Positive solutions for singular p(z)$p(z)$‐equations

Liu, Zhenhai; Papageorgiou, Nikolaos S.

doi:10.1002/mana.202100288

Cited by 8 publications

(8 citation statements)

References 21 publications

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“…Figure c shows a representative particle finding result, with two different types of particles marked separately. The details of the particle finding algorithm can be found in SI Section 4 and in ref . After the centers of all of the particles are identified at different frames, we use the open-source software “trackpy” to track the trajectories of the particles .…”

Section: Methodsmentioning

confidence: 99%

Heterogeneous Dynamics of Sheared Particle-Laden Fluid Interfaces with Janus Particle Doping

Qiao,

Liu,

et al. 2023

Langmuir

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The formation of particle clusters can substantially modify the dynamics and mechanical properties of suspensions in both two and three dimensions. While it has been well established that large network-spanning clusters increase the rigidity of particle systems, it is still unclear how the presence of localized nonpercolating clusters affects the dynamics and mechanical properties of particle suspensions. Here, we introduce self-assembled localized particle clusters at a fluid–fluid interface by mixing a fraction of Janus particles in a monolayer of homogeneous colloids. Each Janus particle binds to a few nearby homogeneous colloids, resulting in numerous small clusters uniformly distributed across the interface. Using a custom magnetic rod interfacial stress rheometer, we apply linear oscillatory shear to the particle-laden fluid interface. By analyzing the local affine deformation of particles from optical microscopy, we show that particles in localized clusters experience substantially lower shear-induced stretching than their neighbors outside clusters. We hypothesize that such heterogeneous dynamics induced by particle clusters increase the effective surface coverage of particles, which in turn enhances the shear moduli of the interface, as confirmed by direct interfacial rheological measurements. Our study illustrates the microscopic dynamics of small clusters in a shear flow and reveals their profound effects on the macroscopic rheology of particle-laden fluid interfaces. Our findings open an avenue for designing interfacial materials with improved mechanical properties via the control of formation of localized particle clusters.

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Section: Methodsmentioning

confidence: 99%

Heterogeneous Dynamics of Sheared Particle-Laden Fluid Interfaces with Janus Particle Doping

Qiao,

Liu,

et al. 2023

Langmuir

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“…Increasingly specific benchmarks are being developed. Examples include G-Eval, a framework using LLMs to evaluate natural language generation output via a CoT paradigm [46], and AmbiEnt, where even advanced models like GPT-4 struggle with correctly disentangling ambiguous meanings [47].…”

Section: Related Workmentioning

confidence: 99%

Large language models as tax attorneys: a case study in legal capabilities emergence

Nay,

Karamardian,

Lawsky

et al. 2024

Phil. Trans. R. Soc. A.

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Better understanding of Large Language Models' (LLMs) legal analysis abilities can contribute to improving the efficiency of legal services, governing artificial intelligence and leveraging LLMs to identify inconsistencies in law. This paper explores LLM capabilities in applying tax law. We choose this area of law because it has a structure that allows us to set up automated validation pipelines across thousands of examples, requires logical reasoning and maths skills, and enables us to test LLM capabilities in a manner relevant to real-world economic lives of citizens and companies. Our experiments demonstrate emerging legal understanding capabilities, with improved performance in each subsequent OpenAI model release. We experiment with retrieving and using the relevant legal authority to assess the impact of providing additional legal context to LLMs. Few-shot prompting, presenting examples of question–answer pairs, is also found to significantly enhance the performance of the most advanced model, GPT-4. The findings indicate that LLMs, particularly when combined with prompting enhancements and the correct legal texts, can perform at high levels of accuracy but not yet at expert tax lawyer levels. As LLMs continue to advance, their ability to reason about law autonomously could have significant implications for the legal profession and AI governance. This article is part of the theme issue ‘A complexity science approach to law and governance’.

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“…HTC technology for the transformation of biomass into sustainable carbon materials under mild reaction conditions is receiving considerable attention because of its simplicity and ability to endow hydrochar with abundant OFGs. 33,34,103 Diverse types of biomass have been subjected to the HTC process, ranging from model substances to intact biomass including cellulose, 104,105 glucose, 104,106 agricultural residue, 107 animal manure, 108 municipal solid waste, 109,110 and sewage sludge. 111 Briey, HTC technology is presumably close to natural coalication 112 and it is oen conducted under moderate conditions in the temperature range of 180-280 °C in a conned system.…”

Section: Hydrothermal Platformsmentioning

confidence: 99%