122 research outputs found
Extreme events in discrete nonlinear lattices
We perform statistical analysis on discrete nonlinear waves generated though
modulational instability in the context of the Salerno model that interpolates
between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable
discrete nonlinear Schrodinger (DNLS) equation. We focus on extreme events in
the form of discrete rogue or freak waves that may arise as a result of rapid
coalescence of discrete breathers or other nonlinear interaction processes. We
find power law dependence in the wave amplitude distribution accompanied by an
enhanced probability for freak events close to the integrable limit of the
equation. A characteristic peak in the extreme event probability appears that
is attributed to the onset of interaction of the discrete solitons of the AL
equation and the accompanied transition from the local to the global
stochasticity monitored through the positive Lyapunov exponent of a nonlinear
map.Comment: 5 pages, 4 figures; reference added, figure 2 correcte
Structure of plastically compacting granular packings
The developing structure in systems of compacting ductile grains were studied
experimentally in two and three dimensions. In both dimensions, the peaks of
the radial distribution function were reduced, broadened, and shifted compared
with those observed in hard disk- and sphere systems. The geometrical
three--grain configurations contributing to the second peak in the radial
distribution function showed few but interesting differences between the
initial and final stages of the two dimensional compaction. The evolution of
the average coordination number as function of packing fraction is compared
with other experimental and numerical results from the literature. We conclude
that compaction history is important for the evolution of the structure of
compacting granular systems.Comment: 12 pages, 12 figure
Role of friction-induced torque in stick-slip motion
We present a minimal quasistatic 1D model describing the kinematics of the
transition from static friction to stick-slip motion of a linear elastic block
on a rigid plane. We show how the kinematics of both the precursors to
frictional sliding and the periodic stick-slip motion are controlled by the
amount of friction-induced torque at the interface. Our model provides a
general framework to understand and relate a series of recent experimental
observations, in particular the nucleation location of micro-slip instabilities
and the build up of an asymmetric field of real contact area.Comment: 6 pages, 5 figure
On the modulation instability development in optical fiber systems
Extensive numerical simulations were performed to investigate all stages of
modulation instability development from the initial pulse of pico-second
duration in photonic crystal fiber: quasi-solitons and dispersive waves
formation, their interaction stage and the further propagation. Comparison
between 4 different NLS-like systems was made: the classical NLS equation, NLS
system plus higher dispersion terms, NLS plus higher dispersion and
self-steepening and also fully generalized NLS equation with Raman scattering
taken into account. For the latter case a mechanism of energy transfer from
smaller quasi-solitons to the bigger ones is proposed to explain the dramatical
increase of rogue waves appearance frequency in comparison to the systems when
the Raman scattering is not taken into account.Comment: 9 pages, 54 figure
Solitary wave interaction in a compact equation for deep-water gravity waves
In this study we compute numerical traveling wave solutions to a compact
version of the Zakharov equation for unidirectional deep-water waves recently
derived by Dyachenko & Zakharov (2011) Furthermore, by means of an accurate
Fourier-type spectral scheme we find that solitary waves appear to collide
elastically, suggesting the integrability of the Zakharov equation.Comment: 8 pages, 5 figures, 23 references. Other author's papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh/ . arXiv admin note:
text overlap with arXiv:1204.288
Landau Damping and Coherent Structures in Narrow-Banded 1+1 Deep Water Gravity Waves
We study the nonlinear energy transfer around the peak of the spectrum of
surface gravity waves by taking into account nonhomogeneous effects. In the
narrow-banded approximation the kinetic equation resulting from a
nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at
the same time the random version of the Benjamin-Feir instability and the
Landau damping phenomenon. We analytically derive the values of the Phillips'
constant and the enhancement factor for which the
narrow-banded approximation of the JONSWAP spectrum is unstable. By performing
numerical simulations of the nonlinear Schr\"{o}dinger equation we check the
validity of the prediction of the related kinetic equation. We find that the
effect of Landau damping is to suppress the formation of coherent structures.
The problem of predicting freak waves is briefly discussed.Comment: 4 pages, 3 figure
Hamiltonian form and solitary waves of the spatial Dysthe equations
The spatial Dysthe equations describe the envelope evolution of the
free-surface and potential of gravity waves in deep waters. Their Hamiltonian
structure and new invariants are unveiled by means of a gauge transformation to
a new canonical form of the evolution equations. An accurate Fourier-type
spectral scheme is used to solve for the wave dynamics and validate the new
conservation laws, which are satisfied up to machine precision. Traveling waves
are numerically constructed using the Petviashvili method. It is shown that
their collision appears inelastic, suggesting the non-integrability of the
Dysthe equations.Comment: 6 pages, 9 figures. Other author's papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
Localized instabilities of the Wigner equation as a model for the emergence of Rogue Waves
In this paper, we model Rogue Waves as localized instabilities emerging from homogeneous and stationary background wavefields, under NLS dynamics. This is achieved in two steps: given any background Fourier spectrum P(k), we use the Wigner transform and Penrose’s method to recover spatially periodic unstable modes, which we call unstable Penrose modes. These can be seen as generalized Benjamin–Feir modes, and their parameters are obtained by resolving the Penrose condition, a system of nonlinear equations involving P(k). Moreover, we show how the superposition of unstable Penrose modes can result in the appearance of localized unstable modes. By interpreting the appearance of an unstable mode localized in an area not larger than a reference wavelength λ0 as the emergence of a Rogue Wave, a criterion for the emergence of Rogue Waves is formulated. Our methodology is applied to δ spectra, where the standard Benjamin–Feir instability is recovered, and to more general spectra. In that context, we present a scheme for the numerical resolution of the Penrose condition and estimate the sharpest possible localization of unstable modes. Keywords: Rogue Waves; Wigner equation; Nonlinear Schrodinger equation; Penrose modes; Penrose conditio
Vlasov simulations of electron acceleration by radio frequency heating near the upper hybrid layer
It is shown by using a combination of Vlasov and test particles simulations that the electron distribution function resulting from energization due to Upper Hybrid (UH) plasma turbulence depends critically on the closeness of the pump wave to the double resonance, defined as omega≈omega_UH≈n omega_ce where n is an integer. For pump frequencies, away from the double resonance the electron distribution function is very close to Maxwellian, while as the pump frequency approaches the double resonance it develops a high energy tail. The simulations show turbulence involving coupling between Lower Hybrid (LH) and UH waves, followed by excitation of Electron Bernstein (EB) modes. For the particular case of a pump with frequency between n=3 and n=4 the EB modes cover the range from the first to the 5th mode. The simulations show that when the injected wave frequency is between the 3rd and 4th electron cyclotron frequency, bulk electron heating occurs due to the interaction between the electrons and large amplitude EB waves, primarily on the first EB branch leading to an essentially thermal distribution. On the other hand, when the frequency is slightly above the 4th electron cyclotron harmonic, the resonant interaction is predominantly due to the UH branch and leads to a further acceleration of high-velocity electrons and a distribution function with a suprathermal tail of energetic electrons. The results are consistent with ionospheric experiments and relevant to the production of Artificial Ionospheric Plasma Layers
Nonlinear wave interaction in coastal and open seas -- deterministic and stochastic theory
We review the theory of wave interaction in finite and infinite depth. Both of these strands of water-wave research begin with the deterministic governing equations for water waves, from which simplified equations can be derived to model situations of interest, such as the mild slope and modified mild slope equations, the Zakharov equation, or the nonlinear Schr\"odinger equation. These deterministic equations yield accompanying stochastic equations for averaged quantities of the sea-state, like the spectrum or bispectrum. We discuss several of these in depth, touching on recent results about the stability of open ocean spectra to inhomogeneous disturbances, as well as new stochastic equations for the nearshore
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