Symplectic-energy-momentum preserving variational integrators

The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving. To do this, a space–time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy. Criteria for the solvability of the time steps and some numerical examples are given

Frictional Collisions Off Sharp Objects

This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. Such situations arise in the early stage of fragmentation when a number of angular fragments undergo complex collision sequences before eventually scattering. Such situations precludes the application of most contact algorithms proposed to date

Asynchronous Variational Integrators

We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; (ii) the algorithms derive from a spacetime form of a discrete version of Hamilton’s variational principle. As a consequence of this variational structure, the algorithms conserve local momenta and a local discrete multisymplectic structure exactly. To guide the development of the discretizations, a spacetime multisymplectic formulation of elastodynamics is presented. The variational principle used incorporates both configuration and spacetime reference variations. This allows a unified treatment of all the conservation properties of the system.A discrete version of reference configuration is also considered, providing a natural definition of a discrete energy. The possibilities for discrete energy conservation are evaluated. Numerical tests reveal that, even when local energy balance is not enforced exactly, the global and local energy behavior of the AVIs is quite remarkable, a property which can probably be traced to the symplectic nature of the algorith

Variational integrators, the Newmark scheme, and dissipative systems

Variational methods are a class of symplectic-momentum integrators for ODEs. Using these schemes, it is shown that the classical Newmark algorithm is structure preserving in a non-obvious way, thus explaining the observed numerical behavior. Modifications to variational methods to include forcing and dissipation are also proposed, extending the advantages of structure preserving integrators to non-conservative systems

Nonsmooth Lagrangian mechanics and variational collision integrators

Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated

First observations and magnitude measurement of Starlink's Darksat

Measure the Sloan g' magnitudes of the Starlink's STARLINK-1130 (Darksat) and 1113 LEO communication satellites and determine the effectiveness of the Darksat darkening treatment at 475.4\,nm. Two observations of the Starlink's Darksat LEO communication satellite were conducted on 2020/02/08 and 2020/03/06 using a Sloan r' and g' filter respectively. While a second satellite, STARLINK-1113 was observed on 2020/03/06 using a Sloan g' filter. The initial observation on 2020/02/08 was a test observation when Darksat was still manoeuvring to its nominal orbit and orientation. Based on the successful test observation, the first main observation was conducted on 2020/03/06 along with an observation of the second Starlink satellite. The calibration, image processing and analysis of the Darksat Sloan g' image gives an estimated Sloan g' magnitude of $7.46\pm0.04$ at a range of 976.50\,km. For STARLINK-1113 an estimated Sloan g' magnitude of $6.59\pm0.05$ at a range of 941.62\,km was found. When scaled to a range of 550\,km and corrected for the solar and observer phase angles, a reduction by a factor of two is seen in the reflected solar flux between Darksat and STARLINK-1113. The data and results presented in this work, show that the special darkening coating used by Starlink for Darksat has darkened the Sloan g' magnitude by $0.77\pm0.05$\,mag, when the range is equal to a nominal orbital height (550\,km). This result will serve members of the astronomical community modelling the satellite mega-constellations, to ascertain their true impact on both the amateur and professional astronomical communities. Concurrent and further observations are planned to cover the full optical and NIR spectrum, from an ensemble of instruments, telescopes and observatories.Comment: Accepted for publication in A&A Letters. 5 pages, 2 figures and 4 table

A subsystem-independent generalization of entanglement

We introduce a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such a subspace if its expectations are a proper mixture of those of other states. Many information-theoretic aspects of entanglement can be extended to the general setting, suggesting new ways of measuring and classifying entanglement in multipartite systems. By going beyond the distinguishable-subsystem framework, generalized entanglement also provides novel tools for probing quantum correlations in interacting many-body systems.Comment: 5 pages, 1 encapsulated color figure, REVTeX4 styl

Machine learning techniques to select Be star candidates. An application in the OGLE-IV Gaia south ecliptic pole field

Statistical pattern recognition methods have provided competitive solutions for variable star classification at a relatively low computational cost. In order to perform supervised classification, a set of features is proposed and used to train an automatic classification system. Quantities related to the magnitude density of the light curves and their Fourier coefficients have been chosen as features in previous studies. However, some of these features are not robust to the presence of outliers and the calculation of Fourier coefficients is computationally expensive for large data sets. We propose and evaluate the performance of a new robust set of features using supervised classifiers in order to look for new Be star candidates in the OGLE-IV Gaia south ecliptic pole field. We calculated the proposed set of features on six types of variable stars and on a set of Be star candidates reported in the literature. We evaluated the performance of these features using classification trees and random forests along with K-nearest neighbours, support vector machines, and gradient boosted trees methods. We tuned the classifiers with a 10-fold cross-validation and grid search. We validated the performance of the best classifier on a set of OGLE-IV light curves and applied this to find new Be star candidates. The random forest classifier outperformed the others. By using the random forest classifier and colour criteria we found 50 Be star candidates in the direction of the Gaia south ecliptic pole field, four of which have infrared colours consistent with Herbig Ae/Be stars. Supervised methods are very useful in order to obtain preliminary samples of variable stars extracted from large databases. As usual, the stars classified as Be stars candidates must be checked for the colours and spectroscopic characteristics expected for them