Discovering an active subspace in a single-diode solar cell model

Predictions from science and engineering models depend on the values of the model's input parameters. As the number of parameters increases, algorithmic parameter studies like optimization or uncertainty quantification require many more model evaluations. One way to combat this curse of dimensionality is to seek an alternative parameterization with fewer variables that produces comparable predictions. The active subspace is a low-dimensional linear subspace defined by important directions in the model's input space; input perturbations along these directions change the model's prediction more, on average, than perturbations orthogonal to the important directions. We describe a method for checking if a model admits an exploitable active subspace, and we apply this method to a single-diode solar cell model with five input parameters. We find that the maximum power of the solar cell has a dominant one-dimensional active subspace, which enables us to perform thorough parameter studies in one dimension instead of five

Where post-Newtonian and numerical-relativity waveforms meet

We analyze numerical-relativity (NR) waveforms that cover nine orbits (18 gravitational-wave cycles) before merger of an equal-mass system with low eccentricity, with numerical uncertainties of 0.25 radians in the phase and less than 2% in the amplitude; such accuracy allows a direct comparison with post-Newtonian (PN) waveforms. We focus on one of the PN approximants that has been proposed for use in gravitational-wave data analysis, the restricted 3.5PN ``TaylorT1'' waveforms, and compare these with a section of the numerical waveform from the second to the eighth orbit, which is about one and a half orbits before merger. This corresponds to a gravitational-wave frequency range of $M\omega = 0.0455$ to 0.1. Depending on the method of matching PN and NR waveforms, the accumulated phase disagreement over this frequency range can be within numerical uncertainty. Similar results are found in comparisons with an alternative PN approximant, 3PN ``TaylorT3''. The amplitude disagreement, on the other hand, is around 6%, but roughly constant for all 13 cycles that are compared, suggesting that only 4.5 orbits need be simulated to match PN and NR waves with the same accuracy as is possible with nine orbits. If, however, we model the amplitude up to 2.5PN order, the amplitude disagreement is roughly within numerical uncertainty up to about 11 cycles before merger.Comment: 14 pages, 18 figures. Modifications resulting from bug fixes in LAL, and extended analysis of numerical errors and phase agreement with PN, now including the 3PN TaylorT3 approximant. No change to main conclusion

Stock Market Simulation

During this project the group performed a ten-week stock market simulation in which they experimented with different investing strategies to learn how to navigate the stock market. They researched six different investing and trading methods in order to better understand investing. The experience gained from this project will help them become better investors in the future and help them manage their personal finances wisely

Accretion onto a Supermassive Black Hole Binary Before Merger

While supermassive binary black holes (SMBBHs) inspiral toward merger they may also accrete significant amounts of matter. To study the dynamics of such a system requires simultaneously describing the evolving spacetime and the dynamics of magnetized plasma. Here we present the first relativistic calculation simulating two equal-mass, non-spinning black holes as they inspiral from an initial separation of $20M$ ($G=c=1$) almost to merger, $\simeq 9M$, while accreting gas from a surrounding disk, where $M$ is the total binary mass. We find that the accretion rate $\dot M$ onto the black holes first decreases during this period and then reaches a plateau, dropping by only a factor of $\sim 3$ despite its rapid inspiral. An estimated bolometric light curve follows the same profile. The minidisks through which the accretion reaches the black holes are very non-standard. Reynolds, not Maxwell, stresses dominate, and they oscillate between two distinct structural states. In one part of the cycle, ``sloshing" streams transfer mass from one minidisk to the other through the L1 point at a rate $\sim 0.1\times$ the accretion rate, carrying kinetic energy at a rate that can be as large as the peak minidisk bolometric luminosity. We also discover that the minidisks have time-varying tilts with respect to the orbital plane similar in magnitude to the circumbinary disk's aspect ratio. The unsigned poloidal flux on the black hole event horizon is roughly constant at a dimensionless level $\phi\sim 2-3$, but doubles just before merger; if the black holes had significant spin, this flux could support jets whose power could approach the radiated luminosity. This simulation is the first to employ our multipatch infrastructure \pwmhd, decreasing computational expense per physical time to $\sim 3\%$ of similar runs using conventional single-grid methods.Comment: Comments welcom

Modeling the source of GW150914 with targeted numerical-relativity simulations

In fall of 2015, the two LIGO detectors measured the gravitational wave signal GW150914, which originated from a pair of merging black holes. In the final 0.2 seconds (about 8 gravitational-wave cycles) before the amplitude reached its maximum, the observed signal swept up in amplitude and frequency, from 35 Hz to 150 Hz. The theoretical gravitational-wave signal for merging black holes, as predicted by general relativity, can be computed only by full numerical relativity, because analytic approximations fail near the time of merger. Moreover, the nearly-equal masses, moderate spins, and small number of orbits of GW150914 are especially straightforward and efficient to simulate with modern numerical-relativity codes. In this paper, we report the modeling of GW150914 with numerical-relativity simulations, using black-hole masses and spins consistent with those inferred from LIGO's measurement. In particular, we employ two independent numerical-relativity codes that use completely different analytical and numerical methods to model the same merging black holes and to compute the emitted gravitational waveform; we find excellent agreement between the waveforms produced by the two independent codes. These results demonstrate the validity, impact, and potential of current and future studies using rapid-response, targeted numerical-relativity simulations for better understanding gravitational-wave observations.Comment: 11 pages, 3 figures, submitted to Classical and Quantum Gravit

Can Cosmic Parallax Distinguish Between Anisotropic Cosmologies?

In an anisotropic universe, observers not positioned at a point of special symmetry should observe cosmic parallax - the relative angular motion of test galaxies over cosmic time. It was recently argued that the non-observance of this effect in upcoming precision astrometry missions such as Gaia may be used to place strong bounds on the position of off-center observers in a void-model universe described by the Lemaitre-Tolman-Bondi metric. We consider the analogous effect in anisotropic cosmological models described by an axisymmetric homogeneous Bianchi type I metric and discuss whether any observation of cosmic parallax would distinguish between different anisotropic evolutions.Comment: 24 pages, 6 figure