Effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems

We study the effect of randomness and anisotropy on Turing patterns in reaction-diffusion systems. For this purpose, the Gierer-Meinhardt model of pattern formation is considered. The cases we study are: (i)randomness in the underlying lattice structure, (ii)the case in which there is a probablity p that at a lattice site both reaction and diffusion occur, otherwise there is only diffusion and lastly, the effect of (iii) anisotropic and (iv) random diffusion coefficients on the formation of Turing patterns. The general conclusion is that the Turing mechanism of pattern formation is fairly robust in the presence of randomness and anisotropy.Comment: 11 pages LaTeX, 14 postscript figures, accepted in Phys. Rev.

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

Submillimeter mapping and analysis of cold dust condensations in the Orion M42 star forming complex

We present here the continuum submillimeter maps of the molecular cloud around the M42 Nebula in the Orion region. These have been obtained in four wavelength bands (200, 260, 360 and 580 microns) with the ProNaOS two meter balloon-borne telescope. The area covered is 7 parsecs wide (50 arcmin at a distance of 470 pc) with a spatial resolution of about 0.4 parsec. Thanks to the high sensitivity to faint surface brightness gradients, we have found several cold condensations with temperatures ranging from 12 to 17 K, within 3 parsecs of the dense ridge. The statistical analysis of the temperature and spectral index spatial distribution shows an evidence of an inverse correlation between these two parameters. Being invisible in the IRAS 100 micron survey, some cold clouds are likely to be the seeds for future star formation activity going on in the complex. We estimate their masses and we show that two of them have masses higher than their Jeans masses, and may be gravitationally unstable.Comment: 4 figures, The Astrophysical Journal, Main Journal, in pres

Dynamical effects induced by long range activation in a nonequilibrium reaction-diffusion system

We both show experimentally and numerically that the time scales separation introduced by long range activation can induce oscillations and excitability in nonequilibrium reaction-diffusion systems that would otherwise only exhibit bistability. Namely, we show that the Chlorite-Tetrathionate reaction, where autocatalytic species diffuses faster than the substrates, the spatial bistability domain in the nonequilibrium phase diagram is extended with oscillatory and excitability domains. A simple model and a more realistic model qualitatively account for the observed behavior. The latter model provides quantitative agreement with the experiments.Comment: 19 pages + 9 figure

Deuterated water in the solar-type protostars NGC 1333 IRAS 4A and IRAS 4B

Aims. The aim of this paper is to study deuterated water in the solar-type protostars NGC1333 IRAS4A and IRAS4B, to compare their HDO abundance distribution with other star-forming regions, and to constrain their HDO/H2O ratios. Methods. Using the Herschel/HIFI instrument as well as ground-based telescopes, we observed several HDO lines covering a large excitation range (Eup/k=22-168 K) towards these protostars and an outflow position. Non-LTE radiative transfer codes were then used to determine the HDO abundance profiles in these sources. Results. The HDO fundamental line profiles show a very broad component, tracing the molecular outflows, in addition to a narrower emission component and a narrow absorbing component. In the protostellar envelope of NGC1333 IRAS4A, the HDO inner (T>100 K) and outer (T<100 K) abundances with respect to H2 are estimated at 7.5x10^{-9} and 1.2x10^{-11}, respectively, whereas, in NGC1333 IRAS4B, they are 1.0x10^{-8} and 1.2x10^{-10}, respectively. Similarly to the low-mass protostar IRAS16293-2422, an absorbing outer layer with an enhanced abundance of deuterated water is required to reproduce the absorbing components seen in the fundamental lines at 465 and 894 GHz in both sources. This water-rich layer is probably extended enough to encompass the two sources as well as parts of the outflows. In the outflows emanating from NGC1333 IRAS4A, the HDO column density is estimated at about (2-4)x10^{13} cm^{-2}, leading to an abundance of about (0.7-1.9)x10^{-9}. An HDO/H2O ratio between 7x10^{-4} and 9x10^{-2} is derived in the outflows. In the warm inner regions of these two sources, we estimate the HDO/H2O ratios at about 1x10^{-4}-4x10^{-3}. This ratio seems higher (a few %) in the cold envelope of IRAS4A, whose possible origin is discussed in relation to formation processes of HDO and H2O.Comment: 16 pages, 13 figure

Turing Instability in a Boundary-fed System

The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations (Turing instability) in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis which neglects longitudinal diffusion is inappropriate for predicting the linear stability of these patterns. Using a fully nonuniform analysis, we investigate the structure of the patterns formed along the gradients and their stability to transverse Turing pattern formation as a function of the values of two control parameters: the malonic acid feed concentration and the size of the reactor in the dimension along the gradients. The results from this investigation are compared with existing experiments.Comment: 41 pages, 18 figures, to be published in Physical Review

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth

Photodissociation regions and star formation in the Carina Nebula

We have obtained wide-field thermal infrared (IR) images of the Carina Nebula, using the SPIREX/Abu telescope at the South Pole. Emission from poly-cyclic aromatic hydrocarbons (PAHs) at 3.29um, a tracer of photodissociation regions (PDRs), reveals many interesting well defined clumps and diffuse regions throughout the complex. Near-IR images (1--2um), along with images from the Midcourse Space Experiment (MSX) satellite (8--21um) were incorporated to study the interactions between the young stars and the surrounding molecular cloud in more detail. Two new PAH emission clumps have been identified in the Keyhole Nebula and were mapped in 12CO(2--1) and (1--0) using the SEST. Analysis of their physical properties reveals they are dense molecular clumps, externally heated with PDRs on their surfaces and supported by external pressure in a similar manner to the other clumps in the region. A previously identified externally heated globule containing IRAS 10430-5931 in the southern molecular cloud, shows strong 3.29-, 8- and 21-um emission, the spectral energy distribution (SED) revealing the location of an ultra-compact (UC) HII region. The northern part of the nebula is complicated, with PAH emission inter-mixed with mid-IR dust continuum emission. Several point sources are located here and through a two-component black-body fit to their SEDs, we have identified 3 possible UC HII regions as well as a young star surrounded by a circumstellar disc. This implies that star formation in this region is on-going and not halted by the intense radiation from the surrounding young massive stars.Comment: 14 pages, 12 figures. Accepted by MNRAS. Higher resolution figures available at http://www.phys.unsw.edu.au/~jmr/papers.htm

Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems

The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The derivation applies to the bistable, excitable, and the Turing unstable regimes. In the bistable case stability thresholds are obtained for the Eckhaus and the zigzag instabilities and for the transition to traveling waves. Neutral stability curves demonstrate the destabilization of stationary planar patterns at low wavenumbers to zigzag and traveling modes. Numerical solutions of the model system support the theoretical findings

Massive Quiescent Cores in Orion. I. Temperature Structure

We have mapped four massive cores in Orion using the \ammonia (J,K) = (1,1) and (J,K) = (2,2) inversion transitions, as part of our effort to study the pre--protostellar phase of massive star formation. These cores were selected to be quiescent, i.e. they contain no apparent IR sources and are not associated with any molecular outflows. These cores are one order of magnitude more massive than dark cloud cores and have about twice the line width. This paper focuses on their temperature structure. We find a statistically significant correlation between the gas kinetic temperature and the gas column density. The general trend is for the gas to be colder where the column density is higher, which we interpret to mean that the interiors of these cores are colder than the regions surrounding them. This is in contrast with dark cloud cores, which exhibit relatively flat temperature profiles. The temperature gradient within the massive quiescent Orion cores is consistent with an external radiation source heating the dust, and dust--gas collisions providing relatively close coupling between dust and gas temperatures. From linewidth and temperature, we also obtained the spatial distribution of the turbulence. An anticorrelation is found between the intensity of emission and the degree of turbulence. Thus, we suggest that the initial stage of massive pre--protostellar cloud cores is relatively quiescent condensations which are cooler than their surroundings.Comment: 32 pages, 10 figures, accepted by Ap