13,671 research outputs found
Analysis of data on the relation between eddies and streaky structures in turbulent flows using the placebo method
An artificially synthesized velocity field with known properties is used as a test data set in analyzing and interpreting the turbulent flow velocity fields. The objective nature of this approach is utilized for studying the relation between streaky and eddy structures. An analysis shows that this relation may be less significant than is customarily supposed
The Quantum Spectrum of the Conserved Charges in Affine Toda Theories
The exact eigenvalues of the infinite set of conserved charges on the
multi-particle states in affine Toda theories are determined. This is done by
constructing a free field realization of the Zamolodchikov-Faddeev algebra in
which the conserved charges are realized as derivative operators. The resulting
eigenvalues are renormalization group (RG) invariant, have the correct
classical limit and pass checks in first order perturbation theory. For
one recovers the (RG invariant form of the) quantum masses of Destri and
DeVega.Comment: 38p, 1 fig. included, MPI-Ph/93-92, LATE
SLE for theoretical physicists
This article provides an introduction to Schramm(stochastic)-Loewner
evolution (SLE) and to its connection with conformal field theory, from the
point of view of its application to two-dimensional critical behaviour. The
emphasis is on the conceptual ideas rather than rigorous proofs.Comment: 43 pages, to appear in Annals of Physics; v.2: published version with
minor correction
Conformal Curves in Potts Model: Numerical Calculation
We calculated numerically the fractal dimension of the boundaries of the
Fortuin-Kasteleyn clusters of the -state Potts model for integer and
non-integer values of on the square lattice.
In addition we calculated with high accuracy the fractal dimension of the
boundary points of the same clusters on the square domain. Our calculation
confirms that this curves can be described by SLE.Comment: 11 Pages, 4 figure
N=2 Supersymmetry, Painleve III and Exact Scaling Functions in 2D Polymers
We discuss in this paper various aspects of the off-critical model in
two dimensions. We find the ground-state energy conjectured by Zamolodchikov
for the unitary minimal models, and extend the result to some non-unitary
minimal cases. We apply our results to the discussion of scaling functions for
polymers on a cylinder. We show, using the underlying N=2 supersymmetry, that
the scaling function for one non-contractible polymer loop around the cylinder
is simply related to the solution of the Painleve III differential equation. We
also find the ground-state energy for a single polymer on the cylinder. We
check these results by numerically simulating the polymer system. We also
analyze numerically the flow to the dense polymer phase. We find there
surprising results, with a function that is not monotonous and
seems to have a roaming behavior, getting very close to the values 81/70 and
7/10 between its UV and IR values of 1.Comment: 20 pages (with 2 figures included
(Discrete) Almansi Type Decompositions: An umbral calculus framework based on symmetries
We introduce the umbral calculus formalism for hypercomplex variables
starting from the fact that the algebra of multivariate polynomials
\BR[\underline{x}] shall be described in terms of the generators of the
Weyl-Heisenberg algebra. The extension of \BR[\underline{x}] to the algebra
of Clifford-valued polynomials gives rise to an algebra of
Clifford-valued operators whose canonical generators are isomorphic to the
orthosymplectic Lie algebra .
This extension provides an effective framework in continuity and discreteness
that allow us to establish an alternative formulation of Almansi decomposition
in Clifford analysis (c.f. \cite{Ryan90,MR02,MAGU}) that corresponds to a
meaningful generalization of Fischer decomposition for the subspaces .
We will discuss afterwards how the symmetries of \mathfrak{sl}_2(\BR) (even
part of ) are ubiquitous on the recent approach of
\textsc{Render} (c.f. \cite{Render08}), showing that they can be interpreted in
terms of the method of separation of variables for the Hamiltonian operator in
quantum mechanics.Comment: Improved version of the Technical Report arXiv:0901.4691v1; accepted
for publication @ Math. Meth. Appl. Sci
http://www.mat.uc.pt/preprints/ps/p1054.pdf (Preliminary Report December
2010
Watersheds are Schramm-Loewner Evolution curves
We show that in the continuum limit watersheds dividing drainage basins are
Schramm-Loewner Evolution (SLE) curves, being described by one single parameter
. Several numerical evaluations are applied to ascertain this. All
calculations are consistent with SLE, with ,
being the only known physical example of an SLE with . This lies
outside the well-known duality conjecture, bringing up new questions regarding
the existence and reversibility of dual models. Furthermore it constitutes a
strong indication for conformal invariance in random landscapes and suggests
that watersheds likely correspond to a logarithmic Conformal Field Theory (CFT)
with central charge .Comment: 5 pages and 4 figure
First observation of Cherenkov rings with a large area CsI-TGEM-based RICH prototype
We have built a RICH detector prototype consisting of a liquid C6F14 radiator
and six triple Thick Gaseous Electron Multipliers (TGEMs), each of them having
an active area of 10x10 cm2. One triple TGEM has been placed behind the liquid
radiator in order to detect the beam particles, whereas the other five have
been positioned around the central one at a distance to collect the Cherenkov
photons. The upstream electrode of each of the TGEM stacks has been coated with
a 0.4 micron thick CsI layer.
In this paper, we will present the results from a series of laboratory tests
with this prototype carried out using UV light, 6 keV photons from 55Fe and
electrons from 90Sr as well as recent results of tests with a beam of charged
pions where for the first time Cherenkov Ring images have been successfully
recorded with TGEM photodetectors. The achieved results prove the feasibility
of building a large area Cherenkov detector consisting of a matrix of TGEMs.Comment: Presented at the International Conference NDIP-11, Lyon,July201
Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation
with reflecting boundary conditions which is relevant to the Temperley--Lieb
model of loops on a strip. By use of integral formulae we prove conjectures
relating it to the weighted enumeration of Cyclically Symmetric Transpose
Complement Plane Partitions and related combinatorial objects
Finite-size left-passage probability in percolation
We obtain an exact finite-size expression for the probability that a
percolation hull will touch the boundary, on a strip of finite width. Our
calculation is based on the q-deformed Knizhnik--Zamolodchikov approach, and
the results are expressed in terms of symplectic characters. In the large size
limit, we recover the scaling behaviour predicted by Schramm's left-passage
formula. We also derive a general relation between the left-passage probability
in the Fortuin--Kasteleyn cluster model and the magnetisation profile in the
open XXZ chain with diagonal, complex boundary terms.Comment: 21 pages, 8 figure
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