Search results for "pattern"

Deformations of higher order Peregrine breathers and monstrous polynomials.

2013

International audience; In the following, we present two new results about the focusing one dimensional NLS equation : 1. We construct solutions of NLS equation in terms of wronskians. Then performing a special passage to the limit when a parameter tends to 0, we obtain quasi-rational solutions of NLS equation. 2. We construct quasi-rational solutions in terms of determinants without of a limit. Which is new is that we obtain at order N, solutions depending on 2N-2 parameters. 3. When all these parameters are equal to zeros, we recover Peregrine breathers; it is the reason why we call these solutions deformations of Peregrine breathers. \\ Then we deduce new patterns of solutions in the (x,…

Solutions to the NLS equation : differential relations and their different representations

2020

Solutions to the focusing nonlinear Schrödinger equation (NLS) of order N depending on 2N − 2 real parameters in terms of wronskians and Fredholm determinants are given. These solutions give families of quasirational solutions to the NLS equation denoted by vN and have been explicitly constructed until order N = 13. These solutions appear as deformations of the Peregrine breather PN as they can be obtained when all parameters are equal to 0. These quasi rational solutions can be expressed as a quotient of two polynomials of degree N (N + 1) in the variables x and t and the maximum of the modulus of the Peregrine breather of order N is equal to 2N + 1. Here we give some relations between sol…

Families of solutions of order nine to the NLS equation with sixteen parameters

2015

We construct new deformations of the Peregrine breather (P9) of order 9 with 16 real parameters. With this method, we obtain explicitly new families of quasi-rational solutions to the NLS equation in terms of a product of an exponential depending on t by a ratio of two polynomials of degree 90 in x and t; when all the parameters are equal to 0, we recover the classical P9 breather. We construct new patterns of different types of rogue waves as triangular configurations of 45 peaks as well as rings and concentric rings.

Determinant representation of NLS equation, Ninth Peregrine breather and multi-rogue waves

2012

This article is a continuation of a recent paper on the solutions of the focusing NLS equation. The representation in terms of a quotient of two determinants gives a very efficient method of determination of famous Peregrine breathers and its deformations. Here we construct Peregrine breathers of order $N=9$ and multi-rogue waves associated by deformation of parameters. The analytical expression corresponding to Peregrine breather is completely given.

Tenth Peregrine breather solution of the NLS equation.

2012

We go on in this paper, in the study of the solutions of the focusing NLS equation. With a new representation given in a preceding paper, a very compact formulation without limit as a quotient of two determinants, we construct the Peregrine breather of order N=10. The explicit analytical expression of the Akhmediev's solution is completely given.

The role of landscape, topography, and geodiversity in explaining vascular plant species richness in a fragmented landscape

2016

We explained vascular plant species richness patterns in a 286 km(2) fragmented landscape with a notable human influence. The objective of this study was two-fold: to test the relative importance of landscape, topography and geodiversity measures, and to compare three different landscape-type variables in species richness modeling. Moreover, we tested if results differ when only native species are considered. We used generalized linear modeling based variation partitioning and generalized additive models with different explanatory variable sets. Landscape and topography explained the majority of the variation but the relative importance of topography and geodiversity was higher in explainin…

Preliminary study of coach verbal behaviour according to game actions

2012

Guzman JF, Calpe-Gomez V. Preliminary study of coach verbal behaviour according to game actions. J. Hum. Sport Exerc. Vol. 7, No. 2, pp. 376-382, 2012. The aim of this study was to analyse the interaction between game actions in high-level handball and verbal behaviour performed by the coach. For this purpose, a match of the 1 st National Division of male Spanish handball was analysed. The type of behaviour and the content of the message reported by the coach were recorded using a modified version of Coaching Behaviour Assessment System (CBAS) and Coach Analysis and Intervention System (CAIS). About game actions, they were grouped into positive and negative. Statistically significant differ…

ADVANCES IN VEGETABLE GRAFTING AND NEW NURSERY PATTERNS FOR GRAFTED PLANT PRODUCTION

2014

Nanostructuring thin Au films on transparent conductive oxide substrates

2013

Fabrication processes of Au nanostructures on indium-tin-oxide (ITO) surface by simple, versatile, and low-cost bottom-up methodologies are investigated in this work. A first methodology exploits the patterning effects induced by nanosecond laser irradiations on thin Au films deposited on ITO surface. We show that after the laser irradiations, the Au film break-up into nanoclusters whose mean size and surface density are tunable by the laser fluence. A second methodology exploits, instead, the patterning effects of standard furnace thermal processes on the Au film deposited on the ITO. We observe, in this case, a peculiar shape evolution from pre-formed nanoclusters during the Au deposition…

Growth of low-density vertical quantum dot molecules with control in energy emission

2010

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License.-- This article is part of the series 8th International Workshop on Epitaxial Semiconductors on Patterned Substrates and Novel Index Surfaces.