6,823 research outputs found
Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation
We study a reaction diffusion model recently proposed in [5] to describe the spatiotemporal evolution of the bacterium Bacillus subtilis on agar plates containing nutrient. An interesting mathematical feature of the model, which is a coupled pair of partial differential equations, is that the bacterial density satisfies a degenerate nonlinear diffusion equation. It was shown numerically that this model can exhibit quasi-one-dimensional constant speed travelling wave solutions. We present an analytic study of the existence and uniqueness problem for constant speed travelling wave solutions. We find that such solutions exist only for speeds greater than some threshold speed giving minimum speed waves which have a sharp profile. For speeds greater than this minimum speed the waves are smooth. We also characterise the dependence of the wave profile on the decay of the front of the initial perturbation in bacterial density. An investigation of the partial differential equation problem establishes,via a global existence and uniqueness argument, that these waves are the only long time solutions supported by the problem. Numerical solutions of the partial differential equation problem are presented and they confirm the results of the analysis
Massive planet migration: Theoretical predictions and comparison with observations
We quantify the utility of large radial velocity surveys for constraining
theoretical models of Type II migration and protoplanetary disk physics. We
describe a theoretical model for the expected radial distribution of extrasolar
planets that combines an analytic description of migration with an empirically
calibrated disk model. The disk model includes viscous evolution and mass loss
via photoevaporation. Comparing the predicted distribution to a uniformly
selected subsample of planets from the Lick / Keck / AAT planet search
programs, we find that a simple model in which planets form in the outer disk
at a uniform rate, migrate inward according to a standard Type II prescription,
and become stranded when the gas disk is dispersed, is consistent with the
radial distribution of planets for orbital radii 0.1 AU < a < 2.5 AU and planet
masses greater than 1.65 Jupiter masses. Some variant models are disfavored by
existing data, but the significance is limited (~95%) due to the small sample
of planets suitable for statistical analysis. We show that the favored model
predicts that the planetary mass function should be almost independent of
orbital radius at distances where migration dominates the massive planet
population. We also study how the radial distribution of planets depends upon
the adopted disk model. We find that the distribution can constrain not only
changes in the power-law index of the disk viscosity, but also sharp jumps in
the efficiency of angular momentum transport that might occur at small radii.Comment: ApJ, in press. References updated to match published versio
MHD simulations of the collapsar model for GRBs
We present results from axisymmetric, time-dependent magnetohydrodynamic
(MHD) simulations of the collapsar model for gamma-ray bursts. Our main
conclusion is that, within the collapsar model, MHD effects alone are able to
launch, accelerate and sustain a strong polar outflow. We also find that the
outflow is Poynting flux-dominated, and note that this provides favorable
initial conditions for the subsequent production of a baryon-poor fireball.Comment: 4 pages, to appear in proceedings of "2003 GRB Conference" (Santa Fe,
NM, September 8-12, 2003), needs aipprocs LaTeX class, movies are available
at http://rocinante.colorado.edu/~proga
Feedback control architecture & the bacterial chemotaxis network
Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to ‘reset’ (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a ‘cascade control’ feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance
Reduction of Effective Terahertz Focal Spot Size By Means Of Nested Concentric Parabolic Reflectors
An ongoing limitation of terahertz spectroscopy is that the technique is
generally limited to the study of relatively large samples of order 4 mm across
due to the generally large size of the focal beam spot. We present a nested
concentric parabolic reflector design which can reduce the terahertz focal spot
size. This parabolic reflector design takes advantage of the feature that
reflected rays experience a relative time delay which is the same for all
paths. The increase in effective optical path for reflected light is equivalent
to the aperture diameter itself. We have shown that the light throughput of an
aperture of 2 mm can be increased by a factor 15 as compared to a regular
aperture of the same size at low frequencies. This technique can potentially be
used to reduce the focal spot size in terahertz spectroscopy and enable the
study of smaller samples
Astrometric signatures of self-gravitating protoplanetary discs
We use high resolution numerical simulations to study whether gravitational
instabilities within circumstellar discs can produce astrometrically detectable
motion of the central star. For discs with masses of M_disc = 0.1 M_star, which
are permanantly stable against fragmentation, we find that the magnitude of the
astrometric signal depends upon the efficiency of disc cooling. Short cooling
times produce prominent filamentary spiral structures in the disc, and lead to
stellar motions that are potentially observable with future high precision
astrometric experiments. For a disc that is marginally unstable within radii of
\~10 au, we estimate astrometric displacements of 10-100 microarcsec on decade
timescales for a star at a distance of 100 pc. The predicted displacement is
suppressed by a factor of several in more stable discs in which the cooling
time exceeds the local dynamical time by an order of magnitude. We find that
the largest contribution comes from material in the outer regions of the disc
and hence, in the most pessimistic scenario, the stellar motions caused by the
disc could confuse astrometric searches for low mass planets orbiting at large
radii. They are, however, unlikely to present any complications in searches for
embedded planets orbiting at small radii, relative to the disc size, or Jupiter
mass planets or greater orbiting at large radii.Comment: 6 pages, 9 figures, accepted for publication in MNRA
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