CP-violating transport theory for electroweak baryogenesis with thermal corrections

We derive CP-violating transport equations for fermions for electroweak baryogenesis from the CTP-formalism including thermal corrections at the one-loop level. We consider both the VEV-insertion approximation (VIA) and the semiclassical (SC) formalism. We show that the VIA-method is based on an assumption that leads to an ill-defined source term containing a pinch singularity, whose regularisation by thermal effects leads to ambiguities including spurious ultraviolet and infrared divergences. We then carefully review the derivation of the semiclassical formalism and extend it to include thermal corrections. We present the semiclassical Boltzmann equations for thermal WKB-quasiparticles with source terms up to the second order in gradients that contain both dispersive and finite width corrections. We also show that the SC-method reproduces the current divergence equations and that a correct implementation of the Fick's law captures the semiclassical source term even with conserved total current ∂μ j μ = 0. Our results show that the VIA-source term is not just ambiguous, but that it does not exist. Finally, we show that the collisional source terms reported earlier in the semiclassical literature are also spurious, and vanish in a consistent calculation.

Estimates of Gradients in Radar Moments Using a Linear Least Squares Derivative Technique

The local, linear, least squares derivative (LLSD) approach to radar analysis is a method of quantifying gradients in radar data by fitting a least squares plane to a neighborhood of range bins and finding its slope. When applied to radial velocity fields, for example, LLSD yields part of the azimuthal (rotational) and radial (divergent) components of horizontal shear, which, under certain geometric assumptions, estimate one-half of the two-dimensional vertical vorticity and horizontal divergence equations, respectively. Recent advances in computational capacity as well as increased usage of LLSD products by the meteorological community have motivated an overhaul of the LLSD methodology’s application to radar data. This paper documents the mathematical foundation of the updated LLSD approach, including a complete derivation of its equation set, discussion of its limitations, and considerations for other types of implementation. In addition, updated azimuthal shear calculations are validated against theoretical vorticity using simulated circulations. Applications to nontraditional radar data and new applications to nonvelocity radar data including reflectivity at horizontal polarization, spectrum width, and polarimetric moments are also explored. These LLSD gradient calculations may be leveraged to identify and interrogate a wide variety of severe weather phenomena, either directly by operational forecasters or indirectly as part of future automated algorithms.

Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains

We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.