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1. Alignment complete relational Hoare logics for some and all

   https://doi.org/10.46298/lmcs-21(4:21)2025  

   Nagasamudram, Ramana; Banerjee, Anindya; Naumann, David A (November 2025, Logical Methods in Computer Science)

   In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various alignments of executions. Seemingly more flexible alignments can be expressed in terms of product automata based on program transition relations. A single degenerate alignment rule (sequential composition), atop a complete Hoare logic, comprises a RHL for $$\forall\forall$$ properties that is complete in the sense of Cook. The notion of alignment completeness was previously proposed as an additional measure, and some rules were shown to be alignment complete with respect to a few ad hoc forms of alignment automata. This paper proves alignment completeness with respect to a general class of $$\forall\forall$$ alignment automata, for a RHL comprised of standard rules together with a rule of semantics-preserving rewrites based on Kleene algebra with tests. A new logic for $$\forall\exists$$ properties is introduced and shown to be sound and alignment complete for a new general class of automata. The $$\forall\forall$$ and $$\forall\exists$$ automata are shown to be semantically complete. Thus both logics are complete in the sense of Cook. The paper includes discussion of why alignment is not the only important principle for relational reasoning and proposes entailment completeness as further means to evaluate RHLs. 

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2. Stability and error analysis of a semi-implicit scheme for incompressible flows with variable density and viscosity

   https://doi.org/10.1515/jnma-2024-0033  

   Vu, An; Cappanera, Loic (November 2024, Journal of Numerical Mathematics)

   Abstract We study the stability and convergence properties of a semi-implicit time stepping scheme for the incompressible Navier–Stokes equations with variable density and viscosity. The density is assumed to be approximated in a way that conserves the minimum-maximum principle. The scheme uses a fractional time-stepping method and the momentum, which is equal to the product of the density and velocity, as a primary unknown. The semi-implicit algorithm for the coupled momentum-pressure is shown to be conditionally stable and the velocity is shown to converge inL²norm with order one in time. Numerical illustrations confirm that the algorithm is stable and convergent under classic CFL condition even for sharp density profiles. 

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3. Barren plateaus from learning scramblers with local cost functions

   https://doi.org/10.1007/JHEP01(2023)090  

   Garcia, Roy J.; Zhao, Chen; Bu, Kaifeng; Jaffe, Arthur (January 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> The existence of barren plateaus has recently revealed new training challenges in quantum machine learning (QML). Uncovering the mechanisms behind barren plateaus is essential in understanding the scope of problems that QML can efficiently tackle. Barren plateaus have recently been shown to exist when learning global properties of random unitaries, which is relevant when learning black hole dynamics. Establishing whether local cost functions can circumvent these barren plateaus is pertinent if we hope to apply QML to quantum many-body systems. We prove a no-go theorem showing that local cost functions encounter barren plateaus in learning random unitary properties. 

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4. Additive manufacturing of refractory metals and carbides for extreme environments: an overview

   https://doi.org/10.1177/13621718241235471  

   Mukherjee, Poulomi; Gabourel, Ashlee; Firdosy, Samad A; Hofmann, Douglas C; Moridi, Atieh (March 2024, Science and Technology of Welding and Joining)

   Refractory metals and their carbides possess extraordinary properties when subjected to high temperatures and extreme environments. Consequently, they can act as key material systems for advancing many sectors, including space, energy and defence. However, it has been difficult to process these materials using the conventional routes of manufacturing. Additive manufacturing (AM) has shown a lot of potential to overcome the challenges and develop new material systems with tailored properties. This review provides a fundamental understanding of the challenges in the processing of refractory metals and their carbides, including microcracking, formation of brittle oxide phases and high ductile to brittle transition temperature (DBTT). We also highlight some of the novel approaches that have been taken to improve the processability of these challenging material systems using AM. These include in-situ reactive printing, ultrasonic vibration, laser beam shaping, multi-laser deposition and substrate pre-heating with a focus on microstructural changes to improve the properties of printed parts. 

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5. Characterization of oscillation modes in levitated droplets using image and non-image based techniques

   https://doi.org/10.1038/s41526-023-00254-7  

   Brosius, Nevin; Livesay, Jason; Karpinski, Zachary; Singiser, Robert; SanSoucie, Michael; Phillips, Brandon; Narayanan, Ranga (December 2023, npj Microgravity)

   n/a (Ed.)

   Abstract The dynamics of levitated liquid droplets can be used to measure their thermophysical properties by correlating the frequencies at which normal modes of oscillation most strongly resonate when subject to an external oscillatory force. In two preliminary works, it was shown via electrostatic levitation and processing of various metals and alloys that (1) the resonance of the first principal mode of oscillation (moden = 2) can be used to accurately measure surface tension and (2) that so-called “higher-order resonance” ofn = 3 is observable at a predictable frequency. It was also shown, in the context of future space-based experimentation on the Electrostatic Levitation Furnace (ELF), a setup on the International Space Station (ISS) operated by Japan Aerospace Exploration Agency (JAXA), that while the shadow array method in which droplet behavior is visualized would be challenging to identify then = 3 resonance, the normal moden = 4 was predicted to be more easily identifiable. In this short communication, experimental evidence of the first three principal modes of oscillation is provided using molten samples of Tin and Indium and it is subsequently shown that, as predicted, an “image-less approach can be used to identify bothn = 2 andn = 4 resonances in levitated liquid droplets. This suggests that the shadow array method may be satisfactorily used to obtain a self-consistent benchmark of thermophysical properties by comparing results from two successive even-mode natural frequencies. 

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