13,753 research outputs found

### Structure of large random hypergraphs

The theme of this paper is the derivation of analytic formulae for certain
large combinatorial structures. The formulae are obtained via fluid limits of
pure jump type Markov processes, established under simple conditions on the
Laplace transforms of their Levy kernels. Furthermore, a related Gaussian
approximation allows us to describe the randomness which may persist in the
limit when certain parameters take critical values. Our method is quite
general, but is applied here to vertex identifiability in random hypergraphs. A
vertex v is identifiable in n steps if there is a hyperedge containing v all of
whose other vertices are identifiable in fewer than n steps. We say that a
hyperedge is identifiable if every one of its vertices is identifiable. Our
analytic formulae describe the asymptotics of the number of identifiable
vertices and the number of identifiable hyperedges for a Poisson random
hypergraph on a set of N vertices, in the limit as N goes to infinity.Comment: Revised version with minor conceptual improvements and additional
discussion. 32 pages, 5 figure

### Differential equation approximations for Markov chains

We formulate some simple conditions under which a Markov chain may be
approximated by the solution to a differential equation, with quantifiable
error probabilities. The role of a choice of coordinate functions for the
Markov chain is emphasised. The general theory is illustrated in three
examples: the classical stochastic epidemic, a population process model with
fast and slow variables, and core-finding algorithms for large random
hypergraphs.Comment: Published in at http://dx.doi.org/10.1214/07-PS121 the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org

### Proton-Electron Hyperfine Coupling Constants of the Chlorophyll a Cation Radical by ENDOR Spectroscopy

In this paper we describe the assignment of the major coupling constants in monomer chlorophyll a cation free radical
by ENDOR spectroscopy. To facilitate chemical manipulation methylpyrochlorophyllide a has been used as a stand-in,
and a suite of six selectively deuterated derivatives have been subjected to ENDOR investigation. Details of the synthesis of
these compounds are described. To study the effect of structural features on the spin distribution in the free radicals, six additional
chlorophyll derivatives have been studied. Five coupling constants have been assigned, which account for about 80% of
the observed electron spin resonance line width in the chlorophyll a monomer cation radical. The spin distribution appears to
be highly asymmetric

### A high pressure, high temperature combustor and turbine-cooling test facility

A new test facility is being constructed for developing turbine-cooling and combustor technology for future generation aircraft gas turbine engines. Prototype engine hardware will be investigated in this new facility at gas stream conditions up to 2480 K average turbine inlet temperature and 4.14 x 10 to the 6th power n sq m turbine inlet pressure. The facility will have the unique feature of fully automated control and data acquisition through the use of an integrated system of mini-computers and programmable controllers which will result in more effective use of operating time, will limit the number of operators required, and will provide built in self protection safety systems. The facility and the planning and design considerations are described

### Calibration of Tests for Time Dilation in GRB Pulse Structures

Two tests for cosmological time dilation in $\gamma$-ray bursts -- the peak
alignment and auto-correlation statistics -- involve averaging information near
the times of peak intensity. Both tests require width corrections, assuming
cosmological origin for bursts, since narrower temporal structure from higher
energy would be redshifted into the band of observation, and since intervals
between pulse structures are included in the averaging procedures. We analyze
long ($>$ 2 s) BATSE bursts and estimate total width corrections for trial
time-dilation factors (TDF = [1+$z_{\rm dim}$]/[1+$z_{\rm brt}$]) by
time-dilating and redshifting bright bursts. Both tests reveal significant
trends of increasing TDF with decreasing peak flux, but neither provides
sufficient discriminatory power to distinguish between actual TDFs in the range
2--3.Comment: 5 pages in LATeX, REVTEX style, 2 embedded figures. To appear in
Third Huntsville GRB Workshop Proceeding

### Test for Time Dilation of Intervals Between Pulse Structures in GRBs

If $\gamma$-ray bursts are at cosmological distances, then not only their
constituent pulses but also the intervals between pulses should be
time-dilated. Unlike time-dilation measures of pulse emission, intervals would
appear to require negligible correction for redshift of narrower temporal
structure from higher energy into the band of observation. However, stretching
of pulse intervals is inherently difficult to measure without incurring a
timescale-dependent bias since, as time profiles are stretched, more structure
can appear near the limit of resolution. This problem is compounded in dimmer
bursts because identification of significant structures becomes more
problematic. We attempt to minimize brightness bias by equalizing
signal-to-noise (s/n) level of all bursts. We analyze wavelet-denoised burst
profiles binned to several resolutions, identifying significant fluctuations
between pulse structures and interjacent valleys. When bursts are ranked by
peak flux, an interval time-dilation signature is evident, but its magnitude
and significance are dependent upon temporal resolution and s/n level.Comment: 5 pages in LATeX, REVTEX style, 2 embedded figures. To appear in
Third Huntsville GRB Workshop Proceeding

### A Model for Short Gamma-Ray Bursts: Heated Neutron Stars in Close Binary Systems

In this paper we present a model for the short (< second) population of
gamma-ray bursts (GRBs). In this model heated neutron stars in a close binary
system near their last stable orbit emit neutrinos at large luminosities (~
10^53 ergs/sec). A fraction of these neutrinos will annihilate to form an
electron-positron pair plasma wind which will, in turn, expand and recombine to
photons which make the gamma-ray burst. We study neutrino annihilation and show
that a substantial fraction (~ 50%) of energy deposited comes from inter-star
neutrinos, where each member of the neutrino pair originates from each neutron
star. Thus, in addition to the annihilation of neutrinos blowing off of a
single star, we have a new source of baryon free energy that is deposited
between the stars. To model the pair plasma wind between stars, we do
three-dimensional relativistic numerical hydrodynamic calculations.
Preliminary results are also presented of new, fully general relativistic
calculations of gravitationally attracting stars falling from infinity with no
angular momentum. These simulations exhibit a compression effect.Comment: 3 pages, 3 postscript figs (2 color), to appear in "Gamma-Ray Burst
and Afterglow Astronomy 2001", Woods Hole; 5-9 Nov, 200

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