2,479 research outputs found
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
Dynamics of Air-Fluidized Granular System Measured by the Modulated Gradient Spin-echo
The power spectrum of displacement fluctuation of beads in the air-fluidized
granular system is measured by a novel NMR technique of modulated gradient
spin-echo. The results of measurement together with the related spectrum of the
velocity fluctuation autocorrelation function fit well to an empiric formula
based on to the model of bead caging between nearest neighbours; the cage
breaks up after a few collisions \cite{Menon1}. The fit yields the
characteristic collision time, the size of bead caging and the diffusion-like
constant for different degrees of system fluidization. The resulting mean
squared displacement increases proportionally to the second power of time in
the short-time ballistic regime and increases linearly with time in the
long-time diffusion regime as already confirmed by other experiments and
simulations.Comment: 4 figures. Submited to Physical Review Letters, April 200
Singular Scaling Functions in Clustering Phenomena
We study clustering in a stochastic system of particles sliding down a
fluctuating surface in one and two dimensions. In steady state, the
density-density correlation function is a scaling function of separation and
system size.This scaling function is singular for small argument -- it exhibits
a cusp singularity for particles with mutual exclusion, and a divergence for
noninteracting particles. The steady state is characterized by giant
fluctuations which do not damp down in the thermodynamic limit. The
autocorrelation function is a singular scaling function of time and system
size. The scaling properties are surprisingly similar to those for particles
moving in a quenched disordered environment that results if the surface is
frozen.Comment: 8 pages, 3 figures, Invited talk delivered at Statphys 23, Genova,
July 200
A Q-Ising model application for linear-time image segmentation
A computational method is presented which efficiently segments digital
grayscale images by directly applying the Q-state Ising (or Potts) model. Since
the Potts model was first proposed in 1952, physicists have studied lattice
models to gain deep insights into magnetism and other disordered systems. For
some time, researchers have realized that digital images may be modeled in much
the same way as these physical systems (i.e., as a square lattice of numerical
values). A major drawback in using Potts model methods for image segmentation
is that, with conventional methods, it processes in exponential time. Advances
have been made via certain approximations to reduce the segmentation process to
power-law time. However, in many applications (such as for sonar imagery),
real-time processing requires much greater efficiency. This article contains a
description of an energy minimization technique that applies four Potts
(Q-Ising) models directly to the image and processes in linear time. The result
is analogous to partitioning the system into regions of four classes of
magnetism. This direct Potts segmentation technique is demonstrated on
photographic, medical, and acoustic images.Comment: 7 pages, 8 figures, revtex, uses subfigure.sty. Central European
Journal of Physics, in press (2010
Nonequilibrium glass transitions in driven and active matter
The glass transition, extensively studied in dense fluids, polymers, or
colloids, corresponds to a dramatic evolution of equilibrium transport
coefficients upon a modest change of control parameter, like temperature or
pressure. A similar phenomenology is found in many systems evolving far from
equilibrium, such as driven granular media, active and living matter. While
many theories compete to describe the glass transition at thermal equilibrium,
very little is understood far from equilibrium. Here, we solve the dynamics of
a specific, yet representative, class of glass models in the presence of
nonthermal driving forces and energy dissipation, and show that a dynamic
arrest can take place in these nonequilibrium conditions. While the location of
the transition depends on the specifics of the driving mechanisms, important
features of the glassy dynamics are insensitive to details, suggesting that an
`effective' thermal dynamics generically emerges at long time scales in
nonequilibrium systems close to dynamic arrest.Comment: 7 pages, 2 fig
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