Search results for "ExAC"
showing 10 items of 1440 documents
Families of quasi-rational solutions of the NLS equation as an extension of higher order Peregrine breathers.
2011
We construct a multi-parametric family of solutions of the focusing NLS equation from the known result describing the multi phase almost-periodic elementary solutions given in terms of Riemann theta functions. We give a new representation of their solutions in terms of Wronskians determinants of order 2N composed of elementary trigonometric functions. When we perform a special passage to the limit when all the periods tend to infinity, we get a family of quasi-rational solutions. This leads to efficient representations for the Peregrine breathers of orders N=1,, 2, 3, first constructed by Akhmediev and his co-workers and also allows to get a simpler derivation of the generic formulas corres…
Quasi-rational solutions of the NLS equation and rogue waves
2010
We degenerate solutions of the NLS equation from the general formulation in terms of theta functions to get quasi-rational solutions of NLS equations. For this we establish a link between Fredholm determinants and Wronskians. We give solutions of the NLS equation as a quotient of two wronskian determinants. In the limit when some parameter goes to $0$, we recover Akhmediev's solutions given recently It gives a new approach to get the well known rogue waves.
Eighth Peregrine breather solution of the NLS equation and multi-rogue waves
2012
This is a continuation of a paper in which we present a new representation of solutions of the focusing NLS equation as a quotient of two determinants. This work was based on a recent paper in which we had constructed a multi-parametric family of this equation in terms of wronskians. \\ Here we give a more compact formulation without limit. With this method, we construct Peregrine breather of order N=8 and multi-rogue waves associated by deformation of parameters.
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…
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.
BCG Mass Evolution in Cosmological Hydro-Simulations
2018
We analyze the stellar growth of Brightest Cluster Galaxies (BCGs) produced by cosmological zoom-in hydrodynamical simulations of the formation of massive galaxy clusters. The evolution of the stellar mass content is studied considering different apertures, and tracking backwards either the main progenitor of the $z=0$ BCG or that of the cluster hosting the BCG at $z=0$. Both methods lead to similar results up to $z \simeq 1.5$. The simulated BCGs masses at $z=0$ are in agreement with recent observations. In the redshift interval from $z=1$ to $z=0$ we find growth factors 1.3, 1.6 and 3.6 for stellar masses within 30kpc, 50kpc and 10% of $R_{500}$ respectively. The first two factors, and in…
Lotus tenuis x L. corniculatus interspecific hybridization as a means to breed bloat-safe pastures and gain insight into the genetic control of proan…
2014
Background: Proanthocyanidins (PAs) are secondary metabolites that strongly affect plant quality traits. The concentration and the structure of these metabolites influence the palatability and nutritional value of forage legumes. Hence, modulating PAs in the leaves of forage legumes is of paramount relevance for forage breeders worldwide. The lack of genetic variation in the leaf PA trait within the most important forage species and the difficulties in engineering this pathway via the ectopic expression of regulatory genes, prompted us to pursue alternative strategies to enhance this trait in forage legumes of agronomic interest. The Lotus genus includes forage species which accumulate PAs …
High-resolution records of growth temperature and life history of two Nacella limpet species, Tierra del Fuego, Argentina
2020
Stable isotope ratios in patelloid limpets of the genus Patella have been established as proxies for coastal environmental change at sub-monthly resolution along the eastern North Atlantic and Mediterranean Sea. Nacella deaurata (Gmelin, 1791) and N. magellanica (Gmelin, 1791) are common intertidal species of patelloid limpets inhabiting the coast of Tierra del Fuego, Argentina/Chile and are commonly found in Holocene archaeological deposits. Here, we examine oxygen and carbon isotope ratios (δ18Oshell and δ13Cshell, respectively) of modern specimens of N. deaurata and N. magellanica to test the hypotheses that: 1) they form their shells in isotopic equilibrium with ambient water; and 2) pr…
Innovative electronic lithography using self-assembly films in order to modify material surfaces at nanometric scale
2013
The concept of electon beam decomposition has been developed in order to create smaller patterns than those achieved by conventional lithographic methods. This work aimed to go further about this concept through a separation of the involved mechanisms in order to better understand them and thus reach a better control of process.A device was designed and a protocol was defined where the first stage is the adsorption at cryogenic temperature of metal-carbonyl compounds. The adsorbate is then decomposed by a focused electron beam and fragmentation residues are removed through annealing allowing the deposit reorganization. The study of the different steps of the elaboration method was followed …