Internal waves in the sea : a summary of published information with notes on applications to naval operations / O.S. Lee.

Abstract

An example of the mode structure of internal waves. . . 13 3 Observations of temperature at three stations. ..16,17 * Minimum of N is used for convenience with the understanding that a channel can be defined as the region between z and z where N (z) =» N(zJ.

Limits on Models of the Ultrahigh Energy Cosmic Rays Based on Topological Defects

“…1 where we have normalized the spectrum of "observable particles" (nucleons, photons, electrons) to the 3 3 10 11 GeV point (cosmic-ray data are taken from [25], and the highest point is from [2]). Lee [13] has published a spectrum for similar input parameters, and it is in acceptable agreement with the present work except for MeV-PeV g rays where our result is about a factor of 10 lower. We suspect this is because of our lower IR field, and this appears to be confirmed by results presented by Lee which show the g-ray inten- sity to be significantly lower if the IR field is neglected.…”

“…Notice that above 10 11 GeV photons dominate the spectra of observable particles, and that over some ranges of energy electrons dominate the electromagnetic component. Also note that the predicted g-ray flux at GeV energies is comparable to the observed background, and as pointed out by Lee [13], the extragalactic g-ray background at these energies will place a strong constraint on the topological defect models. Figure 2 shows the energy injection rate at the present epoch, such that the intensity of observable particles is normalized to the 3 3 10 11 GeV point, as a function of M X for various extragalactic magnetic fields and evolution models.…”

“…Parameters of TD scenarios include mass of the X particle, energy spectra and final state composition of the decay products, and cosmological evolution of the topological defect injection rate [12,13]. The problem of propagation is more severe than for the case of acceleration scenarios because most of the energy from X-particle decay emerges in electrons, photons, and neutrinos, with only about 3% in nucleons.…”

“…Reference [15] has therefore already ruled out TD as the origin of the ͑2 3͒ 3 10 11 GeV events. Recently, however, Lee [13] and Sigl, Lee, and Coppi [16] have claimed that lower X-particle masses are possible, and adopting M X c 2 10 14 GeV, and a lower magnetic field, suggested the TD scenario is not ruled out. In this Letter we consider several TD scenarios to put limits on the luminosity of the particle fluxes injected by topological defects as a function of the X-particle mass, the cosmological evolution of the topological defects, and the strength of the extragalactic magnetic field, and consider for what range of parameters TD could explain the ͑2 3͒ 3 10 11 GeV events.…”

“…For the infrared background we adopt a spectrum [22] which is based on the model of Stecker et al [23] but constrained at low frequencies by upper limits derived by us from the error bars on the microwave background measured by the FIRAS experiment on COBE [24]. At 3 3 10 23 eV, where the microwave background is decreasing rapidly with energy, our IR spectrum is a factor of 5 lower than that used by Lee [13].…”