[1] The new Horizontal Wind Model (HWM07) provides a statistical representation of the horizontal wind fields of the Earth's atmosphere from the ground to the exosphere (0–500 km). It represents over 50 years of satellite, rocket, and ground-based wind measurements via a compact Fortran 90 subroutine. The computer model is a function of geographic location, altitude, day of the year, solar local time, and geomagnetic activity. It includes representations of the zonal mean circulation, stationary planetary waves, migrating tides, and the seasonal modulation thereof. HWM07 is composed of two components, a quiet time component for the background state described in this paper and a geomagnetic storm time component (DWM07) described in a companion paper.

/pdf/an-empirical-model-of-the-earth-s-horizontal-wind-fields-vm989vom4t.pdf

An empirical model of the Earth's horizontal wind fields: HWM07

We present the first multi-instrumental results on the ionospheric response to the geomagnetic storm of 17–18 March 2015 (the St. Patrick's Day storm) that was up to now the strongest in the 24th solar cycle (minimum SYM-H value of A233 nT). The storm caused complex effects around the globe. The most dramatic positive ionospheric storm occurred at low latitudes in the morning (~100–150% enhancement) and postsunset (~80–100% enhancement) sectors. These significant vertical total electron content increases were observed in different local time sectors and at different universal time, but around the same area of the Eastern Pacific region, which indicates a regional impact of storm drivers. Our analysis revealed that this particular region was most concerned by the increase in the thermospheric O/N 2 ratio. At midlatitudes, we observe inverse hemispheric asymmetries that occurred, despite the equinoctial period, in different longitudinal regions. In the European-African sector, positive storm signatures were observed in the Northern Hemisphere (NH), whereas in the American sector, a large positive storm occurred in the Southern Hemisphere, while the NH experienced a negative storm. The observed asymmetries can be partly explained by the thermospheric composition changes and partly by the hemispherically different nondipolar portions of the geomagnetic field as well as by the IMF By component variations. At high latitudes, negative ionospheric storm effects were recorded in all longitudinal regions, especially the NH of the Asian sector was concerned. The negative storm phase developed globally on 18 March at the beginning of the recovery phase.

https://hal-insu.archives-ouvertes.fr/insu-01514406/document

Ionospheric response to the 2015 St. Patrick's Day storm: A global multi‐instrumental overview

[1] With the current data availability from both ground- and space-based sources, the network of ground-based Global Positioning System (GPS) receivers, GPS occultation receivers, in situ electron density sensors, and dual-frequency beacon transmitters, the time is right for a comprehensive review of the history, current state, and future directions of ionospheric imaging. A brief introduction and history of ionospheric imaging is presented, beginning with computerized ionospheric tomography. Then, a comprehensive review of the current state of ionospheric imaging is presented. The ability of imaging algorithms to ingest multiple types of data and use advanced inverse techniques borrowed from meteorological data assimilation to produce four-dimensional images of electron density is discussed. Particular emphasis is given to the mathematical basis for the different methods. The science that ionospheric imaging addresses is discussed, and the scientific contributions that ionospheric imaging has made are described. Finally, future directions for this research area are outlined.

/pdf/history-current-state-and-future-directions-of-ionospheric-2aok12z48z.pdf

History, current state, and future directions of ionospheric imaging

[1] We present the extension to the thermosphere of a Martian general circulation model, the first able to self-consistently study the whole Martian atmosphere from the surface to the exosphere. We describe the parameterizations developed to include physical processes important for thermospheric altitudes. The results of a simulation covering 1 full Martian year are presented, focusing on the seasonal, diurnal, and day-to-day variability of the temperatures in the exobase region. The seasonal variation of the zonal mean temperatures in the upper atmosphere is of about 100 K, mostly due to the variation of the solar forcing. The temperature of the mesopause ranges between 115 and 130 K, with little seasonal and day-night variations. Its pressure level undergoes significant seasonal and day-night variations. Comparisons with SPICAM observations show that the modeled mesopause is too low and too warm. A similar study for the homopause shows that it is located higher in the atmosphere during solstices, owing to reinforced mixing by a stronger circulation. Important day-night temperature differences are found in the thermosphere, ranging from about 60 K at aphelion to 110 K at perihelion. This diurnal cycle is slightly perturbed by the day-to-day variations of temperature, dominated by waves with periods of 2 to 6 sols and amplitude of 30 K. The model reproduces the observed solar cycle variation in temperatures when using a UV heating efficiency of 16%, slightly lower than the theoretical value. The seasonal variation of temperatures is overestimated by the model, in comparison with the available measurements.

A ground-to-exosphere Martian general circulation model: 1. Seasonal, diurnal, and solar cycle variation of thermospheric temperatures

We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters (k,n,k,@l) we construct sets of n+1 mutually unbiased bases in C^k. We show how to construct these difference sets from commutative semifields and that all known maximal sets of mutually unbiased bases can be obtained in this way, resolving a conjecture about the monomiality of maximal sets. We also relate mutually unbiased bases to spin models.

https://arxiv.org/pdf/quant-ph/0511004.pdf

Equiangular lines, mutually unbiased bases, and spin models

[1] There is great interest in understanding how the thermosphere-ionosphere system responds to geomagnetic storms. New insights are possible using the new generation of fully coupled three-dimensional models, together with extensive ionospheric databases. The period of postsolar maximum geomagnetic storms in October and November 2003 were some of the largest storms ever recorded. In this paper, we explore how the thermosphere-ionosphere system responded to the onset of the 20 November 2003 geomagnetic storm, using the NCAR TIMEGCM. The model simulates dramatic changes in the thermospheric equatorward winds, O/N 2 , and corresponding ionospheric electron densities. The model is used as a framework to interpret an increase in the observed ionospheric total electron content, and F region electron density, in the European and North African sector, in terms of changes in the neutral gas. Corresponding compositional effects observed by the GUVI instrument on the TIMED satellite lend credence to the model results. We describe some of the important physical processes that will affect planning for the utilization of measurements from the Geospace investigations in NASA's Living With a Star Program. The study illustrates the value of measuring both the neutral and ionized gases, of obtaining quasi-global views from imaging instruments, and the synergy between satellite data, ground-based measurements, and models.

Global thermosphere‐ionosphere response to onset of 20 November 2003 magnetic storm

A survey of finite semifields

Spinor spaces can be represented as minimal left ideals of Clifford algebras and they are generated by primitive idempotents. Primitive idempotents of the Clifford algebras Rp, q are shown to be products of mutually nonannihilating commuting idempotent % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabaGaaiaacaqabeaadaqaaqGaaO% qaamaaleaaleaacaaIXaaabaGaaGOmaaaaaaa!3DBD!\[{\textstyle{1 \over 2}}\]2}}\](1+eT), where the k=q−rq−p basis elements eT satisfy eT2=1. The lattice generated by a set of mutually annihilating primitive idempotents is examined. The final result characterizes all Clifford algebras Rp, q with an anti-involution such that each symmetric elements is either a nilpotent or then some right multiple of it is a nonzero symmetric idempotent. This happens when p+q<-3 and (p, q)≠(2, 1).

Idempotent structure of Clifford algebras

This paper reviews Clifford algebras in mathematics and in theoretical physics. In particular, the little-known differential form realization is constructed in detail for the four-dimensional Minkowski space. This setting is then used to describe spinors as differential forms, and to solve the Klein-Gordon and Kahler-Dirac equations. The approach of this paper, in obtaining the solutions directly in terms of differential forms, is much more elegant and concise than the traditional explicit matrix methods. A theorem given here differentiates between the two real forms of the Dirac algebra by showing that spin can be accommodated in only one of them.

The Clifford algebra of differential forms

All division ringsD of 16, 27, 32, 125 and 343 elements are shown to have aright primitive elementp such that

$$\mathcal{D}* = \{ e,ep,(ep)p,...,(...(ep)p...)p\} .$$

That is, the multiplicative loop is the set of all right multiples of the identitye by the elementp. A construction of Dickson [5] is used to show that all commutative division algebras three-dimensional over a finite field not of characteristic 2 have a primitive element. Examples of division rings of 27, 29 and 211 elements with right primitive elements are given. Finally, a “pre-semifield” is exhibited that does not have a right primitive element.

G. P. Wene

Papers

Global thermosphere‐ionosphere response to onset of 20 November 2003 magnetic storm

A survey of finite semifields

Idempotent structure of Clifford algebras

The Clifford algebra of differential forms

On the multiplicative structure of finite division rings