Related papers: Spatio-temporal observation of higher-order modula…
Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…
We deploy a supervised machine-learning model based on a neural network to predict the temporal and spectral reshaping of a simple sinusoidal modulation into a pulse train having a comb structure in the frequency domain, which occurs upon…
Modal linear stability analysis has proven very successful in the analysis of coherent structures of turbulent flows. Formally, it describes the evolution of a disturbance in the limit of infinite time. In this work we apply modal linear…
The performance of autonomous systems heavily relies on their ability to generate a robust representation of the environment. Deep neural networks have greatly improved vision-based perception systems but still fail in challenging…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability (MI) from non-instantaneous nonlinearities in photorefractive crystals.…
Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects. In all models with local…
Nonlinear observer design for systems whose state space evolves on Lie groups is considered. The proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model…
This paper presents a theoretical model for studying the dynamics of ordering in alloys which exhibit modulated phases. The model is different from the standard time-dependent Ginzburg-Landau description of the evolution of a non-conserved…
We propose an observer for rotational dynamics subject to directional and gyroscopic measurements, which simultaneously estimates the gyroscopic biases and attitude rates. We show uniform almost global asymptotic and local exponential…
We present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a…
We obtain and investigate theoretically a broad family of stable and unstable time-periodic orbits-oscillating Turing rolls (OTR)-in the Lugiato-Lefever model of optical cavities. Using the dynamical systems tools developed in fluid…
Local rearrangements are the elements of plastic deformation in an amorphous solid. In oscillatory shear, they can switch reversibly between two distinct configurations. While these repeating relaxations are typically considered in the…
We propose a novel mechanism leading to spatiotemporal oscillations in extended systems that does not rely on local bulk instabilities. Instead, oscillations arise from the interaction of two subsystems of different spatial dimensionality.…
We present a picture of phase transitions of the system with colored multiplicative noise. Considering the noise amplitude as the power-law dependence of the stochastic variable $x^a$ we show the way to phase transitions disorder-order and…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…
The dynamic of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally…
We study the phase diagram of the sine circle map lattice with random initial conditions and identify the various types of dynamical behaviour which appear here. We focus on the regions which show spatio-temporal intermittency and…
We investigate effects of the radiation and the moduli oscillation around the stabilized values on the evolution of a 6-dimensional spacetime compactified on $S^2$. In order to see the transition from the 5-dimensional space to the…