Based on a carefully constructed sample of dwarf stars, a new optical-near infrared photometric calibration to estimate the metallicity of late-type K and early-to-mid-type M dwarfs is presented. The calibration sample has two parts; the first part i
ncludes 18 M dwarfs with metallicities determined by high-resolution spectroscopy and the second part contains 49 dwarfs with metallicities obtained through moderate-resolution spectra. By applying this calibration to a large sample of around 1.3 million M dwarfs from the Sloan Digital Sky Survey and the Two-Micron All Sky Survey, the metallicity distribution of this sample is determined and compared with those of previous studies. Using photometric parallaxes, the Galactic heights of M dwarfs in the large sample are also estimated. Our results show that stars farther from the Galactic plane, on average, have lower metallicity, which can be attributed to the age-metallicity relation. A scarcity of metal-poor dwarf stars in the metallicity distribution relative to the Simple Closed Box Model indicates the existence of the M dwarf problem, similar to the previously known G and K dwarf problems. Several more complicated Galactic chemical evolution models which have been proposed to resolve the G and K dwarf problems are tested and it is shown that these models could, to some extent, mitigate the M dwarf problem as well.
By treating idealized zeolite frameworks as periodic mechanical trusses, we show that the number of flexible folding mechanisms in zeolite frameworks is strongly peaked at the minimum density end of their flexibility window. 25 of the 197 known zeoli
te frameworks exhibit an extensive flexibility, where the number of unique mechanisms increases linearly with the volume when long wavelength mechanisms are included. Extensively flexible frameworks therefore have a maximum in configurational entropy, as large crystals, at their lowest density. Most real zeolites do not exhibit extensive flexibility, suggesting that surface and edge mechanisms are important, likely during the nucleation and growth stage. The prevalence of flexibility in real zeolites suggests that, in addition to low framework energy, it is an important criterion when searching large databases of hypothetical zeolites for potentially useful realizable structures.
We present a family of p-enrichment schemes. These schemes may be separated into two basic classes: the first, called emph{fixed tolerance schemes}, rely on setting global scalar tolerances on the local regularity of the solution, and the second, cal
led emph{dioristic schemes}, rely on time-evolving bounds on the local variation in the solution. Each class of $p$-enrichment scheme is further divided into two basic types. The first type (the Type I schemes) enrich along lines of maximal variation, striving to enhance stable solutions in areas of highest interest. The second type (the Type II schemes) enrich along lines of maximal regularity in order to maximize the stability of the enrichment process. Each of these schemes are tested over a pair of model problems arising in coastal hydrology. The first is a contaminant transport model, which addresses a declinature problem for a contaminant plume with respect to a bay inlet setting. The second is a multicomponent chemically reactive flow model of estuary eutrophication arising in the Gulf of Mexico.
We study a family of generalized slope limiters in two dimensions for Runge-Kutta discontinuous Galerkin (RKDG) solutions of advection--diffusion systems. We analyze the numerical behavior of these limiters applied to a pair of model problems, compar
ing the error of the approximate solutions, and discuss each limiters advantages and disadvantages. We then introduce a series of coupled $p$-enrichment schemes that may be used as standalone dynamic $p$-enrichment strategies, or may be augmented via any in the family of variable-in-$p$ slope limiters presented.
