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Register a new userUniqueness of the $[varphi,vec{e}_{3}]$-catenary cylinders by their asymptotic behaviour
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We establish a uniqueness result for the $[varphi,vec{e}_{3}]$-catenary cylinders by their asymptotic behaviour. Well known examples of such cylinders are the grim reaper translating solitons for the mean curvature flow. For such solitons, F. Martin, J. Perez-Garcia, A. Savas-Halilaj and K. Smoczyk proved that, if $Sigma$ is a properly embedded translating soliton with locally bounded genus, and $mathcal{C}^{infty}$-asymptotic to two vertical planes outside a cylinder, then $Sigma$ must coincide with some grim reaper translating soliton. In this paper, applying the moving plane method of Alexandrov together with a strong maximum principle for elliptic operators, we increase the family of $[varphi,vec{e}_{3}]$-minimal graphs where these types of results hold under different assumption of asymptotic behaviour.
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We establish curvature estimates and a convexity result for mean convex properly embedded $[varphi,vec{e}_{3}]$-minimal surfaces in $mathbb{R}^3$, i.e., $varphi$-minimal surfaces when $varphi$ depends only on the third coordinate of $mathbb{R}^3$. Led by the works on curvature estimates for surfaces in 3-manifolds, due to White for minimal surfaces, to Rosenberg, Souam and Toubiana, for stable CMC surfaces, and to Spruck and Xiao for stable translating solitons in $mathbb{R}^3$, we use a compactness argument to provide curvature estimates for a family of mean convex $[varphi,vec{e}_{3}]$-minimal surfaces in $mathbb{R}^{3}$. We apply this result to generalize the convexity property of Spruck and Xiao for translating solitons. More precisely, we characterize the convexity of a properly embedded $[varphi,vec{e}_{3}]$-minimal surface in $mathbb{R}^{3}$ with non positive mean curvature when the growth at infinity of $varphi$ is at most quadratic.
Polarization transfer in the 4He(e,ep)3H reaction at a Q^2 of 0.4 (GeV/c)^2 was measured at the Mainz Microtron MAMI. The ratio of the transverse to the longitudinal polarization components of the ejected protons was compared with the same ratio for elastic ep scattering. The results are consistent with a recent fully relativistic calculation which includes a predicted medium modification of the proton form factor based on a quark-meson coupling model.
Using isobaric Monte Carlo simulations, we map out the entire phase diagram of a system of hard cylindrical particles of length $L$ and diameter $D$, using an improved algorithm to identify the overlap condition between two cylinders. Both the prolate $L/D>1$ and the oblate $L/D<1$ phase diagrams are reported with no solution of continuity. In the prolate $L/D>1$ case, we find intermediate nematic textrm{N} and smectic textrm{SmA} phases in addition to a low density isotropic textrm{I} and a high density crystal textrm{X} phase, with textrm{I-N-SmA} and textrm{I-SmA-X} triple points. An apparent columnar phase textrm{C} is shown to be metastable as in the case of spherocylinders. In the oblate $L/D<1$ case, we find stable intermediate cubatic textrm{Cub}, nematic textrm{N}, and columnar textrm{C} phases with textrm{I-N-Cub}, textrm{N-Cub-C}, and textrm{I-Cub-C} triple points. Comparison with previous numerical and analytical studies is discussed. The present study, accounting for the explicit cylindrical shape, paves the way to more sophisticated models with important biological applications, such as viruses and nucleosomes.
In this paper, we prove that the round cylinders are rigid in the space of Ricci shrinkers. Namely, any Ricci shrinker that is sufficiently close to $S^{n-1}times mathbb R$ in the pointed-Gromov-Hausdorff topology must itself be isometric to $S^{n-1}times mathbb R$.
The effects of multi-photon-exchange and other higher-order QED corrections on elastic electron-proton scattering have been a subject of high experimental and theoretical interest since the polarization transfer measurements of the proton electromagnetic form factor ratio $G_E^p/G_M^p$ at large momentum transfer $Q^2$ conclusively established the strong decrease of this ratio with $Q^2$ for $Q^2 gtrsim 1$ GeV$^2$. This result is incompatible with previous extractions of this quantity from cross section measurements using the Rosenbluth Separation technique. Much experimental attention has been focused on extracting the two-photon exchange (TPE) effect through the unpolarized $e^+p/e^-p$ cross section ratio, but polarization transfer in polarized elastic scattering can also reveal evidence of hard two-photon exchange. Furthermore, it has a different sensitivity to the generalized TPE form factors, meaning that measurements provide new information that cannot be gleaned from unpolarized scattering alone. Both $epsilon$-dependence of polarization transfer at fixed $Q^2$, and deviations between electron-proton and positron-proton scattering are key signatures of hard TPE. A polarized positron beam at Jefferson Lab would present a unique opportunity to make the first measurement of positron polarization transfer, and comparison with electron-scattering data would place valuable constraints on hard TPE. Here, we propose a measurement program in Hall A that combines the Super BigBite Spectrometer for measuring recoil proton polarization, with a non-magnetic calorimetric detector for triggering on elastically scattered positrons. Though the reduced beam current of the positron beam will restrict the kinematic reach, this measurement will have very small systematic uncertainties, making it a clean probe of TPE.
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