Related papers: Examining the evolution of phase-space elements fo…
This paper extends our previous work~(Szumi\'nski and Maciejewski, 2024), where we explored the dynamics and integrability of the double-spring pendulum. Here, we investigate the variable-length double pendulum, a three-degree-of-freedom…
The comprehensive investigation of the temporal evolution of the diocotron instability of the plane electron strip on the linear stage of its development is performed. By using the Kelvin's method of the shearing modes we elucidate the role…
Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence'. Here, we study these phenomena using the framework of Exact Coherent Structures, which has…
We carry out a systematic study of a novel type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one dimensional model. The chaos is characterized by a smooth interplay of different spatial scales,…
The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with…
The Lyapunov exponents of a dynamical system measure the average rate of exponential stretching along an orbit. Positive exponents are often taken as a defining characteristic of chaotic dynamics. However, the standard…
A fundamental problem in neuroscience is understanding how a network's properties dictate its function. Connectomics provides one avenue to predict nervous system function. To test this explicitly, we systematically measure signal…
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear…
The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the…
Motivated by recent experiments, the isotropic-nematic phase transition in chromonic liquid crystals is studied. As temperature decreases, nematic nuclei nucleate, grow, and coalesce, giving rise to tactoid microstructures in an isotropic…
We exploit flow propagation on the directed neuronal network of the nematode Caenorhabditis elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which…
Partial differential equations, and their chaotic solutions, are pervasive in the modelling of complex systems in engineering, science, and beyond. Data-driven methods can find solutions to partial differential equations with a…
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…
Undulatory locomotion of microorganisms like soil-dwelling worms and spermatozoa, in structured environments, is ubiquitous in nature. They navigate complex environments consisting of fluids and obstacles, negotiating hydrodynamic effects…
A quantitative understanding of how sensory signals are transformed into motor outputs places useful constraints on brain function and helps reveal the brain's underlying computations. We investigate how the nematode C. elegans responds to…
We study the behavior of the elastic polymer, a model of a directed polymer in a continuous Gaussian random environment that is independent in time and correlated in space, as the dimension of the environment is taken to infinity. We give…
We study the properties of a nano-electromechanical system in the coherent regime, where the electronic and vibrational time scales are of the same order. Employing a master equation approach, we obtain the stationary reduced density matrix…
In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…
Nematode species are well-known for their invariant cell lineage pattern during development. Combining knowledge about the fate specification induced by asymmetric division and the anti-correlation between cell cycle length and cell volume…
We analyze speech embeddings from structured clinical interviews of psychotic patients and healthy controls by treating language production as a high-dimensional dynamical process. Lyapunov exponent (LE) spectra are computed from word-level…