On Computing the Translations Norm in the Epipolar Graph

This paper deals with the problem of recovering the unknown norm of relative translations between cameras based on the knowledge of relative rotations and translation directions. We provide theoretical conditions for the solvability of such a problem, and we propose a two-stage method to solve it. First, a cycle basis for the epipolar graph is computed, then all the scaling factors are recovered simultaneously by solving a homogeneous linear system. We demonstrate the accuracy of our solution by means of synthetic and real experiments.Comment: Accepted at 3DV 201

Ionic Kratzer bond theory and vibrational levels for achiral covalent bond HH

A dihydrogen Hamiltonian reduces to the Sommerfeld-Kratzer-potential, adapted for field quantization according to old-quantum theory. Constants omega_e, k_e and r_e needed for the H_2 vibrational system derive solely from hydrogen mass m_H. For H_2, a first principles ionic Kratzer oscillator returns the covalent bond energy within 0,08 % and all levels within 0,02 %, 30 times better than the Dunham oscillator and as accurate as early ab initio QM.Comment: 21 pages, 4 figures, 2 tables, at the institutional archive Ghent University, references and early ab initio QM results added, typo's remove

Design Methodology and Performance Evaluation of New Generation Sounding Rockets

Sounding rockets are currently deployed for the purpose of providing experimental data of the upper atmosphere, as well as for microgravity experiments. This work provides a methodology in order to design, model, and evaluate the performance of new sounding rockets. A general configuration composed of a rocket with four canards and four tail wings is sized and optimized, assuming different payload masses and microgravity durations. The aerodynamic forces are modeled with high fidelity using the interpolation of available data. Three different guidance algorithms are used for the trajectory integration: constant attitude, near radial, and sun-pointing. The sun-pointing guidance is used to obtain the best microgravity performance while maintaining a specified attitude with respect to the sun, allowing for experiments which are temperature sensitive. Near radial guidance has instead the main purpose of reaching high altitudes, thus maximizing the microgravity duration. The results prove that the methodology at hand is straightforward to implement and capable of providing satisfactory performance in term of microgravity duration

A Generalized Variational Principle with Applications to Excited State Mean Field Theory.

We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean field theory, density functional theory, multireference theory, and quantum Monte Carlo. Like the standard variational principle, this generalized variational principle amounts to the optimization of a nonlinear function that, in the limit of an arbitrarily flexible wave function, has the desired Hamiltonian eigenstate as its global minimum. Unlike the standard variational principle, it can target excited states and select individual states in cases of degeneracy or near-degeneracy. As an initial demonstration of how this approach can be useful in practice, we employ it to improve the optimization efficiency of excited state mean field theory by an order of magnitude. With this improved optimization, we are able to demonstrate that the accuracy of the corresponding second-order perturbation theory rivals that of singles-and-doubles equation-of-motion coupled cluster in a substantially broader set of molecules than could be explored by our previous optimization methodology

A numerical canonical transformation approach to quantum many body problems

We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of numerical canonical transformations.Comment: 10 pages, 3 encapsulated figures. Parts of the paper are substantially revised to refer to previous similar method