An accretion-jet model for M87: interpreting the spectral energy distribution and Faraday rotation measure

M87 is arguably the best supermassive black hole (BH) to explore the jet and/or accretion physics due to its proximity and fruitful high-resolution multi-waveband observations. We model the multi-wavelength spectral energy distribution (SED) of M87 core that observed at a scale of 0.4 arcsec ($\sim 10^5R_{\rm g}$, $R_{\rm g}$ is gravitational radius) as recently presented by Prieto et al. Similar to Sgr A*, we find that the millimeter bump as observed by Atacama Large Millimeter/submillimeter Array (ALMA) can be modeled by the synchrotron emission of the thermal electrons in advection dominated accretion flow (ADAF), while the low-frequency radio emission and X-ray emission may dominantly come from the jet. The millimeter radiation from ADAF dominantly come from the region within $10R_{\rm g}$, which is roughly consistent with the recent very long baseline interferometry observations at 230\,GHz. We further calculate the Faraday rotation measure (RM) from both ADAF and jet models, and find that the RM predicted from the ADAF is roughly consistent with the measured value while the RM predicted from the jet is much higher if jet velocity close to the BH is low or moderate (e.g., $v_{\rm jet}\lesssim0.6\,c$). With the constraints from the SED modeling and RM, we find that the accretion rate close to the BH horizon is $\sim (0.2-1)\times10^{-3}{M}_{\odot} \rm yr^{-1}\ll\dot{\it M}_{\rm B}\sim 0.2\it {M}_{\odot} \rm yr^{-1}$ ($\dot{M}_{\rm B}$ is Bondi accretion rate), where the electron density profile, $n_{\rm e}\propto r^{\sim -1}$, in the accretion flow is consistent with that determined from X-ray observation inside the Bondi radius and recent numerical simulations.Comment: 8 pages, 3 figures, accepted for publication in Ap

On the Generalization Effects of Linear Transformations in Data Augmentation

Data augmentation is a powerful technique to improve performance in applications such as image and text classification tasks. Yet, there is little rigorous understanding of why and how various augmentations work. In this work, we consider a family of linear transformations and study their effects on the ridge estimator in an over-parametrized linear regression setting. First, we show that transformations which preserve the labels of the data can improve estimation by enlarging the span of the training data. Second, we show that transformations which mix data can improve estimation by playing a regularization effect. Finally, we validate our theoretical insights on MNIST. Based on the insights, we propose an augmentation scheme that searches over the space of transformations by how uncertain the model is about the transformed data. We validate our proposed scheme on image and text datasets. For example, our method outperforms RandAugment by 1.24% on CIFAR-100 using Wide-ResNet-28-10. Furthermore, we achieve comparable accuracy to the SoTA Adversarial AutoAugment on CIFAR datasets.Comment: International Conference on Machine learning (ICML) 2020. Added experimental results on ImageNe

The Ductile-Brittle Fracture Transition: A Comparison of Macro and Microscopic Observation on Compact Tension Specimens

Rapid development of failure analysis has brought increased attention to the concept of fracture toughness in recent years. The existing criteria for valid plane strain fracture toughness testing based on a macroscopic view have been shown to be conservative in some cases, and for other cases to be of questionable validity. Compact tension specimens of variable thickness were fabricated from annealed 01 tool steel between 0.125 inch and 1.00 inch. Load-COD data and gross plastic flow measurements are compared to scanning electron microscopy (SEM) fracture surface analysis in order to correlate macroscopic observations of the ductile-brittle transition on a macroscopic scale with microscopic data permit the validity of macroscopic criteria for plane strain fracture toughness to be examined. Criteria examined include criteria based on continuum mechanics, shape of the load-crack opening displacement curve, plan view plastic zone size (PZS) and percent slant fracture. Data indicate, for example, that PZS criteria need not be met in order to obtain totally brittle fracture on a microscopic scale, so that this criterion is conservative. Alternatively plane strain fracture toughness does decrease as the percent flat fracture approaches 100 percent, but SEM data indicate that 100 percent macroscopic flat fracture does not correspond to 100 percent microscopic brittle fracture at the minimum thickness required to obtain 100 percent macroscopic flat fracture. This implies that a larger thickness is required than is indicated by macroscopic appearance and that larger thickness must be utilized to obtain a valid plane strain fracture toughness