Singular limits in phase dynamics with physical viscosity and capillarity

Following pioneering work by Fan and Slemrod who studied the effect of artificial viscosity terms, we consider the system of conservation laws arising in liquid-vapor phase dynamics with physical viscosity and capillarity effects taken into account. Following Dafermos we consider self-similar solutions to the Riemann problem and establish uniform total variation bounds, allowing us to deduce new existence results. Our analysis cover both the hyperbolic and the hyperbolic-elliptic regimes and apply to arbitrarily large Riemann data. The proofs rely on a new technique of reduction to two coupled scalar equations associated with the two wave fans of the system. Strong L1 convergence to a weak solution of bounded variation is established in the hyperbolic regime, while in the hyperbolicelliptic regime a stationary singularity near the axis separating the two wave fans, or more generally an almost-stationary oscillating wave pattern (of thickness depending upon the capillarityviscosity ratio) are observed which prevent the solution to have globally bounded variation

Boundary layers in weak solutions of hyperbolic conservation laws. III. Vanishing relaxation limits

This is the third part of a series concerned with boundary layers in solutions of nonlinear hyperbolic systems of conservation laws. We consider here self-similar solutions of the Riemann problem, following a pioneering idea by Dafermos. The system under study is strictly hyperbolic but no assumption of genuine nonlinearity is made. The boundary is possibly characteristic, that the sign of the characteristic speed near the boundary is not known a priori. We investigate the effect of vanishing relaxation terms on the solutions of the Riemann problem. We show that the boundary Riemann problem with relaxation admits continuous solutions that remain uniformly bounded in the total variation norm. Following the second part of this series, we derive the necessary uniform estimates near the boundary which allow us to describe the structure of the boundary layer even when the boundary is characteristic. Our analysis provides still a new approach to the existence of Riemann solutions for systems of conservation laws

Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page

Radiation Driven Implosion and Triggered Star Formation

We present simulations of initially stable isothermal clouds exposed to ionizing radiation from a discrete external source, and identify the conditions that lead to radiatively driven implosion and star formation. We use the Smoothed Particle Hydrodynamics code SEREN (Hubber et al. 2010) and the HEALPix-based photoionization algorithm described in Bisbas et al. (2009). We find that the incident ionizing flux is the critical parameter determining the evolution: high fluxes simply disperse the cloud, whereas low fluxes trigger star formation. We find a clear connection between the intensity of the incident flux and the parameters of star formation.Comment: 4 pages, 2 figures, conference proceedings, IAU Symposium 270 (eds. Alves, Elmegreen, Girart, Trimble

Near-arcsecond resolution observations of the hot corino of the solar type protostar IRAS 16293-2422

Complex organic molecules have previously been discovered in solar type protostars, raising the questions of where and how they form in the envelope. Possible formation mechanisms include grain mantle evaporation, interaction of the outflow with its surroundings or the impact of UV/X-rays inside the cavities. In this Letter we present the first interferometric observations of two complex molecules, CH3CN and HCOOCH3, towards the solar type protostar IRAS16293-2422. The images show that the emission originates from two compact regions centered on the two components of the binary system. We discuss how these results favor the grain mantle evaporation scenario and we investigate the implications of these observations for the chemical composition and physical and dynamical state of the two components.Comment: 5 pages (apjemulate), 2 figures; accepted by ApJ

Broad N2H+ emission towards the protostellar shock L1157-B1

We present the first detection of N2H+ towards a low-mass protostellar outflow, namely the L1157-B1 shock, at about 0.1 pc from the protostellar cocoon. The detection was obtained with the IRAM 30-m antenna. We observed emission at 93 GHz due to the J = 1-0 hyperfine lines. The analysis of the emission coupled with the HIFI CHESS multiline CO observations leads to the conclusion that the observed N2H+(1-0) line originates from the dense (> 10^5 cm-3) gas associated with the large (20-25 arcsec) cavities opened by the protostellar wind. We find a N2H+ column density of few 10^12 cm-2 corresponding to an abundance of (2-8) 10^-9. The N2H+ abundance can be matched by a model of quiescent gas evolved for more than 10^4 yr, i.e. for more than the shock kinematical age (about 2000 yr). Modelling of C-shocks confirms that the abundance of N2H+ is not increased by the passage of the shock. In summary, N2H+ is a fossil record of the pre-shock gas, formed when the density of the gas was around 10^4 cm-3, and then further compressed and accelerated by the shock.Comment: ApJ, in pres

Smooth Gowdy symmetric generalized Taub-NUT solutions

We study a class of S3 Gowdy vacuum models with a regular past Cauchy horizon which we call smooth Gowdy symmetric generalized Taub-NUT solutions. In particular, we prove existence of such solutions by formulating a singular initial value problem with asymptotic data on the past Cauchy horizon. The result of our investigations is that a future Cauchy horizon exists for generic asymptotic data. Moreover, we derive an explicit expression for the metric on the future Cauchy horizon in terms of the asymptotic data on the past horizon. This complements earlier results about S2xS1 Gowdy models.Comment: 56 pages, 1 figure. The new version contains a detailed explanation of the Fuchsian method on the 2-spher

Triggered Star Formation in the Orion Bright-Rimmed Clouds

We have developed an empirical and effective set of criteria, based on the 2MASS colors, to select candidate classical T Tauri stars (CTTS). This provides a useful tool to study the young stellar population in star-forming regions. Here we present our analysis of the bright-rimmed clouds (BRCs) B 35, B 30, IC 2118, LDN 1616, LDN 1634, and Orion East to show how massive stars interact with molecular clouds to trigger star formation. Our results support the radiation-driven implosion model in which the ionization fronts from OB stars compress a nearby cloud until the local density exceeds the critical value, thereby inducing the cloud to collapse to form stars. We find that only BRCs associated with strong IRAS 100 micron emission (tracer of high density) and H-alpha emission (tracer of ionization fronts) show signs of ongoing star formation. Relevant timescales, including the ages of O stars, expanding HII regions, and the ages of CTTS, are consistent with sequential star formation. We also find that CTTS are only seen between the OB stars and the BRCs, with those closer to the BRCs being progressively younger. There are no CTTS leading the ionization fronts, i.e., within the molecular clouds. All these provide strong evidence of triggered star formation and show the major roles massive stars play in sustaining the star-forming activities in the region.Comment: To appear in Ap

Dzyaloshinskii-Moriya interaction in transport through single molecule transistors

The Dzyaloshinskii-Moriya interaction is shown to result in a canting of spins in a single molecule transistor. We predict non-linear transport signatures of this effect induced by spin-orbit coupling for the generic case of a molecular dimer. The conductance is calculated using a master equation and is found to exhibit a non-trivial dependence on the magnitude and direction of an external magnetic field. We show how three-terminal transport measurements allow for a determination of the coupling-vector characterizing the Dzyaloshinskii-Moriya interaction. In particular, we show how its orientation, defining the intramolecular spin chirality, can be probed with ferromagnetic electrodes

Diagnosing shock temperature with NH3_3 and H2_2O profiles

In a previous study of the L1157 B1 shocked cavity, a comparison between NH$_3$(1$_0$-$0_0$) and H$_2$O(1$_{\rm 10}$--1$_{\rm 01}$) transitions showed a striking difference in the profiles, with H$_2$O emitting at definitely higher velocities. This behaviour was explained as a result of the high-temperature gas-phase chemistry occurring in the postshock gas in the B1 cavity of this outflow. If the differences in behaviour between ammonia and water are indeed a consequence of the high gas temperatures reached during the passage of a shock, then one should find such differences to be ubiquitous among chemically rich outflows. In order to determine whether the difference in profiles observed between NH$_3$ and H$_2$O is unique to L1157 or a common characteristic of chemically rich outflows, we have performed Herschel-HIFI observations of the NH$_3$(1$_0$-0$_0$) line at 572.5 GHz in a sample of 8 bright low-mass outflow spots already observed in the H$_2$O(1$_{\rm 10}$--1$_{\rm 01}$) line within the WISH KP. We detected the ammonia emission at high-velocities at most of the outflows positions. In all cases, the water emission reaches higher velocities than NH$_3$, proving that this behaviour is not exclusive of the L1157-B1 position. Comparisons with a gas-grain chemical and shock model confirms, for this larger sample, that the behaviour of ammonia is determined principally by the temperature of the gas.Comment: Accepted for publication in the Monthly Notices of the Royal Astronomical Societ