14,471 research outputs found
Computational problems without computation
Problemen uit de discrete wiskunde lijken op het eerste gezicht vaak erg simpel. Ze kunnen meestal gemakkelijk en zonder gebruik te maken van wiskundige begrippen worden geformuleerd. Toch komt het vaak voor dat zoân ogenschijnlijk eenvoudig probleem nog open is of dat er, zoals bij het handelsreizigersprobleem, wel een oplossing gegeven kan worden,maar alleen een die onbruikbaar is omdat de rekentijd bij grotere getallen te snel groeit. In dit artikel, gebaseerd op zijn voordracht op het NMC 2002, kijkt Gerhard Woeginger naar de tegenovergestelde situatie. Hij introduceert allerlei discrete\ud
problemen die onoplosbaar lijken, maar waarvoor er een simpele oplossing bestaat
Tight bounds for break minimization
We consider round-robin sports tournaments with n teams and n â 1 rounds. We construct an infinite family of opponent schedules for which every home-away assignment induces at least 1/4 n(nâ2) breaks. This construction establishes a matching lower bound for a corresponding upper bound from the literature
Three Mechanisms for Bar Thickening
We present simulations of bar-unstable stellar discs in which the bars
thicken into box/peanut shapes. Detailed analysis of the evolution of each
model revealed three different mechanisms for thickening the bars. The first
mechanism is the well-known buckling instability, the second is the vertical
excitation of bar orbits by passage through the 2:1 vertical resonance, and the
third is a gradually increasing fraction of bar orbits trapped into this
resonance. Since bars in many galaxies may have formed and thickened long ago,
we have examined the models for fossil evidence in the velocity distribution of
stars in the bar, finding a diagnostic to discriminate between a bar that had
buckled from the other two mechanisms.Comment: 18 pages, 17 figures, accepted to appear in MNRAS, comments welcom
Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order
The recently constructed Hamiltonians for spinless binary black holes through
third post-Newtonian order and for spinning ones through formal second
post-Newtonian order, where the spins are counted of zero post-Newtonian order,
are transformed into fully canonical center-of-mass and rest-frame variables.
The mixture terms in the Hamiltonians between center-of-mass and rest-frame
variables are in accordance with the relation between the total linear momentum
and the center-of-mass velocity as demanded by global Lorentz invariance. The
various generating functions for the center-of-mass and rest-frame canonical
variables are explicitly given in terms of the single-particle canonical
variables. The no-interaction theorem does not apply because the world-line
condition of Lorentz covariant position variables is not imposed.Comment: 18 pages, no figure
Dark Matter Problem in Disk Galaxies
In the generic CDM cosmogony, dark-matter halos emerge too lumpy and
centrally concentrated to host observed galactic disks. Moreover, disks are
predicted to be smaller than those observed. We argue that the resolution of
these problems may lie with a combination of the effects of protogalactic
disks, which would have had a mass comparable to that of the inner dark halo
and be plausibly non-axisymmetric, and of massive galactic winds, which at
early times may have carried off as many baryons as a galaxy now contains. A
host of observational phenomena, from quasar absorption lines and intracluster
gas through the G-dwarf problem point to the existence of such winds. Dynamical
interactions will homogenize and smooth the inner halo, and the observed disk
will be the relic of a massive outflow. The inner halo expanded after absorbing
energy and angular momentum from the ejected material. Observed disks formed at
the very end of the galaxy formation process, after the halo had been reduced
to a minor contributor to the central mass budget and strong radial streaming
of the gas had died down.Comment: 5 pages; submitted to MNRA
Triaxial Black-Hole Nuclei
We demonstrate that the nuclei of galaxies containing supermassive black
holes can be triaxial in shape. Schwarzschild's method was first used to
construct self-consistent orbital superpositions representing nuclei with axis
ratios of 1:0.79:0.5 and containing a central point mass representing a black
hole. Two different density laws were considered, with power-law slopes of -1
and -2. We constructed two solutions for each power law: one containing only
regular orbits and the other containing both regular and chaotic orbits.
Monte-Carlo realizations of the models were then advanced in time using an
N-body code to verify their stability. All four models were found to retain
their triaxial shapes for many crossing times. The possibility that galactic
nuclei may be triaxial complicates the interpretation of stellar-kinematical
data from the centers of galaxies and may alter the inferred interaction rates
between stars and supermassive black holes.Comment: 4 pages, 4 postscript figures, uses emulateapj.st
Pair diffusion, hydrodynamic interactions, and available volume in dense fluids
We calculate the pair diffusion coefficient D(r) as a function of the
distance r between two hard-sphere particles in a dense monodisperse
suspension. The distance-dependent pair diffusion coefficient describes the
hydrodynamic interactions between particles in a fluid that are central to
theories of polymer and colloid dynamics. We determine D(r) from the
propagators (Green's functions) of particle pairs obtained from discontinuous
molecular dynamics simulations. At distances exceeding 3 molecular diameters,
the calculated pair diffusion coefficients are in excellent agreement with
predictions from exact macroscopic hydrodynamic theory for large Brownian
particles suspended in a solvent bath, as well as the Oseen approximation.
However, the asymptotic 1/r distance dependence of D(r) associated with
hydrodynamic effects emerges only after the pair distance dynamics has been
followed for relatively long times, indicating non-negligible memory effects in
the pair diffusion at short times. Deviations of the calculated D(r) from the
hydrodynamic models at short distances r reflect the underlying many-body fluid
structure, and are found to be correlated to differences in the local available
volume. The procedure used here to determine the pair diffusion coefficients
can also be used for single-particle diffusion in confinement with spherical
symmetry.Comment: 6 pages, 5 figure
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