56 research outputs found
The structure of typical clusters in large sparse random configurations
The initial purpose of this work is to provide a probabilistic explanation of
a recent result on a version of Smoluchowski's coagulation equations in which
the number of aggregations is limited. The latter models the deterministic
evolution of concentrations of particles in a medium where particles coalesce
pairwise as time passes and each particle can only perform a given number of
aggregations. Under appropriate assumptions, the concentrations of particles
converge as time tends to infinity to some measure which bears a striking
resemblance with the distribution of the total population of a Galton-Watson
process started from two ancestors. Roughly speaking, the configuration model
is a stochastic construction which aims at producing a typical graph on a set
of vertices with pre-described degrees. Specifically, one attaches to each
vertex a certain number of stubs, and then join pairwise the stubs uniformly at
random to create edges between vertices. In this work, we use the configuration
model as the stochastic counterpart of Smoluchowski's coagulation equations
with limited aggregations. We establish a hydrodynamical type limit theorem for
the empirical measure of the shapes of clusters in the configuration model when
the number of vertices tends to . The limit is given in terms of the
distribution of a Galton-Watson process started with two ancestors
Infinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals
Yor's generalized meander is a temporally inhomogeneous modification of the
-dimensional Bessel process with , in which the
inhomogeneity is indexed by . We introduce the
non-colliding particle systems of the generalized meanders and prove that they
are the Pfaffian processes, in the sense that any multitime correlation
function is given by a Pfaffian. In the infinite particle limit, we show that
the elements of matrix kernels of the obtained infinite Pfaffian processes are
generally expressed by the Riemann-Liouville differintegrals of functions
comprising the Bessel functions used in the fractional calculus,
where orders of differintegration are determined by . As special
cases of the two parameters , the present infinite systems
include the quaternion determinantal processes studied by Forrester, Nagao and
Honner and by Nagao, which exhibit the temporal transitions between the
universality classes of random matrix theory.Comment: LaTeX, 35 pages, v3: The argument given in Section 3.2 was
simplified. Minor corrections were mad
Electroexcitation of the at low momentum transfer
We report on new p measurements at the
resonance at the low momentum transfer region. The mesonic
cloud dynamics is predicted to be dominant and rapidly changing in this
kinematic region offering a test bed for chiral effective field theory
calculations. The new data explore the low dependence of the resonant
quadrupole amplitudes while extending the measurements of the Coulomb
quadrupole amplitude to the lowest momentum transfer ever reached. The results
disagree with predictions of constituent quark models and are in reasonable
agreement with dynamical calculations that include pion cloud effects, chiral
effective field theory and lattice calculations. The reported measurements
suggest that improvement is required to the theoretical calculations and
provide valuable input that will allow their refinements
Physics Opportunities with the 12 GeV Upgrade at Jefferson Lab
This white paper summarizes the scientific opportunities for utilization of
the upgraded 12 GeV Continuous Electron Beam Accelerator Facility (CEBAF) and
associated experimental equipment at Jefferson Lab. It is based on the 52
proposals recommended for approval by the Jefferson Lab Program Advisory
Committee.The upgraded facility will enable a new experimental program with
substantial discovery potential to address important topics in nuclear,
hadronic, and electroweak physics.Comment: 64 page
Methods for Optical Calibration of the BigBite Hadron Spectrometer
The techniques for optical calibration of Jefferson Lab's large-acceptance
magnetic hadron spectrometer, BigBite, have been examined. The most consistent
and stable results were obtained by using a method based on singular value
decomposition. In spite of the complexity of the optics, the particles'
positions and momenta at the target have been precisely reconstructed from the
coordinates measured in the detectors by means of a single back-tracing matrix.
The technique is applicable to any similar magnetic spectrometer and any
particle type. For 0.55 GeV/c protons, we have established the vertex
resolution of 1.2 cm, angular resolutions of 7 mrad and 16 mrad (in-plane and
out-of-plane, respectively), and a relative momentum resolution of 1.6%.Comment: 26 pages, 13 figure
Search for three-nucleon short-range correlations in light nuclei
We present new data probing short-range correlations (SRCs) in nuclei through the measurement of electron scattering off high-momentum nucleons in nuclei. The inclusive ^{4}He/^{3}He cross section ratio is observed to be both x and Q^{2} independent for 1.52, our data support the hypothesis that a previous claim of three-nucleon correlation dominance was an artifact caused by the limited resolution of the measurement. While 3N-SRCs appear to have an important contribution, our data show that isolating 3N-SRCs is significantly more complicated than for 2N-SRCs.United States. Department of Energy (Contract DE-AC05-06OR23177)United States. Department of Energy (Contract DE-AC02-06CH11357)United States. Department of Energy (Contract DE-FG02-96ER40950
High Precision Measurement of the Proton Elastic Form Factor Ratio at low
We report a new, high-precision measurement of the proton elastic form factor
ratio \mu_p G_E/G_M for the four-momentum transfer squared Q^2 = 0.3-0.7
(GeV/c)^2. The measurement was performed at Jefferson Lab (JLab) in Hall A
using recoil polarimetry. With a total uncertainty of approximately 1%, the new
data clearly show that the deviation of the ratio \mu_p G_E/G_M from unity
observed in previous polarization measurements at high Q^2 continues down to
the lowest Q^2 value of this measurement. The updated global fit that includes
the new results yields an electric (magnetic) form factor roughly 2% smaller
(1% larger) than the previous global fit in this Q^2 range. We obtain new
extractions of the proton electric and magnetic radii, which are
^(1/2)=0.875+/-0.010 fm and ^(1/2)=0.867+/-0.020 fm. The charge
radius is consistent with other recent extractions based on the electron-proton
interaction, including the atomic hydrogen Lamb shift measurements, which
suggests a missing correction in the comparison of measurements of the proton
charge radius using electron probes and the recent extraction from the muonic
hydrogen Lamb shift.Comment: 12 pages, 3 figure
Track D Social Science, Human Rights and Political Science
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138414/1/jia218442.pd
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