38,257 research outputs found
One Dimensional ary Density Classification Using Two Cellular Automaton Rules
Suppose each site on a one-dimensional chain with periodic boundary condition
may take on any one of the states , can you find out the most
frequently occurring state using cellular automaton? Here, we prove that while
the above density classification task cannot be resolved by a single cellular
automaton, this task can be performed efficiently by applying two cellular
automaton rules in succession.Comment: Revtex, 4 pages, uses amsfont
The dynamic dipole polarizabilities of the Li atom and the Be+ ion
The dynamic dipole polarizabilities for the Li atom and the Be+ ion in the 2s
and 2p states are calculated using the variational method with a Hylleraas
basis. The present polarizabilities represent the definitive values in the
non-relativistic limit. Corrections due to relativistic effects are also
estimated. Analytic representations of the polarizabilities for frequency
ranges encompassing the n=3 excitations are presented. The recommended
polarizabilities for ^7Li and ^9Be+ were 164.11 \pm 0.03 a.u. and 24.489 \pm
0.004 a.u.
Calculations of polarizabilities and hyperpolarizabilities for the Be ion
The polarizabilities and hyperpolarizabilities of the Be ion in the
state and the state are determined. Calculations are performed
using two independent methods: i) variationally determined wave functions using
Hylleraas basis set expansions and ii) single electron calculations utilizing a
frozen-core Hamiltonian. The first few parameters in the long-range interaction
potential between a Be ion and a H, He, or Li atom, and the leading
parameters of the effective potential for the high- Rydberg states of
beryllium were also computed. All the values reported are the results of
calculations close to convergence. Comparisons are made with published results
where available.Comment: 18 pp; added details to Sec. I
A magnetized torus for modeling Sgr A* millimeter images and spectra
Context. The supermassive black hole, Sagittarius (Sgr) A*, in the centre of
our Galaxy has the largest angular size in the sky among all astrophysical
black holes. Its shadow, assuming no rotation, spans ~ 50 microarcsec.
Resolving such dimensions has long been out of reach for astronomical
instruments until a new generation of interferometers being operational during
this decade. Of particular interest is the Event Horizon Telescope (EHT) with
resolution ~ 20 microarcsec in the millimeter-wavelength range 0.87 mm - 1.3
mm. Aims. We investigate the ability of the fully general relativistic
Komissarov (2006) analytical magnetized torus model to account for observable
constraints at Sgr A* in the centimeter and millimeter domains. The impact of
the magnetic field geometry on the observables is also studied. Methods. We
calculate ray-traced centimeter- and millimeter-wavelength synchrotron spectra
and images of a magnetized accretion torus surrounding the central black hole
in Sgr A*. We assume stationarity, axial symmetry, constant specific angular
momentum and polytropic equation of state. A hybrid population of thermal and
non-thermal electrons is considered. Results. We show that the torus model is
capable of reproducing spectral constraints in the millimeter domain, and in
particular in the observable domain of the EHT. However, the torus model is not
yet able to fit the centimeter spectrum. 1.3 mm images at high inclinations are
in agreement with observable constraints. Conclusions. The ability of the torus
model to account for observations of Sgr A* in the millimeter domain is
interesting in the perspective of the future EHT. Such an analytical model
allows very fast computations. It will thus be a suitable test bed for
investigating large domains of physical parameters, as well as non-black-hole
compact object candidates and alternative theories of gravity.Comment: Major changes wrt the June 2014 version. Accepted by A&
Finding The Sign Of A Function Value By Binary Cellular Automaton
Given a continuous function , suppose that the sign of only has
finitely many discontinuous points in the interval . We show how to use
a sequence of one dimensional deterministic binary cellular automata to
determine the sign of where is the (number) density of 1s in
an arbitrarily given bit string of finite length provided that satisfies
certain technical conditions.Comment: Revtex, uses amsfonts, 10 page
Long-range interactions for He()--He and He()--He
The energetically lowest five states of a helium atom are: He(),
He(), He(), He(), and He(). Long-range interaction
coefficients , , , , and for all and
pairs of these states are calculated precisely using correlated wave functions
in Hylleraas coordinates. Finite nuclear isotope mass effects are included
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