Related papers: Non-linear dynamics of multibody systems: a system…
We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…
We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
In this paper, the D2-IBC (Data-Driven Inversion Based Control) approach for nonlinear control is introduced and analyzed. The method does not require any a-priori knowledge of the system dynamics and relies on a two degrees of freedom…
Bond graphs can be used to build thermodynamically-compliant hierarchical models of biomolecular systems. As bond graphs have been widely used to model, analyse and synthesise engineering systems, this paper suggests that they can play the…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
Understanding the dynamics of two inertial bodies coupled via a friction interface is essential for a wide range of systems and motion control applications. Coupling terms within the dynamics of an inertial pair connected via a passive…
Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential…
We study the dynamics of particles coupled to gravity in (2 + 1) dimensions. Using the ADM formalism, we derive the general Hamiltonian for an N-body system and analyze the dynamics of a two-particle system. Non-linear terms are found up to…
Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…
In quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Quite opposed, in classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between…
An asymmetric two-link robot supported atop a flat platform by wheels that roll and pivot freely, but do not slip laterally, will develop forward momentum if the joint between the links is actuated internally. In particular, oscillations in…
We present a framework for constructing physics and causally constrained neural models of turbulent dynamical systems from data. We first formulate a finite-time flow map with strict energy-preserving nonlinearities for stable modeling of…
We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the…
In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteristics. An off-lattice modelling approach is considered…
A generalized formalism of the so-called non-adiabatic quantum molecular dynamics is presented, which applies for atomic many-body systems in external laser fields. The theory treats the nuclear dynamics and electronic transitions…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…
We present a theory of causality in dynamical systems using Koopman operators. Our theory is grounded on a rigorous definition of causal mechanism in dynamical systems given in terms of flow maps. In the Koopman framework, we prove that…
A simple phenomenological model for describing the conformational dynamics of biological macromolecules via the nonlinearity-induced instabilities is proposed. It is shown that the interaction between charges and bending degrees of freedom…
The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to…