4,579 research outputs found
Unknotting numbers and triple point cancelling numbers of torus-covering knots
It is known that any surface knot can be transformed to an unknotted surface
knot or a surface knot which has a diagram with no triple points by a finite
number of 1-handle additions. The minimum number of such 1-handles is called
the unknotting number or the triple point cancelling number, respectively. In
this paper, we give upper bounds and lower bounds of unknotting numbers and
triple point cancelling numbers of torus-covering knots, which are surface
knots in the form of coverings over the standard torus . Upper bounds are
given by using -charts on presenting torus-covering knots, and lower
bounds are given by using quandle colorings and quandle cocycle invariants.Comment: 26 pages, 14 figures, added Corollary 1.7, to appear in J. Knot
Theory Ramification
High frequency dynamics in liquid nickel: an IXS study
Owing to their large relatively thermal conductivity, peculiar,
non-hydrodynamic features are expected to characterize the acoustic-like
excitations observed in liquid metals. We report here an experimental study of
collective modes in molten nickel, a case of exceptional geophysical interest
for its relevance in Earth interior science. Our result shed light on
previously reported contrasting evidences: in the explored energy-momentum
region no deviation from the generalized hydrodynamic picture describing non
conductive fluids are observed. Implications for high frequency transport
properties in metallic fluids are discussed.Comment: 6 pages, 4 figures, to appear in "Journal of Chemical Physics
Does the bonding rule break down in AsSe glass?
The local coordination numbers of AsSe glass were determined by a
combination of anomalous x-ray scattering experiments, reverse Monte Carlo
calculations, and {\it ab initio} molecular dynamics simulations. The
well-known `8- bonding rule' proposed by Mott breaks down around the As
atoms, exceeding the rule by 7--26%. An experimental prediction based on
mean-field theory agrees with the present experimental and theoretical results.
The fourfold coordinated As atoms likely form As-As wrong bond chains rather
than ethan-like configurations, which is identified as the origin for the
breakdown of the `8- bonding rule'.Comment: 6 pages, 6figures, 1table, submitted to Europhysics Letter
Variable Accretion Rates and Fluffy First Stars
We combine the output of hydrodynamical simulations of Population III star
cluster formation with stellar evolution models, and calculate the evolution of
protostars experiencing variable mass accretion rates due to interactions
within a massive disk. We find that the primordial protostars are extended
'fluffy' objects for the bulk of their pre-main-sequence lifetimes. Accretion
luminosity feedback from such objects is high, but as shown in previous work,
has a minimal effect on the star cluster. The extended radii of the protostars,
combined with the observation of close encounters in the simulations, suggests
that mergers will occur in such systems. Furthermore, mass transfer between
close protostellar binaries with extended radii could lead to massive tight
binaries, which are a possible progenitor of gamma ray bursts.Comment: 7 pages, 6 figures, 2 tables. To be published in MNRA
Microlensing of collimated Gamma-Ray Burst afterglows
We investigate stellar microlensing of the collimated gamma-ray burst
afterglows. A spherical afterglow appears on the sky as a superluminally
expanding thin ring (``ring-like'' image), which is maximally amplified as it
crosses the lens. We find that the image of the collimated afterglow becomes
quite uniform (``disk-like'' image) after the jet break time (after the Lorentz
factor of the jet drops below the inverse of the jet opening angle).
Consequently, the amplification peak in the light curve after the break time is
lower and broader. Therefore detailed monitoring of the amplification history
will be able to test whether the afterglows are jets or not, i.e.,
``disk-like'' or not, if the lensing occurs after the break time. We also show
that some proper motion and polarization is expected, peaking around the
maximum amplification. The simultaneous detection of the proper motion and the
polarization will strengthen that the brightening of the light curve is due to
microlensing.Comment: 16 pages, 6 figures, accepted for publication in Ap
Structural and dynamical properties of liquid Si. An orbital-free molecular dynamics study
Several static and dynamic properties of liquid silicon near melting have
been determined from an orbital free {\em ab-initio} molecular dynamics
simulation. The calculated static structure is in good agreement with the
available X-ray and neutron diffraction data. The dynamical structure shows
collective density excitations with an associated dispersion relation which
closely follows recent experimental data. It is found that liquid silicon can
not sustain the propagation of shear waves which can be related to the power
spectrum of the velocity autocorrelation function. Accurate estimates have also
been obtained for several transport coefficients. The overall picture is that
the dynamic properties have many characteristics of the simple liquid metals
although some conspicuous differences have been found.Comment: 12 pages, 11 figure
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