11,876 research outputs found
On the Hierarchical Preconditioning of the PMCHWT Integral Equation on Simply and Multiply Connected Geometries
We present a hierarchical basis preconditioning strategy for the
Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation considering
both simply and multiply connected geometries.To this end, we first consider
the direct application of hierarchical basis preconditioners, developed for the
Electric Field Integral Equation (EFIE), to the PMCHWT. It is notably found
that, whereas for the EFIE a diagonal preconditioner can be used for obtaining
the hierarchical basis scaling factors, this strategy is catastrophic in the
case of the PMCHWT since it leads to a severly ill-conditioned PMCHWT system in
the case of multiply connected geometries. We then proceed to a theoretical
analysis of the effect of hierarchical bases on the PMCHWT operator for which
we obtain the correct scaling factors and a provably effective preconditioner
for both low frequencies and mesh refinements. Numerical results will
corroborate the theory and show the effectiveness of our approach
Efficient solvability of Hamiltonians and limits on the power of some quantum computational models
We consider quantum computational models defined via a Lie-algebraic theory.
In these models, specified initial states are acted on by Lie-algebraic quantum
gates and the expectation values of Lie algebra elements are measured at the
end. We show that these models can be efficiently simulated on a classical
computer in time polynomial in the dimension of the algebra, regardless of the
dimension of the Hilbert space where the algebra acts. Similar results hold for
the computation of the expectation value of operators implemented by a
gate-sequence. We introduce a Lie-algebraic notion of generalized mean-field
Hamiltonians and show that they are efficiently ("exactly") solvable by means
of a Jacobi-like diagonalization method. Our results generalize earlier ones on
fermionic linear optics computation and provide insight into the source of the
power of the conventional model of quantum computation.Comment: 6 pages; no figure
Short-term variability of a sample of 29 trans-Neptunian objects and Centaurs
We present results of 6 years of observations, reduced and analyzed with the
same tools in a systematic way. We report completely new data for 15 objects,
for 5 objects we present a new analysis of previously published results plus
additional data and for 9 objects we present a new analysis of data already
published. Lightcurves, possible rotation periods and photometric amplitudes
are reported for all of them. The photometric variability is smaller than
previously thought: the mean amplitude of our sample is 0.1mag and only around
15% of our sample has a larger variability than 0.15mag. The smaller
variability than previously thought seems to be a bias of previous
observations. We find a very weak trend of faster spinning objects towards
smaller sizes, which appears to be consistent with the fact that the smaller
objects are more collisionally evolved, but could also be a specific feature of
the Centaurs, the smallest objects in our sample. We also find that the smaller
the objects, the larger their amplitude, which is also consistent with the idea
that small objects are more collisionally evolved and thus more deformed.
Average rotation rates from our work are 7.5h for the whole sample, 7.6h for
the TNOs alone and 7.3h for the Centaurs. All of them appear to be somewhat
faster than what one can derive from a compilation of the scientific literature
and our own results. Maxwellian fits to the rotation rate distribution give
mean values of 7.5h (for the whole sample) and 7.3h (for the TNOs only).
Assuming hydrostatic equilibrium we can determine densities from our sample
under the additional assumption that the lightcurves are dominated by shape
effects, which is likely not realistic. The resulting average density is
0.92g/cm^3 which is not far from the density constraint that one can derive
from the apparent spin barrier that we observe.Comment: Accepted for publication in A&
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