Constructing Linear Families from

Generating families of linear models from nonlinear parameter-dependent equations requires explicit analytical characterization of the equilibrium surface. Doing so in terms of the original system parameters is generally not possible. Introducing an alternative parameterization, we propose an efficient method for computing local linear parameter-dependent families. Although local, these families can be constructed anywhere, specifically around bifurcation points where other methods fail

Splitting Methods for the Time-dependent Schrödinger Equation

Cheap and easy to implement fourth-order methods for the Schrodinger equation with time-dependent Hamiltonians are introduced. The methods require evaluations of exponentials of simple unidimensional integrals, and can be considered an averaging technique, preserving many of the qualitative properties of the exact solution

Time-Independent Approaches

1 Similarities and Differences After the success which mean field methods have had for bound state problems in various fields of physics, it was only natural to try the mean field concept for scattering states as well. The original attempt in this direction is the time-dependent Hartree-Fock method (TDHF) developed about 20 years ago [1]. In this method one solves the equation of motion for the one-body density operator ae = ae (t), i _h @ @ t ae = [h; ae] ; (1.1) with an initial condition for ae, ae (ti) = aei; (1.2

Collision risk assessment between UAS and landing aircraft in restricted airspace surrounding an airport using 3D Monte-Carlo simulation

The availability of off the shelf, easy to control, unmanned aerial systems (UAS) on the market has led to an increase in report of UAS incursion into aerodrome. Such incursions would often result in lengthy airport shutdowns and cause disruption to air traffic operations throughout the region. Additionally, advancement in UAS flight control, motor efficiency, and battery life made the UAS more attractive to cargo operators for carrying parcels, both in urban area and near major port of call. While advancements have been made in the past decade in detection and avoidance of UAS traffics, the systems depend on either having fully cooperative traffic or sensor capability beyond what is currently available. This paper presents a 3D collision risk assessment model that was created to assess both the collision risk posed by an intruding non-cooperative UAS, as well as the safety risk associated with UAS operating within the 5km restricted airspace using predetermined route. Monte-Carlo simulations based on the 3D flight dynamics of the UAS are used to calculate the probability of collision at each time-step under the different scenarios.Accepted versionWe would like to thank Air Traffic Management Research Institute for funding this research under Programme 2: Urban Aerial Transport Traffic Management & Systems