Théorie générale des systèmes

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By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

Dynamical flow networks serve as macroscopic models for, e.g., transportation networks, queuing networks, and distribution networks. While the flow dynamics in such networks follow the conservation of mass on the links, the outflow from each link is often ...

This paper deals with the initial value problem for a semilinear wave equation on a bounded domain and solutions are required to vanish on the boundary of this domain. The essential feature of the situation considered here is that the ellipticity of the sp ...

This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...

Beliefs inform the behaviour of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...

We investigate the stability of the steady vertical path and the emerging trajectories of a buoyancy -driven annular disk as the diameter of its central hole is varied. The steady and axisymmetric wake associated with the steady vertical path of the disk, ...

Dynamical system (DS) based motion planning offers collision-free motion, with closed-loop reactivity thanks to their analytical expression. It ensures that obstacles are not penetrated by reshaping a nominal DS through matrix modulation, which is construc ...

This paper proposes a data-driven control design method for nonlinear systems that builds upon the Koopman operator framework. In particular, the Koopman operator is used to lift the nonlinear dynamics to a higher-dimensional space where the so-called obse ...

In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...

One-dimensional materials have gained much attention in the last decades: from carbon nanotubes to ultrathin nanowires to few-atom atomic chains, these can all display unique electronic properties and great potential for next-generation applications. Exfol ...

Dynamic aperture is an important concept for the study of non-linear beam dynamics in circular accelerators. It describes the extent of the phase-space region where a particle's motion remains bounded over a given number of turns. Understanding the feature ...

Since the discovery of dissipative Kerr solitons in optical microresonators, significant progress has been made in the understanding of the underlying physical principles from the fundamental side and generation of broadband coherent optical Kerr frequency ...

We study the drainage of a viscous liquid film coating the outside of a solid horizontal cylinder, where gravity acts vertically. We focus on the limit of large Ohnesorge numbers Oh, where inertia is negligible compared to viscous effects. We first study t ...

Accurate human trajectory prediction is crucial for applications such as autonomous vehicles, robotics, and surveillance systems. Yet, existing models often fail to fully leverage the non-verbal social cues human subconsciously communicate when navigating ...

We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...

Théorie générale des systèmes

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Additive and geometric transversality of fractal sets in the integers

Stability: a search for structure

The Strong Integral Input-to-State Stability Property in Dynamical Flow Networks

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

Stochastic pairwise preference convergence in Bayesian agents

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

Instability and trajectories of buoyancy-driven annular disks: A numerical study

Reactive collision-free motion generation in joint space via dynamical systems and sampling-based MPC

Data-Driven Control Synthesis using Koopman Operator: A Robust Approach

Dynamical system approach to navigation around obstacles

Searching for the Thinnest Metallic Wire

Optimizing Dynamic Aperture Studies with Active Learning

Emergent nonlinear dynamics in photonic lattices

Stability of a liquid layer draining around a horizontal cylinder: Interplay of capillary and gravity forces

Social-Transmotion: Promptable Human Trajectory Prediction

Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

Frustrated magnets in the limit of infinite dimensions: Dynamics and disorder-free glass transition