591 research outputs found
Isoperimetry in two-dimensional percolation
We consider the unique infinite connected component of supercritical bond
percolation on the square lattice and study the geometric properties of
isoperimetric sets, i.e., sets with minimal boundary for a given volume. For
almost every realization of the infinite connected component we prove that, as
the volume of the isoperimetric set tends to infinity, its asymptotic shape can
be characterized by an isoperimetric problem in the plane with respect to a
particular norm. As an application we then show that the anchored isoperimetric
profile with respect to a given point as well as the Cheeger constant of the
giant component in finite boxes scale to deterministic quantities. This settles
a conjecture of Itai Benjamini for the plane.Comment: 40 pages, 2 figs; version to appear in Commun. Pure Appl. Mat
Orbital order in classical models of transition-metal compounds
We study the classical 120-degree and related orbital models. These are the
classical limits of quantum models which describe the interactions among
orbitals of transition-metal compounds. We demonstrate that at low temperatures
these models exhibit a long-range order which arises via an "order by disorder"
mechanism. This strongly indicates that there is orbital ordering in the
quantum version of these models, notwithstanding recent rigorous results on the
absence of spin order in these systems.Comment: 7 pages, 1 eps fi
The Two-Screen Measurement Setup to Indirectly Measure Proton Beam Self-Modulation in AWAKE
The goal of the first phase of the AWAKE \cite{AWAKE1,AWAKE2} experiment at
CERN is to measure the self-modulation \cite{SMI} of the long SPS proton bunch into microbunches after traversing
of plasma with a plasma density of
. The two screen measurement setup
\cite{Turner2016} is a proton beam diagnostic that can indirectly prove the
successful development of the self-modulation of the proton beam by imaging
protons that got defocused by the transverse plasma wakefields after passing
through the plasma, at two locations downstream the end of the plasma. This
article describes the design and realization of the two screen measurement
setup integrated in the AWAKE experiment. We discuss the performance and
background response of the system based on measurements performed with an
unmodulated Gaussian SPS proton bunch during the AWAKE beam commissioning in
September and October 2016. We show that the system is fully commissioned and
adapted to eventually image the full profile of a self-modulated SPS proton
bunch in a single shot measurement during the first phase of the AWAKE
experiment.Comment: 5 pages 8 figure
Indirect Self-Modulation Instability Measurement Concept for the AWAKE Proton Beam
AWAKE, the Advanced Proton-Driven Plasma Wakefield Acceleration Experiment,
is a proof-of-principle R&D experiment at CERN using a 400 GeV/c proton beam
from the CERN SPS (longitudinal beam size sigma_z = 12 cm) which will be sent
into a 10 m long plasma section with a nominal density of approx. 7x10^14
atoms/cm3 (plasma wavelength lambda_p = 1.2mm). In this paper we show that by
measuring the time integrated transverse profile of the proton bunch at two
locations downstream of the AWAKE plasma, information about the occurrence of
the self-modulation instability (SMI) can be inferred. In particular we show
that measuring defocused protons with an angle of 1 mrad corresponds to having
electric fields in the order of GV/m and fully developed self-modulation of the
proton bunch. Additionally, by measuring the defocused beam edge of the
self-modulated bunch, information about the growth rate of the instability can
be extracted. If hosing instability occurs, it could be detected by measuring a
non-uniform defocused beam shape with changing radius. Using a 1 mm thick
Chromox scintillation screen for imaging of the self-modulated proton bunch, an
edge resolution of 0.6 mm and hence a SMI saturation point resolution of 1.2 m
can be achieved.Comment: 4 pages, 4 figures, EAAC conference proceeding
Mean-field driven first-order phase transitions in systems with long-range interactions
We consider a class of spin systems on with vector valued spins
(\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The
interactions are generally spread-out in the sense that the 's exhibit
either exponential or power-law fall-off. Under the technical condition of
reflection positivity and for sufficiently spread out interactions, we prove
that the model exhibits a first-order phase transition whenever the associated
mean-field theory signals such a transition. As a consequence, e.g., in
dimensions , we can finally provide examples of the 3-state Potts model
with spread-out, exponentially decaying interactions, which undergoes a
first-order phase transition as the temperature varies. Similar transitions are
established in dimensions for power-law decaying interactions and in
high dimensions for next-nearest neighbor couplings. In addition, we also
investigate the limit of infinitely spread-out interactions. Specifically, we
show that once the mean-field theory is in a unique ``state,'' then in any
sequence of translation-invariant Gibbs states various observables converge to
their mean-field values and the states themselves converge to a product
measure.Comment: 57 pages; uses a (modified) jstatphys class fil
Optimal designs for rational function regression
We consider optimal non-sequential designs for a large class of (linear and
nonlinear) regression models involving polynomials and rational functions with
heteroscedastic noise also given by a polynomial or rational weight function.
The proposed method treats D-, E-, A-, and -optimal designs in a
unified manner, and generates a polynomial whose zeros are the support points
of the optimal approximate design, generalizing a number of previously known
results of the same flavor. The method is based on a mathematical optimization
model that can incorporate various criteria of optimality and can be solved
efficiently by well established numerical optimization methods. In contrast to
previous optimization-based methods proposed for similar design problems, it
also has theoretical guarantee of its algorithmic efficiency; in fact, the
running times of all numerical examples considered in the paper are negligible.
The stability of the method is demonstrated in an example involving high degree
polynomials. After discussing linear models, applications for finding locally
optimal designs for nonlinear regression models involving rational functions
are presented, then extensions to robust regression designs, and trigonometric
regression are shown. As a corollary, an upper bound on the size of the support
set of the minimally-supported optimal designs is also found. The method is of
considerable practical importance, with the potential for instance to impact
design software development. Further study of the optimality conditions of the
main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory
and additional example
New strategies to measure intracellular sodium concentrations
Fluorescent ion indicators are widely used to measure ion concentrations in living cells. However, despite considerable efforts in synthesizing new compounds, no ratiometric sodium indicator is available that can be excited at visible wavelengths. Ratiometric indicators have an advantage in that measured fluorescence intensities can be corrected for fluctuations of the indicator concentration and the illumination intensity, which is not possible when non-ratiometric indicators are used. One way to circumvent this problem is to measure fluorescence lifetimes, which are independent of these factors. Another way to overcome the disadvantages of a non-ratiometric indicator dye is to embed it, together with a reference dye, into nanoparticles. By relating the indicator fluorescence to the fluorescence of the reference dye, inhomogeneities in the nanosensor concentration or the illumination intensity can be cancelled out reliably. In this study we compare the benefits and drawbacks of these approaches. © 2010 Copyright SPIE - The International Society for Optical Engineering
Annealed lower tails for the energy of a polymer
We consider the energy of a randomly charged polymer. We assume that only
charges on the same site interact pairwise. We study the lower tails of the
energy, when averaged over both randomness, in dimension three or more. As a
corollary, we obtain the correct temperature-scale for the Gibbs measure.Comment: 27 page
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