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The differential operators $iD$ and $-D^2 - p$ are constructed on certain finite directed weighted graphs. Two types of inverse spectral problems are considered. First, information about the graph weights and boundary conditions is extracted from the spectrum of $-D^2$. Second, the compactness of isospectral sets for $-D^2 - p$ is established by computation of the residues of the zeta function. [ABSTRACT FROM AUTHOR]

Poly(dimethylsiloxane) (PDMS) is a common material used in fabricating microfluidic devices. The predominant PDMS fabrication method, soft lithography, relies on photolithography for fabrication of micropatterned molds. In this technical note, we report an alternative molding technique using microscale PLasma Activated Templating (μPLAT). The use of photoresist in soft lithography is replaced by patterned water droplets created using μPLAT. When liquid PDMS encapsulates patterned water and then solidifies, the cavities occupied by water become structures such as microchannels. Using this method, device fabrication is less time consuming, more cost efficient and flexible, and ideal for rapid prototyping. An additional important feature of the water-molding process is that it yields structural profiles that are difficult to achieve using photolithography. [ABSTRACT FROM AUTHOR]

In this paper, we investigate sulfur chemistry in laboratory analogs of Jupiter Trojans and Kuiper Belt Objects (KBOs). Electron irradiation experiments of CH3OH–NH3–H2O and H2S–CH3OH–NH3–H2O ices were conducted to better understand the chemical differences between primordial planetesimals inside and outside the sublimation line of H2S. The main goal of this work is to test the chemical plausibility of the hypothesis correlating the color bimodality in Jupiter Trojans with sulfur chemistry in the incipient solar system. Temperature programmed desorption (TPD) of the irradiated mixtures allows the detection of small sulfur allotropes (S3 and S4) after the irradiation of H2S containing ice mixtures. These small, red polymers are metastable and could polymerize further under thermal processing and irradiation, producing larger sulfur polymers (mainly S8) that are spectroscopically neutral at wavelengths above 500 nm. This transformation may affect the spectral reflectance of Jupiter Trojans in a different way compared to KBOs, thereby providing a useful framework for possibly differentiating and determining the formation and history of small bodies. Along with allotropes, we report the production of organo-sulfur molecules. Sulfur molecules produced in our experiment have been recently detected by Rosetta in the coma of 67P/Churyumov–Gerasimenko. The very weak absorption of sulfur polymers in the infrared range hampers their identification on Trojans and KBOs, but these allotropes strongly absorb light at UV and Visible wavelengths. This suggests that high signal-to-noise ratio UV–Vis spectra of these objects could provide new constraints on their presence. [ABSTRACT FROM AUTHOR]