Crack fronts and damage in glass at the nanometer scale

We have studied the low speed fracture regime for different glassy materials with variable but controlled length scales of heterogeneity in a carefully mastered surrounding atmosphere. By using optical and atomic force microscopy (AFM) techniques we tracked in real-time the crack tip propagation at the nanometer scale on a wide velocity range (mm/s - pm/s and below). The influence of the heterogeneities on this velocity is presented and discussed. Our experiments reveal also -for the first time- that the crack progresses through nucleation, growth and coalescence of nanometric damage cavities within the amorphous phase. This may explain the large fluctuations observed in the crack tip velocities for the smallest values. This behaviour is very similar to what is involved, at the micrometric scale, in ductile fracture. The only difference is very likely due to the related length scales (nanometric instead of micrometric). Consequences of such a nano-ductile fracture mode observed at a temperature far below the glass transition temperature in glass is finally discussed.Comment: 12 pages, 8 figures, submitted to Journal of Physics: Condensed Matter; Invited talk at Glass and Optical Materials Division Fall 2002 Meeting, Pittsburgh, Pa, US

Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

Shock excitation of H2_2 in the James Webb Space Telescope era

(Abridged) H2 is the most abundant molecule in the Universe. Thanks to its widely spaced energy levels, it predominantly lights up in warm gas, T > 100 K, such as shocked regions, and it is one of the key targets of JWST observations. These include shocks from protostellar outflows, all the way up to starburst galaxies and AGN. Shock models are able to simulate H2 emission. We aim to explore H2 excitation using such models, and to test over which parameter space distinct signatures are produced in H2 emission. We present simulated H2 emission using the Paris-Durham shock code over an extensive grid of 14,000 plane-parallel stationary shock models, a large subset of which are exposed to an external UV radiation field. The grid samples 6 input parameters: preshock density, shock velocity, transverse magnetic field strength, UV radiation field strength, cosmic-ray-ionization rate, and PAH abundance. Physical quantities, such as temperature, density, and width, have been extracted along with H2 integrated line intensities. The strength of the transverse magnetic field, set by the scaling factor, b, plays a key role in the excitation of H2. At low values of b (<~ 0.3, J-type shocks), H2 excitation is dominated by vibrationally excited lines; at higher values (b >~ 1, C-type shocks), rotational lines dominate the spectrum for shocks with an external radiation field comparable to (or lower than) the solar neighborhood. Shocks with b >= 1 can be spatially resolved with JWST for nearby objects. When the input kinetic energy flux increases, the excitation and integrated intensity of H2 increases similarly. An external UV field mainly serves to increase the excitation, particularly for shocks where the input radiation energy is comparable to the input kinetic energy flux. These results provide an overview of the energetic reprocessing of input kinetic energy flux and the resulting H2 line emission.Comment: Published in A&

FUSE Observations of the HD Molecule toward HD 73882

The Lyman and Werner band systems of deuterated molecular hydrogen (HD) occur in the far UV range below 1200 A. The high sensitivity of the FUSE mission can give access, at moderate resolution, to hot stars shining through translucent clouds, in the hope of observing molecular cores in which deuterium is essentially in the form of HD. Thus, the measurement of the HD/H2 ratio may become a new powerful tool to evaluate the deuterium abundance, D/H, in the interstellar medium. We report here on the detection of HD toward the high extinction star HD 73882 [E(B-V)=0.72]. A preliminary analysis is presented.Comment: 4 pages + 4 .ps figures. This paper will appear in a special issue of Astrophysical Journal Letters devoted to the first scientific results from the FUSE missio

Photoelectric effect on dust grains across the L1721 cloud in the rho Ophiuchi molecular complex

We present ISO-LWS measurements of the main gas cooling lines, C+ 158 mum and O 63 mum towards a moderate opacity molecular cloud (Av=3), L1721, illuminated by the B2 star nu Sco (X = 5-10). These data are combined with an extinction map and IRAS dust emission images to test our understanding of gas heating and cooling in photo-dissociation regions (PDRs). This nearby PDR is spatially resolved in the IRAS images; variations in the IRAS colors across the cloud indicate an enhanced abundance of small dust grains within the PDR. A spatial correlation between the gas cooling lines and the infrared emission from small dust grains illustrates the dominant role of small dust grains in the gas heating through the photoelectric effect. The photoelectric efficiency, determined from the observations by ratioing the power radiated by gas and small dust grains, is in the range 2 to 3% in close agreement with recent theoretical estimates. The brightness profiles across the PDR in the C+ 158 mum and O 63 mum lines are compared with model calculations where the density profile is constrained by the extinction data and where the gas chemical and thermal balances are solved at each position. We show that abundance variations of small dust grains across the PDR must be considered to account for the LWS observations.Comment: 10 pages, 15 figure

CN and HCN in Dense Interstellar Clouds

We present a theoretical investigation of CN and HCN molecule formation in dense interstellar clouds. We study the gas-phase CN and HCN production efficiencies from the outer photon-dominated regions (PDRs) into the opaque cosmic-ray dominated cores. We calculate the equilibrium densities of CN and HCN, and of the associated species C+, C, and CO, as functions of the far-ultraviolet (FUV) optical depth. We consider isothermal gas at 50 K, with hydrogen particle densities from 10^2 to 10^6 cm^-3. We study clouds that are exposed to FUV fields with intensities 20 to 2*10^5 times the mean interstellar FUV intensity. We assume cosmic-ray H2 ionization rates ranging from 5*10^-17 s^-1, to an enhanced value of 5*10^-16 s^-1. We also examine the sensitivity of the density profiles to the gas-phase sulfur abundance.Comment: Accepted for publication in ApJ, 33 pages, 8 figure

Multifluid, Magnetohydrodynamic Shock Waves with Grain Dynamics II. Dust and the Critical Speed for C Shocks

This is the second in a series of papers on the effects of dust on multifluid, MHD shock waves in weakly ionized molecular gas. We investigate the influence of dust on the critical shock speed, v_crit, above which C shocks cease to exist. Chernoff showed that v_crit cannot exceed the grain magnetosound speed, v_gms, if dust grains are dynamically well coupled to the magnetic field. We present numerical simulations of steady shocks where the grains may be well- or poorly coupled to the field. We use a time-dependent, multifluid MHD code that models the plasma as a system of interacting fluids: neutral particles, ions, electrons, and various ``dust fluids'' comprised of grains with different sizes and charges. Our simulations include grain inertia and grain charge fluctuations but to highlight the essential physics we assume adiabatic flow, single-size grains, and neglect the effects of chemistry. We show that the existence of a phase speed v_phi does not necessarily mean that C shocks will form for all shock speeds v_s less than v_phi. When the grains are weakly coupled to the field, steady, adiabatic shocks resemble shocks with no dust: the transition to J type flow occurs at v_crit = 2.76 v_nA, where v_nA is the neutral Alfven speed, and steady shocks with v_s > 2.76 v_nA are J shocks with magnetic precursors in the ion-electron fluid. When the grains are strongly coupled to the field, v_crit = min(2.76 v_nA, v_gms). Shocks with v_crit < v_s < v_gms have magnetic precursors in the ion-electron-dust fluid. Shocks with v_s > v_gms have no magnetic precursor in any fluid. We present time-dependent calculations to study the formation of steady multifluid shocks. The dynamics differ qualitatively depending on whether or not the grains and field are well coupled.Comment: 43 pages with 17 figures, aastex, accepted by The Astrophysical Journa

Glass breaks like metals, but at the nanometer scale

We report in situ Atomic Force Microscopy experiments which reveal the presence of nanoscale damage cavities ahead of a stress-corrosion crack tip in glass. Their presence might explain the departure from linear elasticity observed in the vicinity of a crack tip in glass. Such a ductile fracture mechanism, widely observed in the case of metallic materials at the micrometer scale, might be also at the origin of the striking similarity of the morphologies of fracture surfaces of glass and metallic alloys at different length scales.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Lett, few minor corrections, Fig. 1b change

Sulphur-bearing species in the star forming region L1689N

We report observations of the expected main S-bearing species (SO, SO2 and H2S) in the low-mass star forming region L1689N. We obtained large scale (~300''x200'') maps of several transitions from these molecules with the goal to study the sulphur chemistry, i.e. how the relative abundances change in the different physical conditions found in L1689N. We identified eight interesting regions, where we carried out a quantitative comparative study: the molecular cloud (as reference position), five shocked regions caused by the interaction of the molecular outflows with the cloud, and the two protostars IRAS16293-2422 and 16293E. In the cloud we carefully computed the gas temperature and density by means of a non-LTE LVG code, while in other regions we used previous results. We hence derived the column density of SO, SO2 and H2S, together with SiO and H2CO - which were observed previously - and their relevant abundance ratios. We find that SiO is the molecule that shows the largest abundance variations in the shocked regions, whereas S-bearing molecules show more moderate variations. Remarkably, the region of the brightest SiO emission in L1689N is undetected in SO2, H2S and H2CO and only marginally detected in SO. In the other weaker SiO shocks, SO2 is enhanced with respect to SO. We propose a schema in which the different molecular ratios correspond to different ages of the shocks. Finally, we find that SO, SO2 and H2S have significant abundance jumps in the inner hot core of IRAS16293-2422 and discuss the implications of the measured abundances.Comment: Accepted 08/10/0

Deuterated Thioformaldehyde in the Barnard 1 Cloud

We present observations of the singly and doubly deuterated species of thioformaldehyde, HDCS and D$_2$CS, towards the dark cloud Barnard 1. This is the first detection of D$_2$CS in Space and in dense and cold prestellar regions. Column densities obtained using rotational diagrams and a Large Velocity Gradient model show an extremely high D-enhancement in thioformaldehyde in Barnard 1. Although the column density of H$_2$CS is smaller than that of H$_2$CO, both species show similar D-enhancements in their singly and doubly deuterated species. A chemical model -including multiply deuterated species- has been used in order to interpret the observations. Predicted rotational frequencies from laboratory data for HDCS and D$_2$CS are significantly in error when compared to the observed frequencies in Space. Consequently, we have derived new rotational constants for these two species and for H$_2$CS and H$_2$C$^{34}$S using the observed frequencies in Barnard 1. The new rotational constants allow to predict the rotational transitions of these species with the accuracy needed for the narrow line emerging from dark clouds. Rotational constants for HDCS and D$_2$CS have been obtained from the observed transitions in the laboratory and in Space.Comment: 33 pages, 6 figures, accepted for publication in Ap