22 research outputs found
On the topological classification of binary trees using the Horton-Strahler index
The Horton-Strahler (HS) index has been shown to
be relevant to a number of physical (such at diffusion limited aggregation)
geological (river networks), biological (pulmonary arteries, blood vessels,
various species of trees) and computational (use of registers) applications.
Here we revisit the enumeration problem of the HS index on the rooted,
unlabeled, plane binary set of trees, and enumerate the same index on the
ambilateral set of rooted, plane binary set of trees of leaves. The
ambilateral set is a set of trees whose elements cannot be obtained from each
other via an arbitrary number of reflections with respect to vertical axes
passing through any of the nodes on the tree. For the unlabeled set we give an
alternate derivation to the existing exact solution. Extending this technique
for the ambilateral set, which is described by an infinite series of non-linear
functional equations, we are able to give a double-exponentially converging
approximant to the generating functions in a neighborhood of their convergence
circle, and derive an explicit asymptotic form for the number of such trees.Comment: 14 pages, 7 embedded postscript figures, some minor changes and typos
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An improved method for measuring muon energy using the truncated mean of dE/dx
The measurement of muon energy is critical for many analyses in large
Cherenkov detectors, particularly those that involve separating
extraterrestrial neutrinos from the atmospheric neutrino background. Muon
energy has traditionally been determined by measuring the specific energy loss
(dE/dx) along the muon's path and relating the dE/dx to the muon energy.
Because high-energy muons (E_mu > 1 TeV) lose energy randomly, the spread in
dE/dx values is quite large, leading to a typical energy resolution of 0.29 in
log10(E_mu) for a muon observed over a 1 km path length in the IceCube
detector. In this paper, we present an improved method that uses a truncated
mean and other techniques to determine the muon energy. The muon track is
divided into separate segments with individual dE/dx values. The elimination of
segments with the highest dE/dx results in an overall dE/dx that is more
closely correlated to the muon energy. This method results in an energy
resolution of 0.22 in log10(E_mu), which gives a 26% improvement. This
technique is applicable to any large water or ice detector and potentially to
large scintillator or liquid argon detectors.Comment: 12 pages, 16 figure
All-particle cosmic ray energy spectrum measured with 26 IceTop stations
We report on a measurement of the cosmic ray energy spectrum with the IceTop
air shower array, the surface component of the IceCube Neutrino Observatory at
the South Pole. The data used in this analysis were taken between June and
October, 2007, with 26 surface stations operational at that time, corresponding
to about one third of the final array. The fiducial area used in this analysis
was 0.122 km^2. The analysis investigated the energy spectrum from 1 to 100 PeV
measured for three different zenith angle ranges between 0{\deg} and 46{\deg}.
Because of the isotropy of cosmic rays in this energy range the spectra from
all zenith angle intervals have to agree. The cosmic-ray energy spectrum was
determined under different assumptions on the primary mass composition. Good
agreement of spectra in the three zenith angle ranges was found for the
assumption of pure proton and a simple two-component model. For zenith angles
{\theta} < 30{\deg}, where the mass dependence is smallest, the knee in the
cosmic ray energy spectrum was observed between 3.5 and 4.32 PeV, depending on
composition assumption. Spectral indices above the knee range from -3.08 to
-3.11 depending on primary mass composition assumption. Moreover, an indication
of a flattening of the spectrum above 22 PeV were observed.Comment: 38 pages, 17 figure
Approaches to the study of hillslope development due to mass movement
Slope-angle histograms have traditionally provided a data base for the evaluation of changing angles over geological time. Ideas relating to hillslope development due to mass movement have considered a lowering in regolith shear resistance due to weathering, producing slope-angle decline. Decreasing values for angles of internal friction, along with increasing pore water pressures, have been suggested to explain slope-angle decline through time. These ideas have considered simple changes in undifferentiated regolith. This article considers the role of progressive pedogenesis in determining the changing stability of slopes. For this it is necessary to evaluate the changes which occur within individual horizons to produce an increasingly differentiated soil cover. Angles of internal friction alter at different rates and in different ways depending on whether the horizon is losing or gaining weathered material through translocation. Furthermore, the increasing internal differentiation of the soil cover has complex effects on its hydrological response. Instead of the two scenarios previously envisaged, one involving the water table below the slip surface and the other involving the water table at the ground surface, slope stability needs to be evaluated in the light of continually changing negative or positive pore water pressures. Each storm produces a different response, and this response alters with soil development, complicating the assessment of failure timing and depth. The study of evolving soil profiles is of fundamental significance to a range of geomorphological processes, requiring closer evaluation in the future