Bifurcations and patterns in the Kuramoto model with inertia

In this work, we analyze the Kuramoto model (KM) with inertia on a convergent family of graphs. It is assumed that the intrinsic frequencies of the individual oscillators are sampled from a probability distribution. In addition, a given graph, which may also be random, assigns network connectivity. As in the original KM, in the model with inertia, the weak coupling regime features mixing, the state of the network when the phases (but not velocities) of all oscillators are distributed uniformly around the unit circle. We study patterns, which emerge when mixing loses stability under the variation of the strength of coupling. We identify a pitchfork (PF) and an Andronov-Hopf (AH) bifurcations in the model with multimodal intrinsic frequency distributions. To this effect, we use a combination of the linear stability analysis and Penrose diagrams, a geometric technique for studying stability of mixing. We show that the type of a bifurcation and a nascent spatiotemporal pattern depend on the interplay of the qualitative properties of the intrinsic frequency distribution and network connectivity.Comment: 20 pages, 8 figures. Revised version accepted to Journal of Nonlinear Science. arXiv admin note: text overlap with arXiv:2105.0754

Transparency of 0.2% GdCl3 Doped Water in a Stainless Steel Test Environment

The possibility of neutron and neutrino detection using water Cerenkov detectors doped with gadolinium holds the promise of constructing very large high-efficiency detectors with wide-ranging application in basic science and national security. This study addressed a major concern regarding the feasibility of such detectors: the transparency of the doped water to the ultraviolet Cerenkov light. We report on experiments conducted using a 19-meter water transparency measuring instrument and associated materials test tank. Sensitive measurements of the transparency of water doped with 0.2% GdCl3 at 337nm, 400nm and 420nm were made using this instrument. These measurements indicate that GdCl3 is not an appropriate dopant in stainless steel constructed water Cerenkov detectors.Comment: 17 pages, 11 figures, corrects typos, changes formatting, adds error bars to figure

Reheating after f(R) inflation

The reheating dynamics after the inflation induced by $R^2$-corrected $f(R)$ model is considered. To avoid the complexity of solving the fourth order equations, we analyze the inflationary and reheating dynamics in the Einstein frame and its analytical solutions are derived. We also perform numerical calculation including the backreaction from the particle creation and compare the results with the analytical solutions. Based on the results, observational constraints on the model are discussed.Comment: 16 pages, 11 figure