Instabilities and Patterns in Coupled Reaction-Diffusion Layers

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the inter-layer coupling. For systems of $n$-component layers and non-identical layers, the linear problem's block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer Brusselator system. The competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system. Selecting a $\sqrt{2}$:1 length scale ratio produces an unusual steady square pattern.Comment: 13 pages, 5 figures, accepted for publication in Phys. Rev.

Revisiting the Cooling Flow Problem in Galaxies, Groups, and Clusters of Galaxies

We present a study of 107 galaxies, groups, and clusters spanning ~3 orders of magnitude in mass, ~5 orders of magnitude in central galaxy star formation rate (SFR), ~4 orders of magnitude in the classical cooling rate (dM/dt) of the intracluster medium (ICM), and ~5 orders of magnitude in the central black hole accretion rate. For each system in this sample, we measure dM/dt using archival Chandra X-ray data and acquire the SFR and systematic uncertainty in the SFR by combining over 330 estimates from dozens of literature sources. With these data, we estimate the efficiency with which the ICM cools and forms stars, finding e_cool = SFR/(dM/dt) = 1.4 +/- 0.4% for systems with dM/dt > 30 Msun/yr. For these systems, we measure a slope in the SFR-dM/dt relation greater than unity, suggesting that the systems with the strongest cool cores are also cooling more efficiently. We propose that this may be related to, on average, higher black hole accretion rates in the strongest cool cores, which could influence the total amount (saturating near the Eddington rate) and dominant mode (mechanical vs radiative) of feedback. For systems with dM/dt < 30 Msun/yr, we find that the SFR and dM/dt are uncorrelated, and show that this is consistent with star formation being fueled at a low (but dominant) level by recycled ISM gas in these systems. We find an intrinsic log-normal scatter in SFR at fixed dM/dt of 0.52 +/- 0.06 dex, suggesting that cooling is tightly self-regulated over very long timescales, but can vary dramatically on short timescales. There is weak evidence that this scatter may be related to the feedback mechanism, with the scatter being minimized (~0.4 dex) in systems for which the mechanical feedback power is within a factor of two of the cooling luminosity.Comment: 16 pages, 10 figures, 6 tables. Submitted to ApJ. Comments welcome

Homogeneous cooling of rough, dissipative particles: Theory and simulations

We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous cooling state. For short times $t$, translational and rotational energy are found to change linearly with $t$. For large times both energies decay like $t^{-2}$ with a ratio independent of time, but not corresponding to equipartition. Good agreement is found between theory and simulations, as long as no clustering instability is observed. System parameters, i.e. density, particle size, and particle mass can be absorbed in a rescaled time, so that the decay of translational and rotational energy is solely determined by normal restitution and surface roughness.Comment: 10 pages, 10 eps-figure

The Impacts of Triclosan on Anaerobic Community Structures, Function, and Antimicrobial Resistance

Triclosan is a widespread antimicrobial agent that accumulates in anaerobic digesters used to treat the residual solids generated at municipal wastewater treatment plants; there is very little information, however, about how triclosan impacts microbial communities in anaerobic digesters. We investigated how triclosan impacts the community structure, function and antimicrobial resistance genes in lab-scale anaerobic digesters. Previously exposed (to triclosan) communities were amended with 5, 50, and 500 mg/kg of triclosan, corresponding to the median, 95th percentile, and 4-fold higher than maximum triclosan concentration that has been detected in U.S. biosolids. Triclosan amendment caused all of the Bacteria and Archaea communities to structurally diverge from that of the control cultures (based on ARISA). At the end of the experiment, all triclosan-amended Archaea communities had diverged from the control communities, regardless of the triclosan concentration added. In contrast, over time the Bacteria communities that were amended with lower concentrations of triclosan (5 mg/kg and 50 mg/kg) initially diverged and then reconverged with the control community structure. Methane production at 500 mg/kg was nearly half the methane production in control cultures. At 50 mg/kg, a large variability in methane production was observed, suggesting that 50 mg/kg may be a tipping point where function begins to fail in some communities. When previously unexposed communities were exposed to 500 mg triclosan/kg, function was maintained, but the abundance of a gene encoding for triclosan resistance (mexB) increased. This research suggests that triclosan could inhibit methane production in anaerobic digesters if concentrations were to increase and may also select for resistant Bacteria. In both cases, microbial community composition and exposure history alter the influence of triclosan