44,671 research outputs found
On the real zeroes of the Hurwitz zeta-function and Bernoulli polynomials
The behaviour of real zeroes of the Hurwitz zeta function is investigated. It is
shown that has no real zeroes in the region for large negative
. In the region the zeroes are
asymptotically located at the lines with integer . If
is the number of real zeroes of with given then
As a corollary we have a
simple proof of Inkeri's result that the number of real roots of the classical
Bernoulli polynomials for large is asymptotically equal to
.Comment: 9 pages, 2 figure
An empirical model for protostellar collapse
We propose a new analytic model for the initial conditions of protostellar
collapse in relatively isolated regions of star formation. The model is
non-magnetic, and is based on a Plummer-like radial density profile as its
initial condition. It fits: the observed density profiles of pre-stellar cores
and Class 0 protostars; recent observations in pre-stellar cores of roughly
constant contraction velocities over a wide range of radii; and the lifetimes
and accretion rates derived for Class 0 and Class I protostars. However, the
model is very simple, having in effect only 2 free parameters, and so should
provide a useful framework for interpreting observations of pre-stellar cores
and protostars, and for calculations of radiation transport and time-dependent
chemistry. As an example, we model the pre-stellar core L1544.Comment: To appear in Astrophysical Journal, Jan 20th, 2001. 18 pages incl. 3
fig
In search for a perfect shape of polyhedra: Buffon transformation
For an arbitrary polygon consider a new one by joining the centres of
consecutive edges. Iteration of this procedure leads to a shape which is affine
equivalent to a regular polygon. This regularisation effect is usually ascribed
to Count Buffon (1707-1788). We discuss a natural analogue of this procedure
for 3-dimensional polyhedra, which leads to a new notion of affine -regular
polyhedra. The main result is the proof of existence of star-shaped affine
-regular polyhedra with prescribed combinatorial structure, under partial
symmetry and simpliciality assumptions. The proof is based on deep results from
spectral graph theory due to Colin de Verdiere and Lovasz.Comment: Slightly revised version with added example of pentakis dodecahedro
Simulating star formation in molecular cloud cores I. The influence of low levels of turbulence on fragmentation and multiplicity
We present the results of an ensemble of simulations of the collapse and
fragmentation of dense star-forming cores. We show that even with very low
levels of turbulence the outcome is usually a binary, or higher-order multiple,
system. We take as the initial conditions for these simulations a typical
low-mass core, based on the average properties of a large sample of observed
cores. All the simulated cores start with a mass of , a
flattened central density profile, a ratio of thermal to gravitational energy
and a ratio of turbulent to gravitational energy
. Even this low level of turbulence is sufficient to
produce multiple star formation in 80% of the cores; the mean number of stars
and brown dwarfs formed from a single core is 4.55, and the maximum is 10. At
the outset, the cores have no large-scale rotation. The only difference between
each individual simulation is the detailed structure of the turbulent velocity
field. The multiple systems formed in the simulations have properties
consistent with observed multiple systems. Dynamical evolution tends
preferentially to eject lower mass stars and brown dwarves whilst hardening the
remaining binaries so that the median semi-major axis of binaries formed is
au. Ejected objects are usually single low-mass stars and brown
dwarfs, yielding a strong correlation between mass and multiplicity. Our
simulations suggest a natural mechanism for forming binary stars that does not
require large-scale rotation, capture, or large amounts of turbulence.Comment: 20 pages, 12 figures submitted to A&
AN ANALYSIS OF THE YIELD-PRICE RISK ASSOCIATED WITH SPECIALTY CROPS
Specialty crops have been cited as means to diversify crop portfolios on the prairies. Lentils, a specialty crop, have high variability in yields and prices but are relatively uncorrelated with the yields and prices of other traditional Saskatchewan crops. In addition, yields and prices of lentils may be negatively correlated. These attributes have important but offsetting effects in crop portfolio selection. The objective of this article is to assess the relative profitability and riskiness of wheat and lentil rotations for a representative Saskatchewan farm and to select appropriate farmers who should consider production of lentils. The cumulative density function of net returns are simulated for both rotations assuming stochastic prices and yields. Stochastic dominance with respect to a function is used to identify the corresponding appropriate profile of agricultural producers for each crop rotation. The results indicate that lentils should be considered by a number of, but not all, Saskatchewan farmers.Crop Production/Industries, Risk and Uncertainty,
Hydrodynamics of photoionized columns in the Eagle Nebula, M 16
We present hydrodynamical simulations of the formation, structure and
evolution of photoionized columns, with parameters based on those observed in
the Eagle Nebula. On the basis of these simulations we argue that there is no
unequivocal evidence that the dense neutral clumps at heads of the columns were
cores in the pre-existing molecular cloud. In our simulations, a variety of
initial conditions leads to the formation and maintenance of near-equilibrium
columns. Therefore, it is likely that narrow columns will often occur in
regions with large-scale inhomogeneities, but that observations of such columns
can tell us little about the processes by which they formed. The manner in
which the columns in our simulations develop suggests that their evolution may
result in extended sequences of radiation-induced star formation.Comment: 12 pages, 9 figures, Latex, MN macros, in press with MNRA
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