224 research outputs found
On the -binomial distribution and the Ising model
A completely new approach to the Ising model in 1 to 5 dimensions is
developed. We employ -binomial coefficients, a generalisation of the
binomial coefficients, to describe the magnetisation distributions of the Ising
model. For the complete graph this distribution corresponds exactly to the
limit case . We take our investigation to the simple -dimensional
lattices for and fit -binomial distributions to our data,
some of which are exact but most are sampled. For and the
magnetisation distributions are remarkably well-fitted by -binomial
distributions. For we are only slightly less successful, while for
we see some deviations (with exceptions!) between the -binomial
and the Ising distribution. We begin the paper by giving results on the
behaviour of the -distribution and its moment growth exponents given a
certain parameterization of . Since the moment exponents are known for the
Ising model (or at least approximately for ) we can predict how
should behave and compare this to our measured . The results speak in
favour of the -binomial distribution's correctness regarding their general
behaviour in comparison to the Ising model. The full extent to which they
correctly model the Ising distribution is not settled though.Comment: 51 pages, 23 figures, submitted to PRB on Oct 23 200
Tachyons in Compact Spaces
We discuss condensations of closed string tachyons localized in compact
spaces. Time evolution of an on-shell condensation is naturally related to the
worldsheet RG flow. Some explicit tachyonic compactifications of Type II string
theory is considered, and some of them are shown to decay into supersymmetric
theories known as the little string theories.Comment: 14 page
Integrable Deformations of Strings in Flux Backgrounds
We study d=2 0A string theory perturbed by tachyon momentum modes in
backgrounds with non-trivial tachyon condensate and Ramond-Ramond (RR) flux. In
the matrix model description, we uncover a complexified Toda lattice hierarchy
constrained by a pair of novel holomorphic string equations. We solve these
constraints in the classical limit for general RR flux and tachyon condensate.
Due to the non-holomorphic nature of the tachyon perturbations, the
transcendental equations which we derive for the string susceptibility are
manifestly non-holomorphic. We explore the phase structure and critical
behavior of the theory.Comment: 39 pages, 4 figure
Heterotic Strings in Two Dimensions and New Stringy Phase Transitions
We discuss heterotic string theories in two dimensions with gauge groups
Spin(24) and Spin(8) x E_8. After compactification the theories exhibit a rich
spectrum of states with both winding and momentum. At special points some of
these stringy states become massless, leading to new first order phase
transitions. For example, the thermal theories exhibit standard thermodynamics
below the phase transition, but novel and peculiar behavior above it. In
particular, when the radius of the Euclidean circle is smaller than the phase
transition point the torus partition function is not given by the thermal trace
over the spacetime Hilbert space. The full moduli space of compactified
theories is 13 dimensional, when Wilson lines are included; the Spin(24) and
Spin(8) x E_8 theories correspond to distinct decompactification limits.Comment: 32 pages; v2: references added, minor change
Holographic Gravitational Anomalies
In the AdS/CFT correspondence one encounters theories that are not invariant
under diffeomorphisms. In the boundary theory this is a gravitational anomaly,
and can arise in 4k+2 dimensions. In the bulk, there can be gravitational
Chern-Simons terms which vary by a total derivative. We work out the
holographic stress tensor for such theories, and demonstrate agreement between
the bulk and boundary. Anomalies lead to novel effects, such as a nonzero
angular momentum for global AdS(3). In string theory such Chern-Simons terms
are known with exact coefficients. The resulting anomalies, combined with
symmetries, imply corrections to the Bekenstein-Hawking entropy of black holes
that agree exactly with the microscopic counting.Comment: 25 page
Matrix Model and Time-like Linear Dilaton Matter
We consider a matrix model description of the 2d string theory whose matter
part is given by a time-like linear dilaton CFT. This is equivalent to the c=1
matrix model with a deformed, but very simple fermi surface. Indeed, after a
Lorentz transformation, the corresponding 2d spacetime is a conventional linear
dilaton background with a time-dependent tachyon field. We show that the tree
level scattering amplitudes in the matrix model perfectly agree with those
computed in the world-sheet theory. The classical trajectories of fermions
correspond to the decaying D-branes in the time-like linear dilaton CFT. We
also discuss the ground ring structure. Furthermore, we study the properties of
the time-like Liouville theory by applying this matrix model description. We
find that its ground ring structure is very similar to that of the minimal
string.Comment: 30 pages, harvmac, typos corrected, acknowledgements and comments
added(v2), published version (v3
Cooperative AUV Navigation using a Single Maneuvering Surface Craft
In this paper we describe the experimental implementation of an online algorithm for cooperative localization of submerged autonomous underwater vehicles (AUVs) supported by an autonomous surface craft. Maintaining accurate localization of an AUV is difficult because electronic signals, such as GPS, are highly attenuated by water. The usual solution to the problem is to utilize expensive navigation sensors to slow the rate of dead-reckoning divergence. We investigate an alternative approach that utilizes the position information of a surface vehicle to bound the error and uncertainty of the on-board position estimates of a low-cost AUV. This approach uses the Woods Hole Oceanographic Institution (WHOI) acoustic modem to exchange vehicle location estimates while simultaneously estimating inter-vehicle range. A study of the system observability is presented so as to motivate both the choice of filtering approach and surface vehicle path planning. The first contribution of this paper is to the presentation of an experiment in which an extended Kalman filter (EKF) implementation of the concept ran online on-board an OceanServer Iver2 AUV while supported by an autonomous surface vehicle moving adaptively. The second contribution of this paper is to provide a quantitative performance comparison of three estimators: particle filtering (PF), non-linear least-squares optimization (NLS), and the EKF for a mission using three autonomous surface craft (two operating in the AUV role). Our results indicate that the PF and NLS estimators outperform the EKF, with NLS providing the best performance.United States. Office of Naval Research (Grant N000140711102)United States. Office of Naval Research. Multidisciplinary University Research InitiativeSingapore. National Research FoundationSingapore-MIT Alliance for Research and Technology. Center for Environmental Sensing and Monitorin
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