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Diffusion of cosmic rays (CRs) is the key process for understanding their propagation and acceleration. We employ the description of spatial separation of magnetic field lines in magnetohydrodynamic turbulence in Lazarian & Vishniac to quantify the divergence of the magnetic field on scales less than the injection scale of turbulence and show that this divergence induces superdiffusion of CR in the direction perpendicular to the mean magnetic field. The perpendicular displacement squared increases, not as the distance x along the magnetic field, which is the case for a regular diffusion, but as the x 3 for freely streaming CRs. The dependence changes to x 3/2 for the CRs propagating diffusively along the magnetic field. In the latter case, we show that it is important to distinguish the perpendicular displacement with respect to the mean field and to the local magnetic field. We consider how superdiffusion changes the acceleration of CRs in shocks and show how it decreases efficiency of the CRs acceleration in perpendicular shocks. We also demonstrate that in the case when the small-scale magnetic field is generated in the pre-shock region, an efficient acceleration can take place for the CRs streaming without collisions along the magnetic loops.
Short period double degenerate white dwarf (WD) binaries with periods of less than similar to 1 day are considered to be one of the likely progenitors of type Ia supernovae. These binaries have undergone a period of common envelope evolution. If the core ignites helium before the envelope is ejected, then a hot subdwarf remains prior to contracting into a WD. Here we present a comparison of two very rare systems that contain two hot subdwarfs in short period orbits. We provide a quantitative spectroscopic analysis of the systems using synthetic spectra from state-of-the-art non-LTE models to constrain the atmospheric parameters of the stars. We also use these models to determine the radial velocities, and thus calculate dynamical masses for the stars in each system.
We review the evidence for a putative early 21st-century divergence between global mean surface temperature (GMST) and Coupled Model Intercomparison Project Phase 5 (CMIP5) projections. We provide a systematic comparison between temperatures and projections using historical versions of GMST products and historical versions of model projections that existed at the times when claims about a divergence were made. The comparisons are conducted with a variety of statistical techniques that correct for problems in previous work, including using continuous trends and a Monte Carlo approach to simulate internal variability. The results show that there is no robust statistical evidence for a divergence between models and observations. The impression of a divergence early in the 21st century was caused by various biases in model interpretation and in the observations, and was unsupported by robust statistics.
Tikhonov regularization with oversmoothing penalty for linear statistical inverse learning problems
(2019)
In this paper, we consider the linear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered in the reproducing kernel Hilbert space framework to reconstruct the estimator from the random noisy data. We discuss the rates of convergence for the regularized solution under the prior assumptions and link condition. For regression functions with smoothness given in terms of source conditions the error bound can explicitly be established.