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A $3$-$(v,\{4,6\},1)$ design is a configuration of $v$ points and a collection of $4$- and $6$-element subsets called blocks, that jointly contain every 3-element subset exactly once. Using an exhaustive computer search on $v\leq 28$ points we investigate the $3$-$(v,\{4,6\},1)$ designs that have a transitive automorphism group and where the blocks of size 6 form a 2-class symmetric design. A 2-class symmetric design with parameters $(v,k{;}\lambda_1,\lambda_2{;}\delta_1,\delta_2)$ is a set-system on $v$ points and $v$ blocks of size $k$, where every pair of points are in $\lambda_1$ or $\lambda_2$ blocks and every pair of blocks intersect in $\delta_1$ or $\delta_2$ points. The 2-class symmetric designs include biplanes, semi-biplanes, and 2-class symmetric partially balanced incomplete block designs.

A groupoid $\Omega \left( \mathcal{B} \right)$ called material groupoid is naturally associated to any simple body $\mathcal{B}$. The material distribution is introduced due to the (possible) lack of differentiability of the material groupoid. Thus, the inclusion of these new objects in the theory of material bodies opens the possibility of studying non-uniform bodies. As an example, the material distribution and its associated singular foliation result in a rigorous and unique subdivision of the material body into strictly smoothly uniform sub-bodies, laminates, filaments and isolated points. Furthermore, the material distribution permits us to present a "measure" of uniformity of a simple body as well as more general definitions of homogeneity for non-uniform bodies., Comment: arXiv admin note: text overlap with arXiv:1711.09022

Associated to each material body $\mathcal{B}$ there exists a groupoid $\Omega \left( \mathcal{B} \right)$ consisting of all the material isomorphisms connecting the points of $\mathcal{B}$. The uniformity character of $\mathcal{B}$ is reflected in the properties of $\Omega \left( \mathcal{B} \right)$: $\mathcal{B}$ is uniform if, and only if, $\Omega \left( \mathcal{B} \right)$ is transitive. Smooth uniformity corresponds to a Lie groupoid and, specifically, to a Lie subgroupoid of the groupoid $\Pi^1\left({\mathcal B}, {\mathcal B} \right)$ of 1-jets of $\mathcal B$. We consider a general situation when $\Omega \left( \mathcal{B} \right)$ is only an algebraic subgroupoid. Even in this case, we can cover $\mathcal{B}$ by a material foliation whose leaves are transitive. The same happens with $\Omega \left( \mathcal{B} \right)$ and the corresponding leaves generate transitive Lie groupoids (roughly speaking, the leaves covering $\mathcal B$). This result opens the possibility to study the homogeneity of general material bodies using geometric instruments.

A Lie groupoid, called \textit{material Lie groupoid}, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called \textit{material algebroid}, is used to characterize the uniformity and the homogeneity properties of the material. The relation to previous results in terms of $G-$structures is discussed in detail. An illustrative example is presented as an application of the theory.

Virtual Compton Scattering (VCS) on the proton has been studied at Jefferson Lab using the exclusive photon electroproduction reaction (e p --> e p gamma). This paper gives a detailed account of the analysis which has led to the determination of the structure functions P_LL-P_TT/epsilon and P_LT, and the electric and magnetic generalized polarizabilities (GPs) alpha_E(Q^2) and beta_M(Q^2) at values of the four-momentum transfer squared Q^2= 0.92 and 1.76 GeV^2. These data, together with the results of VCS experiments at lower momenta, help building a coherent picture of the electric and magnetic GPs of the proton over the full measured Q^2-range, and point to their non-trivial behavior., Comment: version 2: modified according to PRC Editor's and Referee's recommendations. Archival paper for the E93-050 experiment at JLab Hall A. 28 pages, 23 figures, 5 cross-section tables. To be submitted to Phys.Rev.C

Precise measurements of the proton electromagnetic form factor ratio $R = \mu_p G_E^p/G_M^p$ using the polarization transfer method at Jefferson Lab have revolutionized the understanding of nucleon structure by revealing the strong decrease of $R$ with momentum transfer $Q^2$ for $Q^2 \gtrsim 1$ GeV$^2$, in strong disagreement with previous extractions of $R$ from cross section measurements. In particular, the polarization transfer results have exposed the limits of applicability of the one-photon-exchange approximation and highlighted the role of quark orbital angular momentum in the nucleon structure. The GEp-II experiment in Jefferson Lab's Hall A measured $R$ at four $Q^2$ values in the range 3.5 GeV$^2 \le Q^2 \le 5.6$ GeV$^2$. A possible discrepancy between the originally published GEp-II results and more recent measurements at higher $Q^2$ motivated a new analysis of the GEp-II data. This article presents the final results of the GEp-II experiment, including details of the new analysis, an expanded description of the apparatus and an overview of theoretical progress since the original publication. The key result of the final analysis is a systematic increase in the results for $R$, improving the consistency of the polarization transfer data in the high-$Q^2$ region. This increase is the result of an improved selection of elastic events which largely removes the systematic effect of the inelastic contamination, underestimated by the original analysis., Comment: 30 pages, 17 figures, 4 tables. Final version to appear in Phys. Rev. C

A high-resolution (sigma_instr. = 1.5 MeV) search for narrow states (Gamma < 10 MeV) with masses of M_x approx 1500-1850 MeV in ep -> e'K^+ X, e'K^- X and e' pi^+ X electroproduction at small angles and low Q^2 was performed. These states would be candidate partner states of the reported Theta^+(1540) pentaquark. No statistically significant signal was observed in any of the channels at 90% C.L. Upper limits on forward production were determined to be between 0.7% and 4.2% of the Lambda(1520) production cross section, depending on the channel and the assumed mass and width of the state., Comment: 5 pages, 5 figures, to appear in Phys. Rev. C, update with responses to referee suggestions

A formulation of Continuum Mechanics within the context of General Relativity is presented that allows for the incorporation of certain types of anelastic material behaviour, such as viscoelasticity and plasticity. The approach is based on the concept of a four-dimensional body-time complex structured as a principal bundle. The anelastic response is regarded as the result of a continuous distribution of inhomogeneities, whose evolution is dictated by a suggested relativistic version of the Eshelby tensor. The role played by various groups is emphasized throughout the presentation and illustrated by means of the example of an anelastic fluid., Comment: 29 pages

We have measured the 4He(e,e'p)3H reaction at missing momenta of 130-300 MeV/c using the three-spectrometer facility at the Mainz microtron MAMI. Data were taken in perpendicular kinematics to allow us to determine the response function Rlt and the asymmetry term Atl. The data are compared to both relativistic and non-relativistic calculations., Comment: To be published in the European Physical Journal A

Precision studies of the reaction $^{3}$He(e,e$^\prime$p) using the three-spectrometer facility at the Mainz microtron MAMI are presented. All data are for quasielastic kinematics at $|\vec{q} | =685$ MeV/c. Absolute cross sections were measured at three electron kinematics. For the measured missing momenta range from 10 to 165 MeV/c, no strength is observed for missing energies higher than 20 MeV. Distorted momentum distributions were extracted for the two-body breakup and the continuum. The longitudinal and transverse behavior was studied by measuring the cross section for three photon polarizations. The longitudinal and transverse nature of the cross sections is well described by a currently accepted and widely used prescription of the off-shell electron-nucleon cross-section. The results are compared to modern three-body calculations and to previous data., Comment: 4 pages, 3 figures. Submitted for publication in Phys. Rev. Lett

We measured the 12C(e,e'p) cross section as a function of missing energy in parallel kinematics for (q,w) = (970 MeV/c, 330 MeV) and (990 MeV/c, 475 MeV). At w=475 MeV, at the maximum of the quasielastic peak, there is a large continuum (E_m > 50 MeV) cross section extending out to the deepest missing energy measured, amounting to almost 50% of the measured cross section. The ratio of data to DWIA calculation is 0.4 for both the p- and s-shells. At w=330 MeV, well below the maximum of the quasielastic peak, the continuum cross section is much smaller and the ratio of data to DWIA calculation is 0.85 for the p-shell and 1.0 for the s-shell. We infer that one or more mechanisms that increase with $\omega$ transform some of the single-nucleon-knockout into multinucleon knockout, decreasing the valence knockout cross section and increasing the continuum cross section., Comment: 14 pages, 7 figures, Revtex (multicol, prc and aps styles), to appear in Phys Rev C

Recoil proton polarization observables were measured for both the p($\vec {\rm e}$,e$^\prime\vec{\rm p}\,$) and d($\vec {\rm e}$,e$^\prime\vec{\rm p}\,)$n reactions at two values of Q$^2$ using a newly commissioned proton Focal Plane Polarimeter at the M.I.T.-Bates Linear Accelerator Center. The hydrogen and deuterium spin-dependent observables $D_{\ell\ell}$ and $D_{{\ell}t}$, the induced polarization $P_n$ and the form factor ratio $G^p_E/G^p_M$ were measured under identical kinematics. The deuterium and hydrogen results are in good agreement with each other and with the plane-wave impulse approximation (PWIA)., Comment: 9 pages, 1 figure; accepted by Phys. Rev. Lett

The first measurements of the induced proton polarization, P_n, for the 12C (e,e'\vec{p}) reaction are reported. The experiment was performed at quasifree kinematics for energy and momentum transfer (\omega,q) \approx (294 MeV, 756 MeV/c) and sampled a recoil momentum range of 0-250 MeV/c. The induced polarization arises from final-state interactions and for these kinematics is dominated by the real part of the spin-orbit optical potential. The distorted-wave impulse approximation provides good agreement with data for the 1p_{3/2} shell. The data for the continuum suggest that both the 1s_{1/2} shell and underlying l > 1 configurations contribute., Comment: 5 pages LaTeX, 2 postscript figures, accepted by Physical Reveiw Letters

The coincidence cross-section and the interference structure function, R_LT, were measured for the 12C(e,e'p) 11B reaction at quasielastic kinematics and central momentum transfer of q=400 MeV/c. The measurement was at an opening angle of theta_pq=11 degrees, covering a range in missing energy of E_m = 0 to 65 MeV. The R_LT structure function is found to be consistent with zero for E_m > 50 MeV, confirming an earlier study which indicated that R_L vanishes in this region. The integrated strengths of the p- and s-shell are compared with a Distorted Wave Impulse Approximation calculation. The s-shell strength and shape are compared with a Hartree Fock-Random Phase Approximation calculation. The DWIA calculation overestimates the cross sections for p- and s-shell proton knockout as expected, but surprisingly agrees with the extracted R_LT value for both shells. The HF-RPA calculation describes the data more consistently, which may be due to the inclusion of 2-body currents in this calculation., Comment: 8 Pages LaTex, 5 postscript figures. Submitted to Phys. Rev. C

The inclusive A(e,e') cross section for $x \simeq 1$ was measured on $^2$H, C, Fe, and Au for momentum transfers $Q^2$ from 1-7 (GeV/c)$^2$. The scaling behavior of the data was examined in the region of transition from y-scaling to x-scaling. Throughout this transitional region, the data exhibit $\xi$-scaling, reminiscent of the Bloom-Gilman duality seen in free nucleon scattering., Comment: 4 pages, RevTeX; 4 figures (postscript in .tar.Z file)