52,130 research outputs found
Ultra thin gage plastic film
Process utilizing specially modified conventional equipment, with changes in process temperature, pressure, and cooling requirements produces ultra thin 1.56 micron /0.0614 mil/ thick polyethylene film
An Optimal Skorokhod Embedding for Diffusions
Given a Brownian motion and a general target law (not necessarily
centered or even integrable) we show how to construct an embedding of in
. This embedding is an extension of an embedding due to Perkins, and is
optimal in the sense that it simultaneously minimises the distribution of the
maximum and maximises the distribution of the minimum among all embeddings of
. The embedding is then applied to regular diffusions, and used to
characterise the target laws for which a -embedding may be found.Comment: 22 pages, 4 figure
Stability and photochemistry of ClO dimers formed at low temperature in the gas phase
The recent observations of elevated concentrations of the ClO radical in the austral spring over Antarctica have implicated catalytic destruction by chlorine in the large depletions seen in the total ozone column. One of the chemical theories consistent with an elevated concentration of the ClO is a cycle involving the formation of the ClO dimer through the association reaction: ClO + ClO = Cl2O2 and the photolysis of the dimer to give the active Cl species necessary for O3 depletion. Here, researchers report experimental studies designed to characterize the dimer of ClO formed by the association reaction at low temperatures. ClO was produced by static photolysis of several different precursor systems: Cl sub 2 + O sub 3; Cl sub 2 O sub 2; OClO + Cl sub 2 O spectroscopy in the U.V. region, which allowed the time dependence of Cl sub 2, Cl sub 2 O, ClO, OClO, O sub 3 and other absorbing molecules to be determined
Sum of Two Squares - Pair Correlation and Distribution in Short Intervals
In this work we show that based on a conjecture for the pair correlation of
integers representable as sums of two squares, which was first suggested by
Connors and Keating and reformulated here, the second moment of the
distribution of the number of representable integers in short intervals is
consistent with a Poissonian distribution, where "short" means of length
comparable to the mean spacing between sums of two squares. In addition we
present a method for producing such conjectures through calculations in prime
power residue rings and describe how these conjectures, as well as the above
stated result, may by generalized to other binary quadratic forms. While
producing these pair correlation conjectures we arrive at a surprising result
regarding Mertens' formula for primes in arithmetic progressions, and in order
to test the validity of the conjectures, we present numericalz computations
which support our approach.Comment: 3 figure
Parrondo-like behavior in continuous-time random walks with memory
The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass
stochastic processes with memory. In this article we will show how the random
combination of two different unbiased CTRWs can give raise to a process with
clear drift, if one of them is a CTRW with memory. If one identifies the other
one as noise, the effect can be thought as a kind of stochastic resonance. The
ultimate origin of this phenomenon is the same of the Parrondo's paradox in
game theoryComment: 8 pages, 3 figures, revtex; enlarged and revised versio
3D printing dimensional calibration shape: Clebsch Cubic
3D printing and other layer manufacturing processes are challenged by
dimensional accuracy. Several techniques are used to validate and calibrate
dimensional accuracy through the complete building envelope. The validation
process involves the growing and measuring of a shape with known parameters.
The measured result is compared with the intended digital model. Processes with
the risk of deformation after time or post processing may find this technique
beneficial. We propose to use objects from algebraic geometry as test shapes. A
cubic surface is given as the zero set of a 3rd degree polynomial with 3
variables. A class of cubics in real 3D space contains exactly 27 real lines.
We provide a library for the computer algebra system Singular which, from 6
given points in the plane, constructs a cubic and the lines on it. A surface
shape derived from a cubic offers simplicity to the dimensional comparison
process, in that the straight lines and many other features can be analytically
determined and easily measured using non-digital equipment. For example, the
surface contains so-called Eckardt points, in each of which three of the lines
intersect, and also other intersection points of pairs of lines. Distances
between these intersection points can easily be measured, since the points are
connected by straight lines. At all intersection points of lines, angles can be
verified. Hence, many features distributed over the build volume are known
analytically, and can be used for the validation process. Due to the thin shape
geometry the material required to produce an algebraic surface is minimal. This
paper is the first in a series that proposes the process chain to first define
a cubic with a configuration of lines in a given print volume and then to
develop the point cloud for the final manufacturing. Simple measuring
techniques are recommended.Comment: 8 pages, 1 figure, 1 tabl
Supernova Remnant in a Stratified Medium: Explicit, Analytical Approximations for Adiabatic Expansion and Radiative Cooling
We propose simple, explicit, analytical approximations for the kinematics of
an adiabatic blast wave propagating in an exponentially stratified ambient
medium, and for the onset of radiative cooling, which ends the adiabatic era.
Our method, based on the Kompaneets implicit solution and the Kahn
approximation for the radiative cooling coefficient, gives straightforward
estimates for the size, expansion velocity, and progression of cooling times
over the surface, when applied to supernova remnants (SNRs). The remnant shape
is remarkably close to spherical for moderate density gradients, but even a
small gradient in ambient density causes the cooling time to vary substantially
over the remnant's surface, so that for a considerable period there will be a
cold dense expanding shell covering only a part of the remnant. Our
approximation provides an effective tool for identifying the approximate
parameters when planning 2-dimensional numerical models of SNRs, the example of
W44 being given in a subsequent paper.Comment: ApJ accepted, 11 pages, 2 figures embedded, aas style with
ecmatex.sty and lscape.sty package
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