Equipartition of mass distributions by hyperplanes

Central energy equipartition in multi-mass models of globular clusters

In the construction of multi-mass King-Michie models of globular clusters, an approximated central energy equipartition between stars of different masses is usually imposed by scaling the velocity parameter of each mass class inversely with the stellar mass, as if the distribution function were isothermal. In this paper, this ‘isothermal approximation’ (IA) has been checked and its consequences...

Tidal Shocking by Extended Mass Distributions

We derive expressions for the tidal field exerted by a spherically symmetric galaxy having an extended mass distribution, and use our analysis to calculate tidal perturbations and heating of stars in a globular cluster or a satellite galaxy orbiting in the external potential. We consider a Hernquist model and several power-law models for the primary. We integrate the tidal force over accurate o...

Computing hypercircles by moving hyperplanes

Let K be a field of characteristic zero, α algebraic of degree n over K. Given a proper parametrization ψ of a rational curve C, we present a new algorithm to compute the hypercircle associated to the parametrization ψ. As a consequence, we can decide if C is defined over K and, if not, to compute the minimum field of definition of C containing K. The algorithm exploits the conjugate curves of ...

Essential overs of the ube by hyperplanes

The equipartition of curves

In this paper we analyze the problem of partitioning a continuous curve into n parts with equal successive chords, the curve EquiPartition problem (EP). The goal is to locate n− 1 consecutive curve points, so that the curve can be divided into n segments with equal chords under a distance function. We adopt a level set approach to prove that for any continuous injective curve in a metric space ...