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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)

   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.
2. 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)
3. Testing Novel New Drip Emitter with Variable Diameters for a Variable Rate Drip Irrigation

   https://doi.org/10.3390/agriculture11020087  

   AL-agele, Hadi A. ; Nackley, Lloyd ; Higgins, Chad ( February 2021 , Agriculture)

   This research presents a new variable rate drip irrigation (VRDI) emitter design that can monitor individual water drops. Conventional drip systems cannot monitor the individual water flow rate per emitter. Application uniformity for conventional drip emitters can be decreased by clogged emitters, irregular emitter orifices, and decreases in pressure. A VRDI emitter can overcome the irrigation challenges in the field by increasing water application uniformity for each plant and reducing water losses. Flow rate is affected by the diameter of the delivery pipe and the pressure of the irrigation delivery system. This study compares the volumetric water flow rate for conventional drip emitters and new VRDI emitters with variable diameters inner (1 mm, 1.2 mm, 1.4 mm, and 1.6 mm) and outside (3 mm, 3.5 mm, 4 mm, and 4.5 mm) with three pressures (34 kPa, 69 kPa, and 103 kPa). The tests revealed that the new VRDI emitter had flow rates that increased as the operating pressure increased similar to a conventional drip tube. The flow rate was slightly increased in the VRDI with pressure, but even this increase did not show large changes in the flow rate. The flow rate of the conventional drip tube was 88% largermore »than the VRDI emitter for all pressures (p < 0.05). However, operating pressure did not affect the drop sizes at the VRDI emitter, but the generalized linear mixed models (GLM) results show that volume per drop was impacted by the outside diameter of the VRDI outlet (p < 0.05). The interaction between the inner and outside diameter was also significant at p < 0.01, and the interaction between outside diameter and pressure was statistically significant at p < 0.01. The electronic components used to control our VRDI emitter are readily compatible with off-the-shelf data telemetry solutions; thus, each emitter could be controlled remotely and relay data to a centralized data repository or decision-maker, and a plurality of these emitters could be used to enable full-field scale VRDI.« less
4. 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)
5. V2V: A Deep Learning Approach to Variable-to-Variable Selection and Translation for Multivariate Time-Varying Data

   https://doi.org/10.1109/TVCG.2020.3030346  

   Han, Jun ; Zheng, Hao ; Xing, Yunhao ; Chen, Danny Z. ; Wang, Chaoli ( February 2021 , IEEE Transactions on Visualization and Computer Graphics)