Related papers: A new fast multiple-shooting method for computing …
Periodically driven systems provide a powerful platform for quantum multiparameter estimation. Constructing a static effective Hamiltonian in a proper rotating frame is commonly employed to assess the attainable precision. However, such an…
In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of…
The discovery of binary and triple asteroids in addition to the execution of space missions to minor celestial bodies in the past several years have focused increasing attention on periodic orbits around irregular-shaped celestial bodies.…
We present a novel method to compute unstable periodic orbits (UPOs) that optimize the infinite-time average of a given quantity for polynomial ODE systems. The UPO search procedure relies on polynomial optimization to construct nonnegative…
Scattering problems for periodic structures have been studied a lot in the past few years. A main idea for numerical solution methods is to reduce such problems to one periodicity cell. In contrast to periodic settings, scattering from…
Quasi-periodic oscillations (QPOs) discovered in the decaying tails of giant flares of magnetars are believed to be torsional oscillations of neutron stars. These QPOs have a high potential to constrain properties of high-density matter. In…
We describe the algorithms used in the Matlab continuation and bifurcation package pde2path for Hopf bifurcation and continuation of branches of periodic orbits in systems of PDEs in 1, 2, and 3 spatial dimensions, including the computation…
Periodic surface structures are nowadays standard building blocks of optical devices. If such structures are illuminated by aperiodic time-harmonic incident waves as, e.g., Gaussian beams, the resulting surface scattering problem must be…
An algorithm for detecting periodic orbits in chaotic systems [Phys. Rev. E, 60 (1999), pp.~6172--6175], which combines the set of stabilising transformations proposed by Schmelcher and Diakonos [Phys. Rev. Lett., 78 (1997), pp.~4733--4736]…
We consider a Celestial Mechanics model: the spin-orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to compute quasi-periodic…
Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study…
Using methods from symplectic geometry, the second and fifth authors have provided theoretical groundwork and tools aimed at analyzing periodic orbits, their stability and their bifurcations in families, for the purpose of space mission…
In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that only stochastic information of the gradients of the objective function is available via a stochastic first-order oracle…
Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial satellites, leading them to migration of orbits, resonant…
In the framework of the spatial circular Hill three-body problem we illustrate the application of symplectic invariants to analyze the network structure of symmetric periodic orbit families. The extensive collection of families within this…
In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of…
Periodically driven systems offer a perfect breeding ground for out-of-equilibrium engineering of topological boundary states at zero energy ($0$-mode), as well as finite energy ($\pi$-mode), with the latter having no static analog. The…
Recent work has shown that a variety of novel phases of matter arise in periodically driven Floquet systems. Among these are many-body localized phases which spontaneously break global symmetries and exhibit novel multiplets of Floquet…
We present a detailed algorithm to construct symbolic encodings for chaotic attractors of three-dimensional flows. It is based on a topological analysis of unstable periodic orbits embedded in the attractor and follows the approach proposed…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…