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Cross-field chaotic transport of electrons by $\vec E \times \vec B$ electron drift instability in Hall thrustersJul 19 2019One special interest for the industrial development of Hall thruster is characterizing the anomalous cross-field electron transport observed after the channel exit. Since the ionization efficiency is more than 90%, the neutral atom density in that domain ... More

Dynamics of quasiperiodically driven spin systemsJul 17 2019We study the stroboscopic dynamics of a spin-$S$ object subjected to $\delta$-function kicking in the transverse magnetic field which is generated following the Fibonacci sequence. The corresponding classical Hamiltonian map is constructed in the large ... More

Resonance--Assisted Tunneling in Deformed Optical Microdisks with a Mixed Phase SpaceJul 16 2019The life times of optical modes in whispering-gallery cavities crucially depend on the underlying classical ray dynamics and may be spoiled by the presence of classical nonlinear resonances due to resonance--assisted tunneling. Here we present an intuitive ... More

Dynamical thermalization of interacting fermionic atoms in a Sinai-oscillator trapJul 15 2019We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai-oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that for a many-body ... More

Nonlinear dynamics and energy transfer for two rotating dipoles in an external field: A three-dimensional analysisJul 15 2019We investigate the structure and the nonlinear dynamics of two rigid polar rotors coupled through the dipole-dipole interaction in an external homogeneous electric field. In the field-free stable head-tail configuration, an excess energy is provided to ... More

Semiclassical evolution in phase space for a softly chaotic systemJul 15 2019An initial coherent state is propagated exactly by a kicked quantum Hamiltonian and its associated classical stroboscopic map. The classical trajectories within the initial state are regular for low kicking strengths, then bifurcate and become mainly ... More

Blinking chimeras in globally coupled rotatorsJul 14 2019In globally coupled ensembles of identical oscillators so-called chimera states can be observed. The chimera state is a symmetry-broken regime, where a subset of oscillators forms a cluster, a synchronized population, while the rest of the system remains ... More

Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computingJul 12 2019The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, reservoir computing turned out to be a very promising approach especially for the reproduction of the long-term ... More

Heteroclinic and Homoclinic Connections in a Kolmogorov-Like FlowJul 11 2019Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in a weakly turbulent ... More

Statistical Measures and Selective Decay Principle for Generalized Euler DynamicsJul 11 2019We investigate the statistical mechanics of a family of two dimensional (2D) fluid flows, described by the generalized Euler equations, or {\alpha}-models. We aim to study the equilibrium mechanics, using initially a point-vortex approximation and then ... More

On optimal cover and its possible shape for fractals embedded into 2D Euclidian spaceJul 10 2019In this article a definition of optimal cover for fractal structures is proposed. Expression for Minkowsky dimension is rewritten in terms of functional equation on areas of covers that constructed for different scales.Given the definition, the functional ... More

Dual channels of helicity cascade in turbulent flowsJul 08 2019Helicity, as one of only two inviscid invariants in three-dimensional turbulence, plays an important role in the generation and evolution of turbulence. From the traditional viewpoint, there exists only one channel of helicity cascade similar to that ... More

Suppression of Chaos in Mutually Coupled Synchronized Generalized Lorenz SystemsJul 08 2019In this work, the dynamics of a system of mutually coupled Generalized Lorenz systems (GLS) is investigated. The state variables of two Lorenz oscillators are coupled mutually via non-linear controls and synchronization is achieved between the state variables. ... More

There are no deviations for the ergodic averages of the Giulietti-Liverani horocycle flows on the two-torusJul 08 2019We show that the ergodic averages for the horocycle flow on the two-torus associated by Giulietti and Liverani to an Anosov diffeomorphism either grow linearly or are bounded, in other words there are no deviations. For this, we use topological invariance ... More

Tilting and Squeezing: Phase space geometry of Hamiltonian saddle-node bifurcation and its influence on chemical reaction dynamicsJul 07 2019In this article we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics. To achieve this goal, we identify the phase space invariant manifolds using Lagrangian descriptors, ... More

Co-existing climate attractors in a coupled aquaplanetJul 07 2019The first step in exploring the properties of dynamical systems like the Earth climate is to identify the different phase space regions where the trajectories asymptotically evolve, called `attractors'. In a given system, multiple attractors can co-exist ... More

Chimera states for a globally coupled sine circle map lattice: spatiotemporal intermittency and hyperchaosJul 06 2019We study the existence of chimera states, i.e. mixed states, in a globally coupled sine circle map lattice, with different strengths of inter-group and intra-group coupling. We find that at specific values of the parameters of the CML, a completely random ... More

Takens-inspired neuromorphic processor: a downsizing tool for random recurrent neural networks via feature extractionJul 06 2019We describe a new technique which minimizes the amount of neurons in the hidden layer of a random recurrent neural network (rRNN) for time series prediction. Merging Takens-based attractor reconstruction methods with machine learning, we identify a mechanism ... More

From rotating fluid masses and Ziegler's paradox to Pontryagin- and Krein spaces and bifurcation theoryJul 05 2019Three classical systems, the Kelvin gyrostat, the Maclaurin spheroids, and the Ziegler pendulum have directly inspired development of the theory of Pontryagin and Krein spaces with indefinite metric and singularity theory as independent mathematical topics, ... More

Solitary States and Partial Synchrony in Oscillatory Ensembles with Attractive and Repulsive InteractionsJul 05 2019We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, ... More

Phase reduction beyond the first order: the case of the mean-field complex Ginzburg-Landau equationJul 04 2019Phase reduction is a powerful technique that permits to describe the dynamics of a weakly perturbed limit-cycle oscillator in terms of its phase. For ensembles of oscillators, a classical example of phase reduction is the derivation of the Kuramoto model ... More

Can quantum many-body systems behave as strongly chaotic, being completely integrable ?Jun 29 2019We study the paradigmatic Lieb-Liniger (LL) model belonging to the class of integrable quantum many-body systems, by considering its statistical properties in the many-body Hilbert space. We demonstrate that, for a fixed total momentum, the properties ... More

Superdiffusive random laserJun 28 2019The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to constrain ... More

Stochastic Lagrangians for Statistical DynamicsJun 28 2019The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their realization ... More

Harnessing Fluctuations in Thermodynamic Computing via Time-Reversal SymmetriesJun 27 2019We experimentally demonstrate that highly structured distributions of work emerge during even the simple task of erasing a single bit. These are signatures of a refined suite of time-reversal symmetries in distinct functional classes of microscopic trajectories. ... More

Many-body synchronisation in a classical Hamiltonian systemJun 26 2019We study synchronisation between periodically driven, interacting classical spins undergoing a Hamiltonian dynamics. In the thermodynamic limit there is a transition between a regime where all the spins oscillate synchronously for an infinite time with ... More

Extremely High Length-Divergent Thermal Conductivity in Long-Range Interacting Fermi-Pasta-Ulam ChainsJun 26 2019The power-law length ($L$) divergence of thermal conductivity ($\kappa$) in one-dimensional (1D) systems, i.e., $\kappa \sim L^{\alpha}$, has been predicted by theories and also corroborated by experiments. The theoretical predictions of the exponent ... More

Extremely High Length-Divergent Thermal Conductivity in Long-Range Interacting Fermi-Pasta-Ulam ChainsJun 26 2019Jul 03 2019The power-law length ($L$) divergence of thermal conductivity ($\kappa$) in one-dimensional (1D) systems, i.e., $\kappa \sim L^{\alpha}$, has been predicted by theories and also corroborated by experiments. The theoretical predictions of the exponent ... More

Length-Divergent Thermal Conductivity in Long-Range Interacting Fermi-Pasta-Ulam ChainsJun 26 2019Jul 11 2019The power-law length ($L$) divergence of thermal conductivity ($\kappa$) in one-dimensional (1D) systems, i.e., $\kappa \sim L^{\alpha}$, has been predicted by theories and also corroborated by experiments. The theoretical predictions of the exponent ... More

Bounds on chaos from the eigenstate thermalization hypothesisJun 26 2019We show that known bounds on the growth rates of operator complexity and the out-of-time-order four-point correlator in chaotic many-body quantum systems follow directly from the general structure of operator matrix elements in systems that obey the eigenstate ... More

On the intrinsic three-dimensionality of the flow normal to a circular diskJun 25 2019Direct numerical simulations are performed for the steady flow normal to a circular disk at the Reynolds number of 1000. Numerical simulations are conducted with different levels of simplification procedure by reducing the azimuthal extension of the disk. ... More

Quantum dynamics from fixed points and their stabilityJun 25 2019We approach quantum dynamics in one spatial dimension from a systematic study of moments starting from the dynamics of the mean position. This is complementary to the approach of Brizuela whose starting point was generalized recursion relations between ... More

Dynamics of phases and chaos in models of locally coupled conservative or dissipative oscillatorsJun 25 2019We discuss Hamiltonian model of oscillator lattice with local coupling. Model describes spatial modes of nonlinear Schr\"{o}dinger equation with periodic tilted potential. The Hamiltonian system manifests reversibility of Topaj - Pikovsky phase oscillator ... More

Aspects of Nosé and Nosé-Hoover Dynamics ElucidatedJun 25 2019Some paradoxical aspects of the Nos\'e and Nos\'e-Hoover dynamics of 1984 and Dettmann's dynamics of 1996 are elucidated. Phase-space descriptions of thermostated harmonic oscillator dynamics can be simultaneously expanding, incompressible, or contracting, ... More

Universal mechanism of low-frequency brain rhythm formation through nonlinear coupling of high-frequency spiking-like activityJun 24 2019A universal mechanism of emergence of synchronized low frequency brain wave field activity is presented as a result of nonlinear coupling with flat frequency neuronal forcing. The mechanism utilizes a unique dispersion properties of weakly-evanescent ... More

Circulant networks of identical Kuramoto oscillators: Seeking dense networks that do not globally synchronize and sparse ones that doJun 22 2019Jun 26 2019There is a critical connectivity $0<\mu_c<1$ for systems of identical Kuramoto oscillators. Any network of size $n$ in which each oscillator interacts with at least $\mu(n-1)$ others is globally synchronizing if $\mu\geq\mu_c$; otherwise, it may not be. ... More

Circulant networks of identical Kuramoto oscillators: Seeking dense networks that do not globally synchronize and sparse ones that doJun 22 2019There is a critical connectivity $0<\mu_c<1$ for systems of identical Kuramoto oscillators. Any network of size $n$ in which each oscillator interacts with at least $\mu(n-1)$ others is globally synchronizing if $\mu\geq\mu_c$; otherwise, it may not be. ... More

A Study of the Dynamics of a new Piecewise Smooth MapJun 22 2019In this article, we have studied a 1D map, which is formed by combining the two well-known maps i.e. the tent and the logistic maps in the unit interval i.e. [0, 1]. The proposed map can behave as the piecewise smooth or non-smooth maps (depending on ... More

Control of eigenfunctions on surfaces of variable curvatureJun 21 2019We prove a microlocal lower bound on the mass of high energy eigenfunctions of the Laplacian on compact surfaces of negative curvature, and more generally on surfaces with Anosov geodesic flows. This implies controllability for the Schr\"odinger equation ... More

Data-driven prediction of a multi-scale Lorenz 96 chaotic system using a hierarchy of deep learning methods: Reservoir computing, ANN, and RNN-LSTMJun 20 2019Jul 01 2019In this paper, the performance of three deep learning methods for predicting short-term evolution and reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state network (a type of reservoir ... More

Data-driven prediction of a multi-scale Lorenz 96 chaotic system using a hierarchy of deep learning methods: Reservoir computing, ANN, and RNN-LSTMJun 20 2019In this paper, the performance of three deep learning methods for predicting short-term evolution and reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The three methods are: echo state network (a type ... More

Horizon Visibility Graphs and Time Series Merge Trees are DualJun 20 2019In this paper we introduce the horizon visibility graph, a simple extension to the popular horizontal visibility graph representation of a time series, and show that it possesses a rigorous mathematical foundation in computational algebraic topology. ... More

Coherent Riemannian-geometric description of Hamiltonian order and chaos with Jacobi metricJun 19 2019By identifying Hamiltonian flows with geodesic flows of suitably chosen Riemannian manifolds, it is possible to explain the origin of chaos in classical Newtonian dynamics and to quantify its strength. There are several possibilities to geometrize Newtonian ... More

Interevent time distributions of avalanche dynamicsJun 19 2019Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus on the interevent ... More

Gauging classical and quantum integrability through out-of-time ordered correlatorsJun 18 2019Out-of-time-order correlators (OTOCs) have been proposed as a probe of chaos in quantum mechanics, on the basis of their short-time exponential growth found in some particular set-ups. However, it has been seen that this behavior is not universal. Therefore, ... More

State transitions in the Morris-Lecar model under stable Lévy noiseJun 18 2019This paper considers the state transition of the stochastic Morris-Lecar neuronal model driven by symmetric $\alpha$-stable L\'evy noise. The considered system is bistable: a stable fixed point (resting state) and a stable limit cycle (oscillating state), ... More

Phase synchronization in coupled bistable oscillatorsJun 18 2019Jun 24 2019We introduce a simple model system to study synchronization theoretically in quantum oscillators that are not just in limit-cycle states, but rather display a more complex bistable dynamics. Our oscillator model is purely dissipative, with a two-photon ... More

Phase synchronization in coupled bistable oscillatorsJun 18 2019We introduce a simple model system to study synchronization theoretically in quantum oscillators that are not just in limit-cycle states, but rather display a more complex bistable dynamics. Our oscillator model is purely dissipative, with a two-photon ... More

Comparative terrestrial atmospheric circulation regimes in simplified global circulation models: II. energy budgets and spectral transfersJun 18 2019The energetics of possible global atmospheric circulation patterns in an Earth-like atmosphere are explored using a simplified GCM based on the University of Hamburg's Portable University Model for the Atmosphere. Results from a series of simulations, ... More

Comparative terrestrial atmospheric circulation regimes in simplified global circulation models: I. from cyclostrophic super-rotation to geostrophic turbulenceJun 18 2019The regimes of possible global atmospheric circulation patterns in an Earth-like atmosphere are explored using a simplified GCM based on the University of Hamburg's Portable University Model for the Atmosphere with simplified (linear) boundary layer friction, ... More

Control of chaotic systems by Deep Reinforcement LearningJun 16 2019Deep Reinforcement Learning (DRL) is applied to control a nonlinear, chaotic system governed by the one-dimensional Kuramoto-Sivashinsky (KS) equation. DRL uses reinforcement learning principles for the determination of optimal control solutions and deep ... More

Quantum approach to the dynamical systems modelingJun 14 2019We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian) dissipative dynamical ... More

Identifying four wave resonant interactions in a surface gravity wave turbulence experimentJun 14 2019The nonlinear dynamics of waves at the sea surface is believed to be ruled by the Weak Turbulence framework. In order to investigate the nonlinear coupling among gravity surface waves, we developed an experiment in the Coriolis facility which is a 13-m ... More

Universality classes of surface wave turbulence as probed by laser Doppler velocimetry in viscous fluidsJun 13 2019By taking advantage of laser Doppler velocimetry (LDV), we explore the existence of discrete wave cascades on fluid interfaces excited upon monochromatic excitation. We study viscous liquids of variable capillarity spanning a broad range of frictional ... More

Self-organized critical balanced networks: a unified frameworkJun 13 2019Asynchronous irregular (AI) and critical states are two competing frameworks proposed to explain spontaneous neuronal activity. Here, we propose a mean-field model with simple stochastic neurons that generalizes the integrate-and-fire network of Brunel ... More

Time scales in stock marketsJun 13 2019Different investment strategies are adopted in short-term and long-term depending on the time scales, even though time scales are adhoc in nature. Empirical mode decomposition based Hurst exponent analysis and variance technique have been applied to identify ... More

Multifractality of open quantum systemsJun 12 2019We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify ... More

Kapitza resistance in basic chain models with isolated defectsJun 12 2019Kapitza thermal resistance is a common feature of material interfaces. It is defined as the ratio of the thermal drop at the interface to the heat flux flowing across the interface. One expects that this resistance will depend on the structure of the ... More

Normalization of Hamiltonian and Nonlinear Stability of the Triangular Equilibrium Points in Non-resonance Case with PerturbationsJun 11 2019For the study of nonlinear stability of a dynamical system, normalized Hamiltonian of the system is very important to discuss the dynamics in the vicinity of invariant objects. In general, it represents a nonlinear approximation to the dynamics, which ... More

Normalization of Hamiltonian and nonlinear stability of triangular equilibrium points in the photogravitational restricted three body problem with P-R drag in non-resonance caseJun 11 2019Normal forms of Hamiltonian are very important to analyze the nonlinear stability of a dynamical system in the vicinity of invariant objects. This paper presents the normalization of Hamiltonian and the analysis of nonlinear stability of triangular equilibrium ... More

Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbationJun 11 2019When dynamical systems producing rhythmic behavior operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface. Examples include heel-ground ... More

Finding extremal periodic orbits with polynomial optimisation, with application to a nine-mode model of shear flowJun 10 2019Tobasco et al. [Physics Letters A, 382:382-386, 2018] recently suggested that trajectories of ODE systems which optimise the infinite-time average of a certain observable can be localised using sublevel sets of a function that arise when bounding such ... More

An automatic dynamic balancer in a rotating mechanism with time-varying angular velocityJun 10 2019We consider the system of a two ball automatic dynamic balancer attached to a rotating disc with nonconstant angular velocity. We directly compare the scenario of constant angular velocity with that when the acceleration of the rotor is taken into consideration. ... More

Magnetotransport in a perturbed periodic antidot superlatticeJun 09 2019We study a 2-dimensional model for an antidot periodic superlattice with perturbed positions of the antidots. To do so we use a quasiperiodic LG model obtained from a 3-dimensional billiard model. Our results show that infinite drifting trajectories present ... More

Closed-loop adaptive control of extreme events in a turbulent flowJun 07 2019Extreme events that arise spontaneously in chaotic dynamical systems often have an adverse impact on the system or the surrounding environment. As such, their mitigation is highly desirable. Here, we introduce a novel control strategy for mitigating extreme ... More

The route to chaos in routing games: Population increase drives period-doubling instability, chaos & inefficiency with Price of Anarchy equal to oneJun 06 2019We study a learning dynamic model of routing (congestion) games to explore how an increase in the total demand influences system performance. We focus on non-atomic routing games with two parallel edges of linear cost, where all agents evolve using Multiplicative ... More

Bifurcation without parameters in a chaotic system with a memristive elementJun 06 2019We investigate the effect of memory on a chaotic system experimentally and theoretically. For this purpose, we use Chua's oscillator as an electrical model system showing chaotic dynamics extended by a memory element in form of a double-barrier memristive ... More

Computation of kinematic and magnetic $α$-effect and eddy diffusivity tensors by Padé approximationJun 04 2019We present examples of Pad\'e approximation of the $\alpha$-effect and eddy viscosity/diffusivity tensors in various flows. Expressions for the tensors derived in the framework of the standard multiscale formalism are employed. Algebraically the simplest ... More

Bifurcation analysis of a TaO memristor modelJun 04 2019This paper presents a study of bifurcation in the time-averaged dynamics of TaO memristors driven by narrow pulses of alternating polarities. The analysis, based on a physics-inspired model, focuses on the stable fixed points and on how these are affected ... More

Dimensional scaling of flame propagation in discrete particulate cloudsJun 04 2019The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidizer is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate sources are ... More

Eigenvalue Statistics for Generalized Symmetric and Hermitian MatricesJun 03 2019The Nearest Neighbour Spacing (NNS) distribution can be computed for generalized symmetric 2x2 matrices having different variances in the diagonal and in the off-diagonal elements. Tuning the relative value of the variances we show that the distributions ... More

Many-body Chaos in a Thermalised FluidMay 31 2019We use a new measure of many-body chaos for classical systems---cross-correlators---to show that in a thermalised fluid (obtained from a non-linear, prototypical equation of hydrodynamics sharing formal similarities with models of turbulence) characterised ... More

Stability and control of power grids with diluted network topologyMay 31 2019In the present study we consider a random network of Kuramoto oscillators with inertia in order to mimic and investigate the dynamics emerging in high-voltage power grids. The corresponding natural frequencies are assumed to be bimodally Gaussian distributed, ... More

Chaos and Complexity in Quantum MechanicsMay 31 2019Jun 10 2019We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order correlators. ... More

Chaos and Complexity in Quantum MechanicsMay 31 2019Jul 02 2019We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order correlators. ... More

Chaos and Complexity in Quantum MechanicsMay 31 2019We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order correlators. ... More

Linear response in neuronal networks: from neurons dynamics to collective responseMay 31 2019We review two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitely, including network parameters dependence. This is done in a statistical physics-like approach where one associates to the ... More

Uncorrelated Configurations and Field Uniformity in Reverberation Chambers Stirred by Tunable MetasurfacesMay 29 2019Reverberation chambers are currently used to test electromagnetic compatibility as well as to characterize antenna efficiency, wireless devices, and MIMO systems. The related measurements are based on statistical averages and their fluctuations. We introduce ... More

Bohmian trajectories in an entangled two-qubit systemMay 29 2019Jun 08 2019In this paper we examine the evolution of Bohmian trajectories in the presence of quantum entanglement. We study a simple two-qubit system composed of two coherent states and investigate the impact of quantum entanglement on chaotic and ordered trajectories ... More

Bohmian trajectories in an entangled two-qubit systemMay 29 2019In this paper we examine the evolution of Bohmian trajectories in the presence of quantum entanglement. We study a simple two-qubit system composed of two coherent states and investigate the impact of quantum entanglement on chaotic and ordered trajectories ... More

Building a Maxey--Riley framework for surface ocean inertial particle dynamicsMay 29 2019Jun 05 2019A Maxey-Riley set for surface ocean inertial (i.e., buoyant, finite-size) particle dynamics is derived by vertically integrating the original Maxey-Riley set, adapted to account for Earth's rotation and sphericity effects, across a sufficiently small ... More

Building a Maxey--Riley framework for surface ocean inertial particle dynamicsMay 29 2019A Maxey-Riley set for surface ocean inertial (i.e., buoyant, finite-size) particle dynamics is derived by vertically integrating the original Maxey-Riley set, adapted to account for Earth's rotation and sphericity effects, across a sufficiently small ... More

Extreme value theory of evolving phenomena in complex dynamical systems: firing cascades in a model of neural networkMay 28 2019We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of many individual ... More

Self-oscillations in an Alpha Stirling Engine: a bifurcation analysisMay 26 2019We study a thermo-mechanical system comprised of an alpha Stirling engine and a flywheel from the perspective of dynamical systems theory. Thermodynamics establish a static relation between the flywheel's angle and the forces exerted by the two power ... More

The statistical properties of turbulence in the presence of a smart small-scale controlMay 24 2019By means of high-resolution numerical simulations, we compare the statistical properties of homogeneous and isotropic turbulence to those of the Navier-Stokes equation where small-scale vortex filaments are strongly depleted, thanks to a non-linear extra ... More

Sensitivity computation of statistically stationary quantities in turbulent flowsMay 22 2019It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not suitable for turbulent flows. The reason is that turbulent flows exhibit ... More

Sensitivity computation of statistically stationary quantities in turbulent flowsMay 22 2019Jul 03 2019It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not suitable for turbulent flows. The reason is that turbulent flows exhibit ... More

Dynamic mode decomposition for analytic mapsMay 22 2019Extended dynamic mode decomposition (EDMD) provides a class of algorithms to identify patterns and effective degrees of freedom in complex dynamical systems. We show that the modes identified by EDMD correspond to those of compact Perron-Frobenius and ... More

Bichaoticity Induced by Inherent Birhythmicity during the Oscillatory Electrodissolution of SiliconMay 21 2019The electrodissolution of p-type silicon in a fluoride-containing electrolyte is a prominent electrochemical oscillator with a still unknown oscillation mechanism. In this article, we present a study of its dynamical states occurring in a wide range of ... More

Extreme spatial clustering by fractal catastrophesMay 21 2019We analyse the spatial inhomogeneities ('spatial clustering') in the distribution of inertial particles accelerated by a space-time dependent random force. To quantify spatial clustering, the phase-space dynamics of the particles must be projected to ... More

On the perturbed photogravitational restricted five-body problem: the analysis of fractal basins of convergenceMay 20 2019In the framework of photogravitational version of the restricted five-body problem, the existence and stability of the in-plane equilibrium points, the possible regions for motion are explored and analysed numerically, under the combined effect of small ... More

Explicit Third-Order Model Reduction Formulas for General Nonlinear Mechanical SystemsMay 19 2019For general nonlinear mechanical systems, we derive closed-form, reduced-order models up to cubic order based on rigorous invariant manifold results. For conservative systems, the reduction is based on Lyapunov Subcenter Manifold (LSM) theory, whereas ... More

The partial visibility curve of the Feigenbaum cascade to chaosMay 17 2019A family of classical mathematical problems considers the visibility properties of geometric figures in the plane, e.g. curves or polygons. In particular, the {\it domination problem} tries to find the minimum number of points that are able to dominate ... More

When the goal is to generate a series of activities: A self-organized simulated robot armMay 17 2019Behavior is characterized by sequences of goal-oriented conducts, such as food uptake, socializing and resting. Classically, one would define for each task a corresponding satisfaction level, with the agent engaging, at a given time, in the activity having ... More

How Entropic Regression Beats the Outliers Problem in Nonlinear System IdentificationMay 16 2019System identification (SID) is central in science and engineering applications whereby a general model form is assumed, but active terms and parameters must be inferred from observations. Most methods for SID rely on optimizing some metric-based cost ... More

On the Automatic Parameter Selection for Permutation EntropyMay 15 2019Permutation Entropy (PE) has been shown to be a useful tool for time series analysis due to its low computational cost and noise robustness. This has drawn for its successful application in many fields. Some of these include damage detection, disease ... More

Impact of Network Topology on the Stability of DC Power GridsMay 15 2019We probe the stability of Watts-Strogatz DC power grids, in which droop-controlled producers, constant power load consumers and power lines obey Kirchhoff's circuit laws. The concept of survivability is employed to evaluate the system's response to voltage ... More

High harmonic generation with nearly circular polarized pulsesMay 15 2019According to conventional wisdom, increasing ellipticity reduces high harmonic generation by several orders because the recollision probability decreases. This is the obvious conclusion drawn from the motion of an electron in a laser field without an ... More

On the Wave Turbulence Theory for the Nonlinear Schrödinger Equation with Random PotentialsMay 14 2019We derive a new kinetic and a porous medium equations from the nonlinear Schr\"odinger equation with random potentials. The kinetic equation has a very similar form with the 4-wave turbulence kinetic equation in the wave turbulence theory. Moreover, we ... More

Dynamics of Tipping Cascades on Complex NetworksMay 14 2019Tipping points occur in a lot of systems in various disciplines such as ecology, climate science, economy or engineering. Tipping points are critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative ... More