Search results for "Parametric statistics"

Emergence of extreme events in fiber-based nonlinear devices

2010

We review our experimental and theoretical results showing the emergence of rogue events during light propagation in fiber-based nonlinear systems. Distinct statistical properties are underlined through parametric and Raman amplifications, supercontinuum generation and optical turbulence.

Parametric frequency conversion of optical simulton pulses

2007

We present an analytical description of the parametric frequency conversion of short solitary wave optical pulses in quadratic nonlinear crystals controlled by means of a continuous wave background.

Generalized modulational instability in multimode fibers: Wideband multimode parametric amplification

2015

In this paper intermodal modulational instability (IM-MI) is analyzed in a multimode fiber where several spatial and polarization modes propagate. The coupled nonlinear Schr\"odinger equations describing the modal evolution in the fiber are linearized and reduced to an eigenvalue problem. As a result, the amplification of each mode can be described by means of the eigenvalues and eigenvectors of a matrix that stores the information about the dispersion properties of the modes and the modal power distribution of the pump. Some useful analytical formulas are also provided that estimate the modal amplification as function of the system parameters. Finally, the impact of third-order dispersion …

Demonstration of polarization pulling using a fiber-optic parametric amplifier

2012

International audience; We report the observation of all-optical polarization pulling of an initially polarization-scrambled signal using parametric amplification in a highly nonlinear optical fiber. Broadband polarization pulling has been achieved both for the signal and idler waves with up to 25 dB gain using the strong polarization sensitivity of parametric amplifiers. We further derive the probability distribution function for the final polarization state, assuming a randomly polarized initial state, and we show that it agrees well with the experiments.

Nonlinear Resonance Effects in Pattern Formation in Optical Parametric Oscillators

2005

Weibull Prediction Limits for a Future Number of Failures Under Parametric Uncertainty

2012

In this paper, we present an accurate procedure, called “within-sample prediction of order statistics,” to obtain prediction limits for the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the first in-service inspection of the same sample. The failure-time of such units is modeled with a two-parameter Weibull distribution indexed by scale and shape parameters β and δ, respectively. It will be noted that in the literature only the case is considered when the scale parameter β is unknown, but the shape parameter δ is known. As a rule, in practice the Weibull shape parameter δ is not known. Instead it is estimated subjectively …

Design and Digital Fabrication of a Parametric Joint for Bamboo Sustainable Structures

2019

The study deepens the design of a joining system for bamboo spatial structure by proposing new and advanced solutions that guarantee maximum freedom of composition to the designer. The joint allows to determine and control parametrically the adaptability to any spatial grid configuration of culms with heterogeneous dimensions. Despite the bamboo being one of the main natural building materials in the field of sustainable architecture, currently, it is not used enough due to the lack of adequate connection systems. Bamboo is a rapidly growing renewable resource, naturally available, which is quite strong and lends itself to structural applications. The paper proposes an innovative approach t…

Parametric Solitons in Two-Dimensional Lattices of Purely Nonlinear Origin

2008

We demonstrate spatial solitons via twin-beam second-harmonic generation in hexagonal lattices realized by poling lithium niobate planar waveguides. These simultons can be steered by acting on power, direction, and wavelength of the fundamental frequency input.

An Automatic Differentiation Based Approach to the Level Set Method

2015

This paper discusses an implementation of the parametric level set method. Adjoint approach is used to perform the sensitivity analysis, but contrary to standard implementations, the state problem is differentiated in its discretized form. The required partial derivatives are computed using tools of automatic differentiation, which avoids the need to derive the adjoint problem from the governing partial differential equation. The augmented Lagrangian approach is used to enforce volume constraints, and a gradient based optimization method is used to solve the subproblems. Applicability of the method is demonstrated by repeating well known compliance minimization studies of a cantilever beam …

Stochastic ship roll motion via path integral method

2010

ABSTRACTThe response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple …