Related papers: The special concave toric domain for the rotating …
The dynamics near the Lagrange equilibria $L_1$ and $L_2$ of the Circular Restricted Three-body Problem has gained attention in the last decades due to its relevance in some topics such as the temporary captures of comets and asteroids and…
We study the Quadratic Cycle Cover Problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and…
In this paper, we consider the rigid spacecraft with an internal rotor as a regular point reducible regular controlled Hamiltonian (RCH) system. In the cases of coincident and non-coincident centers of buoyancy and gravity, we give…
We present a tidal model for treating the rotational evolution in the general three-body problem with arbitrary viscosities, in which all the masses are considered to be extended and all the tidal interactions between pairs are taken into…
An important problem in the breeding of livestock, crops, and forest trees is the optimum of selection of genotypes that maximizes genetic gain. The key constraint in the optimal selection is a convex quadratic constraint that ensures…
We address the longstanding challenge in quantum many-body theory of reconciling unitary dynamics with irreversible relaxation. In classical chaos, the unitary evolution operator develops Ruelle-Pollicott (RP) resonances inside the unit…
Transition from regular to chaotic dynamics in a crystal made of singular scatterers $U(r)=\lambda |r|^{-\sigma}$ can be reached by varying either sigma or lambda. We map the problem to a localization problem, and find that in all space…
The generalized relativistic effective core potential (GRECP) approach is employed in the framework of multireference single- and double-excitation configuration interaction (MRD-CI) method to calculate the spin-orbit (SO) splitting in the…
Using the Euclidean path integral approach with functional methods, we discuss the $(g_{0} \phi^{p})_{d}$ self-interacting scalar field theory, in the strong-coupling regime. We assume the presence of macroscopic boundaries confining the…
The collective dynamics of objects moving through a viscous fluid is complex and counterintuitive. A key to understanding the role of nontrivial particle shape in this complexity is the interaction of a pair of sedimenting spheroids. We…
Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework…
In this article we give an extention of the L^2-theory of anisotropic singular perturbations for elliptic problems. We study a linear and some nonlinear problems involving L^p data (1<p<2). Convergences in pseudo Sobolev spaces are proved…
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…
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…
In this paper we look at a class of random optimization problems that arise in the forms typically known in statistical physics as Little models. In \cite{BruParRit92} the Little models were studied by means of the well known tool from the…
The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g. the three-body problem). The main…
We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…
By using the \emph{Rydberg--Klein--Rees} (RKR) formulas to solve the inverse Schr\"{o}dinger problem, we found a confining bottom-up potential from a given eigenvalue spectrum. To illustrate this methodology, we consider the vector meson…
We investigate the Kepler problem using a symplectic structure consistent with the commutation rules of the noncommutative quantum mechanics. We show that a noncommutative parameter of the order of $10^{-58} \text m^2$ gives observable…
We determine analytically the phase diagram of the toric code model in a parallel magnetic field which displays three distinct regions. Our study relies on two high-order perturbative expansions in the strong- and weak-field limit, as well…