due to oblique perturbations. Using direct numerical
simulations of the Euler equations, it is here demonstrated that oblique side
bands are capable of triggering modulational instability and eventually
leading to the formation of rogue waves also for <i>kh</i> ≤ 1.36. Results,
nonetheless, indicate that modulational instability cannot sustain a
substantial wave growth for <i>kh</i> < 0.8
On the computation of the Benjamin-Feir Index
Recently it has been shown theoretically, numerically and experimentally that the statistical properties (probability density function of wave amplitude and wave height)of long crested surface gravity waves depend not only on steepness
but also on the Benjamin-Feir Index (BFI), which is the ratio between wave steepness and spectral bandwidth. The computation of this index requires the estimation of a number of parameters such as the spectral bandwidth and the peak frequency. For a given time series or a wave spectrum those parameters can be calculated using different methods, thus leading to different numerical values of the BFI. We analyze different approaches for computing the BFI and, based on numerical experiments with simulated spectra, we outline a unique robust methodology for its computation
- …