An Adaptive Algorithm for Synchronization in Diffusively Coupled Systems

We present an adaptive algorithm that guarantees synchronization in diffusively coupled systems. We first consider compartmental systems of ODEs, where each compartment represents a spatial domain of components interconnected through diffusion terms with like components in different compartments. Each set of like components may have its own weighted undirected graph describing the topology of the interconnection between compartments. The link weights are updated adaptively according to the magnitude of the difference between neighboring agents connected by the link. We next consider reaction-diffusion PDEs with Neumann boundary conditions, and derive an analogous algorithm guaranteeing spatial homogenization of solutions. We provide a numerical example demonstrating the results

Guaranteeing Spatial Uniformity in Diffusively-Coupled Systems

We present a condition that guarantees spatially uniformity in the solution trajectories of a diffusively-coupled compartmental ODE model, where each compartment represents a spatial domain of components interconnected through diffusion terms with like components in different compartments. Each set of like components has its own weighted undirected graph describing the topology of the interconnection between compartments. The condition makes use of the Jacobian matrix to describe the dynamics of each compartment as well as the Laplacian eigenvalues of each of the graphs. We discuss linear matrix inequalities that can be used to verify the condition guaranteeing spatial uniformity, and apply the result to a coupled oscillator network. Next we turn to reaction-diffusion PDEs with Neumann boundary conditions, and derive an analogous condition guaranteeing spatial uniformity of solutions. The paper contributes a relaxed condition to check spatial uniformity that allows individual components to have their own specific diffusion terms and interconnection structures

Cosmic-Ray Heating of Molecular Gas in the Nuclear Disk: Low Star Formation Efficiency

Understanding the processes occurring in the nuclear disk of our Galaxy is interesting in its own right, as part of the Milky Way Galaxy, but also because it is the closest galactic nucleus. It has been more than two decades since it was recognized that the general phenomenon of higher gas temperature in the inner few hundred parsecs by comparison with local clouds in the disk of the Galaxy. This is one of the least understood characteristics of giant molecular clouds having a much higher gas temperature than dust temperature in the inner few degrees of the Galactic center. We propose that an enhanced flux of cosmic-ray electrons, as evidenced recently by a number of studies, are responsible for directly heating the gas clouds in the nuclear disk, elevating the temperature of molecular gas ($\sim$ 75K) above the dust temperature ($\sim$ 20K). In addition we report the detection of nonthermal radio emission from Sgr B2-F based on low-frequency GMRT and VLA observations. The higher ionization fraction and thermal energy due to the impact of nonthermal electrons in star forming sites have important implications in slowing down star formation in the nuclear disk of our galaxy and nuclei of galaxies.Comment: 12 pages, one figure, ApJL (in press

An Inverse Compton Scattering Origin of X-ray Flares from Sgr A*

The X-ray and near-IR emission from Sgr A* is dominated by flaring, while a quiescent component dominates the emission at radio and sub-mm wavelengths. The spectral energy distribution of the quiescent emission from Sgr A* peaks at sub-mm wavelengths and is modeled as synchrotron radiation from a thermal population of electrons in the accretion flow, with electron temperatures ranging up to $\sim 5-20$\,MeV. Here we investigate the mechanism by which X-ray flare emission is produced through the interaction of the quiescent and flaring components of Sgr A*. The X-ray flare emission has been interpreted as inverse Compton, self-synchrotron-Compton, or synchrotron emission. We present results of simultaneous X-ray and near-IR observations and show evidence that X-ray peak flare emission lags behind near-IR flare emission with a time delay ranging from a few to tens of minutes. Our Inverse Compton scattering modeling places constraints on the electron density and temperature distributions of the accretion flow and on the locations where flares are produced. In the context of this model, the strong X-ray counterparts to near-IR flares arising from the inner disk should show no significant time delay, whereas near-IR flares in the outer disk should show a broadened and delayed X-ray flare.Comment: 22 pages, 6 figures, 2 tables, AJ (in press

Shocked molecular hydrogen towards the Tornado nebula

We present near-infrared and millimetre-line observations of the Tornado nebula (G357.7-0.1). We detected 2.12 micron_m H2 1-0 S(1) line emission towards the suspected site of interaction with a molecular cloud revealed by the presence of an OH(1720 MHz) maser. The distribution of the H2 emission is well correlated with the nonthermal radio continuum emission from the Tornado, and the velocity of the H2 emission spans over 100 km/s, which both imply that the H2 emission is shock excited. We also detected millimetre-lines from 12CO and 13CO transitions at the velocity of the maser, and mapped the distribution of the molecular cloud in a 2 x 2 arcmin^2 region around the maser. The peak of the molecular cloud aligns well with an indentation in the nebula's radio continuum distribution, suggesting that the nebula's shock is being decelerated at this location, which is consistent with the presence of the OH(1720 MHz) maser and shocked H2 emission at that location.Comment: 10 pages, 8 figures, minor changes, accepted to MNRA

Shocked molecular gas towards the SNR G359.1-0.5 and the Snake

We have found a bar of shocked molecular hydrogen (H2) towards the OH(1720 MHz) maser located at the projected intersection of supernova remnant (SNR) G359.1-0.5 and the nonthermal radio filament, known as the Snake. The H2 bar is well aligned with the SNR shell and almost perpendicular to the Snake. The OH(1720 MHz) maser is located inside the sharp western edge of the H2 emission, which is consistent with the scenario in which the SNR drives a shock into a molecular cloud at that location. The spectral-line profiles of 12CO, HCO+ and CS towards the maser show broad-line absorption, which is absent in the 13CO spectra and most probably originates from the pre-shock gas. A density gradient is present across the region and is consistent with the passage of the SNR shock while the H2 filament is located at the boundary between the pre--shocked and post-shock regions.Comment: 8 pages, 12 figures, accepted by the MNRAS, typos fixe