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We argue that the alignment of Lyapunov vectors provides a quantitative criterion to predict catastrophes , i.e. the imminence of large-amplitude events in chaotic time-series of observables generated by sets of ordinary differential equations. Explicit predictions are reported for a Rössler oscillator and for a semiconductor laser with optoelectronic feedback.

Recently, Jánosi et al. (2019) introduced the concept of a “vortex proxy” based on an observation of strong correlations between integrated kinetic energy and integrated enstrophy over a large enough surface area. When mesoscale vortices are assumed to exhibit a Gaussian shape, the two spatial integrals have particularly simple functional forms, and a ratio of them defines an effective radius of a “proxy vortex”. In the original work, the idea was tested over a restricted area in the Californian Current System. Here we extend the analysis to global scale by means of 25 years of AVISO altimetry data covering the (ice-free) global ocean. The results are compared with a global vortex database containing over 64 million mesoscale eddies. We demonstrate that the proxy vortex representation of surface flow fields also works globally and provides a quick and reliable way to obtain coarse-grained vortex statistics. Estimated mean eddy sizes (effective radii) are extracted in very good agreement with the data from the vortex census. Recorded eddy amplitudes are directly used to infer the kinetic energy transported by the mesoscale vortices. The ratio of total and eddy kinetic energies is somewhat higher than found in previous studies. The characteristic westward drift velocities are evaluated by a time-lagged cross-correlation analysis of the kinetic energy fields. While zonal mean drift speeds are in good agreement with vortex trajectory evaluation in the latitude bands 30–5∘ S and 5–30∘ N, discrepancies are exhibited mostly at higher latitudes on both hemispheres. A plausible reason for somewhat different drift velocities obtained by eddy tracking and cross-correlation analysis is the fact that the drift of mesoscale eddies is only one component of the surface flow fields. Rossby wave activities, coherent currents, and other propagating features on the ocean surface apparently contribute to the zonal transport of kinetic energy.

Evaluating passive tracer advection is a common tool to study flow structures, particularly Lagrangian trajectories ranging from molecular scales up to the atmosphere and oceans. Here we report on numerical experiments in the region of the tropical Pacific (20∘ S–20∘ N), where 6600 tracer parcels are advected from a regular initial configuration (along a meridional line at 110∘ W between 15∘ S and 15∘ N) during periods of 1 year for 25 years altogether. We exploit AVISO surface flow fields and solve the kinematic equation for passive tracer movement in the 2D advection tests. We demonstrate that the strength of the advection defined by mean monthly westward displacements of the tracer clouds exhibit surprisingly large inter- and intra-annular variabilities. Furthermore, an analysis of cross-correlations between advection strength and the El-Niño and Southern Oscillation (SOI) indices reveal a significant anticorrelation between advection intensity and ONI (the Oceanic Niño Index) and a weaker positive correlation with SOI, both with a time lag of about 3 months (the two indices are strongly anticorrelated near real time). The statistical properties of advection (time-dependent mean squared displacement and first passage time distribution) suggest that the westward-moving tracers can be mapped into a simple 1D stochastic process, namely fractional Brownian motion. We fit the model parameters and show by numerical simulations of the fractional Brownian motion model that it is able to reproduce the observed statistical properties of the tracers' trajectories well. We argue that a traditional explanation based on the superposition of ballistic drift and a diffusion term yields different statistics and is incompatible with our observations.

This Technical Design Report presents a detailed description of all aspects of the LUXE (Laser Und XFEL Experiment), an experiment that will combine the high-quality and high-energy electron beam of the European XFEL with a high-intensity laser, to explore the uncharted terrain of strong-field quantum electrodynamics characterised by both high energy and high intensity, reaching the Schwinger field and beyond. The further implications for the search of physics beyond the Standard Model are also discussed.

The dynamics of two mutually delay-coupled semiconductor lasers has been frequently studied experimentally, numerically, and analytically either for weak or strong detuning between the lasers. Here, we present a systematic numerical investigation spanning all detuning ranges. We report high-resolution stability diagrams for wide ranges of the main control parameters of the laser, as described by the Lang-Kobayashi model. In particular, we detail the parameter influence on dynamical performance and map the distribution of chaotic pulsations and self-generated periodic spiking with arbitrary periodicity. Special attention is given to the unfolding of regular pulse packages for both symmetric and non-symmetric configurations with respect to detuning. The influence of the delay -time on the self-organization of periodic and chaotic laser phases as a function of the coupling and detuning is also described in detail.

Ratchets are simple mechanical devices which combine spatial asymmetry and nonequilibrium to produce counterintuitive transport of particles. The operation and properties of linear ratchets have already been extensively explored. However, very little is known about circular granular ratchets, startling devices able to convert vertical vibrations into rotations of the device. Here, we report results of systematic numerical investigations of the operational characteristics of circular granular ratchets. Several distinct behaviors are identified and explained in terms of the inner flow fields of the ratchet. All dynamical regimes found are robust and should not be difficult to observe in laboratory experiments.

Taming chaos arising from dissipative non-autonomous nonlinear systems by applying additional harmonic excitations is a reliable and widely used procedure nowadays. But the suppressory effectiveness of generic non-harmonic periodic excitations continues to be a significant challenge both to our theoretical understanding and in practical applications. Here we show how the effectiveness of generic suppressory excitations is optimally enhanced when the impulse transmitted by them (time integral over two consecutive zeros) is judiciously controlled in a not obvious way. Specifically, the effective amplitude of the suppressory excitation is minimal when the impulse transmitted is maximum. Also, by lowering the impulse transmitted one obtains larger regularization areas in the initial phase difference-amplitude control plane, the price to be paid being the requirement of larger amplitudes. These two remarkable features, which constitute our definition of optimum control, are demonstrated experimentally by means of an analog version of a paradigmatic model, and confirmed numerically by simulations of such a damped driven system including the presence of noise. Our theoretical analysis shows that the controlling effect of varying the impulse is due to a subsequent variation of the energy transmitted by the suppressory excitation.

In this mini-review, we present evidence from the vast literature that one essential part of the coupled atmosphere–ocean system that makes life on Earth possible, the water cycle, is exhibiting changes along with many attributes of the global climate. Our starting point is the 6th Assessment Report of the IPCC, which appeared in 2021, where the almost monograph-size Chapter 8, with over 1800 references, is devoted entirely to the water cycle. In addition to listing the main observations on the Earth globally, we focus on Europe, particularly on the Carpathian (Pannonian) Basin. We collect plausible explanations of the possible causes behind an observably accelerating and intensifying water cycle. Some authors still suggest that changes in the natural boundary conditions, such as solar irradiance or Earth’s orbital parameters, explain the observations. In contrast, most authors attribute such changes to the increasing greenhouse gas concentrations since the industrial revolution. The hypothesis being tested, and which has already yielded convincing affirmative answers, is that the hydrological cycle intensifies due to anthropogenic impacts. The Carpathian Basin, a part of the Danube watershed, including the sub-basin of the Tisza River, is no exception to these changes. The region is experiencing multiple drivers contributing to alterations in the water cycle, including increasing temperatures, shifting precipitation regimes, and various human impacts.

A study of the distribution of spikes in periodic oscillations is reported for an optically injected laser diode proxy, as a function of the injected field strength and detuning. A novel and unexpected feature reported here is an abundance of overlapping adding-doubling complexification cascades. Two-parameter spikes complexification cascades of the laser proxy are found to mimic phenomena also found in a state-of-the-art semiconductor laser model. Such cascades should not be difficult to observe experimentally, either in lasers or in other complex oscillators.