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We study the stability of circular orbits of the electromagnetic two-body problem in an electromagnetic setting that includes retarded and advanced interactions. We give a method to derive the equations of tangent dynamics about circular…
We study the maximum of Branching Brownian motion (BBM) with branching rates that vary in space, via a periodic function of a particle's location. This corresponds to a variant of the F-KPP equation in a periodic medium, extensively studied…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…
The motion of three bodies can be solved perturbatively when a tightly bound inner binary is orbited by a distant perturber, giving rise for example to the well-known Kozai-Lidov oscillations. We propose to study the relativistic…
In this paper we use the planar circular restricted three-body problem where one of the primary bodies is an oblate spheroid or an emitter of radiation in order to determine the basins of attraction associated with the equilibrium points.…
We study extremal curves associated with a functional which is linear in the curve's torsion. The functional in question is known to capture the properties of entanglement entropy for two-dimensional conformal field theories with chiral…
We propose a fluid-rigid body interaction benchmark problem, consisting of a solid spherical obstacle in a Newtonian fluid, whose centre of mass is fixed but is free to rotate. A number of different problems are defined for both two and…
Next-generation planetary tracking methods, such as interplanetary laser ranging (ILR) and same-beam interferometry (SBI) promise an orders-of-magnitude increase in the accuracy of measurements of solar system dynamics. This requires a…
The three-body problem has been studied for more than three centuries [1,2], and has received much attention in recent years [3-5]. It shows complex dynamical phenomena due to the mutual gravitational interaction of the three bodies. Triple…
In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem…
The three-body Schr\"odinger equation of the H$_2^+$ hydrogen molecular ion with Coulomb potentials is solved in perimetric coordinates using the Lagrange-mesh method. The Lagrange-mesh method is an approximate variational calculation with…
We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the…
We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with…
The possible observations of Trojan-like extrasolar planets stimulate the deeper understanding of the stability behaviour of the co-orbital resonant motion. By using Hill's equations and the energy-rate method an analysis of the stability…
Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at…
We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitude, is expanded in power series of eccentricities and…
We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…
We investigate the appearance of mobility edges in a one-dimensional non-Hermitian tight-banding model with alternating hopping constants and slowly varying quasi-periodic on-site potentials. Due to the presence of slowly varying exponent,…
We extract all the invariants (i.e. all the functions which do not depend on the choice of phase-space coordinates) of the dynamics of two point-masses, at the third post-Newtonian (3PN) approximation of general relativity. We start by…
A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total…