Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices

For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly- decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrödinger, where the linear operator of the Schrödinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice.Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía and EU (FEDER program 2014-2020) project P18-RT-3480Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía and EU (FEDER program 2014-2020) project US-1380977MICINN and AEI project PID2019-110430GB-C21MICINN and AEI project PID2020-112620GB-I00Ministerio de Ciencia, Innovación y Universidades (MICIU, Spain) and FEDER funds Project No. PID2019-108508GB-I0

Treatment with tocilizumab or corticosteroids for COVID-19 patients with hyperinflammatory state: a multicentre cohort study (SAM-COVID-19)

Objectives: The objective of this study was to estimate the association between tocilizumab or corticosteroids and the risk of intubation or death in patients with coronavirus disease 19 (COVID-19) with a hyperinflammatory state according to clinical and laboratory parameters. Methods: A cohort study was performed in 60 Spanish hospitals including 778 patients with COVID-19 and clinical and laboratory data indicative of a hyperinflammatory state. Treatment was mainly with tocilizumab, an intermediate-high dose of corticosteroids (IHDC), a pulse dose of corticosteroids (PDC), combination therapy, or no treatment. Primary outcome was intubation or death; follow-up was 21 days. Propensity score-adjusted estimations using Cox regression (logistic regression if needed) were calculated. Propensity scores were used as confounders, matching variables and for the inverse probability of treatment weights (IPTWs). Results: In all, 88, 117, 78 and 151 patients treated with tocilizumab, IHDC, PDC, and combination therapy, respectively, were compared with 344 untreated patients. The primary endpoint occurred in 10 (11.4%), 27 (23.1%), 12 (15.4%), 40 (25.6%) and 69 (21.1%), respectively. The IPTW-based hazard ratios (odds ratio for combination therapy) for the primary endpoint were 0.32 (95%CI 0.22-0.47; p < 0.001) for tocilizumab, 0.82 (0.71-1.30; p 0.82) for IHDC, 0.61 (0.43-0.86; p 0.006) for PDC, and 1.17 (0.86-1.58; p 0.30) for combination therapy. Other applications of the propensity score provided similar results, but were not significant for PDC. Tocilizumab was also associated with lower hazard of death alone in IPTW analysis (0.07; 0.02-0.17; p < 0.001). Conclusions: Tocilizumab might be useful in COVID-19 patients with a hyperinflammatory state and should be prioritized for randomized trials in this situatio

Body motion in a resistive medium: an exactly solvable model

We introduce and solve in closed form, using momentum and kinetic energy balance, a simplified microscopic model of a body propagating in a one dimensional resistive medium. For a whole family of collisions with varying degree of inelasticities, we find that the effective resistive force on the moving body is opposite to and proportional to the square of the body's velocity

Saturable impurity in an optical array: Green function approach

© 2018 American Physical Society. We examine a one-dimensional linear waveguide array containing a single saturable waveguide. By using the formalism of lattice Green functions, we compute in closed form the localized mode and the transmission across the impurity in closed form. For the single saturable impurity in the bulk, we find that an impurity state is always possible, independent of the impurity strength. For the surface saturable impurity case, a minimum nonlinearity strength is necessary to create a bound state. The transmission coefficient across the impurity shows a sublinear behavior with an absence of any resonance. The dynamical self-trapping at the bulk impurity site shows no self-trapping transition, and it resembles the behavior of a weak linear impurity. For the surface impurity, however, there is a self-trapping transition at a critical nonlinearity value. The asymptotic propagation of the optical power shows a ballistic character in both cases, with a speed that de

Bounded dynamics in finite PT -symmetric magnetic metamaterials

Artículo de publicación ISIWe examine the PT-symmetry-breaking transition for amagnetic metamaterial of a finite extent, modeled as an array of coupled split-ring resonators in the equivalent circuit model approximation. Small-size arrays are solved completely in closed form, while for arrays larger than N = 5 results were computed numerically for several gain and loss spatial distributions. In all cases, it is found that the parameter stability window decreases rapidly with the size of the array, until at N = 20 approximately it is not possible to support a stable PT -symmetric phase.This work was supported in part by Fondo Nacional de Ciencia y Tecnolog´ıa (Grant No. 1120123), Programa Iniciativa Cient´ıfica Milenio (Grant No. P10-030-F), and Programa de Financiamiento Basal (Grant No. FB0824/2008)

Boundary-induced Anderson localization in photonic lattices

We analyze numerically localization of light in linear square waveguide arrays restricted in one dimension ("ribbons"), whose boundaries are disordered in propagation constant and/or coupling. We find that the disordered boundary induces a localization tendency in the bulk even for relatively wide ribbons. © 2011 Elsevier B.V. All rights reserved

Solitons in a modified discrete nonlinear Schrödinger equation

© 2018 The Author(s). We study the bulk and surface nonlinear modes of a modified one-dimensional discrete nonlinear Schrödinger (mDNLS) equation. A linear and a modulational stability analysis of the lowest-order modes is carried out. While for the fundamental bulk mode there is no power threshold, the fundamental surface mode needs a minimum power level to exist. Examination of the time evolution of discrete solitons in the limit of strongly localized modes, suggests ways to manage the Peierls-Nabarro barrier, facilitating in this way a degree of soliton steering. The long-time propagation of an initially localized excitation shows that, at long evolution times, nonlinear effects become negligible and as a result, the propagation becomes ballistic. The qualitative similarity of the results for the mDNLS to the ones obtained for the standard DNLS, suggests that this kind of discrete soliton is an robust entity capable of transporting an excitation across a generic discrete medium tha

Computing areas and integrals with random numbers

We introduce the basics of the Monte Carlo method that allows computing areas and definite integrals, by means of the generation of long sequences of random numbers. The areas of some nontrivial shapes are computed, showing the convergence towards their exact values. The application of the method to the computation of definite integrals is also given, showing an important example of the kinematics of a particle under the action of an arbitrary timedependent force

Fano resonances in magnetic metamaterials

We study the scattering of magnetoinductive plane waves by internal (external) capacitive (inductive) defects coupled to a one-dimensional split-ring resonator array. We examine a number of simple defect configurations where Fano resonances occur and study the behavior of the transmission coefficient as a function of the controllable external parameters. We find that for embedded capacitive defects, the addition of a small amount of coupling to second neighbors is necessary for the occurrence of Fano resonance. For external inductive defects, Fano resonances are commonplace, and they can be tuned by changing the relative orientation or distance between the defect and the SSR array. © 2011 American Physical Society

Seltrapping in flat band lattices with nonlinear disorder

We study the transport properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. In the weak nonlinearity regime, the dynamics is controlled by the degeneracy of the bands leading to a linear form of selftrapping. In the strong nonlinearity regime, the dynamics of the excitations depends strongly on the local environment around the initial excitation site that leads to a highly fluctuating selfrapping profile. For a binary nonlinear disorder, it is shown that the spreading of the flat band fundamental mode, is completely inhibited for a finite fraction of all cases. This fraction corresponds to the fraction of times the same value of (random) nonlinearity is assigned to all sites of the fundamental mode