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 $\infty$. 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 $2(\nu+1)$-dimensional Bessel process with $\nu > -1$, in which the inhomogeneity is indexed by $\kappa \in [0, 2(\nu+1))$. 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 $J_{\nu}$ used in the fractional calculus, where orders of differintegration are determined by $\nu-\kappa$. As special cases of the two parameters $(\nu, \kappa)$, 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 Δ+(1232)\Delta^{+}(1232) at low momentum transfer

We report on new p$(e,e^\prime p)\pi^\circ$ measurements at the $\Delta^{+}(1232)$ 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 $Q^2$ 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 μpGE/GM\mu_pG_E/G_M at low Q2Q^2

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