1,984 research outputs found
A Canonical Form for Positive Definite Matrices
We exhibit an explicit, deterministic algorithm for finding a canonical form
for a positive definite matrix under unimodular integral transformations. We
use characteristic sets of short vectors and partition-backtracking graph
software. The algorithm runs in a number of arithmetic operations that is
exponential in the dimension , but it is practical and more efficient than
canonical forms based on Minkowski reduction
System balance analysis for vector computers
The availability of vector processors capable of sustaining computing rates of 10 to the 8th power arithmetic results pers second raised the question of whether peripheral storage devices representing current technology can keep such processors supplied with data. By examining the solution of a large banded linear system on these computers, it was found that even under ideal conditions, the processors will frequently be waiting for problem data
Slider-Block Friction Model for Landslides: Application to Vaiont and La Clapiere Landslides
Accelerating displacements preceding some catastrophic landslides have been
found empirically to follow a time-to-failure power law, corresponding to a
finite-time singularity of the velocity [{\it Voight},
1988]. Here, we provide a physical basis for this phenomenological law based on
a slider-block model using a state and velocity dependent friction law
established in the laboratory and used to model earthquake friction. This
physical model accounts for and generalizes Voight's observation: depending on
the ratio of two parameters of the rate and state friction law and on the
initial frictional state of the sliding surfaces characterized by a reduced
parameter , four possible regimes are found. Two regimes can account for
an acceleration of the displacement. We use the slider-block friction model to
analyze quantitatively the displacement and velocity data preceding two
landslides, Vaiont and La Clapi\`ere. The Vaiont landslide was the catastrophic
culmination of an accelerated slope velocity. La Clapi\`ere landslide was
characterized by a peak of slope acceleration that followed decades of ongoing
accelerating displacements, succeeded by a restabilizing phase. Our inversion
of the slider-block model on these data sets shows good fits and suggest to
classify the Vaiont (respectively La Clapi\`ere) landslide as belonging to the
velocity weakening unstable (respectively strengthening stable) sliding regime.Comment: shortened by focusing of the frictional model, Latex document with
AGU style file of 14 pages + 11 figures (1 jpeg photo of figure 6 given
separately) + 1 tabl
Computing automorphic forms on Shimura curves over fields with arbitrary class number
We extend methods of Greenberg and the author to compute in the cohomology of
a Shimura curve defined over a totally real field with arbitrary class number.
Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke
eigenvalues associated to Hilbert modular forms of arbitrary level over a
totally real field of odd degree. We conclude with two examples which
illustrate the effectiveness of our algorithms.Comment: 15 pages; final submission to ANTS I
Towards Landslide Predictions: Two Case Studies
In a previous work [Helmstetter, 2003], we have proposed a simple physical
model to explain the accelerating displacements preceding some catastrophic
landslides, based on a slider-block model with a state and velocity dependent
friction law. This model predicts two regimes of sliding, stable and unstable
leading to a critical finite-time singularity. This model was calibrated
quantitatively to the displacement and velocity data preceding two landslides,
Vaiont (Italian Alps) and La Clapi\`ere (French Alps), showing that the former
(resp. later) landslide is in the unstable (resp. stable) sliding regime. Here,
we test the predictive skills of the state-and-velocity-dependent model on
these two landslides, using a variety of techniques. For the Vaiont landslide,
our model provides good predictions of the critical time of failure up to 20
days before the collapse. Tests are also presented on the predictability of the
time of the change of regime for la Clapi\`ere landslide.Comment: 30 pages with 12 eps figure
Coverage and Characteristics of the Affymetrix GeneChip Human Mapping 100K SNP Set
Improvements in technology have made it possible to conduct genome-wide association mapping at costs within reach of academic investigators, and experiments are currently being conducted with a variety of high-throughput platforms. To provide an appropriate context for interpreting results of such studies, we summarize here results of an investigation of one of the first of these technologies to be publicly available, the Affymetrix GeneChip Human Mapping 100K set of single nucleotide polymorphisms (SNPs). In a systematic analysis of the pattern and distribution of SNPs in the Mapping 100K set, we find that SNPs in this set are undersampled from coding regions (both nonsynonymous and synonymous) and oversampled from regions outside genes, relative to SNPs in the overall HapMap database. In addition, we utilize a novel multilocus linkage disequilibrium (LD) coefficient based on information content (analogous to the information content scores commonly used for linkage mapping) that is equivalent to the familiar measure r (2) in the special case of two loci. Using this approach, we are able to summarize for any subset of markers, such as the Affymetrix Mapping 100K set, the information available for association mapping in that subset, relative to the information available in the full set of markers included in the HapMap, and highlight circumstances in which this multilocus measure of LD provides substantial additional insight about the haplotype structure in a region over pairwise measures of LD
Pressure Dependence of the Elastic Moduli in Aluminum Rich Al-Li Compounds
I have carried out numerical first principles calculations of the pressure
dependence of the elastic moduli for several ordered structures in the
Aluminum-Lithium system, specifically FCC Al, FCC and BCC Li, L1_2 Al_3Li, and
an ordered FCC Al_7Li supercell. The calculations were performed using the full
potential linear augmented plane wave method (LAPW) to calculate the total
energy as a function of strain, after which the data was fit to a polynomial
function of the strain to determine the modulus. A procedure for estimating the
errors in this process is also given. The predicted equilibrium lattice
parameters are slightly smaller than found experimentally, consistent with
other LDA calculations. The computed elastic moduli are within approximately
10% of the experimentally measured moduli, provided the calculations are
carried out at the experimental lattice constant. The LDA equilibrium shear
modulus C11-C12 increases from 59.3 GPa in Al, to 76.0 GPa in Al_7Li, to 106.2
GPa in Al_3Li. The modulus C_44 increases from 38.4 GPa in Al to 46.1 GPa in
Al_7Li, then falls to 40.7 GPa in Al_3Li. All of the calculated elastic moduli
increase with pressure with the exception of BCC Li, which becomes elastically
unstable at about 2 GPa, where C_11-C_12 vanishes.Comment: 17 pages (REVTEX) + 7 postscript figure
Tri-critical behavior in rupture induced by disorder
We discover a qualitatively new behavior for systems where the load transfer
has limiting stress amplification as in real fiber composites. We find that the
disorder is a relevant field leading to tri--criticality, separating a
first-order regime where rupture occurs without significant precursors from a
second-order regime where the macroscopic elastic coefficient exhibit power law
behavior. Our results are based on analytical analysis of fiber bundle models
and numerical simulations of a two-dimensional tensorial spring-block system in
which stick-slip motion and fracture compete.Comment: Revtex, 10 pages, 4 figures available upon reques
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ARAC simulations of the ash plume from the December 1997 eruption of Soufriere Hills Volcano, Montserrat
Ash clouds generated by erupting volcanoes represent a serious hazard to military and civil aviation. The dispersion modeling system of the Atmospheric Release Advisory Capability (ARAC) has been used to model the cloud resulting from the eruption of the Soufriere Hills volcano, Montserrat in December 1997. A clone of parts of the ARAC system, now being installed at the Air Force Weather Agency (AFWA), will enable AFWA to provide hazard guidance to military operations in the vicinity of erupting volcanoes. This paper presents ARAC� s modeling results and discusses potential application of similar calculations for AFWA support during future events
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