Search results for "Nonlinear"
showing 10 items of 3684 documents
Plasmon-driven Bessel beams
2012
We report on subwavelength diffraction-free beams with grazing propagation in metal-dielectric devices. The nondiffracting beams are resonantly transmitted through the nanostructured medium leading to light confinement and wave amplification around the beam axis.
A thermodynamical model of inhomogeneous superfluid turbulence
2007
In this paper we perform a thermodynamical derivation of a nonlinear hydrodynamical model of inhomogeneous superfluid turbulence. The theory chooses as fundamental fields the density, the velocity, the energy density, the heat flux and the averaged vortex line length per unit volume. The restrictions on the constitutive quantities are derived from the entropy principle, using the Liu method of Lagrange multipliers. The mathematical and physical consequences deduced by the theory are analyzed both in the linear and in the nonlinear regime. Field equations are written and the wave propagation is studied with the aim to describe the mutual interactions between the second sound and the vortex t…
Hydrodynamic equations of anisotropic, polarized and inhomogeneous superfluid vortex tangles
2008
We include the effects of anisotropy and polarization in the hydrodynamics of inhomogeneous vortex tangles, thus generalizing the well known Hall-Vinen-Bekarevich-Khalatnikov equations, which do not take them in consideration. These effects contribute to the mutual friction force ${\bf F}_{ns}$ between normal and superfluid components and to the vortex tension force $\rho_s{\bf T}$. These equations are complemented by an evolution equation for the vortex line density $L$, which takes into account these contributions. These equations are expected to be more suitable than the usual ones for rotating counterflows, or turbulence behind a cylinder, or turbulence produced by a grid of parallel th…
Introduction to Wave Turbulence Formalisms for Incoherent Optical Waves
2016
We provide an introduction to different wave turbulence formalisms describing the propagation of partially incoherent optical waves in nonlinear media. We consider the nonlinear Schrodinger equation as a representative model accounting for a nonlocal or a noninstantaneous nonlinearity, as well as higher-order dispersion effects. We discuss the wave turbulence kinetic equation describing, e.g., wave condensation or wave thermalization through supercontinuum generation; the Vlasov formalism describing incoherent modulational instabilities and the formation of large scale incoherent localized structures in analogy with long-range gravitational systems; and the weak Langmuir turbulence formalis…
Turbulent mixing and dispersion mechanisms over flexible and dense vegetation
2019
The present study investigates flow turbulence and dispersion processes in the presence of flexible and dense vegetation on the bed. The turbulent dispersion coefficients and the terms of the turbulent kinetic energy equation are determined by using data collected in a straight laboratory channel with living vegetation on the bed. Results show that the turbulent integral lengths assume an order of magnitude comparable to the stems’ characteristic dimension independently by the direction and the turbulence assumes an isotropic behavior. The coefficients of dispersion have a trend similar to that of the turbulent lengths and assume low values in the longitudinal, transversal and vertical dire…
Pattern selection in the 2D FitzHugh–Nagumo model
2018
We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.
Two-parameter determinant representation of seventh order rogue wave solutions of the NLS equation
2013
We present a new representation of solutions of focusing nonlinear Schrodinger equation (NLS) equation as a quotient of two determinants. We construct families of quasi-rational solutions of the NLS equation depending on two parameters, a and b. We construct, for the first time, analytical expressions of Peregrine breather of order 7 and multi-rogue waves by deformation of parameters. These expressions make possible to understand the behavior of the solutions. In the case of the Peregrine breather of order 7, it is shown for great values of parameters a or b the appearance of the Peregrine breather of order 5. 35Q55; 37K10
Few Cycle Dissipative Soliton Pulses
2006
We find a novel class of stable dissipative solitary waves with discrete velocities and few cycle temporal duration in a composite medium containing active and passive atoms.
Mixed-Valence Magnetic Molecular Cell for Quantum Cellular Automata: Prospects of Designing Multifunctional Devices through Exploration of Double Exc…
2020
In this article, we propose to use multielectron square-planar mixed-valence (MV) molecules as molecular cells for quantum cellular automata (QCA) devices. As distinguished from previous proposals ...
Long-time dynamics of modulated waves in a nonlinear discrete LC transmission line.
2003
International audience; The long-time dynamics of modulated waves in a nonlinear LC transmission line is investigated. Considering the higher-order nonlinear Schrodinger equation, we define analytically the conditions leading to the instability of modulated waves. We show that two kinds of instabilities may develop in the network depending on the frequency range of the chosen carrier wave and on the magnitude of its initial amplitude, which is confirmed by our numerical simulations. The nonreproducibility of numerical experiments on modulated waves is also considered.