Stable localized patterns in thin liquid films

We study a 2-D nonlinear evolution equation which describes the 3-D spatiotemporal behavior of the air-liquid interface of a thin liquid film lying on the underside of a cooled horizontal plate. We show that the Marangoni effect can stabilize the destabilizing effect of gravity (the Rayleigh-Taylor instability) allowing for the existence of stable localized axisymmetric solutions for a wide range of parameter values. Various properties of these structures are discussed

AGN Feedback models: Correlations with star formation and observational implications of time evolution

We examine the correlation between the star formation rate (SFR) and black hole accretion rate (BHAR) across a suite of different AGN feedback models, using the time evolution of a merger simulation. By considering three different stages of evolution, and a distinction between the nuclear and outer regions of star formation, we consider 63 different cases. Despite many of the feedback models fitting the M-\sigma\ relationship well, there are often distinct differences in the SFR-BHAR correlations, with close to linear trends only being present after the merger. Some of the models also show evolution in the SFR-BHAR parameter space that is at times directly across the long-term averaged SFR-BHAR correlation. This suggests that the observational SFR-BHAR correlation found for ensembles of galaxies is an approximate statistical trend, as suggested by Hickox et al. Decomposing the SFR into nuclear and outer components also highlights notable differences between models and there is only modest agreement with observational studies examining this in Seyfert galaxies. For the fraction of the black hole mass growth from the merger event relative to the final black hole mass, we find as much as a factor of three variation among models. This also translates into a similar variation in the post-starburst black hole mass growth. Overall, we find that while qualitative features are often similar amongst models, precise quantitative analysis shows there can be quite distinct differences.Comment: Accepted to MNRAS. Comments welcom

Persistence of Tripartite Nonlocality for Non-inertial Observers

We consider the behaviour of bipartite and tripartite non-locality between fermionic entangled states shared by observers, one of whom uniformly accelerates. We find that while fermionic entanglement persists for arbitrarily large acceleration, the Bell/CHSH inequalities cannot be violated for sufficiently large but finite acceleration. However the Svetlichny inequality, which is a measure of genuine tripartite non-locality, can be violated for any finite value of the acceleration.Comment: 4 pages, pdflatex, 2 figure

Under-dominance constrains the evolution of negative autoregulation in diploids

Regulatory networks have evolved to allow gene expression to rapidly track changes in the environment as well as to buffer perturbations and maintain cellular homeostasis in the absence of change. Theoretical work and empirical investigation in Escherichia coli have shown that negative autoregulation confers both rapid response times and reduced intrinsic noise, which is reflected in the fact that almost half of Escherichia coli transcription factors are negatively autoregulated. However, negative autoregulation is exceedingly rare amongst the transcription factors of Saccharomyces cerevisiae. This difference is all the more surprising because E. coli and S. cerevisiae otherwise have remarkably similar profiles of network motifs. In this study we first show that regulatory interactions amongst the transcription factors of Drosophila melanogaster and humans have a similar dearth of negative autoregulation to that seen in S. cerevisiae. We then present a model demonstrating that this fundamental difference in the noise reduction strategies used amongst species can be explained by constraints on the evolution of negative autoregulation in diploids. We show that regulatory interactions between pairs of homologous genes within the same cell can lead to under-dominance - mutations which result in stronger autoregulation, and decrease noise in homozygotes, paradoxically can cause increased noise in heterozygotes. This severely limits a diploid's ability to evolve negative autoregulation as a noise reduction mechanism. Our work offers a simple and general explanation for a previously unexplained difference between the regulatory architectures of E. coli and yeast, Drosophila and humans. It also demonstrates that the effects of diploidy in gene networks can have counter-intuitive consequences that may profoundly influence the course of evolution

Walking Stabilization Using Step Timing and Location Adjustment on the Humanoid Robot, Atlas

While humans are highly capable of recovering from external disturbances and uncertainties that result in large tracking errors, humanoid robots have yet to reliably mimic this level of robustness. Essential to this is the ability to combine traditional "ankle strategy" balancing with step timing and location adjustment techniques. In doing so, the robot is able to step quickly to the necessary location to continue walking. In this work, we present both a new swing speed up algorithm to adjust the step timing, allowing the robot to set the foot down more quickly to recover from errors in the direction of the current capture point dynamics, and a new algorithm to adjust the desired footstep, expanding the base of support to utilize the center of pressure (CoP)-based ankle strategy for balance. We then utilize the desired centroidal moment pivot (CMP) to calculate the momentum rate of change for our inverse-dynamics based whole-body controller. We present simulation and experimental results using this work, and discuss performance limitations and potential improvements

Towards More Precise Photometric Redshifts: Calibration Via CCD Photometry

We present the initial results from a deep, multi-band photometric survey of selected high Galactic latitude redshift fields. Previous work using the photographic data of Koo and Kron demonstrated that the distribution of galaxies in the multi-dimensional flux space U B R I is nearly planar. The position of a galaxy within this plane is determined by its redshift, luminosity and spectral type. Using recently acquired deep CCD photometry in existing, published redshift fields, we have redetermined the distribution of galaxies in this four-dimensional magnitude space. Furthermore, from our CCD photometry and the published redshifts, we have quantified the photometric-redshift relation within the standard AB magnitude system. This empirical relation has a measured dispersion of approximately 0.02 for z < 0.4. With this work we are reaching the asymptotic intrinsic dispersions that were predicted from simulated distributions of galaxy colors.Comment: submitted to the Astrophysical Journal Letter

Size-independence of statistics for boundary collisions of random walks and its implications for spin-polarized gases

A bounded random walk exhibits strong correlations between collisions with a boundary. For an one-dimensional walk, we obtain the full statistical distribution of the number of such collisions in a time t. In the large t limit, the fluctuations in the number of collisions are found to be size-independent (independent of the distance between boundaries). This occurs for any inter-boundary distance, including less and greater than the mean-free-path, and means that this boundary effect does not decay with increasing system-size. As an application, we consider spin-polarized gases, such as 3-Helium, in the three-dimensional diffusive regime. The above results mean that the depolarizing effect of rare magnetic-impurities in the container walls is orders of magnitude larger than a Smoluchowski assumption (to neglect correlations) would imply. This could explain why depolarization is so sensitive to the container's treatment with magnetic fields prior to its use.Comment: 5 page manuscript with extra details in appendices (additional 3 pages