9,068 research outputs found
On the Inversion of High Energy Proton
Inversion of the K-fold stochastic autoconvolution integral equation is an
elementary nonlinear problem, yet there are no de facto methods to solve it
with finite statistics. To fix this problem, we introduce a novel inverse
algorithm based on a combination of minimization of relative entropy, the Fast
Fourier Transform and a recursive version of Efron's bootstrap. This gives us
power to obtain new perspectives on non-perturbative high energy QCD, such as
probing the ab initio principles underlying the approximately negative binomial
distributions of observed charged particle final state multiplicities, related
to multiparton interactions, the fluctuating structure and profile of proton
and diffraction. As a proof-of-concept, we apply the algorithm to ALICE
proton-proton charged particle multiplicity measurements done at different
center-of-mass energies and fiducial pseudorapidity intervals at the LHC,
available on HEPData. A strong double peak structure emerges from the
inversion, barely visible without it.Comment: 29 pages, 10 figures, v2: extended analysis (re-projection ratios,
2D
Stability of discrete dark solitons in nonlinear Schrodinger lattices
We obtain new results on the stability of discrete dark solitons bifurcating
from the anti-continuum limit of the discrete nonlinear Schrodinger equation,
following the analysis of our previous paper [Physica D 212, 1-19 (2005)]. We
derive a criterion for stability or instability of dark solitons from the
limiting configuration of the discrete dark soliton and confirm this criterion
numerically. We also develop detailed calculations of the relevant eigenvalues
for a number of prototypical configurations and obtain very good agreement of
asymptotic predictions with the numerical data.Comment: 11 pages, 5 figure
Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map
We present an efficient procedure for computing resonances and resonant modes
of Helmholtz problems posed in exterior domains. The problem is formulated as a
nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use
of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains.
We consider a variational formulation and show that the spectrum consists of
isolated eigenvalues of finite multiplicity that only can accumulate at
infinity. The proposed method is based on a high order finite element
discretization combined with a specialization of the Tensor Infinite Arnoldi
method. Using Toeplitz matrices, we show how to specialize this method to our
specific structure. In particular we introduce a pole cancellation technique in
order to increase the radius of convergence for computation of eigenvalues that
lie close to the poles of the matrix-valued function. The solution scheme can
be applied to multiple resonators with a varying refractive index that is not
necessarily piecewise constant. We present two test cases to show stability,
performance and numerical accuracy of the method. In particular the use of a
high order finite element discretization together with TIAR results in an
efficient and reliable method to compute resonances
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