Logical operations with Localized Structures

We show how to exploit excitable regimes mediated by localized structures (LS) to perform AND, OR, and NOT logical operations providing full logical functionality. Our scheme is general and can be implemented in any physical system displaying LS. In particular, LS in nonlinear photonic devices can be used for all-optical computing applications where several reconfigurable logic gates can be implemented in the transverse plane of a single device, allowing for parallel computing.Comment: 11 pages, 6 figure

Stable droplets and growth laws close to the modulational instability of a domain wall

We consider the curvature driven dynamics of a domain wall separating two equivalent states in systems displaying a modulational instability of a flat front. We derive an amplitude equation for the dynamics of the curvature close to the bifurcation point from growing to schrinking circular droplets. We predict the existence of stable droplets with a radius $R$ that diverges at the bifurcation point, where a curvature driven growth law $R(t) \approx t^{1/4}$ is obtained. Our general analytical predictions, which are valid for a wide variety of systems including models of nonlinear optical cavities and reaction-diffusion systems, are illustrated in the parametrically driven complex Ginzburg-Landau equation.Comment: 4 pages, 4 figure

Third-order chromatic dispersion stabilizes Kerr frequency combs

Using numerical simulations of an extended Lugiato-Lefever equation, we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.Comment: 4 pages and 4 figure

Patterns, localized structures and fronts in a reduced model of clonal plant growth

A simplified model of clonal plant growth is formulated, motivated by observations of spatial structures in Posidonia oceanica meadows in the Mediterranean Sea. Two levels of approximation are considered for the scale-dependent feedback terms. Both take into account mortality and clonal, or vegetative, growth as well as competition and facilitation, but the first version is nonlocal in space while the second is local. Study of the two versions of the model in the one-dimensional case reveals that both cases exhibit qualitatively similar behavior (but quantitative differences) and describe the competition between three spatially extended states, the bare soil state, the populated state, and a pattern state, and the associated spatially localized structures. The latter are of two types, holes in the populated state and vegetation patches on bare ground, and are organized within distinct snaking bifurcation diagrams. Fronts between the three extended states are studied and a transition between pushed and pulled fronts identified. Numerical simulations in one spatial dimension are used to determine front speeds and confront the predictions from the marginal stability condition for pulled fronts.Comment: 14 pages, 18 figures. To appear in Physica

The potential impact of climate change on the efficiency and reliability of solar, hydro, and wind energy sources

Climate change impacts the electric power system by affecting both the load and generation. It is paramount to understand this impact in the context of renewable energy as their market share has increased and will continue to grow. This study investigates the impact of climate change on the supply of renewable energy through applying novel metrics of intermittency, power production and storage required by the renewable energy plants as a function of historical climate data variability. Here we focus on and compare two disparate locations, Palma de Mallorca in the Balearic Islands and Cordova, Alaska. The main results of this analysis of wind, solar radiation and precipitation over the 1950–2020 period show that climate change impacts both the total supply available and its variability. Importantly, this impact is found to vary significantly with location. This analysis demonstrates the feasibility of a process to evaluate the local optimal mix of renewables, the changing needs for energy storage as well as the ability to evaluate the impact on grid reliability regarding both penetration of the increasing renewable resources and changes in the variability of the resource. This framework can be used to quantify the impact on both transmission grids and microgrids and can guide possible mitigation paths.P.C. and D.G. acknowledge financial support from Ministerio de Ciencia e Innovación (Spain), the Agencia Estatal de Investigación (AEI, Spain), and the Fondo Europeo de Desarrollo Regional (FEDER, EU) under grant PACSS (RTI2018-093732-B-C22) and the Maria de Maeztu program for Units of Excellence in R&D (MDM-2017-0711). D.N. gratefully acknowledges support from DOE Project GMLC 1.5.02—Resilient Alaskan Distribution system Improvements using Automation, Network analysis, Control, and Energy storage (RADIANCE). U.S.B. acknowledges support from the National Science Foundation under award #OIA-1753748 and by the State of Alaska for material which this work is based upon

Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators

Using the Lugiato-Lefever model, we analyze the effects of third-order chromatic dispersion on the existence and stability of dark- and bright-soliton Kerr frequency combs in the normal dispersion regime. While in the absence of third-order dispersion only dark solitons exist over an extended parameter range, we find that third-order dispersion allows for stable dark and bright solitons to coexist. Reversibility is broken and the shape of the switching waves connecting the top and bottom homogeneous solutions is modified. Bright solitons come into existence thanks to the generation of oscillations in the switching-wave profiles. Temporal oscillatory instabilities of dark solitons are suppressed in the presence of sufficiently strong third-order dispersion, while bright solitons are never found to oscillate in time. As a result of third-order dispersion both bright and dark solitons are found to move with a velocity that depends on their width.status: publishe

Bifurcation structure of dissipative solitons

In this paper we analyze in detail the structure of the phase space of a reversible dynamical system describing the stationary solutions of a model for a nonlinear optical cavity. We compare our results with the general picture described in [P.D. Woods, A.R. Champneys, Physica D 129 (1999) 147; P. Coullet, C. Riera, C. Tresser, Phys. Rev. Lett. 84 (2000) 3069] and find that the stable and unstable manifolds of homogeneous and patterned solutions present a much higher level of complexity than predicted, including the existence of additional localized solutions and fronts. This extra complexity arises due to homoclinic and heteroclinic intersections of the invariant manifolds of low-amplitude periodic solutions, and to the fact that these periodic solutions together with the high-amplitude ones constitute a one-parameter family generating a closed line on the symmetry plane. (c) 2006 Elsevier B.V. All rights reserved