Related papers: Successive Continuation for Locating Connecting Or…
We give a method to determine relative periodic orbits in point vortex systems: it consists mainly into perform a symplectic reduction on a fixed point submanifold in order to obtain a two-dimensional reduced phase space. The method is…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
Orbit determination of spacecraft in orbit has been mostly dependent on either GNSS satellite signals or ground station telemetry. Both methods present their limitations, however: GNSS signals can only be used effectively in earth orbit,…
An extended interference pattern close to surface may result in both a transmissive or evanescent surface fields for large area manipulation of trapped particles. The affinity of differing particle sizes to a moving standing wave light…
We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance, the algorithm identifies candidate eigenpairs for which…
We propose a distributed positioning algorithm to estimate the unknown positions of a number of target nodes, given distance measurements between target nodes and between target nodes and a number of reference nodes at known positions.…
The Obreshkov method is a single-step multi-derivative method used in the numerical solution of differential equations and has been used in recent years in efficient circuit simulation. It has been shown that it can be made of arbitrary…
A method for determining the orbital parameters of interacting pairs of galaxies is presented and evaluated using artificial data. The method consists of a genetic algorithm which can search efficiently through the very large space of…
In this paper, we explore the radial projection method for locally finite point sets and provide numerical examples for different types of order. The main question is whether the method is suitable to analyse order in a quantitive way. Our…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
We propose a method for computation of stable and unstable sets associated to hyperbolic equilibria of nonautonomous ODEs and for computation of specific type of connecting orbits in nonautonomous singular ODEs. We apply the method to a…
We present local distributed, stochastic algorithms for \emph{alignment} in self-organizing particle systems (SOPS) on two-dimensional lattices, where particles occupy unique sites on the lattice, and particles can make spatial moves to…
The proposed article is devoted to the study of the problem of constructing phase trajectories in the vicinity of a singular point. This paper presents a more expanded view of this problem in comparison with those previously considered by…
The ability of robots to estimate their location is crucial for a wide variety of autonomous operations. In settings where GPS is unavailable, measurements of transmissions from fixed beacons provide an effective means of estimating a…
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we…
Low earth orbit satellite constellations with intersatellite links (ISLs) are currently being developed and deployed. The availability of ISLs provides the capability to route across the satellite constellation, rather than using the…
We consider methods based on the topological degree theory to compute periodic orbits of area preserving maps. Numerical approximations of the Kronecker integral and the application of Stenger's method allows us to compute the value of the…
The application of radio-based positioning systems is ever increasing. In light of the dissemination of the Internet of Things and location-aware communication systems, the demands on localization architectures and amount of possible use…
A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…
In this paper, we propose a parallel optimization method for electronic structure calculations based on a single orbital-updating approximation. It is shown by our numerical experiments that the method is efficient and reliable for atomic…