Horizon Tunneling Revisited: The Case of Higher Dimensional Black Holes

We study the tunneling of massless scalars across black hole horizons in any number of spacetime dimensions greater than three. Our analysis finds that corrections due to backreaction and the inverse dimensional expansion are naturally concomitant, and furnishes a simple proof of the classic relation between entropy and area in all spacetime dimensions, finite or infinite. We conclude with a discussion of the limit in which the the number of spacetime dimensions is taken to infinity, where we find that thermodynamic quantities are related to the "thickness" of the membrane on which all the curvature is localized.Comment: 22 page

Polynomial mechanics and optimal control

We describe a new algorithm for trajectory optimization of mechanical systems. Our method combines pseudo-spectral methods for function approximation with variational discretization schemes that exactly preserve conserved mechanical quantities such as momentum. We thus obtain a global discretization of the Lagrange-d'Alembert variational principle using pseudo-spectral methods. Our proposed scheme inherits the numerical convergence characteristics of spectral methods, yet preserves momentum-conservation and symplecticity after discretization. We compare this algorithm against two other established methods for two examples of underactuated mechanical systems; minimum-effort swing-up of a two-link and a three-link acrobot.Comment: Final version to EC

Optimal strategies for throwing accurately

Accuracy of throwing in games and sports is governed by how errors at projectile release are propagated by flight dynamics. To address the question of what governs the choice of throwing strategy, we use a simple model of throwing with an arm modelled as a hinged bar of fixed length that can release a projectile at any angle and angular velocity. We show that the amplification of deviations in launch parameters from a one parameter family of solution curves is quantified by the largest singular value of an appropriate Jacobian. This allows us to predict a preferred throwing style in terms of this singular value, which itself depends on target location and the target shape. Our analysis also allows us to characterize the trade-off between speed and accuracy despite not including any effects of signal-dependent noise. Using nonlinear calculations for propagating finite input-noise, we find that an underarm throw to a target leads to an undershoot, but an overarm throw does not. Finally, we consider the limit of the arm-length vanishing, i.e. shooting a projectile, and find that the most accurate shooting angle bifurcates as the ratio of the relative noisiness of the initial conditions crosses a threshold.Comment: 18 pages, 8 figure

A Temperature and Abundance Retrieval Method for Exoplanet Atmospheres

We present a new method to retrieve molecular abundances and temperature profiles from exoplanet atmosphere photometry and spectroscopy. We run millions of 1D atmosphere models in order to cover the large range of allowed parameter space, and present error contours in the atmospheric properties, given the data. In order to run such a large number of models, we have developed a parametric pressure-temperature (P-T) profile coupled with line-by-line radiative transfer, hydrostatic equilibrium, and energy balance, along with prescriptions for non-equilibrium molecular composition and energy redistribution. We apply our temperature and abundance retrieval method to the atmospheres of two transiting exoplanets, HD 189733b and HD 209458b, which have the best available Spitzer and HST observations. For HD 189733b, we find efficient day-night redistribution of energy in the atmosphere, and molecular abundance constraints confirming the presence of H2O, CO, CH4, and CO2. For HD 209458b, we confirm and constrain the day-side thermal inversion in an average 1D temperature profile. We also report independent detections of H$_2$O, CO, CH$_4$ and CO$_2$ on the dayside of HD 209458b, based on six-channel Spitzer photometry. We report constraints for HD 189733b due to individual data sets separately; a few key observations are variable in different data sets at similar wavelengths. Moreover, a noticeably strong carbon dioxide absorption in one data set is significantly weaker in another. We must, therefore, acknowledge the strong possibility that the atmosphere is variable, both in its energy redistribution state and in the chemical abundances.Comment: 20 pages in emulateapj format, 11 figures. Final version, after proof correction

Tromino: Demand and DRF Aware Multi-Tenant Queue Manager for Apache Mesos Cluster

Apache Mesos, a two-level resource scheduler, provides resource sharing across multiple users in a multi-tenant cluster environment. Computational resources (i.e., CPU, memory, disk, etc. ) are distributed according to the Dominant Resource Fairness (DRF) policy. Mesos frameworks (users) receive resources based on their current usage and are responsible for scheduling their tasks within the allocation. We have observed that multiple frameworks can cause fairness imbalance in a multiuser environment. For example, a greedy framework consuming more than its fair share of resources can deny resource fairness to others. The user with the least Dominant Share is considered first by the DRF module to get its resource allocation. However, the default DRF implementation, in Apache Mesos' Master allocation module, does not consider the overall resource demands of the tasks in the queue for each user/framework. This lack of awareness can result in users without any pending task receiving more resource offers while users with a queue of pending tasks starve due to their high dominant shares. We have developed a policy-driven queue manager, Tromino, for an Apache Mesos cluster where tasks for individual frameworks can be scheduled based on each framework's overall resource demands and current resource consumption. Dominant Share and demand awareness of Tromino and scheduling based on these attributes can reduce (1) the impact of unfairness due to a framework specific configuration, and (2) unfair waiting time due to higher resource demand in a pending task queue. In the best case, Tromino can significantly reduce the average waiting time of a framework by using the proposed Demand-DRF aware policy

Exploring the Fairness and Resource Distribution in an Apache Mesos Environment

Apache Mesos, a cluster-wide resource manager, is widely deployed in massive scale at several Clouds and Data Centers. Mesos aims to provide high cluster utilization via fine grained resource co-scheduling and resource fairness among multiple users through Dominant Resource Fairness (DRF) based allocation. DRF takes into account different resource types (CPU, Memory, Disk I/O) requested by each application and determines the share of each cluster resource that could be allocated to the applications. Mesos has adopted a two-level scheduling policy: (1) DRF to allocate resources to competing frameworks and (2) task level scheduling by each framework for the resources allocated during the previous step. We have conducted experiments in a local Mesos cluster when used with frameworks such as Apache Aurora, Marathon, and our own framework Scylla, to study resource fairness and cluster utilization. Experimental results show how informed decision regarding second level scheduling policy of frameworks and attributes like offer holding period, offer refusal cycle and task arrival rate can reduce unfair resource distribution. Bin-Packing scheduling policy on Scylla with Marathon can reduce unfair allocation from 38\% to 3\%. By reducing unused free resources in offers we bring down the unfairness from to 90\% to 28\%. We also show the effect of task arrival rate to reduce the unfairness from 23\% to 7\%