Related papers: CHASSIS - Inverse Modelling of Relaxed Dynamical S…
In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with…
The approach of dynamical systems is a useful tool to investigate the cosmological history that follows from modified theories of gravity. It provides qualitative information on the typical background solutions in a parametrized family of…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…
This article is devoted to the study of the dynamical behavior of a collisionless kinetic gas in d=1,2,3 space dimensions which is trapped in a rotationally symmetric potential well. Although at the microscopic level the trajectories of…
Seismic full waveform inversion (FWI) is a powerful technique to generate high resolution images of the Earth's interior. However, significant uncertainty exists in all FWI solutions due to imperfect acquisition geometries, inherent noise…
Controlling the state of motion of optically levitated nanoparticles is crucial for the advancement of precision sensing, fundamental tests of physics, and the development of hybrid classical-quantum technologies. Experimentally, such…
In Newtonian gravity, a self-gravitating collisionless gas around a massive object such as a star or a planet is modeled via the Vlasov--Poisson system with an external Kepler potential. The presence of this attractive potential allows for…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system…
A discrete and exact algorithm for obtaining planetary systems is derived in a recent article (Eur. Phys. J. Plus 2022, 137:99). Here the algorithm is used to obtain planetary systems with forces different from the Newtonian inverse square…
High-quality nanomechanical oscillators can sensitively probe force, mass, or displacement in experiments bridging the gap between the classical and quantum domain. Dynamics of these stochastic systems is inherently determined by the…
Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas and wave-particle systems. These systems, adequately described by the…
The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability --…
In this paper, we have presented a power law cosmological model and its dynamical system analysis in $f(T,\phi)$ gravity, where $T$ is the torsion scalar and $\phi$ is the canonical scalar field. The two well-motivated forms of the…
State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in…
A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
We consider the dynamical system \begin{equation*}\left\{ \begin{array}{ll} v(t)\in\partial\phi(x(t))\\ \lambda\dot x(t) + \dot v(t) + v(t) + \nabla \psi(x(t))=0, \end{array}\right.\end{equation*} where $\phi:\R^n\to\R\cup\{+\infty\}$ is a…