Related papers: Analytic Solution for Perturbed Keplerian Motion U…

We consider a singular perturbation for a family of analytic symplectic maps of the annulus possessing a KAM torus. The perturbation introduces dissipation and contains an adjustable parameter. By choosing the adjustable parameter, one can…

The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared to diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is…

We study the small-mass asymptotic behavior of so-called angular integrals, appearing in phase-space calculations in perturbative quantum field theory. For this purpose we utilize the strategy of expansion by regions, which is a universal…

We consider the propagation of acoustic time-harmonic waves in a homogeneous media containing periodic lattices of spherical or cylindrical inclusions. It is assumed that the wavelength has the order of the periods of the lattice while the…

As periodic orbit theory works badly on computing the observable averages of dynamical systems with intermittency, we propose a scheme to cooperate with cycle expansion and perturbation theory so that we can deal with intermittent systems…

This work presents an analytical perturbation method to define and study the dynamics of frozen orbits under the perturbation effects produced by the oblatness of the main celestial body. This is done using a perturbation method purely…

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…

The long-term dynamics of perturbed Keplerian motion is usually analyzed in simplified models as part of the preliminary design of artificial satellites missions. It is commonly approached by averaging procedures that deal with literal…

High-frequency wave propagation is often modelled by nonlinear Friedrichs systems where both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, which causes oscillations with wavelengths…

The spacecraft attitude tracking problem is addressed with actuator faults and uncertainties among inertias, external disturbances, and, in particular, state estimates. A continuous sliding mode attitude controller is designed using…

The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…

The description of the cosmological expansion and its possible local manifestations via treating the proper conformal transformations as a coordinate transformation from a comoving Lorentz reference frame (RF) to an uniformly accelerated RF…

The problem of the time required for a diffusing molecule, within a large bounded domain, to first locate a small target is prevalent in biological modeling. Here we study this problem for a small spherical target. We develop uniform in…

In this paper, we study time-asymptotic propagation phenomena for a class of dispersive equations on the line by exploiting precise estimates of oscillatory integrals. We propose first an extension of the van der Corput Lemma to the case of…

In galactic nuclei, the gravitational potential is dominated by the central supermassive black hole, so stars follow quasi-Keplerian orbits. These orbits are distorted by gravitational forces from other stars, leading to long-term orbital…

We provide a rigorous derivation of an asymptotic formula for perturbations in the resonance values caused by the presence of finite number of anisotropic imperfections of small shapes with constitutive parameters different from the…

In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…

Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians. The error of the algorithm is the sum of each error Hamiltonian's perturbation on the exact solution.…

We present a method to study the time variation of the orbital parameters of a Post-Keplerian binary system undergoing a generic external perturbation. The method is the relativistic extension of the planetary Lagrangian equations. The…

We apply expansion methods to obtain an approximate expression in terms of elementary functions for the space and time dependence of wave packets in a dispersive medium. The specific application to pulses in a cold plasma is considered in…