Search results for "NLS"
showing 10 items of 31 documents
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.
Tenth order solutions to the NLS equation with eighteen parameters
2015
We present here new solutions of the focusing one dimensional non linear Schrödinger equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric as found for the lower orders.
Statistica o fortuna ? Un modo per vincere giocando a dadi…
2018
Statistics or luck ? A way to win by playing dice ... · The paper describes a didactic activity included in the National Scientific Graduation Plan (PNLS) realized in a Scientific College of Palermo. The aims are to underline the importance of Statistics skills owned by citizen and students in Italy and to support them for a good choice of the university course. This paper describes a didactic path of 60 hours where 18 hours are dedicated to an interaction with the teacher, to improve the Statistic skills in the students.
The fifth order Peregrine breather and its eight-parameters deformations solutions of the NLS equation.
2013
We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters. This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.
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…
Molecular determinants of large cargo transport into the nucleus
2020
Nucleocytoplasmic transport is tightly regulated by the nuclear pore complex (NPC). Among the thousands of molecules that cross the NPC, even very large (>15 nm) cargoes such as pathogens, mRNAs and pre-ribosomes can pass the NPC intact. For these cargoes, there is little quantitative understanding of the requirements for their nuclear import, especially the role of multivalent binding to transport receptors via nuclear localisation sequences (NLSs) and the effect of size on import efficiency. Here, we assayed nuclear import kinetics of 30 large cargo models based on four capsid-like particles in the size range of 17–36 nm, with tuneable numbers of up to 240 NLSs. We show that the requireme…
Multi-rogue solutions to the focusing NLS equation
2010
The study of rogue waves is a booming topic mainly in oceanography but also in other fields. In this thesis I construct via Darboux transform a multi-parametric family of smooth quasi-rational solutions of the nonlinear Schödinger equation that present a behavior of rogue waves. For a general choice of parameters the second-order solutions give a model of "three sisters" (three higher than expected waves in a row) while for a particular choice of parameters we obtain the solutions given by Akhmediev et al. in a serie of articles in 2009. Then these solutions allow me to construct rational solutions of the KP-I equation that describe waves in shallow water.
A Deletion of the Nuclear Localization Signal Domain in the Fus Protein Induces Stable Post-stress Cytoplasmic Inclusions in SH-SY5Y Cells
2021
Mutations in Fused-in-Sarcoma (FUS) gene involving the nuclear localization signal (NLS) domain lead to juvenile-onset Amyotrophic Lateral Sclerosis (ALS). The mutant protein mislocalizes to the cytoplasm, incorporating it into Stress Granules (SG). Whether SGs are the first step to the formation of stable FUS-containing aggregates is still unclear. In this work, we used acute and chronic stress paradigms to study the SG dynamics in a human SH-SY5Y neuroblastoma cell line carrying a deletion of the NLS domain of the FUS protein (homozygous: ΔNLS–/–; heterozygous: ΔNLS+/–). Wild-type (WT) cells served as controls. We evaluated the subcellular localization of the mutant protein through immuno…
The effect of nanoparticle size and NLS density on nuclear targeting in cancer and normal cells; impaired nuclear import and aberrant nanoparticle in…
2017
The cell nucleus is an interesting target in many diseases with particular interest in cancer. Previously, nuclear targeted small and large chitosan nanoparticles (S-NPs≈25nm, and L-NPs≈150nm respectively), modified with low, intermediate and high densities of NLS (L-NLS, I-NLS and H-NLS) were developed and assessed in L929 fibroblasts. However, to evade apoptosis and stimulate tumor growth cancer cells are capable of manipulating the nuclear-cytoplasmic transport on many levels, making NPs that are capable of nuclear targeting in normal cells incapable of doing so in cancer. For such reason, here, the nuclear delivery efficiency of S-NPs and L-NPs was assessed as a function of their NLS de…