134 research outputs found
Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states
Scroll waves are three-dimensional analogs of spiral waves. The linear
stability spectrum of untwisted and twisted scroll waves is computed for a
two-variable reaction-diffusion model of an excitable medium. Different bands
of modes are seen to be unstable in different regions of parameter space. The
corresponding bifurcations and bifurcated states are characterized by
performing direct numerical simulations. In addition, computations of the
adjoint linear stability operator eigenmodes are also performed and serve to
obtain a number of matrix elements characterizing the long-wavelength
deformations of scroll waves.Comment: 30 pages 16 figures, submitted to Phys. Rev.
Formation and Evolution of Supermassive Black Holes
The correlation between the mass of supermassive black holes in galaxy nuclei
and the mass of the galaxy spheroids or bulges (or more precisely their central
velocity dispersion), suggests a common formation scenario for galaxies and
their central black holes. The growth of bulges and black holes can commonly
proceed through external gas accretion or hierarchical mergers, and are both
related to starbursts. Internal dynamical processes control and regulate the
rate of mass accretion. Self-regulation and feedback are the key of the
correlation. It is possible that the growth of one component, either BH or
bulge, takes over, breaking the correlation, as in Narrow Line Seyfert 1
objects. The formation of supermassive black holes can begin early in the
universe, from the collapse of Population III, and then through gas accretion.
The active black holes can then play a significant role in the re-ionization of
the universe. The nuclear activity is now frequently invoked as a feedback to
star formation in galaxies, and even more spectacularly in cooling flows. The
growth of SMBH is certainly there self-regulated. SMBHs perturb their local
environment, and the mergers of binary SMBHs help to heat and destroy central
stellar cusps. The interpretation of the X-ray background yields important
constraints on the history of AGN activity and obscuration, and the census of
AGN at low and at high redshifts reveals the downsizing effect, already
observed for star formation. History appears quite different for bright QSO and
low-luminosity AGN: the first grow rapidly at high z, and their number density
decreases then sharply, while the density of low-luminosity objects peaks more
recently, and then decreases smoothly.Comment: 31 pages, 13 figures, review paper for Astrophysics Update
A shooting algorithm for problems with singular arcs
In this article we propose a shooting algorithm for a class of optimal
control problems for which all control variables appear linearly. The shooting
system has, in the general case, more equations than unknowns and the
Gauss-Newton method is used to compute a zero of the shooting function. This
shooting algorithm is locally quadratically convergent if the derivative of the
shooting function is one-to-one at the solution. The main result of this paper
is to show that the latter holds whenever a sufficient condition for weak
optimality is satisfied. We note that this condition is very close to a second
order necessary condition. For the case when the shooting system can be reduced
to one having the same number of unknowns and equations (square system) we
prove that the mentioned sufficient condition guarantees the stability of the
optimal solution under small perturbations and the invertibility of the
Jacobian matrix of the shooting function associated to the perturbed problem.
We present numerical tests that validate our method.Comment: No. RR-7763 (2011); Journal of Optimization, Theory and Applications,
published as 'Online first', January 201
Multi-Institution Research and Education Collaboration Identifies New Antimicrobial Compounds
New antibiotics are urgently needed to address increasing rates of multidrug resistant infections. Seventy-six diversely functionalized compounds, comprising five structural scaffolds, were synthesized and tested for their ability to inhibit microbial growth. Twenty-six compounds showed activity in the primary phenotypic screen at the Community for Open Antimicrobial Drug Discovery (CO-ADD). Follow-up testing of active molecules confirmed that two unnatural dipeptides inhibit the growth of Cryptococcus neoformans with a minimum inhibitory concentration (MIC) ≤ 8 μg/mL. Syntheses were carried out by undergraduate students at five schools implementing Distributed Drug Discovery (D3) programs. This report showcases that a collaborative research and educational process is a powerful approach to discover new molecules inhibiting microbial growth. Educational gains for students engaged in this project are highlighted in parallel to the research advances. Aspects of D3 that contribute to its success, including an emphasis on reproducibility of procedures, are discussed to underscore the power of this approach to solve important research problems and to inform other coupled chemical biology research and teaching endeavors
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