Search results for "probability"
showing 10 items of 3417 documents
Stable control of pulse speed in parametric three-wave solitons.
2006
International audience; We analyze the control of the propagation speed of three wave packets interacting in a medium with quadratic nonlinearity and dispersion. We find analytical expressions for mutually trapped pulses with a common velocity in the form of a three-parameter family of solutions of the three-wave resonant interaction. The stability of these novel parametric solitons is simply related to the value of their common group velocity.
Stationary and pulsating dissipative light bullets from a collective variable approach
2009
A collective variable approach is used to map domains of existence for (3+1) -dimensional spatiotemporal soliton solutions of a complex cubic-quintic Ginzburg-Landau equation. A rich variety of evolution behaviors, which include stationary and pulsating dissipative soliton dynamics, is revealed. Comparisons between the results obtained by the semianalytical approach of collective variables, and those obtained by a purely numerical approach show good agreement for a wide range of equation parameters. This also demonstrates the relevance of the semianalytical method for a systematic search of stability domains for spatiotemporal solitons, leading to a dramatic reduction of the computation tim…
Temporal dynamics of incoherent waves in noninstantaneous response nonlinear Kerr media
2012
International audience; We consider the temporal evolution of an incoherent optical wave that propagates in a noninstantaneous response nonlinear medium, such as single mode optical fibers. In contrast with the expected Raman-like spectral redshift due to a delayed nonlinear response, we show that a highly noninstantaneous response leads to a genuine modulational instability of the incoherent optical wave. We derive a Vlasov-like kinetic equation that provides a detailed description of this process of incoherent modulational instability in the temporal domain.
Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics
2014
International audience; The nonlinear propagation of coherent optical fields has been extensively explored in the framework of nonlinear optics, while the linear propagation of incoherent fields has been widely studied in the framework of statistical optics. However, these two fundamental fields of optics have been mostly developed independently of each other, so that a satisfactory understanding of statistical nonlinear optics is still lacking. This article is aimed at reviewing a unified theoretical formulation of statistical nonlinear optics on the basis of the wave turbulence theory, which provides a nonequilibrium thermodynamic description of the system of incoherent nonlinear waves. W…
A study on the distribution of the envelope and the capacity of underwater acoustic channels
2014
This paper deals with the statistical analysis of the instantaneous capacity of shallow underwater acoustic communication (UWAC) channels under the assumption that the scatterers are randomly distributed on the surface and bottom of the ocean. We start by deriving exact closed-form expressions for the probability density function (PDF) of the total propagation path length from which the PDF of the path gains is obtained. Then, we study the distributions of the channel envelope and the capacity under line-of-sight (LOS) conditions. By performing the chi-square goodness-of-fit test, it is shown that the channel envelope is Rice distributed. Moreover, we investigate the effect of the ocean dep…
Operation conditions and stability of a degenerate two-photon laser
1993
Abstract The presence of a far off-resonant intermediate level in a degenerate three-level two-photon laser model manifests through a steady pump-dependent and a dynamic frequency shift on the laser equations. The steady shift strongly affects the pump threshold necessary for emission, preventing it in certain cases. The dynamic shift makes the frequency pulling/pushing to be intensity-dependent and substantially modify the domains of existence and stability of the lasing solution permitting stable operation for large cavity losses in certain cases.
Dissipative rogue waves: extreme pulses generated by passively mode-locked lasers.
2011
We study numerically rogue waves in dissipative systems, taking as an example a unidirectional fiber laser in a nonstationary regime of operation. The choice of specific set of parameters allows the laser to generate a chaotic sequence of pulses with a random distribution of peak amplitudes. The probability density function for the intensity maxima has an elevated tail at higher intensities. We have found that the probability of producing extreme pulses in this setup is higher than in any other system considered so far. © 2011 American Physical Society.
Noise-induced effects in population dynamics
2002
We investigate the role of noise in the nonlinear relaxation of two ecosystems described by generalized Lotka-Volterra equations in the presence of multiplicative noise. Specifically we study two cases: (i) an ecosystem with two interacting species in the presence of periodic driving; (ii) an ecosystem with a great number of interacting species with random interaction matrix. We analyse the interplay between noise and periodic modulation for case (i) and the role of the noise in the transient dynamics of the ecosystem in the presence of an absorbing barrier in case (ii). We find that the presence of noise is responsible for the generation of temporal oscillations and for the appearance of s…
High redshift galaxies in the ALHAMBRA survey
2015
Context. Most observational results on the high redshift restframe UV-bright galaxies are based on samples pinpointed using the so called dropout technique or Ly-alpha selection. However, the availability of multifilter data allows now replacing the dropout selections by direct methods based on photometric redshifts. In this paper we present the methodology to select and study the population of high redshift galaxies in the ALHAMBRA survey data. Aims. Our aim is to develop a less biased methodology than the traditional dropout technique to study the high redshift galaxies in ALHAMBRA and other multifilter data. Thanks to the wide area ALHAMBRA covers, we especially aim at contributing in th…
Transient behavior of a population dynamical model
2005
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic dynamical regimes and the role of the external noise on the probability distribution of the local field.