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Understanding the dynamics of a methane bubble in a liquid metal bubble column reactor is important for optimizing the reactor design and improving efficiency. To better understand methane bubble dynamics and the reaction to produce hydrogen, we employ ANSYS Fluent to investigate the gas-liquid interface, to relate the surface area where reaction occurs to bubble size, and to determine coalescing behavior as a function of dimensionless numbers. Once the simulation is verified by comparing bubble velocity [1], shape [2], and coalescing distance [3] for a water-air system, a methane bubble in liquid bismuth at 1000 k is examined [4] [5]. Experimentally obtained kinetic parameters for the reaction are used in the computations. The bubble interfacial area to volume ratio is maximized at a diameter of 4mm and does not induce breakage of the bubble. The coalescing distance for two bubbles of methane in bismuth is a third of the distance for air in water bubbles. REFERENCES 1. S. Baz-Rodríguez, A. Aguilar-Corona, and A. Soria, Rev. Mex. Ing. Quím. 8, 213 (2009). 2. R. Clift, J. R. Grace, and M. E. Weber, Bubbles, Drops, and Particles (Academic Press, New York, 1978). 3. T. Otake, S. Tone, K. Nakao, and Y. Mitsuhashi, Chem. Eng. Sci. 32, 377 (1977). 4. M. J. Assael, K. Gialou, K. Kakosimos, and I. Metaxa, High Temp. High Press. 41, 101 (2012). 5. Engineering ToolBox (2004), https://www.engineeringtoolbox.com/methane-d_1420.html. Funding acknowledgement The support of the US National Science Foundation under grant number 2317726 is gratefully acknowledged. 

In today’s era of big data, robust least-squares regression becomes a more challenging problem when considering the extremely corrupted labels along with explosive growth of datasets. Traditional robust methods can handle the noise but suffer from several challenges when applied in huge dataset including (1) computational infeasibility of handling an entire dataset at once, (2) existence of heterogeneously distributed corruption, and (3) difficulty in corruption estimation when data cannot be entirely loaded. This article proposes online and distributed robust regression approaches, both of which can concurrently address all the above challenges. Specifically, the distributed algorithm optimizes the regression coefficients of each data block via heuristic hard thresholding and combines all the estimates in a distributed robust consolidation. In addition, an online version of the distributed algorithm is proposed to incrementally update the existing estimates with new incoming data. Furthermore, a novel online robust regression method is proposed to estimate under a biased-batch corruption. We also prove that our algorithms benefit from strong robustness guarantees in terms of regression coefficient recovery with a constant upper bound on the error of state-of-the-art batch methods. Extensive experiments on synthetic and real datasets demonstrate that our approaches are superior to those of existing methods in effectiveness, with competitive efficiency.