Modeling single-scattering properties of small cirrus particles by use of a size-shape distribution of ice spheroids and cylinders

In this study, we model single-scattering properties of small cirrus crystals using mixtures of polydisperse, randomly oriented spheroids and cylinders with varying aspect ratios and with a refractive index representative of water ice at a wavelength of 1.88 μm. The Stokes scattering matrix elements averaged over wide shape distributions of spheroids and cylinders are compared with those computed for polydisperse surface-equivalent spheres. The shape-averaged phase function for a mixture of oblate and prolate spheroids is smooth, featureless, and nearly flat at side-scattering angles and closely resembles those typically measured for cirrus. Compared with the ensemble-averaged phase function for spheroids, that for a shape distribution of cylinders shows a relatively deeper minimum at side-scattering angles. This may indicate that light scattering from realistic cirrus crystals can be better represented by a shape mixture of ice spheroids. Interestingly, the single-scattering properties of shape-averaged oblate and prolate cylinders are very similar to those of compact cylinders with a diameter-to-length ratio of unity. The differences in the optical cross sections, single-scattering albedo, and asymmetry parameter between the spherical and the nonspherical particles studied appear to be relatively small. This may suggest that for a given optical thickness, the influence of particle shape on the radiative forcing caused by a cloud composed of small ice crystals can be negligible.     

Eigenmode structure in solar-wind Langmuir waves

We show that observed spatial- and frequency-domain signatures of intense solar-wind Langmuir waves can be described as eigenmodes trapped in a parabolic density well. Measured solar-wind electric field spectra and waveforms are compared with 1D linear solutions and, in many cases, can be represented by 1-3 low-order eigenstates. To our knowledge, this report is the first observational confirmation of Langmuir eigenmodes in space. These results suggest that linear eigenmodes may be the starting point of the nonlinear evolution, critical for producing solar type II and type III radio bursts.     

Numerical simulations of type-III solar radio bursts

The first numerical simulations are presented for type-III solar radio bursts in the inhomogeneous solar corona and interplanetary space, that include microscale quasilinear and nonlinear processes, intermediate-scale driven ambient density fluctuations, and large scale evolution of electron beams, Langmuir and ion sound waves, and fundamental and harmonic electromagnetic emission. Bidirectional coronal emission is asymmetric between the upward and downward directions, and harmonic emission dominates fundamental emission. In interplanetary space, fundamental and/or harmonic emission can be important. Langmuir and ion sound waves are bursty and the statistics of Langmuir wave energy agree well with the predictions of stochastic growth theory.     

Outerplanar Thrackles

We show that a graph drawing is an outerplanar thrackle if and only if, up to an inversion in the plane, it is Reidemeister equivalent to an odd musquash. This establishes Conway’s thrackle conjecture for outerplanar thrackles. We also extend this result in two directions. First, we show that no pair of vertices of an outerplanar thrackle can be joined by an edge in such a way that the resulting graph drawing is a thrackle. Secondly, we introduce the notion of crossing rank; drawings with crossing rank 0 are generalizations of outerplanar drawings. We show that all thrackles of crossing rank 0 are outerplanar. We also introduce the notion of an alternating cycle drawing, and we show that a thrackled cycle is alternating if and only if it is outerplanar.     

Generalized Thrackle Drawings of Non-bipartite Graphs

A graph drawing is called a generalized thrackle if every pair of edges meets an odd number of times. In a previous paper, we showed that a bipartite graph G can be drawn as a generalized thrackle on an oriented closed surface M if and only if G can be embedded in M. In this paper, we use Lins’ notion of a parity embedding and show that a non-bipartite graph can be drawn as a generalized thrackle on an oriented closed surface M if and only if there is a parity embedding of G in a closed non-orientable surface of Euler characteristic χ(M)−1. As a corollary, we prove a sharp upper bound for the number of edges of a simple generalized thrackle.     

Toward unified satellite climatology of aerosol properties: What do fully compatible MODIS and MISR aerosol pixels tell us?

Because of the global nature of aerosol effects on climate, satellite observations have been and will be an indispensable source of information about aerosol characteristics for use in various assessments of climate and climate change. There have been parallel claims of unprecedented accuracy of aerosol retrievals with the moderate-resolution imaging spectroradiometer (MODIS) and multiangle imaging spectroradiometer (MISR). These claims have been based on limited comparisons with ground-based observations which, however, are not necessarily indicative of the actual global performance of these satellite sensors. Fortunately, both instruments have been flown for many years on the same Terra platform, which provides a unique opportunity to compare fully collocated pixel-level MODIS and MISR aerosol retrievals directly and globally. Our present extensive analysis of ～8 years of the MODIS-Terra and MISR aerosol data documents unexpected significant disagreements at the pixel level as well as between long-term and spatially averaged aerosol properties. The only point on which both datasets seem to fully agree is that there may have been a weak increasing tendency in the globally averaged aerosol optical thickness (AOT) over the land and no long-term AOT tendency over the oceans. Overall our new results suggest that the current knowledge of the global distribution of the AOT and, especially, aerosol microphysical characteristics remains unsatisfactory.     

New regimes of stochastic wave growth

Stochastic-growth theory (SGT) of bursty waves is generalized and it is shown that the previously separate theory of "elementary bursts" is a limiting case. New regimes of SG are found and elucidated, and results are compared with the first relevant simulations via quasilinear theory and a reduced-parameter model. Both display stochastic behavior with the expected properties--the first simulations to demonstrate SGT behavior explicitly. Reexamination of data and simulations previously analyzed using SGT or elementary burst theory also shows good agreement with the new predictions.     

Curvature properties of metric nilpotent Lie algebras which are independent of metric

This paper consists of two parts. First, motivated by classic results, we determine the subsets of a given nilpotent Lie algebra \(\mathfrak {g}\) (respectively, of the Grassmannian of two-planes of \(\mathfrak {g}\)) whose sign of Ricci (respectively, sectional) curvature remains unchanged for an arbitrary choice of a positive definite inner product on \(\mathfrak {g}\). In the second part we study the subsets of \(\mathfrak {g}\) which are, for some inner product, the eigenvectors of the Ricci operator with the maximal and with the minimal eigenvalue, respectively. We show that the closure of these subsets is the whole algebra \(\mathfrak {g}\), apart from two exceptional cases: when \(\mathfrak {g}\) is two-step nilpotent and when \(\mathfrak {g}\) contains a codimension one abelian ideal.