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

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

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

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

High spectral resolution observations of HNC3 and HCCNC in the L1544 prestellar core

HCCNC and HNC3 are less commonly found isomers of cyanoacetylene, HC3N, a molecule that is widely found in diverse astronomical sources. We want to know if HNC3 is present in sources other than the dark cloud TMC-1 and how its abundance is relative to that of related molecules. We used the ASAI unbiased spectral survey at IRAM 30m towards the prototypical prestellar core L1544 to search for HNC3 and HCCNC which are by-product of the HC3NH+ recombination, previously detected in this source. We performed a combined analysis of published HNC3 microwave rest frequencies with thus far unpublished millimeter data because of issues with available rest frequency predictions. We determined new spectroscopic parameters for HNC3, produced new predictions and detected it towards L1544. We used a gas-grain chemical modelling to predict the abundances of N-species and compare with the observations. The modelled abundances are consistent with the observations, considering a late stage of the evolution of the prestellar core. However the calculated abundance of HNC3 was found 5-10 times higher than the observed one. The HC3N, HNC3 and HCCNC versus HC3NH+ ratios are compared in the TMC-1 dark cloud and the L1544 prestellar core.Comment: Accepted in MNRAS letters. 5 pages plus 2 additional pages for the on-line materia

The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes

We propose a new, augmented formulation of the coupled Euler–Einstein equations for perfect fluids on plane-symmetric Gowdy spacetimes. The unknowns of the augmented system are the density and velocity of the fluid and the first- and second-order spacetime derivatives of the metric. We solve the Riemann problem for the augmented system, allowing propagating discontinuities in both the fluid variables and the first- and second-order derivatives of the geometry coefficients. Our main result, based on Glimm's random choice scheme, is the existence of solutions with bounded total variation of the Euler–Einstein equations, up to the first time where a blow-up singularity (unbounded first-order derivatives of the geometry coefficients) occurs. We demonstrate the relevance of the augmented system for numerical relativity. We also consider general vacuum spacetimes and solve a Riemann problem, by relying on a theorem by Rendall on the characteristic value problem for the Einstein equations

Analysis on Aging in the Generalized Random Energy Model

A new dynamics more natural than that proposed by Bouchaud and Dean is introduced to the Generalized Random Energy Model, and the master equation for the dynamics is solved exactly to calculate the time correlation function. Although our results are very similar to those obtained by Bouchaud and Dean qualitatively, the exponents for power law relaxation are different. The Zero-Field-Cooled magnetization is also calculated with a relation between the correlation function and the response function which holds even if the relaxation is non-equilibrium. The validity of these analytic results are confirmed by numerical simulations.Comment: 12 pages, 5 figures, submitted to J. Phys. Sci. Jp

Discovery of deuterated water in a young proto-planetary disk

We report the first detection of the ground transition of the deuterated water at 464 GHz in the young proto-planetary disk surrounding the solar type protostar DM Tau. The line is observed in absorption against the continuum from the cold dust in the disk midplane, with a line to continuum ratio close to unity. The observation implies that deuterated gaseous water is present, with a relatively large abundance ($\sim 3\times10^{-9}$), in the outer disk above the midplane, where the density is, within a factor ten, $\sim 10^6$ cm$^{-3}$ and the temperature is lower than about 25 K. In these conditions, the H$_2$O condensation timescale is much smaller than the DM Tau disk age, and, therefore, water should be fully frozen onto the grain mantles. We suggest that UV photons and/or X-rays sublimate part of the mantles re-injecting the ices into the gas phase. Even though there is currently no measurement of H$_2$O, we provide arguments that the HDO/H$_2$O ratio should be about 0.01 or larger, which would be hundreds of times larger than the values measured in Solar System objects. This suggests the need of strong caution in comparing and linking the HDO/H$_2$O in Solar System and star forming environments.Comment: Accepted to be published in ApJ Letter

Silicon Superconducting Quantum Interference Device

We have studied a Superconducting Quantum Interference SQUID device made from a single layer thin film of superconducting silicon. The superconducting layer is obtained by heavily doping a silicon wafer with boron atoms using the Gas Immersion Laser Doping (GILD) technique. The SQUID device is composed of two nano-bridges (Dayem bridges) in a loop and shows magnetic flux modulation at low temperature and low magnetic field. The overall behavior shows very good agreement with numerical simulations based on the Ginzburg-Landau equations.Comment: Published in Applied Physics Letters (August 2015

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