Electron and Photon Interactions in the Regime of Strong LPM Suppression

Most searches for ultra-high energy (UHE) astrophysical neutrinos look for radio emission from the electromagnetic and hadronic showers produced in their interactions. The radio frequency spectrum and angular distribution depend on the shower development, so are sensitive to the interaction cross sections. At energies above about 10^{16} eV (in ice), the Landau-Pomeranchuk-Migdal (LPM) effect significantly reduces the cross sections for the two dominant electromagnetic interactions: bremsstrahlung and pair production. At higher energies, above about 10^{20} eV, the photonuclear cross section becomes larger than that for pair production, and direct pair production and electronuclear interactions become dominant over bremsstrahlung. The electron interaction length reaches a maximum around 10^{21} eV, and then decreases slowly as the electron energy increases further. In this regime, the growth in the photon cross section and electron energy loss moderates the rise in nu_e shower length, which rises from ~10 m at 10^{16} eV to ~50 m at 10^{19} eV and ~100 m at 10^{20} eV, but only to ~1 km at 10^{24} eV. In contrast, without photonuclear and electronuclear interactions, the shower length would be over 10 km at 10^{24} eV.Comment: 10 pages, 9 figures. Submitted to Physical Review

Non-scale-invariant inverse curvature flows in Euclidean space

We consider the inverse curvature flows $\dot x=F^{-p}\nu$ of closed star-shaped hypersurfaces in Euclidean space in case $0<p\not=1$ and prove that the flow exists for all time and converges to infinity, if $0<p<1$, while in case $p>1$, the flow blows up in finite time, and where we assume the initial hypersurface to be strictly convex. In both cases the properly rescaled flows converge to the unit sphere.Comment: 21 pages, this is the published versio

Microstructure and mechanical properties of bamboo in compression

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 34).Bamboo has received much interest recently as a construction material due to its strength, rapid growth, and abundance in developing nations such as China, India, and Brazil. The main obstacle to the widespread use of bamboo as a structural material is the lack of adequate information on the mechanical properties of bamboo. In this work, the microstructure and mechanical properties of Phyllostachis dulcis bamboo are studied to help produce a model for the mechanical properties of bamboo. Specifically, a linear relationship is established between the density of bamboo samples, which is known to vary radially, and their strength in compression. Nanoindentation of vascular bundles in various positions in bamboo samples revealed that the Young's modulus and hardness of the bundles vary in the radial direction but not around the circumference. The compressive strength of bamboo samples was found to vary from 40 to 95 MPa, while nanoindentation results show the Young's modulus of vascular bundles ranges from 15 to 18 GPa and the hardness ranges from 380 to 530 MPa.by Michael R. Gerhardt.S.B