Related papers: Self-Consistent Spin, Tidal and Dynamical Equation…
The first attempt at developing a fully self-consistent code coupling dynamics and collisions to study debris discs (Kral, Thebault, Charnoz, 2013) is presented. So far, these two crucial mechanisms were studied separately, with N-body and…
Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…
When simulating partial differential equations, hybrid solvers combine coarse numerical solvers with learned correctors. They promise accelerated simulations while adhering to physical constraints. However, as shown in our theoretical…
Gravitational waves emitted in the late inspiral of binary neutron stars are affected by their tidal deformation. We study the tidal dynamics in full general relativity through matched-asymptotic expansions and prove that the dynamical…
We obtain a new exact equilibrium solution to the N-body problem in a one-dimensional relativistic self-gravitating system. It corresponds to an expanding/contracting spacetime of a circle with N bodies at equal proper separations from one…
Tidal and riverine hydrokinetic turbines offer promising solutions for renewable energy generation in aquatic environments. However, their ecological impact, especially on fish behavior, warrants a thorough investigation. This study…
We consider third-order dynamic systems which have an integral feedback action and discontinuous relay disturbance. More specifically for the applications, the focus is on the integral plus state-feedback control of the motion systems with…
We introduce our new code, SMERCURY-T, which is based on existing codes SMERCURY (Lissauer et al. 2012) and Mercury-T (Bolmont et al. 2015). The result is a mixed-variable symplectic N-body integrator that can compute the orbital and spin…
A rigorous derivation and validation for linear fluid-structure-interaction (FSI) equations for a rigid-body-motion problem is performed in an Eulerian framework. We show that the added-stiffness terms arising in the formulation of Fanion…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird…
In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm…
Robotic manipulation and locomotion often entail nearly-simultaneous collisions -- such as heel and toe strikes during a foot step -- with outcomes that are extremely sensitive to the order in which impacts occur. Robotic simulators…
Effective equation of motion of a rattleback is obtained from the basic equation of motion with viscous friction depending on slip velocity. This effective equation of motion is used to estimate the number of spin reversals and the…
Moving grids are of interest in the numerical solution of hydrodynamical problems and in numerical relativity. We show that conventional integration methods for the simple wave equation in one and more than one dimension exhibit a number of…
We study how tides in a binary system induce some specific internal shear mixing, able to substantially modify the evolution of close binaries prior to mass transfer. We construct numerical models accounting for tidal interactions,…
We present a new approach for boundary integral equations for the wave equation with zero initial conditions. Unlike previous attempts, our mathematical formulation allows us to prove that the associated boundary integral operators are…
Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…
Tidal effects have an important impact on the late inspiral of compact binary systems containing neutron stars. Most current models of tidal deformations of neutron stars assume that the tidal bulge is directly related to the tidal field…