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1. Inverting the variable fractional order in a variable-order space-fractional diffusion equation with variable diffusivity: analysis and simulation

   https://doi.org/10.1515/jiip-2019-0040  

   Zheng, Xiangcheng ; Li, Yiqun ; Cheng, Jin ; Wang, Hong ( April 2021 , Journal of Inverse and Ill-posed Problems)

   null (Ed.)

   Abstract Variable-order space-fractional diffusion equations provide very competitive modeling capabilities of challenging phenomena, including anomalously superdiffusive transport of solutes in heterogeneous porous media, long-range spatial interactions and other applications, as well as eliminating the nonphysical boundary layers of the solutions to their constant-order analogues.In this paper, we prove the uniqueness of determining the variable fractional order of the homogeneous Dirichlet boundary-value problem of the one-sided linear variable-order space-fractional diffusion equation with some observed values of the unknown solutions near the boundary of the spatial domain.We base on the analysis to develop a spectral-Galerkin Levenberg–Marquardt method and a finite difference Levenberg–Marquardt method to numerically invert the variable order.We carry out numerical experiments to investigate the numerical performance of these methods. 

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2. Enhanced Variable Stiffness and Variable Stretchability Enabled by Phase‐Changing Particulate Additives

   https://doi.org/10.1002/adfm.201903368  

   Buckner, Trevor L. ; Yuen, Michelle C. ; Kim, Sang Yup ; Kramer‐Bottiglio, Rebecca ( October 2019 , Advanced Functional Materials)
3. The ASAS-SN catalogue of variable stars IX: The spectroscopic properties of Galactic variable stars

   https://doi.org/10.1093/mnras/stab114  

   Jayasinghe, T ; Kochanek, C S ; Stanek, K Z ; Shappee, B J ; Holoien, T W-S ; Thompson, Todd A ; Prieto, J L ; Dong, Subo ; Pawlak, M ; Pejcha, O ; et al ( March 2021 , Monthly Notices of the Royal Astronomical Society)

   null (Ed.)

   ABSTRACT The All-Sky Automated Survey for Supernovae provides long baseline (∼4 yr) V-band light curves for sources brighter than V≲ 17 mag across the whole sky. We produced V-band light curves for a total of ∼61.5 million sources and systematically searched these sources for variability. We identified ∼426 000 variables, including ∼219 000 new discoveries. Most (${\sim }74{ per\ cent}$) of our discoveries are in the Southern hemisphere. Here, we use spectroscopic information from LAMOST, GALAH, RAVE, and APOGEE to study the physical and chemical properties of these variables. We find that metal-poor eclipsing binaries have orbital periods that are shorter than metal-rich systems at fixed temperature. We identified rotational variables on the main-sequence, red giant branch, and the red clump. A substantial fraction (${\gtrsim }80{ per\ cent}$) of the rotating giants have large $v$rot or large near-ultraviolet excesses also indicative of fast rotation. The rotational variables have unusual abundances suggestive of analysis problems. Semiregular variables tend to be lower metallicity ($\rm [Fe/H]{\sim }-0.5$) than most giant stars. We find that the APOGEE DR16 temperatures of oxygen-rich semiregular variables are strongly correlated with the WRP − WJK colour index for $\rm T_{eff}\lesssim 3800$ K. Using abundance measurements from APOGEE DR16, we find evidence for Mg and N enrichment in the semiregular variables. We find that the Aluminum abundances of the semiregular variables are strongly correlated with the pulsation period, where the variables with $\rm P\gtrsim 60$ d are significantly depleted in Al. 

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4. A Novel Variable Stiffness Compliant Robotic Link Based on Discrete Variable Stiffness Units for Safe Human–Robot Interaction

   https://doi.org/10.1115/1.4056957  

   Fu, Jiaming ; Yu, Ziqing ; Lin, Han ; Zheng, Lianxi ; Gan, Dongming ( January 2024 , Journal of Mechanisms and Robotics)

   Abstract Variable stiffness manipulators balance the trade-off between manipulation performance needing high stiffness and safe human–robot interaction desiring low stiffness. Variable stiffness links enable this flexible manipulation function during human–robot interaction. In this paper, we propose a novel variable stiffness link based on discrete variable stiffness units (DSUs). A DSU is a parallel guided beam that can adjust stiffness discretely by changing the cross-sectional area properties of the hollow beam segments. The variable stiffness link (Tri-DSU) consists of three tandem DSUs to achieve eight stiffness modes and a stiffness ratio of 31. To optimize the design, stiffness analysis of the DSU and Tri-DSU under various configurations and forces was performed by a derived linear analytical model which applies to small/intermediate deflections. The model is derived using the approach of serially connected beams and superposition combinations. 3D-Printed prototypes were built to verify the feature and performance of the Tri-DSU in comparison with the finite element analysis and analytical model results. It’s demonstrated that our model can accurately predict the stiffnesses of the DSU and Tri-DSU within a certain range of parameters. Impact tests were also conducted to validate the performance of the Tri-DSU. The developed method and analytical model are extendable to multiple DSUs with parameter configurations to achieve modularization and customization, and also provide a tool for the design of reconfigurable collaborative robot (cobot) manipulators. 

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5. Variable phosphorus uptake rates and allocation across microbial groups in the oligotrophic Gulf of Mexico: Variable microbial phosphorus uptake rate and allocation

   https://doi.org/10.1111/1462-2920.12932  

   Popendorf, Kimberly J. ; Duhamel, Solange ( October 2015 , Environmental Microbiology)