208 research outputs found
Ostwald Ripening in Two Dimensions: Treatment with Pairwise Interactions
We present a systematic extension of mean field models for Ostwald ripening
in two dimensions. We derived, using a mean field type approximation, an
analytic expression for pairwise interactions between the minority phase
droplets. These interactions appear in dynamic equations for the droplets'
radii and positions, which are solved numerically for systems of tens of
thousands of droplets, yielding very good agreement with recent experiments.Comment: 4 pages, RevTex, 3 eps figure
Michael E. Fisher - teacher, mentor, colleague and friend: a (very) personal account
The only rational way of educating is to be an example. If one cant help it,
a warning example. Albert Einstein. I had the good fortune and privilege of
having Michael Fisher as my teacher, supervisor, mentor and friend. During my
years as a scientist, teacher and supervisor of about one hundred students and
post docs I found myself innumerable times realizing that I am following or at
least trying to follow Michaels example. These pages are my attempt to convey
recollections of my association with Michael, focusing on how he served as an
example for me.Comment: 13 pages, 2 figures, Michael Fisher Memorial volum
Recovery of Protein Structure from Contact Maps
We present an efficient algorithm to recover the three dimensional structure
of a protein from its contact map representation. First we show that when a
physically realizable map is used as target, our method generates a structure
whose contact map is essentially similar to the target. Furthermore, the
reconstructed and original structures are similar up to the resolution of the
contact map representation. Next we use non-physical target maps, obtained by
corrupting a physical one; in this case our method essentially recovers the
underlying physical map and structure. Hence our algorithm will help to fold
proteins, using dynamics in the space of contact maps. Finally we investigate
the manner in which the quality of the recovered structure degrades when the
number of contacts is reduced.Comment: 27 pages, RevTex, 12 figures include
Data clustering using a model granular magnet
We present a new approach to clustering, based on the physical properties of
an inhomogeneous ferromagnet. No assumption is made regarding the underlying
distribution of the data. We assign a Potts spin to each data point and
introduce an interaction between neighboring points, whose strength is a
decreasing function of the distance between the neighbors. This magnetic system
exhibits three phases. At very low temperatures it is completely ordered; all
spins are aligned. At very high temperatures the system does not exhibit any
ordering and in an intermediate regime clusters of relatively strongly coupled
spins become ordered, whereas different clusters remain uncorrelated. This
intermediate phase is identified by a jump in the order parameters. The
spin-spin correlation function is used to partition the spins and the
corresponding data points into clusters. We demonstrate on three synthetic and
three real data sets how the method works. Detailed comparison to the
performance of other techniques clearly indicates the relative success of our
method.Comment: 46 pages, postscript, 15 ps figures include
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