Nonlinear stiffness, Lyapunov exponents, and attractor dimension

I propose that stiffness may be defined and quantified for nonlinear systems using Lyapunov exponents, and demonstrate the relationship that exists between stiffness and the fractal dimension of a strange attractor: that stiff chaos is thin chaos.Comment: See home page http://lec.ugr.es/~julya

Fuzzy Control of Chaos

We introduce the idea of the fuzzy control of chaos: we show how fuzzy logic can be applied to the control of chaos, and provide an example of fuzzy control used to control chaos in Chua's circuit

Thermo-kinetic explosions: safety first or safety last?

Gas and vapour explosions have been involved in industrial accidents since the beginnings of industry. A century ago, at 11:55 am on Friday 24th September 1920, the petroleum barge Warwick exploded in London's docklands and seven men were killed. Understanding what happened when it blew up as it was being refurbished, and how to prevent similar explosions, involves fluid mechanics and thermodynamics plus chemistry. I recount the 1920 accident as an example, together with the history of thermo-kinetic explosions prior to 1920 and up to the present day, and I review the history and the actual state of the science of explosion and the roles of fluid mechanics, thermodynamics, and chemistry in that science. The science of explosions has been aware of its societal implications from the beginning, but, despite advances in health and safety over the past century, is there still work to do

Universality in Three-Frequency Resonances

We investigate the hierarchical structure of three-frequency resonances in nonlinear dynamical systems with three interacting frequencies. We hypothesize an ordering of these resonances based on a generalization of the Farey tree organization from two frequencies to three. In experiments and numerical simulations we demonstrate that our hypothesis describes the hierarchies of three-frequency resonances in representative dynamical systems. We conjecture that this organization may be universal across a large class of three-frequency systems

Burridge-Knopoff Models as Elastic Excitable Media

We construct a model of an excitable medium with elastic rather than the usual diffusive coupling. We explore the dynamics of elastic excitable media, which we find to be dominated by low dimensional structures, including global oscillations, period-doubled pacemakers, and propagating fronts. We suggest that examples of elastic excitable media are to be found in such diverse physical systems as Burridge-Knopoff models of frictional sliding, electronic transmission lines, and active optical waveguides

Noise and Inertia-Induced Inhomogeneity in the Distribution of Small Particles in Fluid Flows

The dynamics of small spherical neutrally buoyant particulate impurities immersed in a two-dimensional fluid flow are known to lead to particle accumulation in the regions of the flow in which rotation dominates over shear, provided that the Stokes number of the particles is sufficiently small. If the flow is viewed as a Hamiltonian dynamical system, it can be seen that the accumulations occur in the nonchaotic parts of the phase space: the Kolmogorov--Arnold--Moser tori. This has suggested a generalization of these dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use a bailout embedding of the standard map to mimic the dynamics of impurities subject not only to drag but also to fluctuating forces modelled as white noise. We find that the generation of inhomogeneities associated with the separation of particle from fluid trajectories is enhanced by the presence of noise, so that they appear in much broader ranges of the Stokes number than those allowing spontaneous separation

Three-frequency resonances in dynamical systems

We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental device (an electronic oscillator). We compare the hierarchies of three-frequency resonances we find in each of these systems. All three show similar qualitative behaviour, suggesting the existence of generic features in the parameter-space organization of three-frequency resonances.Comment: See home page http://lec.ugr.es/~julya

Fuzzy Control of Chaos

IWe introduce the idea of the fuzzy control of chaos: we show how fuzzy logic can be applied to the control of chaos, and provide an example of fuzzy control used to control chaos in Chua’s circuit.Instituto de Investigaciones en Electrónica, Control y Procesamiento de SeñalesComisión de Investigaciones Científicas de la provincia de Buenos Aire

Hybrid organic–inorganic structures trigger the formation of primitive cell-like compartments

We would like to thank COST action Chemobrionics (CA17120) and DYNALIFE (CA21169) for giving us the opportunity to meet and conceive important ideas crucial for the manuscript preparation. We would also like to thank Department CIBIO Core Facilities which are supported by the European Regional Development Fund 2014 to 2020. This work was funded in part from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 824060 (project ACDC).Alkaline hydrothermal vents have become a candidate setting for the origins of life on Earth and beyond. This is due to several key features including the presence of gradients of temperature, redox potential, pH, the availability of inorganic minerals, and the existence of a network of inorganic pore spaces that could have served as primitive compartments. Chemical gardens have long been used as experimental proxies for hydrothermal vents. This paper investigates-10pc]Please note that the spelling of the following author name in the manuscript differs from the spelling provided in the article metadata: Richard J. G. Löffler. The spelling provided in the manuscript has been retained; please confirm. a set of prebiotic interactions between such inorganic structures and fatty alcohols. The integration of a medium-chain fatty alcohol, decanol, within these inorganic minerals, produced a range of emergent 3 dimensions structures at both macroscopic and microscopic scales. Fatty alcohols can be considered plausible prebiotic amphiphiles that might have assisted the formation of protocellular structures such as vesicles. The experiments presented herein show that neither chemical gardens nor decanol alone promote vesicle formation, but chemical gardens grown in the presence of decanol, which is then integrated into inorganic mineral structures, support vesicle formation. These observations suggest that the interaction of fatty alcohols and inorganic mineral structures could have played an important role in the emergence of protocells, yielding support for the evolution of living cells.COST (CA17120)DYNALIFE (CA21169)European Regional Development Fund 2014 to 2020European Union’s Horizon 2020 research and innovation programme 824060 (project ACDC