On the variational structure of breather solutions

In this paper we give a systematic and simple account that put in evidence that many breather solutions of integrable equations satisfy suitable variational elliptic equations, which also implies that the stability problem reduces in some sense to $(i)$ the study of the spectrum of explicit linear systems (\emph{spectral stability}), and $(ii)$ the understanding of how bad directions (if any) can be controlled using low regularity conservation laws. We exemplify this idea in the case of the modified Korteweg-de Vries (mKdV), Gardner, and sine-Gordon (SG) equations. Then we perform numerical simulations that confirm, at the level of the spectral problem, our previous rigorous results, where we showed that mKdV breathers are $H^2$ and $H^1$ stable, respectively. In a second step, we also discuss the Gardner and the Sine-Gordon cases, where the spectral study of a fourth-order linear matrix system is the key element to show stability. Using numerical methods, we confirm that all spectral assumptions leading to the $H^2\times H^1$ stability of SG breathers are numerically satisfied, even in the ultra-relativistic, singular regime. In a second part, we study the periodic mKdV case, where a periodic breather is known from the work of Kevrekidis et al. We rigorously show that these breathers satisfy a suitable elliptic equation, and we also show numerical spectral stability. However, we also identify the source of nonlinear instability in the case described in Kevrekidis et al. Finally, we present a new class of breather solution for mKdV, believed to exist from geometric considerations, and which is periodic in time and space, but has nonzero mean, unlike standard breathers.Comment: 55 pages; This paper is an improved version of our previous paper 1309.0625 and hence we replace i

On the nonlinear stability of mKdV breathers

A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.Comment: 7 p

Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model

A collective coordinate theory is develop for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete non-linear equation. The evolution of these two collective coordinates, obtained by means of the Generalized Travelling Wave Method, explains the mechanism underlying the soliton ratchet and captures qualitatively all the main features of this phenomenon. The theory accounts for the existence of a non-zero depinning threshold, the non-sinusoidal behaviour of the average velocity as a function of the difference phase between the harmonics of the driver, the non-monotonic dependence of the average velocity on the damping and the existence of non-transporting regimes beyond the depinning threshold. In particular it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space

Review on the Stability of the Peregrine and Related Breathers

In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show that these breathers are unstable according to a standard definition of stability. Suitable Lyapunov functionals are described, as well as their underlying spectral properties. As an immediate consequence of the first variation of these functionals, we also present the corresponding nonlinear ODEs fulfilled by these nonlinear Schrödinger breathers. The notion of global stability for each breather mentioned above is finally discussed. Some open questions are also briefly mentioned

The Akhmediev breather is unstable

In this note, we give a rigorous proof that the NLS periodic Akhmediev breather is unstable. The proof follows the ideas in Muñoz (Proyecciones (Antofagasta) 36(4):653–683, 2017), in the sense that a suitable modification of the Stokes wave is the global attractor of the local Akhmediev dynamics for sufficiently large time, and therefore the latter cannot be stable in any suitable finite energy periodic Sobolev space

A selective strategy for targeting primary hyperoxaluria diseases

Funding Information: Authors wish to thank the Centro de Instrumentación Científico-Técnica (CICT) of the University of Jaén, Spain, for partial financial support. A.A.-A. is grateful for the postdoctoral fellowship from Fundación Alfonso Martín Escudero. Authors acknowledge the use of the National Facility ELECMI ICTS, node “Laboratorio de Microscopias Avanzadas” at Universidad de Zaragoza. This research has also partially been supported by the Spanish Ministerio de Ciencia, Innovación y Universidades (grant RTI2018-098560-B-C22) and by the Andalusian Consejería de Economía y Conocimiento (FEDER program 2014-2020: grant number 1380682). This work was partially supported by the Associate Laboratory for Green Chemistry-LAQV, which is financed by national funds from FCT/MCTES (UIDB/50006/2020). Funding Information: This research has also partially been supported by the Spanish Ministerio de Ciencia, Innovación y Universidades (grant RTI2018-098560-B-C22) and by the Andalusian Consejería de Economía y Conocimiento (FEDER program 2014-2020: grant number 1380682). This work was partially supported by the Associate Laboratory for Green Chemistry-LAQV, which is financed by national funds from FCT/MCTES (UIDB/50006/2020). Funding Information: Authors wish to thank the Centro de Instrumentación Científico-Técnica (CICT) of the University of Jaén, Spain, for partial financial support. A.A.-A. is grateful for the postdoctoral fellowship from Fundación Alfonso Martín Escudero. Authors acknowledge the use of the National Facility ELECMI ICTS, node “Laboratorio de Microscopias Avanzadas” at Universidad de Zaragoza. Publisher Copyright: © 2022 The Author(s)Primary hyperoxalurias (PHs) are a group of inherited alterations of the hepatic glyoxylate metabolism that result in an excess of oxalate production by the oxidation of glyoxylate by the human lactate dehydrogenase A enzyme (hLDHA). The selective liver inhibition of this enzyme is one of the therapeutic strategies followed in the treatment of this disease. Even though several efforts have been recently performed using gene silencing by the RNA interference approach, small-molecule inhibitors that selectively reach hepatocytes are preferred since they present the advantages of a lower production cost and better pharmacological properties. In that sense, the design, synthesis, and physicochemical characterization by NMR, FTIR, DLS and TEM of two nanocarriers based on chitosan conjugates (1, non-redox-sensitive; 2, redox-sensitive) have been performed to (i) achieve the selective transport of hLDHA inhibitors into hepatocytes and (ii) their disruption once they reach the hepatocytes cytosol. Polymer 2 self-assembled into micelles in water and showed high drug loadings (19.8–24.5 %) and encapsulation efficiencies (31.9–40.8%) for the hLDHA inhibitors (I-III) tested. The non-redox-sensitive micelle 1 remained stable under different glutathione (GSH) concentrations (10 μM and 10 mM), and just a residual release of the inhibitor encapsulated was observed (less than 10 %). On the other hand, micelle 2 was sufficiently stable under in vitro physiological conditions (10 μM, GSH) but it quickly disassembled under the simulated reducing conditions present inside hepatocytes (10 mM GSH), achieving a 60 % release of the hLDHA inhibitor encapsulated after 24 h, confirming the responsiveness of the developed carrier to the high levels of intracellular GSH.publishersversionpublishe

Scalability of GHZ and random-state entanglement in the presence of decoherence

We derive analytical upper bounds for the entanglement of generalized Greenberger-Horne-Zeilinger states coupled to locally depolarizing and dephasing environments, and for local thermal baths of arbitrary temperature. These bounds apply for any convex quantifier of entanglement, and exponential entanglement decay with the number of constituent particles is found. The bounds are tight for depolarizing and dephasing channels. We also show that randomly generated initial states tend to violate these bounds, and that this discrepancy grows with the number of particles.Comment: 9 pages, 3 figure

Recent advances in laser-driven neutron sources

Due to the limited number and high cost of large-scale neutron facilities, there has been a growing interest in compact accelerator-driven sources. In this context, several potential schemes of laser-driven neutron sources are being intensively studied employing laser-accelerated electron and ion beams. In addition to the potential of delivering neutron beams with high brilliance, directionality and ultra-short burst duration, a laser-driven neutron source would offer further advantages in terms of cost-effectiveness, compactness and radiation confinement by closed-coupled experiments. Some of the recent advances in this field are discussed, showing improvements in the directionality and flux of the laser-driven neutron beams

Selective Deuterium Ion Acceleration Using the Vulcan PW Laser

We report on the successful demonstration of selective acceleration of deuterium ions by target-normal sheath acceleration (TNSA) with a high-energy petawatt laser. TNSA typically produces a multi-species ion beam that originates from the intrinsic hydrocarbon and water vapor contaminants on the target surface. Using the method first developed by Morrison, et al.,$^{1}$ an ion beam with $>$99$\%$ deuterium ions and peak energy 14 MeV/nucleon is produced with a 200 J, 700 fs, $>10^{20} W/cm^{2}$ laser pulse by cryogenically freezing heavy water (D$_{2}$O) vapor onto the rear surface of the target prior to the shot. Within the range of our detectors (0-8.5$^{\circ}$), we find laser-to-deuterium-ion energy conversion efficiency of 4.3$\%$ above 0.7 MeV/nucleon while a conservative estimate of the total beam gives a conversion efficiency of 9.4$\%$.Comment: 5 pages, 5 figure

One-dimensional thermal pressure-driven expansion of a pair cloud into an electron-proton plasma

Recently a filamentation instability was observed when a laser-generated pair cloud interacted with an ambient plasma. The magnetic field it drove was strong enough to magnetize and accelerate the ambient electrons. It is of interest to determine if and how pair cloud-driven instabilities can accelerate ions in the laboratory or in astrophysical plasma. For this purpose, the expansion of a localized pair cloud with the temperature 400 keV into a cooler ambient electron-proton plasma is studied by means of one-dimensional particle-in-cell (PIC) simulations. The cloud's expansion triggers the formation of electron phase space holes that accelerate some protons to MeV energies. Forthcoming lasers might provide the energy needed to create a cloud that can accelerate protons.Comment: 5 pages 4 figures, accepted for publication in Physics of Plasma