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Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle…
In hierarchical triple systems, the inner binary is slowly perturbed by a distant companion, giving rise to large-scale oscillations in eccentricity and inclination, known as von-Zeipel-Lidov-Kozai (ZLK) oscillations. Stable systems with a…
Full relativistic simulations in three dimensions invariably develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. Recently, we introduced a numerical method…
This paper is a sequel to "Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey…
The Hannay angle has been previously studied for a celestial circular restricted three-body system by means of an adiabatic approach. In the present work, three main results are obtained. Firstly, a formal connection between perturbation…
These notes are based on lectures held at the Lanzhou university (China) during a CIMPA summer school in july 2004 but benefit from recent devellopements. Our aim is to explain some perturbations technics that allow to study the long time…
We present a theoretical method to generate a highly accurate {\em time-independent} Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which…
A variational treatment of the Gutzwiller - renormalized t-J Hamiltonian combined with the mean-field (MF) approximation is proposed, with a simultaneous inclusion of additional consistency conditions. Those conditions guarantee that the…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
A steady state plane problem of an inhomogeneous half-plane subjected to a load running along the boundary at subsonic speed is analyzed. The Lame coefficients and the density of the half-plane are assumed to be power functions of depth.…
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
For many applications, critical information about system dynamics is encoded in associated eigenvalue problems that can be posed as linear Hamiltonian systems with suitable boundary conditions. Motivated by examples from hydrodynamics,…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the…
In this paper we construct the non-trivial, renormalized Hamiltonian for a class of spin-boson models with supercritical form factors, including the one describing the Weisskopf-Wigner spontaneous emission. The renormalization is performed…
The aim of this paper is to study the relationship between Hamiltonian dynamics and constrained variational calculus. We describe both using the notion of Lagrangian submanifolds of convenient symplectic manifolds and using the so-called…
We present the conservative effective two-body Hamiltonian at the third order in the post-Newtonian expansion with gravitoelectric quadrupolar dynamical tidal-interactions. Our derivation of the effective two-body Lagrangian is based on the…
We propose an algorithm for simulating the dynamics of a geometrically local Hamiltonian $A$ under a small geometrically local perturbation $\alpha B$. In certain regimes, the algorithm achieves the optimal scaling and outperforms the…