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   https://doi.org/10.1016/j.mechatronics.2023.103073  

   Iqbal, Amir ; Veer, Sushant ; Gu, Yan ( December 2023 , Mechatronics)

   Sun, Weichao ; Yao, Bin (Ed.)

   This paper introduces an analytically tractable and computationally efficient model for legged robot dynamics during locomotion on a dynamic rigid surface (DRS), along with an approximate analytical solution and a real-time walking pattern generator synthesized based on the model and solution. By relaxing the static-surface assumption, we extend the classical, time-invariant linear inverted pendulum (LIP) model for legged locomotion on a static surface to dynamic-surface locomotion, resulting in a time-varying LIP model termed as “DRS-LIP”. Sufficient and necessary stability conditions of the time-varying DRS-LIP model are obtained based on the Floquet theory. This model is also transformed into Mathieu’s equation to derive an approximate analytical solution that provides reasonable accuracy with a relatively low computational cost. Using the extended model and its solution, a walking pattern generator is developed to efficiently plan physically feasible trajectories for quadrupedal walking on a vertically oscillating surface. Finally, simulations and hardware experiments from a Laikago quadrupedal robot walking on a pitching treadmill (with a maximum vertical acceleration of 1 m/s ) confirm the accuracy and efficiency of the proposed analytical solution, as well as the efficiency, feasibility, and robustness of the pattern generator, under various surface motions and gait parameters. 

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2. Damping Acoustic Modes in Compressible Horizontally Explicit Vertically Implicit (HEVI) and Split-Explicit Time Integration Schemes

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   Klemp, Joseph B. ; Skamarock, William C. ; Ha, Soyoung ( June 2018 , Monthly Weather Review)
3. A performance study of horizontally explicit vertically implicit (HEVI) time-integrators for non-hydrostatic atmospheric models

   https://doi.org/10.1016/j.jcp.2024.113275  

   Giraldo, Francis X ; de_Bragança_Alves, Felipe AV ; Kelly, James F ; Kang, Soonpil ; Reinecke, P Alex ( October 2024 , Journal of Computational Physics)
4. WISHE‐Moisture Mode in a Vertically Resolved Model

   https://doi.org/10.1029/2019MS001839  

   Fuchs‐Stone, Željka ( February 2020 , Journal of Advances in Modeling Earth Systems)
5. Thermal-Hydraulic Analytical Models of Split-Flow Microchannel Liquid-Cooled Cold Plates With Flow Impingement

   https://doi.org/10.1115/IPACK2021-73283  

   Kisitu, Deogratius ; Ortega, Alfonso ( October 2021 , Proceedings of the 2021 ASME InterPACK)

   Impingement split flow liquid-cooled microchannel cold plates are one of several flow configurations used for single-phase liquid cooling. Split flow or top-in/side-exit (TISE) cold plates divide the flow into two branches thus resulting in halved or reduced flow rates and flow lengths, compared to traditional side-in /side-exit (SISE) or parallel flow cold plates. This has the effect of reducing the pressure drop because of the shorter flow length and lower flow rate and increasing the heat transfer coefficient due to thermally developing as opposed to fully developed flow. It is also claimed that the impinging flow increases the heat transfer coefficient on the base plate in the region of impingement. Because of the downward impinging and turning flow, there are no exact analytical models for this flow configuration. Computational and experimental studies have been performed, but there are no useful compact analytical models in the literature that can be used to predict the performance of these impingement cold plates. Results are presented for novel physics-based laminar flow models for a TISE microchannel cold plate based on an equivalent parallel channel flow approach. We show that the new models accurately predict the thermal-hydraulic performance over a wide range of parameters.

    

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