On the normal exponential map in singular conformal metrics

Brake orbits and homoclinics of autonomous dynamical systems correspond, via Maupertuis principle, to geodesics in Riemannian manifolds endowed with a metric which is singular on the boundary (Jacobi metric). Motivated by the classical, yet still intriguing in many aspects, problem of establishing multiplicity results for brake orbits and homoclinics, as done in [6, 7, 10], and by the development of a Morse theory in [8] for geodesics in such kind of metric, in this paper we study the related normal exponential map from a global perspective.Comment: 10 page

Functions on the sphere with critical points in pairs and orthogonal geodesic chords

Using an estimate on the number of critical points for a Morse-even function on the sphere $\mathbb S^m$, $m\ge1$, we prove a multiplicity result for orthogonal geodesic chords in Riemannian manifolds with boundary that are diffeomorphic to Euclidean balls. This yields also a multiplicity result for brake orbits in a potential well.Comment: 12 pages, 3 figure

Morse Theory for geodesics in singular conformal metrics

Motivated by the use of degenerate Jacobi metrics for the study of brake orbits and homoclinics, we develop a Morse theory for geodesics in conformal metrics having conformal factors vanishing on a regular hypersurface of a Riemannian manifold.Comment: 22 pages. To appear in Communications in Analysis and Geometr

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.Comment: 39 pages, LaTeX2e, amsar

Curvature estimates for submanifolds in warped products

We give estimates on the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.Comment: 21 page

Human operator performance of remotely controlled tasks: Teleoperator research conducted at NASA's George C. Marshal Space Flight Center

The capabilities within the teleoperator laboratories to perform remote and teleoperated investigations for a wide variety of applications are described. Three major teleoperator issues are addressed: the human operator, the remote control and effecting subsystems, and the human/machine system performance results for specific teleoperated tasks

Traveling Traders' Exchange Problem: Stochastic Modeling Framework and Two-Layer Model Identification Strategy

The Travelling Traders’ Exchange Problem (TTEP) is formalised, aiming at studying the collision-exchange systems found in various research areas. As an example of the TTEP models, a 1-D model is developed and characterised in detail. The computational stochastic simulation of the 1-D TTEP model relies on a stochastic simulation algorithm implemented based on the Monte Carlo method. A model identification framework is proposed where the money distribution in the system obtained from the stochastic model is characterised in terms of (a) standard deviation of the money redistribution; (b) its probability density function. Results indicate that the expressions of the estimated functions for (a) and (b) are tightly related to the system input conditions. The example of curve fitting on the probability density function shows how the variation of money redistribution in the system in time is driven by different values of the parameters describing the interaction mechanism

A stochastic modelling approach for the characterisation of collision exchange processes

Collision-exchange process is a common physical process where system members interact with each other to exchange materials and these individual interactions cumulatively drive a macroscopic system evolution in time. In this paper, a compartment-based stochastic model is formulated to study the collision-exchange process between members in a system. The discrete Markov analysis on the stochastic model presents the analytical results that show the independence of the system equilibrium on its initial distribution, and the derived differential equations reveal the deterministic time evolution of material amount on system members. As a specific example of a physical system that can be described via this model, a seed coating process is presented where the inter-particle coating variability is expressed by the stochastic model parameters. The promising agreement between simulation predictions and experimental results demonstrates the feasibility of stochastic modelling on the collision-exchange process and facilitates further model identification and applications to industrial processes