Spatiotemporal analyses of soil moisture from point to footprint scale in two different hydroclimatic regions

This paper presents time stability analyses of soil moisture at different spatial measurement support scales (point scale and airborne remote sensing (RS) footprint scale 800 m × 800 m) in two different hydroclimatic regions. The data used in the analyses consist of in situ and passive microwave remotely sensed soil moisture data from the Southern Great Plains Hydrology Experiments 1997 and 1999 (SGP97 and SGP99) conducted in the Little Washita (LW) watershed, Oklahoma, and the Soil Moisture Experiments 2002 and 2005 (SMEX02 and SMEX05) in the Walnut Creek (WC) watershed, Iowa. Results show that in both the regions soil properties (i.e., percent silt, percent sand, and soil texture) and topography (elevation and slope) are significant physical controls jointly affecting the spatiotemporal evolution and time stability of soil moisture at both point and footprint scales. In Iowa, using point‐scale soil moisture measurements, the WC11 field was found to be more time stable (TS) than the WC12 field. The common TS points using data across the 3 year period (2002–2005) were mostly located at moderate to high elevations in both the fields. Furthermore, the soil texture at these locations consists of either loam or clay loam soil. Drainage features and cropping practices also affected the field‐scale soil moisture variability in the WC fields. In Oklahoma, the field having a flat topography (LW21) showed the worst TS features compared to the fields having gently rolling topography (LW03 and LW13). The LW13 field (silt loam) exhibited better time stability than the LW03 field (sandy loam) and the LW21 field (silt loam). At the RS footprint scale, in Iowa, the analysis of variance (ANOVA) tests show that the percent clay and percent sand are better able to discern the TS features of the footprints compared to the soil texture. The best soil indicator of soil moisture time stability is the loam soil texture. Furthermore, the hilltops (slope ∼0%–0.45%) exhibited the best TS characteristics in Iowa. On the other hand, in Oklahoma, ANOVA results show that the footprints with sandy loam and loam soil texture are better indicators of the time stability phenomena. In terms of the hillslope position, footprints with mild slope (0.93%–1.85%) are the best indicators of TS footprints. Also, at both point and footprint scales in both the regions, land use–land cover type does not influence soil moisture time stability

Wave propagation through a coherently amplifying random medium

We report a detailed and systematic numerical study of wave propagation through a coherently amplifying random one-dimensional medium. The coherent amplification is modeled by introducing a uniform imaginary part in the site energies of the disordered single-band tight binding Hamiltonian. Several distinct length scales (regimes), most of them new, are identified from the behavior of transmittance and reflectance as a function of the material parameters. We show that the transmittance is a non-self-averaging quantity with a well defined mean value. The stationary distribution of the super reflection differs qualitatively from the analytical results obtained within the random phase approximation in strong disorder and amplification regime. The study of the stationary distribution of the phase of the reflected wave reveals the reason for this discrepancy. The applicability of random phase approximation is discussed. We emphasize the dual role played by the lasing medium, as an amplifier as well as a reflector.Comment: 33 pages RevTex, 14 EPS figures included, Accepted for publication in IJMP-

Sustainable Recycling of Insoluble Rust Waste for the Synthesis of Iron-Containing Perovskite-Type Catalysts

Insoluble rust waste from the scraping of rusted iron-containing materials represents a cheap, eco-friendly, and available source of iron. LaFeO3 perovskite-type powders were successfully prepared by solution combustion synthesis using rust waste from an electricity transmission tower manufacturer. Solution combustion synthesis enabled introduction of this insoluble iron precursor directly into the final product, bypassing complex extraction procedures. Catalytic activity in the propylene oxidation of the waste-derived LaFeO3 with stoichiometric Fe/La ratio was almost identical to the commercial iron nitrate-derived LaFeO3 , thus demonstrating the viability of this recycling solution. The amount of waste iron precursor was varied and its effect on the powder properties was investigated. A lesser stoichiometric amount of precursor produced a LaFeO3 -La2O3 binary system, whereas a higher stoichiometric amount led to a LaFeO3 -Fe2O3 binary system. Catalytic activity of iron-rich compositions in the propylene oxidation was only slightly lower than the stoichiometric one, whereas iron-poor compositions were much less active. This eco-friendly methodology can be easily extended to other iron perovskites with different chemical compositions and to other iron-containing compounds

Singular normal form for the Painlev\'e equation P1

We show that there exists a rational change of coordinates of Painlev\'e's P1 equation $y''=6y^2+x$ and of the elliptic equation $y''=6y^2$ after which these two equations become analytically equivalent in a region in the complex phase space where $y$ and $y'$ are unbounded. The region of equivalence comprises all singularities of solutions of P1 (i.e. outside the region of equivalence, solutions are analytic). The Painlev\'e property of P1 (that the only movable singularities are poles) follows as a corollary. Conversely, we argue that the Painlev\'e property is crucial in reducing P1, in a singular regime, to an equation integrable by quadratures