18,101 research outputs found
The Tails of the Crossing Probability
The scaling of the tails of the probability of a system to percolate only in
the horizontal direction was investigated numerically for correlated
site-bond percolation model for .We have to demonstrate that the
tails of the crossing probability far from the critical point have shape
where is the correlation
length index, is the probability of a bond to be closed. At
criticality we observe crossover to another scaling . Here is a scaling index describing the
central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical
change
Use of stochastic adaptation in block method to estimate deformation field for image sequence
The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
We consider the application of the DRA method to the case of several master
integrals in a given sector. We establish a connection between the homogeneous
part of dimensional recurrence and maximal unitarity cuts of the corresponding
integrals: a maximally cut master integral appears to be a solution of the
homogeneous part of the dimensional recurrence relation. This observation
allows us to make a necessary step of the DRA method, the construction of the
general solution of the homogeneous equation, which, in this case, is a coupled
system of difference equations.Comment: 17 pages, 2 figure
Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams
It is shown how strictly four-dimensional integration by parts combined with
differential renormalization and its infrared analogue can be applied for
calculation of Feynman diagrams.Comment: 6 pages, late
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
Planar box diagram for the (N_F = 1) 2-loop QED virtual corrections to Bhabha scattering
In this paper we present the master integrals necessary for the analytic
calculation of the box diagrams with one electron loop (N_{F}=1) entering in
the 2-loop (\alpha^3) QED virtual corrections to the Bhabha scattering
amplitude of the electron. We consider on-shell electrons and positrons of
finite mass m, arbitrary squared c.m. energy s, and momentum transfer t; both
UV and soft IR divergences are regulated within the continuous D-dimensional
regularization scheme. After a brief overview of the method employed in the
calculation, we give the results, for s and t in the Euclidean region, in terms
of 1- and 2-dimensional harmonic polylogarithms, of maximum weight 3. The
corresponding results in the physical region can be recovered by analytical
continuation. For completeness, we also provide the analytic expression of the
1-loop scalar box diagram including the first order in (D-4).Comment: Misprints in Eqs. (36), (38), (39), and (B.9) have been corrected.
The results are now available at http://pheno.physik.uni-freiburg.de/~bhabha,
as FORM input file
Exactly solvable model of the 2D electrical double layer
We consider equilibrium statistical mechanics of a simplified model for the
ideal conductor electrode in an interface contact with a classical
semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of
pointlike unit charges in the stability-against-collapse regime of
reduced inverse temperatures . If there is a potential difference
between the bulk interior of the electrolyte and the grounded interface, the
electrolyte region close to the interface (known as the electrical double
layer) carries some nonzero surface charge density. The model is mappable onto
an integrable semi-infinite sine-Gordon theory with Dirichlet boundary
conditions. The exact form-factor and boundary state information gained from
the mapping provide asymptotic forms of the charge and number density profiles
of electrolyte particles at large distances from the interface. The result for
the asymptotic behavior of the induced electric potential, related to the
charge density via the Poisson equation, confirms the validity of the concept
of renormalized charge and the corresponding saturation hypothesis. It is
documented on the non-perturbative result for the asymptotic density profile at
a strictly nonzero that the Debye-H\"uckel limit is a
delicate issue.Comment: 14 page
A Comparative Numerical Study on GEM, MHSP and MSGC
In this work, we have tried to develop a detailed understanding of the
physical processes occurring in those variants of Micro Pattern Gas Detectors
(MPGDs) that share micro hole and micro strip geometry, like GEM, MHSP and MSGC
etc. Some of the important and fundamental characteristics of these detectors
such as gain, transparency, efficiency and their operational dependence on
different device parameters have been estimated following detailed numerical
simulation of the detector dynamics. We have used a relatively new simulation
framework developed especially for the MPGDs that combines packages such as
GARFIELD, neBEM, MAGBOLTZ and HEED. The results compare closely with the
available experimental data. This suggests the efficacy of the framework to
model the intricacies of these micro-structured detectors in addition to
providing insight into their inherent complex dynamical processes
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