4,462 research outputs found
Laughlin states on the Poincare half-plane and its quantum group symmetry
We find the Laughlin states of the electrons on the Poincare half-plane in
different representations. In each case we show that there exist a quantum
group symmetry such that the Laughlin states are a representation of
it. We calculate the corresponding filling factor by using the plasma analogy
of the FQHE.Comment: 9 pages,Late
Heterogeneous Bond Percolation on Multitype Networks with an Application to Epidemic Dynamics
Considerable attention has been paid, in recent years, to the use of networks
in modeling complex real-world systems. Among the many dynamical processes
involving networks, propagation processes -- in which final state can be
obtained by studying the underlying network percolation properties -- have
raised formidable interest. In this paper, we present a bond percolation model
of multitype networks with an arbitrary joint degree distribution that allows
heterogeneity in the edge occupation probability. As previously demonstrated,
the multitype approach allows many non-trivial mixing patterns such as
assortativity and clustering between nodes. We derive a number of useful
statistical properties of multitype networks as well as a general phase
transition criterion. We also demonstrate that a number of previous models
based on probability generating functions are special cases of the proposed
formalism. We further show that the multitype approach, by naturally allowing
heterogeneity in the bond occupation probability, overcomes some of the
correlation issues encountered by previous models. We illustrate this point in
the context of contact network epidemiology.Comment: 10 pages, 5 figures. Minor modifications were made in figures 3, 4
and 5 and in the text. Explanations and references were adde
The Hyperbolic Heisenberg and Sigma Models in (1+1)-dimensions
Hyperbolic versions of the integrable (1+1)-dimensional Heisenberg
Ferromagnet and sigma models are discussed in the context of topological
solutions classifiable by an integer `winding number'. Some explicit solutions
are presented and the existence of certain classes of such winding solutions
examined.Comment: 13 pages, 1 figure, Latex, personal style file included tensind.sty,
Proof in section 3 altered, no changes to conclusion
Generation of ultra-short light pulses by a rapidly ionizing thin foil
A thin and dense plasma layer is created when a sufficiently strong laser
pulse impinges on a solid target. The nonlinearity introduced by the
time-dependent electron density leads to the generation of harmonics. The pulse
duration of the harmonic radiation is related to the risetime of the electron
density and thus can be affected by the shape of the incident pulse and its
peak field strength. Results are presented from numerical
particle-in-cell-simulations of an intense laser pulse interacting with a thin
foil target. An analytical model which shows how the harmonics are created is
introduced. The proposed scheme might be a promising way towards the generation
of attosecond pulses.
PACS number(s): 52.40.Nk, 52.50.Jm, 52.65.RrComment: Second Revised Version, 13 pages (REVTeX), 3 figures in ps-format,
submitted for publication to Physical Review E, WWW:
http://www.physik.tu-darmstadt.de/tqe
Recovering the state sequence of hidden Markov models using mean-field approximations
Inferring the sequence of states from observations is one of the most
fundamental problems in Hidden Markov Models. In statistical physics language,
this problem is equivalent to computing the marginals of a one-dimensional
model with a random external field. While this task can be accomplished through
transfer matrix methods, it becomes quickly intractable when the underlying
state space is large.
This paper develops several low-complexity approximate algorithms to address
this inference problem when the state space becomes large. The new algorithms
are based on various mean-field approximations of the transfer matrix. Their
performances are studied in detail on a simple realistic model for DNA
pyrosequencing.Comment: 43 pages, 41 figure
Kinetics of ballistic annihilation and branching
We consider a one-dimensional model consisting of an assembly of two-velocity
particles moving freely between collisions. When two particles meet, they
instantaneously annihilate each other and disappear from the system. Moreover
each moving particle can spontaneously generate an offspring having the same
velocity as its mother with probability 1-q. This model is solved analytically
in mean-field approximation and studied by numerical simulations. It is found
that for q=1/2 the system exhibits a dynamical phase transition. For q<1/2, the
slow dynamics of the system is governed by the coarsening of clusters of
particles having the same velocities, while for q>1/2 the system relaxes
rapidly towards its stationary state characterized by a distribution of small
cluster sizes.Comment: 10 pages, 11 figures, uses multicol, epic, eepic and eepicemu. Also
avaiable at http://mykonos.unige.ch/~rey/pubt.htm
Preliminary analysis of an extensive one year survey of trace elements and compounds in the suspended particulate matter in Cleveland, Ohio
Beginning in 1971 a cooperative program has been carried on by the City of Cleveland Division of Air Pollution Control and NASA Lewis Research Center to study the trace element and compound concentrations in the ambient suspended particulate matter in Cleveland Ohio as a function of source, monitoring location and meteorological conditions. The major objectives were to determine the ambient concentration levels at representative urban sites and to develop a technique using trace element and compound data in conjunction with meteorological conditions to identify specific pollution sources which could be developed into a practical system that could be readily utilized by an enforcement agency
Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality
The Fourier transform is often used to connect the Lorentzian energy
distribution for resonance scattering to the exponential time dependence for
decaying states. However, to apply the Fourier transform, one has to bend the
rules of standard quantum mechanics; the Lorentzian energy distribution must be
extended to the full real axis instead of being bounded from
below (``Fermi's approximation''). Then the Fourier transform
of the extended Lorentzian becomes the exponential, but only for times , a time asymmetry which is in conflict with the unitary group time evolution
of standard quantum mechanics. Extending the Fourier transform from
distributions to generalized vectors, we are led to Gamow kets, which possess a
Lorentzian energy distribution with and have exponential
time evolution for only. This leads to probability predictions
that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.
Search for universality in one-dimensional ballistic annihilation kinetics
We study the kinetics of ballistic annihilation for a one-dimensional ideal
gas with continuous velocity distribution. A dynamical scaling theory for the
long time behavior of the system is derived. Its validity is supported by
extensive numerical simulations for several velocity distributions. This leads
us to the conjecture that all the continuous velocity distributions \phi(v)
which are symmetric, regular and such that \phi(0) does not vanish, are
attracted in the long time regime towards the same Gaussian distribution and
thus belong to the same universality class. Moreover, it is found that the
particle density decays as n(t)~t^{-\alpha}, with \alpha=0.785 +/- 0.005.Comment: 8 pages, needs multicol, epsf and revtex. 8 postscript figures
included. Submitted to Phys. Rev. E. Also avaiable at
http://mykonos.unige.ch/~rey/publi.html#Secon
Simultaneous 3D measurement of the translation and rotation of finite size particles and the flow field in a fully developed turbulent water flow
We report a novel experimental technique that measures simultaneously in
three dimensions the trajectories, the translation, and the rotation of finite
size inertial particles together with the turbulent flow. The flow field is
analyzed by tracking the temporal evolution of small fluorescent tracer
particles. The inertial particles consist of a super-absorbent polymer that
renders them index and density matched with water and thus invisible. The
particles are marked by inserting at various locations tracer particles into
the polymer. Translation and rotation, as well as the flow field around the
particle are recovered dynamically from the analysis of the marker and tracer
particle trajectories. We apply this technique to study the dynamics of
inertial particles much larger in size (Rp/{\eta} \approx 100) than the
Kolmogorov length scale {\eta} in a von K\'arm\'an swirling water flow
(R{\lambda} \approx 400). We show, using the mixed (particle/fluid) Eulerian
second order velocity structure function, that the interaction zone between the
particle and the flow develops in a spherical shell of width 2Rp around the
particle of radius Rp. This we interpret as an indication of a wake induced by
the particle. This measurement technique has many additional advantages that
will make it useful to address other problems such as particle collisions,
dynamics of non-spherical solid objects, or even of wet granular matter.Comment: 18 pages, 7 figures, submitted to "Measurement Science and
Technology" special issue on "Advances in 3D velocimetry
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