A computational study of high-speed microdroplet impact onto a smooth solid surface

Numerical solutions of high-speed microdroplet impact onto a smooth solid surface are computed, using the interFoam VoF solver of the OpenFOAM CFD package. Toward the solid surface, the liquid microdroplet is moving with an impinging gas flow, simulating the situation of ink droplets being deposited onto substrate with a collimated mist jet in the Optomec Aerosol Jet printing process. The computed values of maximum spread factor, for the range of parameters of practical interest to Aerosol Jet printing, were found in very good agreement with some of the correlation formulas proposed by previous authors in the literature. Combining formulas selected from different authors with appropriate modifications yields a maximum spread factor formula that can be used for first-order evaluations of deposited in droplet size during the Aerosol Jet technology development. The computational results also illustrate droplet impact dynamics with lamella shape evolution throughout the spreading, receding-relaxation, and wetting equilibrium phases, consistent with that observed and described by many previous authors. This suggests a scale-invariant nature of the basic droplet impact behavior such that experiments with larger droplets at the same nondimensional parameter values may be considered for studying microdroplet impact dynamics. Significant free surface oscillations can be observed when the droplet viscosity is relatively low. The border line between periodic free surface oscillations and aperiodic creeping to capillary equilibrium free surface shape appears at the value of Ohnesorge number around 0.25. Droplet bouncing after receding is prompted with large contact angles at solid surface (as consistent with findings reported in the literature), but can be suppressed by increasing the droplet viscosity

Deficient Reasoning for Dark Matter in Galaxies

Astronomers have been using the measured luminosity to estimate the {\em luminous mass} of stars, based on empirically established mass-to-light ratio which seems to be only applicable to a special class of stars---the main-sequence stars---with still considerable uncertainties. Another basic tool to determine the mass of a system of stars or galaxies comes from the study of their motion, as Newton demonstrated with his law of gravitation, which yields the {\em gravitational mass}. Because the luminous mass can at best only represent a portion of the gravitational mass, finding the luminous mass to be different or less than the gravitational mass should not be surprising. Using such an apparent discrepancy as a compelling evidence for the so-called dark matter, which has been believed to possess mysterious nonbaryonic properties and present a dominant amount in galaxies and the universe, seems to be too far a stretch when seriously examining the facts and uncertainties in the measurement techniques. In our opinion, a galaxy with star type distribution varying from its center to edge may have a mass-to-light ratio varying accordingly. With the thin-disk model computations based on measured rotation curves, we found that most galaxies have a typical mass density profile that peaks at the galactic center and decreases rapidly within $\sim 5$ of the cut-off radius, and then declines nearly exponentially toward the edge. The predicted mass density in the Galactic disk is reasonably within the reported range of that observed in interstellar medium. This leads us to believe that ordinary baryonic matter can be sufficient for supporting the observed galactic rotation curves; speculation of large amount of non-baryonic matter may be based on an ill-conceived discrepancy between gravitational mass and luminous mass which appears to be unjustified

Optical design for a balloon-borne magnetograph

This report details activities performed in order to accomplish the optical design of a balloon-borne solar vector magnetograph

PROFITABILITY AND RISK OF U.S. AGRICULTURAL BANKS

Study of profitability and risk of agricultural banks is very important in assessing the ability to adequately finance agricultural production and rural development. A recursive system of profitability and risk equations is estimated to compare the performance of agricultural with nonagricultural banks and to identify factors which affect performance. A linear regression model which measures risk-adjusted profitability confirms the results from the recursive system. Results show that agricultural banks perform better than nonagricultural counterparts on average even after controlling for risks and other factors. Further, off-balance-sheet business is found to be negatively related to the risk-adjusted profitability of agricultural banks.Financial Economics,

Nonexistence of reflexive ideals in Iwasawa algebras of Chevalley type

Let $\Phi$ be a root system and let \Phi(\Zp) be the standard Chevalley \Zp-Lie algebra associated to $\Phi$. For any integer $t\geq 1$, let $G$ be the uniform pro-$p$ group corresponding to the powerful Lie algebra p^t \Phi(\Zp) and suppose that $p\geq 5$. Then the Iwasawa algebra $\Omega_G$ has no nontrivial reflexive two-sided ideals. This was previously proved by the authors for the root system $A_1$.Comment: Minor changes made, mostly due to helpful comments from the refere