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1. C*-algebras of a Cantor system with finitely many minimal subsets: structures, K-theories, and the index map

   https://doi.org/10.1017/etds.2020.12  

   BEZUGLYI, SERGEY ; NIU, ZHUANG ; SUN, WEI ( May 2021 , Ergodic Theory and Dynamical Systems)

   We study homeomorphisms of a Cantor set with$k$($k<+\infty$) minimal invariant closed (but not open) subsets; we also study crossed product C*-algebras associated to these Cantor systems and certain of their orbit-cut sub-C*-algebras. In the case where$k\geq 2$, the crossed product C*-algebra is stably finite, has stable rank 2, and has real rank 0 if in addition$(X,\unicode[STIX]{x1D70E})$is aperiodic. The image of the index map is connected to certain directed graphs arising from the Bratteli–Vershik–Kakutani model of the Cantor system. Using this, it is shown that the ideal of the Bratteli diagram (of the Bratteli–Vershik–Kakutani model) must have at least$k$vertices at each level, and the image of the index map must consist of infinitesimals.

    

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2. Understanding PDF uncertainty in W boson mass measurements*

   https://doi.org/10.1088/1674-1137/ac930b  

   Gao, Jun ; Liu, Dianyu ; Xie, Keping ( December 2022 , Chinese Physics C)

   We study the dependence of the transverse mass distribution of charged leptons and the missing energy on parton distributions (PDFs) adapted toWboson mass measurements at the CDF and ATLAS experiments. We compare the shape variations of the distribution induced by different PDFs and find that the spread of predictions from different PDF sets can be significantly larger than the PDF uncertainty predicted by a specific PDF set. We suggest analyzing the experimental data using up-to-date PDFs to gain a better understanding of the PDF uncertainties inWboson mass measurements. We also perform a series of Lagrange multiplier scans to identify the constraints on the transverse mass distribution imposed by individual data sets in the CT18 global analysis. In the case of the CDF measurement, the distribution is mostly sensitive tod-quark PDFs in the intermediatexregion, which are largely constrained by DIS and Drell-Yan data on deuteron targets and Tevatron lepton charge asymmetry data.

    

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3. DESCRIPTIVE COMPLEXITY IN CANTOR SERIES

   https://doi.org/10.1017/jsl.2021.77  

   AIREY, DYLAN ; JACKSON, STEVE ; MANCE, BILL ( September 2022 , The Journal of Symbolic Logic)

   Abstract A Cantor series expansion for a real number x with respect to a basic sequence $Q=(q_1,q_2,\dots )$ , where $q_i \geq 2$ , is a generalization of the base b expansion to an infinite sequence of bases. Ki and Linton in 1994 showed that for ordinary base b expansions the set of normal numbers is a $\boldsymbol {\Pi }^0_3$ -complete set, establishing the exact complexity of this set. In the case of Cantor series there are three natural notions of normality: normality, ratio normality, and distribution normality. These notions are equivalent for base b expansions, but not for more general Cantor series expansions. We show that for any basic sequence the set of distribution normal numbers is $\boldsymbol {\Pi }^0_3$ -complete, and if Q is $1$ -divergent then the sets of normal and ratio normal numbers are $\boldsymbol {\Pi }^0_3$ -complete. We further show that all five non-trivial differences of these sets are $D_2(\boldsymbol {\Pi }^0_3)$ -complete if $\lim _i q_i=\infty $ and Q is $1$ -divergent. This shows that except for the trivial containment that every normal number is ratio normal, these three notions are as independent as possible. 

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4. Method of Distributions for Two‐Phase Flow in Heterogeneous Porous Media

   https://doi.org/10.1029/2022WR032607  

   Yang, Hyung Jun ; Tchelepi, Hamdi A. ; Tartakovsky, Daniel M. ( December 2022 , Water Resources Research)

   Multiscale heterogeneity and insufficient characterization data for a specific subsurface formation of interest render predictions of multi‐phase fluid flow in geologic formations highly uncertain. Quantification of the uncertainty propagation from the geomodel to the fluid‐flow response is typically done within a probabilistic framework. This task is computationally demanding due to, for example, the slow convergence of Monte Carlo simulations (MCS), especially when computing the tails of a distribution that are necessary for risk assessment and decision‐making under uncertainty. The frozen streamlines method (FROST) accelerates probabilistic predictions of immiscible two‐phase fluid flow problems; however, FROST relies on MCS to compute the travel‐time distribution, which is then used to perform the transport (phase saturation) computations. To alleviate this computational bottleneck, we replace MCS with a deterministic equation for the cumulative distribution function (CDF) of travel time. The resulting CDF‐FROST approach yields the CDF of the saturation field without resorting to sampling‐based strategies. Our numerical experiments demonstrate the high accuracy of CDF‐FROST in computing the CDFs of both saturation and travel time. For the same accuracy, it is about 5 and 10 times faster than FROST and MCS, respectively.

    

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5. High-throughput Alloy and Process Design for Metal Additive Manufacturing

   Sheikh, S. ; Vela, B. ; Honarmandi, P. ; Morcos, P. ; Shoukr, D. ; Abdelrahman, M. K. ; Karaman, I. ; Elwany, A. ; Arroyave, R. ( April 2023 , arXivorg)

   Designing alloys for additive manufacturing (AM) presents significant opportunities. Still, the chemical composition and processing conditions required for printability (ie., their suitability for fabrication via AM) are challenging to explore using solely experimental means. In this work, we develop a high-throughput (HTP) computational framework to guide the search for highly printable alloys and appropriate processing parameters. The framework uses material properties from stateof- the-art databases, processing parameters, and simulated melt pool profiles to predict processinduced defects, such as lack-of-fusion, keyholing, and balling. We accelerate the printability assessment using a deep learning surrogate for a thermal model, enabling a 1,000-fold acceleration in assessing the printability of a given alloy at no loss in accuracy when compared with conventional physics-based thermal models. We verify and validate the framework by constructing printability maps for the CoCrFeMnNi Cantor alloy system and comparing our predictions to an exhaustive ’in-house’ database. The framework enables the systematic investigation of the printability of a wide range of alloys in the broader Co-Cr-Fe-Mn-Ni HEA system. We identified the most promising alloys that were suitable for high-temperature applications and had the narrowest solidification ranges, and that was the least susceptible to balling, hot-cracking, and the formation of macroscopic printing defects. A new metric for the global printability of an alloy is constructed and is further used for the ranking of candidate alloys. The proposed framework is expected to be integrated into ICME approaches to accelerate the discovery and optimization of novel high-performance, printable alloys. 

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