The Removal of Numerical Drift from Scientific Models

Computer programs often behave differently under different compilers or in different computing environments. Relative debugging is a collection of techniques by which these differences are analysed. Differences may arise because of different interpretations of errors in the code, because of bugs in the compilers or because of numerical drift, and all of these were observed in the present study. Numerical drift arises when small and acceptable differences in values computed by different systems are integrated, so that the results drift apart. This is well understood and need not degrade the validity of the program results. Coding errors and compiler bugs may degrade the results and should be removed. This paper describes a technique for the comparison of two program runs which removes numerical drift and therefore exposes coding and compiler errors. The procedure is highly automated and requires very little intervention by the user. The technique is applied to the Weather Research and Forecasting model, the most widely used weather and climate modelling code.Comment: 12 page

Improving Aircraft Engines Prognostics and Health Management via Anticipated Model-Based Validation of Health Indicators

The aircraft engines manufacturing industry is subjected to many dependability constraints from certification authorities and economic background. In particular, the costs induced by unscheduled maintenance and delays and cancellations impose to ensure a minimum level of availability. For this purpose, Prognostics and Health Management (PHM) is used as a means to perform online periodic assessment of the engines’ health status. The whole PHM methodology is based on the processing of some variables reflecting the system’s health status named Health Indicators. The collecting of HI is an on-board embedded task which has to be specified before the entry into service for matters of retrofit costs. However, the current development methodology of PHM systems is considered as a marginal task in the industry and it is observed that most of the time, the set of HI is defined too late and only in a qualitative way. In this paper, the authors propose a novel development methodology for PHM systems centered on an anticipated model-based validation of HI. This validation is based on the use of uncertainties propagation to simulate the distributions of HI including the randomness of parameters. The paper defines also some performance metrics and criteria for the validation of the HI set. Eventually, the methodology is applied to the development of a PHM solution for an aircraft engine actuation loop. It reveals a lack of performance of the original set of HI and allows defining new ones in order to meet the specifications before the entry into service

Maximum Likelihood Estimation for Single Particle, Passive Microrheology Data with Drift

Volume limitations and low yield thresholds of biological fluids have led to widespread use of passive microparticle rheology. The mean-squared-displacement (MSD) statistics of bead position time series (bead paths) are either applied directly to determine the creep compliance [Xu et al (1998)] or transformed to determine dynamic storage and loss moduli [Mason & Weitz (1995)]. A prevalent hurdle arises when there is a non-diffusive experimental drift in the data. Commensurate with the magnitude of drift relative to diffusive mobility, quantified by a P\'eclet number, the MSD statistics are distorted, and thus the path data must be "corrected" for drift. The standard approach is to estimate and subtract the drift from particle paths, and then calculate MSD statistics. We present an alternative, parametric approach using maximum likelihood estimation that simultaneously fits drift and diffusive model parameters from the path data; the MSD statistics (and consequently the compliance and dynamic moduli) then follow directly from the best-fit model. We illustrate and compare both methods on simulated path data over a range of P\'eclet numbers, where exact answers are known. We choose fractional Brownian motion as the numerical model because it affords tunable, sub-diffusive MSD statistics consistent with typical 30 second long, experimental observations of microbeads in several biological fluids. Finally, we apply and compare both methods on data from human bronchial epithelial cell culture mucus.Comment: 29 pages, 12 figure

How to form planetesimals from mm-sized chondrules and chondrule aggregates

The size distribution of asteroids and Kuiper belt objects in the solar system is difficult to reconcile with a bottom-up formation scenario due to the observed scarcity of objects smaller than $\sim$100 km in size. Instead, planetesimals appear to form top-down, with large $100-1000$ km bodies forming from the rapid gravitational collapse of dense clumps of small solid particles. In this paper we investigate the conditions under which solid particles can form dense clumps in a protoplanetary disk. We use a hydrodynamic code to model the interaction between solid particles and the gas inside a shearing box inside the disk, considering particle sizes from sub-millimeter-sized chondrules to meter-sized rocks. We find that particles down to millimeter sizes can form dense particle clouds through the run-away convergence of radial drift known as the streaming instability. We make a map of the range of conditions (strength of turbulence, particle mass-loading, disk mass, and distance to the star) which are prone to producing dense particle clumps. Finally, we estimate the distribution of collision speeds between mm-sized particles. We calculate the rate of sticking collisions and obtain a robust upper limit on the particle growth timescale of $\sim$$10^5$ years. This means that mm-sized chondrule aggregates can grow on a timescale much smaller than the disk accretion timescale ($\sim$$10^6 - 10^7$ years). Our results suggest a pathway from the mm-sized grains found in primitive meteorites to fully formed asteroids. We speculate that asteroids may form from a positive feedback loop in which coagualation leads to particle clumping driven by the streaming instability. This clumping, in turn reduces collision speeds and enhances coagulation.} Future simulations should model coagulation and the streaming instability together to explore this feedback loop further.Comment: 20 pages. Accepted for publication in A&

What Next-Generation 21 cm Power Spectrum Measurements Can Teach Us About the Epoch of Reionization

A number of experiments are currently working towards a measurement of the 21 cm signal from the Epoch of Reionization. Whether or not these experiments deliver a detection of cosmological emission, their limited sensitivity will prevent them from providing detailed information about the astrophysics of reionization. In this work, we consider what types of measurements will be enabled by a next-generation of larger 21 cm EoR telescopes. To calculate the type of constraints that will be possible with such arrays, we use simple models for the instrument, foreground emission, and the reionization history. We focus primarily on an instrument modeled after the $\sim 0.1~\rm{km}^2$ collecting area Hydrogen Epoch of Reionization Array (HERA) concept design, and parameterize the uncertainties with regard to foreground emission by considering different limits to the recently described "wedge" footprint in k-space. Uncertainties in the reionization history are accounted for using a series of simulations which vary the ionizing efficiency and minimum virial temperature of the galaxies responsible for reionization, as well as the mean free path of ionizing photons through the IGM. Given various combinations of models, we consider the significance of the possible power spectrum detections, the ability to trace the power spectrum evolution versus redshift, the detectability of salient power spectrum features, and the achievable level of quantitative constraints on astrophysical parameters. Ultimately, we find that $0.1~\rm{km}^2$ of collecting area is enough to ensure a very high significance ($\gtrsim30\sigma$) detection of the reionization power spectrum in even the most pessimistic scenarios. This sensitivity should allow for meaningful constraints on the reionization history and astrophysical parameters, especially if foreground subtraction techniques can be improved and successfully implemented.Comment: 27 pages, 18 figures, updated SKA numbers in appendi

The physical oceanography of the transport of floating marine debris

Marine plastic debris floating on the ocean surface is a major environmental problem. However, its distribution in the ocean is poorly mapped, and most of the plastic waste estimated to have entered the ocean from land is unaccounted for. Better understanding of how plastic debris is transported from coastal and marine sources is crucial to quantify and close the global inventory of marine plastics, which in turn represents critical information for mitigation or policy strategies. At the same time, plastic is a unique tracer that provides an opportunity to learn more about the physics and dynamics of our ocean across multiple scales, from the Ekman convergence in basin-scale gyres to individual waves in the surfzone. In this review, we comprehensively discuss what is known about the different processes that govern the transport of floating marine plastic debris in both the open ocean and the coastal zones, based on the published literature and referring to insights from neighbouring fields such as oil spill dispersion, marine safety recovery, plankton connectivity, and others. We discuss how measurements of marine plastics (both in situ and in the laboratory), remote sensing, and numerical simulations can elucidate these processes and their interactions across spatio-temporal scales

Impact of Numerical Relativity information on effective-one-body waveform models

We present a comprehensive comparison of the spin-aligned effective-one-body (EOB) waveform model of Nagar et al. [Phys. Rev. D93, 044046 (2016)], informed using 40 numerical-relativity (NR) datasets, against a set of 149, $\ell=m=2$, NR waveforms freely available through the Simulation Extreme Spacetime (SXS) catalog. We find that, without further calibration, these EOBNR waveforms have unfaithfulness (at design Advanced-LIGO sensitivity and evaluated with total mass $M$ varying as $10M_\odot\leq M \leq 200M_\odot$) always below $1\%$ against all NR waveforms except for three outliers, that still never exceed the $3\%$ level; with a minimal retuning of the (effective) next-to-next-to-next-to-leading-order spin-orbit coupling parameter for the non-equal-mass and non-equal-spin sector, that only needs three more NR waveforms, one is left with another two (though different) outliers, with maximal unfaithfulness of up to only $2\%$ for a total mass of $200M_\odot$. We show this is the effect of slight inaccuracies in the phenomenological description of the postmerger waveform of Del Pozzo and Nagar [arXiv:1606.03952] that was constructed by interpolating over only 40NR simulations. We argue that this is easily fixed by using either an alternative ringdown description (e.g., the superposition of quasi-normal-modes) or an improved version of the phenomenological representation. By analyzing a NR waveform with mass ratio $8$ and dimensionless spins $+0.85$ obtained with the BAM code, we conclude that the model would benefit from NR simulations specifically targeted at improving the postmerger-ringdown phenomenological fits for mass ratios $\gtrsim 8$ and spins $\gtrsim 0.8$.Comment: 24 pages, 20 figures, submitted to Phys. Rev.

Dust outflows and inner gaps generated by massive planets in debris disks

Main sequence stars are commonly surrounded by debris disks, formed by cold far-IR-emitting dust that is thought to be continuously replenished by a reservoir of undetected dust-producing planetesimals. We have investigated the orbital evolution of dust particles in debris disks harboring massive planets. Small dust grains are blown out by radiation pressure, as is well known; in addition, gravitational scattering by the giant planets also creates an outflow of large grains. We describe the characteristics of this large-particle outflow in different planetary architectures and for different particle sizes. In addition, the ejection of particles is responsible for the clearing of dust inside the orbit of the planet. We study the efficiency of particle ejection and the resulting dust density contrast inside and outside the orbit of the planet, as a function of the planet's mass and orbital elements and the particle size. We discuss its implications for exo-planetary debris disks and for the interpretation of in-situ dust detection experiments on space probes traveling in the outer solar system.Comment: 32 pages (pre-print format), including 12 figures. Accepted to ApJ (2005). Due to space constrains Fig. 3-6 are at very low resolutio