768,747 research outputs found
An Anisotropic Ballistic Deposition Model with Links to the Ulam Problem and the Tracy-Widom Distribution
We compute exactly the asymptotic distribution of scaled height in a
(1+1)--dimensional anisotropic ballistic deposition model by mapping it to the
Ulam problem of finding the longest nondecreasing subsequence in a random
sequence of integers. Using the known results for the Ulam problem, we show
that the scaled height in our model has the Tracy-Widom distribution appearing
in the theory of random matrices near the edges of the spectrum. Our result
supports the hypothesis that various growth models in dimensions that
belong to the Kardar-Parisi-Zhang universality class perhaps all share the same
universal Tracy-Widom distribution for the suitably scaled height variables.Comment: 5 pages Revtex, 3 .eps figures included, new references adde
Locating the source of projectile fluid droplets
The ill-posed projectile problem of finding the source height from spattered
droplets of viscous fluid is a longstanding obstacle to accident reconstruction
and crime scene analysis. It is widely known how to infer the impact angle of
droplets on a surface from the elongation of their impact profiles. However,
the lack of velocity information makes finding the height of the origin from
the impact position and angle of individual drops not possible. From aggregate
statistics of the spatter and basic equations of projectile motion, we
introduce a reciprocal correlation plot that is effective when the polar launch
angle is concentrated in a narrow range. The vertical coordinate depends on the
orientation of the spattered surface, and equals the tangent of the impact
angle for a level surface. When the horizontal plot coordinate is twice the
reciprocal of the impact distance, we can infer the source height as the slope
of the data points in the reciprocal correlation plot. If the distribution of
launch angles is not narrow, failure of the method is evident in the lack of
linear correlation. We perform a number of experimental trials, as well as
numerical calculations and show that the height estimate is insensitive to
aerodynamic drag. Besides its possible relevance for crime investigation,
reciprocal-plot analysis of spatter may find application to volcanism and other
topics and is most immediately applicable for undergraduate science and
engineering students in the context of crime-scene analysis.Comment: To appear in the American Journal of Physics (ms 23338). Improved
readability and organization in this versio
The RHESSI Microflare Height Distribution
We present the first in-depth statistical survey of flare source heights
observed by RHESSI. Flares were found using a flare-finding algorithm designed
to search the 6-10 keV count-rate when RHESSI's full sensitivity was available
in order to find the smallest events (Christe et al., 2008). Between March 2002
and March 2007, a total of 25,006 events were found. Source locations were
determined in the 4-10 keV, 10-15 keV, and 15-30 keV energy ranges for each
event. In order to extract the height distribution from the observed projected
source positions, a forward-fit model was developed with an assumed source
height distribution where height is measured from the photosphere. We find that
the best flare height distribution is given by g(h) \propto exp(-h/{\lambda})
where {\lambda} = 6.1\pm0.3 Mm is the scale height. A power-law height
distribution with a negative power-law index, {\gamma} = 3.1 \pm 0.1 is also
consistent with the data. Interpreted as thermal loop top sources, these
heights are compared to loops generated by a potential field model (PFSS). The
measured flare heights distribution are found to be much steeper than the
potential field loop height distribution which may be a signature of the flare
energization process
The Role of Solid Friction in the Sedimentation of Strongly Attractive Colloidal Gels
We study experimentally and theoretically the sedimentation of gels made of
strongly aggregated colloidal particles, focussing on the long time behavior,
when mechanical equilibrium is asymptotically reached. The asymptotic gel
height is found to vary linearly with the initial height, a finding in stark
contrast with a recent study on similar gels [Manley \textit{et al.} 2005
\textit{Phys. Rev. Lett.} \textbf{94} 218302]. We show that the asymptotic
compaction results from the balance between gravity pull, network elasticity,
and solid friction between the gel and the container walls. Based on these
ingredients, we propose a simple model to account for the dependence of the
height loss on the initial height and volume fraction. As a result of our
analysis, we show that the static friction coefficient between the gel and the
container walls strongly depends on volume fraction: the higher the volume
fraction, the weaker the solid friction. This nonintuitive behavior is
explained using simple scaling arguments.Comment: 13 pages, 5 figures. Submitted to JSTA
A surface electrode point Paul trap
We present a model as well as experimental results for a surface electrode
radio-frequency Paul trap that has a circular electrode geometry well-suited
for trapping of single ions and two-dimensional planar ion crystals. The trap
design is compatible with microfabrication and offers a simple method by which
the height of the trapped ions above the surface may be changed \emph{in situ}.
We demonstrate trapping of single and few Sr+ ions over an ion height range of
200-1000 microns for several hours under Doppler laser cooling, and use these
to characterize the trap, finding good agreement with our model.Comment: 10 pages, 11 figures, 1 tabl
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Length limited coding and optimal height-limited binary trees
A new O(nL)-time algorithm is given for finding an optimal prefix-free binary code for a weighted alphabet of size n, with the restriction that no code string be longer than L. An O(nL logn)-time algorithm is given for the corresponding alphabetic problem problem, which is equivalent to optimizing a dictionary of n words, implemented as a binary tree of height
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