Determination of convection terms and quasi-linearities appearing in diffusion equations

We consider the highly nonlinear and ill posed inverse problem of determining some general expression appearing in the a diffusion equation from measurements of solutions on the lateral boundary. We consider both linear and nonlinear expression. In the linear case, the equation is a convection-diffusion equation and our inverse problem corresponds to the unique recovery, in some suitable sense, of a time evolving velocity field associated with the moving quantity as well as the density of the medium in some rough setting described by non-smooth coefficients on a Lipschitz domain. In the nonlinear case, we prove the recovery of more general quasilinear expression appearing in a non-linear parabolic equation. Our result give a positive answer to the unique recovery of a general vector valued first order coefficient, depending on both time and space variable, and to the unique recovery inside the domain of quasilinear terms, from measurements restricted to the lateral boundary, for diffusion equations

Vacuum-UV spectroscopy of interstellar ice analogs. II. Absorption cross-sections of nonpolar ice molecules

Dust grains in cold circumstellar regions and dark-cloud interiors at 10-20 K are covered by ice mantles. A nonthermal desorption mechanism is invoked to explain the presence of gas-phase molecules in these environments, such as the photodesorption induced by irradiation of ice due to secondary ultraviolet photons. To quantify the effects of ice photoprocessing, an estimate of the photon absorption in ice mantles is required. In a recent work, we reported the vacuum-ultraviolet (VUV) absorption cross sections of nonpolar molecules in the solid phase. The aim was to estimate the VUV-absorption cross sections of nonpolar molecular ice components, including CH4, CO2, N2, and O2. The column densities of the ice samples deposited at 8 K were measured in situ by infrared spectroscopy in transmittance. VUV spectra of the ice samples were collected in the 120-160 nm (10.33-7.74 eV) range using a commercial microwave-discharged hydrogen flow lamp. We found that, as expected, solid N2 has the lowest VUV-absorption cross section, which about three orders of magnitude lower than that of other species such as O2, which is also homonuclear. Methane (CH4) ice presents a high absorption near Ly-alpha (121.6 nm) and does not absorb below 148 nm. Estimating the ice absorption cross sections is essential for models of ice photoprocessing and allows estimating the ice photodesorption rates as the number of photodesorbed molecules per absorbed photon in the ice.Comment: 9 pages, 6 figures, 7 table

Photo-desorption of H2O:CO:NH3 circumstellar ice analogs: Gas-phase enrichment

We study the photo-desorption occurring in H$_2$O:CO:NH$_3$ ice mixtures irradiated with monochromatic (550 and 900 eV) and broad band (250--1250 eV) soft X-rays generated at the National Synchrotron Radiation Research Center (Hsinchu, Taiwan). We detect many masses photo-desorbing, from atomic hydrogen (m/z = 1) to complex species with m/z = 69 (e.g., C$_3$H$_3$NO, C$_4$H$_5$O, C$_4$H$_7$N), supporting the enrichment of the gas phase. At low number of absorbed photons, substrate-mediated exciton-promoted desorption dominates the photo-desorption yield inducing the release of weakly bound (to the surface of the ice) species; as the number of weakly bound species declines, the photo-desorption yield decrease about one order of magnitude, until porosity effects, reducing the surface/volume ratio, produce a further drop of the yield. We derive an upper limit to the CO photo-desorption yield, that in our experiments varies from 1.4 to 0.007 molecule photon$^{-1}$ in the range $\sim 10^{15} - 10^{20}$~absorbed photons cm$^{-2}$. We apply these findings to a protoplanetary disk model irradiated by a central T~Tauri star