Lower bounds on the lowest spectral gap of singular potential Hamiltonians

We analyze Schr\"odinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two eigenvalues below its essential spectrum we derive estimates on the lowest spectral gap. In the case where the sub-manifold is a finite curve in two dimensional Euclidean space the size of the gap depends only on the following parameters: the length, diameter and maximal curvature of the curve, a certain parameter measuring the injectivity of the curve embedding, and a compact sub-interval of the open, negative energy half-axis which contains the two lowest eigenvalues.Comment: 24 pages. To appear in slightly different form in Annales Henri Poincar

Polynomial coefficients of thermochemical data for the C-H-O-N system

Thermodynamic data are required input for the finite kinetics and equilibrium computer programs needed for modeling the combustion of hydrocarbons in the fields of energy and pollution research. Least squares determined coefficients of the curve-fitted thermodynamic data for 193 species in the C-H-O-N system are presented in card image form and are of suitable format for use by common computer programs

Interactive design of constrained variational curves

A constrained variational curve is a curve that minimizes some energy functional under certain interpolation constraints. Modeling curves using constrained variational principles is attractive, because the designer is not bothered with the precise representation of the curve (e.g. control points). Until now, the modeling of variational curves is mainly done by means of constraints. If such a curve of least energy is deformed locally (e.g. by moving its control points) the concept of energy minimization is lost. In this paper we introduce deform operators with built-in energy terms. We have tested our ideas in a prototype system for modeling uniform B-spline curves

The Jacobi-Maupertuis Principle in Variational Integrators

In this paper, we develop a hybrid variational integrator based on the Jacobi-Maupertuis Principle of Least Action. The Jacobi-Maupertuis principle states that for a mechanical system with total energy E and potential energy V(q), the curve traced out by the system on a constant energy surface minimizes the action given by ∫√[2(E-V(q))] ds where ds is the line element on the constant energy surface with respect to the kinetic energy of the system. The key feature is that the principle is a parametrization independent geodesic problem. We show that this principle can be combined with traditional variational integrators and can be used to efficiently handle high velocity regions where small time steps would otherwise be required. This is done by switching between the Hamilton principle and the Jacobi-Maupertuis principle depending upon the kinetic energy of the system. We demonstrate our technique for the Kepler problem and discuss some ongoing and future work in studying the energy and momentum behavior of the resulting integrator

Forecasting technology costs via the Learning Curve – Myth or Magic?

To further our understanding of the effectiveness of learning or experience curves to forecast technology costs, a statistical analysis using historical data has been carried out. Three hypotheses have been tested using available data sets that together shed light on the ability of experience curves to forecast future technology costs. The results indicate that the Single Factor Learning Curve is a highly effective estimator of future costs with little bias when errors were viewed in their log format. However it was also found that due to the convexity of the log curve an overestimation of potential cost reductions arises when returned to their monetary units. Furthermore the effectiveness of increasing weights for more recent data was tested using Weighted Least Squares with exponentially increasing weights. This resulted in forecasts that were typically less biased than when using Ordinary Least Square and highlighted the potential benefits of this method.Forecasting, Learning curves, Renewable energy

J004457+4123 (Sharov 21): not a remarkable nova in M31 but a background quasar with a spectacular UV flare

We announce the discovery of a quasar behind the disk of M31, which was previously classified as a remarkable nova in our neighbour galaxy. The paper is primarily aimed at the outburst of J004457+4123 (Sharov 21), with the first part focussed on the optical spectroscopy and the improvement in the photometric database. Both the optical spectrum and the broad band spectral energy distribution of Sharov 21 are shown to be very similar to that of normal, radio-quiet type 1 quasars. We present photometric data covering more than a century and resulting in a long-term light curve that is densely sampled over the past five decades. The variability of the quasar is characterized by a ground state with typical fluctuation amplitudes of ~0.2 mag around B~20.5, superimposed by a singular flare of ~2 yr duration (observer frame) with the maximum at 1992.81 where the UV flux has increased by a factor of ~20. The total energy in the flare is at least three orders of magnitudes higher than the radiated energy of the most luminous supernovae, provided that it comes from an intrinsic process and the energy is radiated isotropically. The profile of the flare light curve appears to be in agreement with the standard predictions for a stellar tidal disruption event where a ~10 M_sun giant star was shredded in the tidal field of a ~2...5 10^8 M_sun black hole. The short fallback time derived from the light curve requires an ultra-close encounter where the pericentre of the stellar orbit is deep within the tidal disruption radius. Gravitational microlensing provides an alternative explanation, though the probability of such a high amplification event is very low.Comment: Accepted for publication in Astronomy and Astrophysics, 14 pages, 11 figure