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Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). The latter…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
For diffeomorphisms or for non-singular flows, there are many results relating properties persistent under C1 perturbations and global structures for the dynamics ( such as hyperbolicity, partial hyperbolicity, dominated splitting).…
We present an experimental investigation of the dynamics and flow-coupling of convective turbulent flows in a cylindrical Rayleigh-Benard convection cell with two immiscible fluids, water and fluorinert FC-77 electronic liquid (FC77). It is…
Lagrangian Neural Networks (LNNs) can learn arbitrary Lagrangians from trajectory data, but their unusual optimization objective leads to significant training instabilities that limit their application to complex systems. We propose several…
The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the…
The interaction between a turbulent convective boundary layer (CBL) and the underlying land surface is an important research problem in the geosciences. In order to model this interaction adequately, it is necessary to develop tools which…
To each flat conformal structure (FCS) of hyperbolic type in the sense of Kulkarni-Pinkall, we associate, for all $\theta\in[(n-1)\pi/2,n\pi/2[$ and for all $r>\opTan(\theta/n)$ a unique immersed hypersurface…
Emergence, a global property of complex adaptive systems (CASs) constituted by interactive agents, is prevalent in real-world dynamic systems, e.g., network-level traffic congestions. Detecting its formation and evaporation helps to monitor…
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…
Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak…
Hyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are…
At low Reynolds numbers, the hydrodynamic interaction between dumbbells driven by an external rotating field can be attractive or repulsive. Dumbbells of dissimilar asymmetric shape or different coupling to the external field undergo…
We study a three-dimensional fluid model describing rapidly rotating convection that takes place in tall columnar structures. The purpose of this model is to investigate the cyclonic and anticyclonic coherent structures. Global existence,…
Probabilistic decoding in Large Language Models (LLMs) often yields inconsistent outputs, particularly on complex or long-form questions. Self-Consistency (SC) mitigates this for short-form QA by majority voting over exact strings, whereas…
Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the…
Spiral waves are considered to be one of the potential mechanisms that maintains complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the…
Every volume-preserving centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (1) has two distinct centre Lyapunov exponents, or (2) exhibits an invariant continuous line field (or pair of line fields) tangent…
It has been known for some time that there exist $5$ essentially different real forms of the complex affine Kac-Moody algebra of type $A_2^{(2)}$ and that one can associate $4$ of these real forms with certain classes of "integrable…
The Riemannian product of two hyperbolic planes of constant Gaussian curvature -1 has a natural K\"ahler structure. In fact, it can be identified with the complex hyperbolic quadric of complex dimension two. In this paper we study…