Verification of the accuracy of the SIR model in forecasting based on the improved SIR model with a constant ratio of recovery to infection rate by comparing with monitored second wave data.

The temporal evolution of second and subsequent waves of epidemics such as Covid-19 is investigated. Analytic expressions for the peak time and asymptotic behaviours, early doubling time, late half decay time, and a half-early peak law, characterizing the dynamical evolution of number of cases and fatalities, are derived, where the pandemic evolution exhibiting multiple waves is described by the semi-time SIR model. The asymmetry of the epidemic wave and its exponential tail are affected by the initial conditions, a feature that has no analogue in the all-time SIR model. Our analysis reveals that the immunity is very strongly increasing in several countries during the second Covid-19 wave. Wave-specific SIR parameters describing infection and recovery rates we find to behave in a similar fashion. Still, an apparently moderate change of their ratio can have significant consequences. As we show, the probability of an additional wave is however low in several countries due to the fraction of immune inhabitants at the end of the second wave, irrespective of the ongoing vaccination efforts. We compare with alternate approaches and data available at the time of submission. Most recent data serves to demonstrate the successful forecast and high accuracy of the SIR model in predicting the evolution of pandemic outbreaks as long as the assumption underlying our analysis, an unchanged situation of the distribution of variants of concern and the fatality fraction, do not change dramatically during a wave. With the rise of the α variant at the time of submission the second wave did not terminate in some countries, giving rise to a superposition of waves that is not treated by the present contribution.

Weak turbulence theory for collisional plasmas.

Plasma is an ionized gas in which the collective behavior dominates over the individual particle interactions. For this reason, plasma is often treated as collisionless or collision-free. However, the discrete nature of the particles can be important, and often, the description of plasmas is incomplete without properly taking the discrete particle effects into account. The weak turbulence theory is a perturbative nonlinear theory, whose essential formalism was developed in the late 1950s and 1960s and continued on through the early 1980s. However, the standard material found in the literature does not treat the discrete particle effects and the associated fluctuations emitted spontaneously by thermal particles completely. Plasma particles emit electromagnetic fluctuations in all frequencies and wave vectors, but in the standard literature, the fluctuations are approximately treated by considering only those frequency-wave number regimes corresponding to the eigenmodes (or normal modes) satisfying the dispersion relations, while ignoring contributions from noneigenmodes. The present paper shows that the noneigenmode fluctuations modify the particle kinetic equation so that the generalized equation includes the Balescu-Lénard-Landau collision integral and also modify the wave kinetic equation to include not only the collisional damping term but also a term that depicts the bremsstrahlung emission of plasma normal modes.

Cosmic magnetization: from spontaneously emitted aperiodic turbulent to ordered equipartition fields.

It is shown that an unmagnetized nonrelativistic thermal electron-proton plasma spontaneously emits aperiodic turbulent magnetic field fluctuations of strength |δB|=3.5ß(e)g(1/3)W(e)(1/2) G, where ß(e) is the normalized thermal electron temperature, W(e) the thermal plasma energy density, and g the plasma parameter. For the unmagnetized intergalactic medium, immediately after the reionization onset, the field strengths from this mechanism are about 2×10(-16) G in cosmic voids and 2×10(-10) G in protogalaxies, both too weak to affect the dynamics of the plasma. Accounting for simultaneous viscous damping reduces these estimates to 2×10(-21) G in cosmic voids and 2×10(-12) G in protogalaxies. The shear and/or compression of the intergalactic and protogalactic medium exerted by the first supernova explosions locally amplify these seed fields and make them anisotropic, until the magnetic restoring forces affect the gas dynamics at ordered plasma betas near unity.

Modified temperature-anisotropy instability thresholds in the solar wind.

The proton and electron temperature anisotropies in the solar wind are constrained by the instability thresholds for temperature-anisotropy-driven kinetic plasma instabilities. The modifications to the marginal instability conditions from accounting for the influence of damping connected with the collisional effects in the solar wind plasma are calculated for right- and left-handed polarized parallel propagating Alfvén waves and mirror and firehose fluctuations. These modifications provide tighter threshold constraints compared to the marginal thresholds but do not fully explain the observations at small values of the parallel plasma beta.

Quasars, blazars, and gamma rays.

Before the launch of the Compton Gamma Ray Observatory (CGRO), the only source of >100-megaelectron volt (MeV) gamma radiation known outside our galaxy was the quasar 3C 273. After less than a year of observing, 13 other extragalactic sources have been discovered with the Energetic Gamma Ray Experiment Telescope (EGRET) on CGRO, and it is expected that many more will be found before the full sky survey is complete. All 14 sources show evidence of blazar properties at other wavelengths; these properties include high optical polarization, extreme optical variability, flat-spectrum radio emission associated with a compact core, and apparent superluminal motion. Such properties are thought to be produced by those few, rare extragalactic radio galaxies and quasars that are favorably aligned to permit us to look almost directly down a relativistically outflowing jet of matter expelled from a supermassive black hole. Although the origin of the gamma rays from radio jets is a subject of much controversy, the gamma-ray window probed by CGRO is providing a wealth of knowledge about the central engines of active galactic nuclei and the most energetic processes occurring in nature.