arXiv subjects

Joseph Gordon

Publications and source records attributed to Joseph Gordon.

6 recordsLinked to original sources

arXiv2025

Degrees in the $\beta$- and $\beta'$-Delaunay graphs

We investigate the typical cells $\widehat{Z}$ and $\widehat{Z}^\prime$ of $\beta$- and $\beta'$-Voronoi tessellations in $\mathbb{R}^d$, establishing a Complementary Theorem which entails: 1) a gamma distribution of the $\Phi$-content (a suitable homogeneous functional) of the typical cell with $n$-facets; 2) the independence of this $\Phi$-content with the shape of the cell; 3) a practical integral representation of the distribution of $Z^{(\prime)}$. We exploit the latter to derive bounds on the distribution of the facet numbers. Using duality, we get bounds on the typical degree distributions of $\beta$- and $\beta'$-Delaunay triangulations. For $\beta'$-Delaunay, the resulting exponential lower bound seems to be the first of its kind for random spatial graphs arising as the skeletons of random tessellations. For $\beta$-Delaunay, matching super-exponential bounds allow us to show concentration of the maximal degree in a growing window to only a finite number of deterministic values (in particular, only two values for $d=2$).

math.PR↗

arXiv2021

Neutron Response of the EJ-254 Boron-Loaded Plastic Scintillator

Organic scintillators doped with capture agents provide a detectable signal for neutrons over a broad energy range. This work characterizes the fast and slow neutron response of EJ-254, an organic plastic scintillator with 5% natural boron loading by weight. For fast neutrons, the primary mechanism for light generation in organic scintillators is n-p elastic scattering. To study the fast neutron response, the proton light yield of EJ-254 was measured at the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory. Using a broad-spectrum neutron source and a double time-of-flight technique, the EJ-254 proton light yield was obtained over the energy range of approximately 270 keV to 4.5 MeV and determined to be in agreement with other plastic scintillators comprised of the same polymer base. To isolate the slow neutron response, an AmBe source with polyethylene moderator was made incident on the EJ-254 scintillator surrounded by an array of EJ-309 observation detectors. Events in the EJ-254 target coincident with the signature 477.6 keV $\gamma$ ray (resulting from deexcitation of the residual $^{7}$Li nucleus following boron neutron capture) were identified. Pulse shape discrimination was used to evaluate the temporal differences in the response of EJ-254 scintillation signals arising from $\gamma$-ray and fast/slow neutron interactions. Clear separation between $\gamma$-ray and fast neutrons signals was not achieved and the neutron capture feature was observed to overlap both the $\gamma$-ray and fast neutron bands. Taking into account the electron light nonproportionality, the neutron-capture light yield in EJ-254 was determined to be 89.4$\pm$1.1 keVee.

physics.ins-det↗

arXiv2019

Beam Distortion Effects upon focusing an ultrashort Petawatt Laser Pulse to greater than 10$^{22}$ W/cm$^{2}$

When an ultrashort laser pulse is tightly focused to a size approaching its central wavelength, the properties of the focused spot diverge from the diffraction limited case. Here we report on this change in behavior of a tightly focused Petawatt class laser beam by an F/1 off-axis paraboloid (OAP). Considering the effects of residual aberration, the spatial profile of the near field and pointing error, we estimate the deviation in peak intensities of the focused spot from the ideal case. We verify that the estimated peak intensity values are within an acceptable error range of the measured values. With the added uncertainties in target alignment, we extend the estimation to infer on-target peak intensities of $\geq$ 10$^{22}$ W/cm$^{2}$ for a target at the focal plane of this F/1 OAP.

physics.optics↗

arXiv2018

Diagonal complexes for surfaces of finite type and surfaces with involution

Two related constructions are studied: (1) The diagonal complex $\mathcal{D}$ and its barycentric subdivision $\mathcal{BD}$ related to a \textit{punctured} oriented surface $F$ equipped with a number of labeled marked points. (2) The symmetric diagonal complex $\mathcal{D}^{inv}$ and its barycentric subdivision $\mathcal{BD}^{inv}$ related to a symmetric (=with an involution) oriented surface $F$ equipped with a number of (symmetrically placed) labeled marked points. Eliminating a puncture gives rise to a bundle whose fibers are homeomorphic to a surgery of the surface $F$. The bundle can be viewed as the "universal curve with holes". The symmetric complex is shown to be homotopy equivalent to the complex of a punctured surface obtained by a surgery of the initial symmetric surface.

math.GT↗

arXiv2017

Polygons with prescribed edge slopes: configuration space and extremal points of perimeter

We describe the configuration space $\mathbf{S}$ of polygons with prescribed edge slopes, and study the perimeter $\mathcal{P}$ as a Morse function on $\mathbf{S}$. We characterize critical points of $\mathcal{P}$ (these are \textit{tangential} polygons) and compute their Morse indices. This setup is motivated by a number of results about critical points and Morse indices of the oriented area function defined on the configuration space of polygons with prescribed edge lengths (flexible polygons). As a by-product, we present an independent computation of the Morse index of the area function (obtained earlier by G. Panina and A. Zhukova).

math.GT↗

arXiv2017

Diagonal complexes

Given an $n$-gon, the poset of all collections of pairwise non-crossing diagonals is isomorphic to the face poset of some convex polytope called \textit{associahedron}. We replace in this setting the $n$-gon (viewed as a disc with $n$ marked points on the boundary) with an arbitrary oriented surface with a number of labeled marked points ("vertices"). With appropriate definitions we arrive at cell complexes $\mathcal{D}$ (generalization of) and its barycentric subdivision $\mathcal{BD}$. The complex $\mathcal{D}$ generalizes the associahedron. If the surface is closed, the complex $\mathcal{D}$ (as well as $\mathcal{BD}$) is homotopy equivalent to the space of metric ribbon graphs $RG_{g,n}^{met}$, or, equivalently, to the decorated moduli space $\widetilde{\mathcal{M}}_{g,n}$. For bordered surfaces, we prove the following: (1) Contraction of a boundary edge does not change the homotopy type of the support of the complex. (2) Contraction of a boundary component to a new marked point yields a forgetful map between two diagonal complexes which is homotopy equivalent to the Kontsevich's tautological circle bundle. Thus, contraction of a boundary component gives a natural simplicial model for the tautological bundle. As an application, we compute the psi-class, that is, the first Chern class in combinatorial terms. The latter result is an application of the local combinatorial formula. (3) In the same way, contraction of several boundary components corresponds to Whitney sum of the tautological bundles.

math.GT↗