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Pressure Poisson equation (PPE) reformulations of the incompressible Navier–Stokes equations (NSE) replace the incompressibility constraint by a Poisson equation for the pressure and a suitable choice of boundary conditions. This yields a time-evolution equation for the velocity field only, with the pressure gradient acting as a nonlocal operator. Thus, numerical methods based on PPE reformulations are representatives of a class of methods that have no principal limitations in achieving high order. In this paper, it is studied to what extent high-order methods for the NSE can be obtained from a specific PPE reformulation with electric boundary conditions (EBC). To that end, implicit–explicit (IMEX) time-stepping is used to decouple the pressure solve from the velocity update, while avoiding a parabolic time-step restriction; and mixed finite elements are used in space, to capture the structure imposed by the EBC. Via numerical examples, it is demonstrated that the methodology can yield at least third order accuracy in space and time.

Abstract The dispersive sweep of fast radio bursts (FRBs) has been used to probe the ionized baryon content of the intergalactic medium 1 , which is assumed to dominate the total extragalactic dispersion. Although the host-galaxy contributions to the dispersion measure appear to be small for most FRBs 2 , in at least one case there is evidence for an extreme magneto-ionic local environment 3,4 and a compact persistent radio source 5 . Here we report the detection and localization of the repeating FRB 20190520B, which is co-located with a compact, persistent radio source and associated with a dwarf host galaxy of high specific-star-formation rate at a redshift of 0.241 ± 0.001. The estimated host-galaxy dispersion measure of approximately $${903}_{-111}^{+72}$$ 903 − 111 + 72 parsecs per cubic centimetre, which is nearly an order of magnitude higher than the average of FRB host galaxies 2,6 , far exceeds the dispersion-measure contribution of the intergalactic medium. Caution is thus warranted in inferring redshifts for FRBs without accurate host-galaxy identifications.

As promising alternatives to lithium-ion batteries, rechargeable anion-shuttle batteries (ASBs) with anions as charge carriers stand out because of their low cost, long cyclic lifetime, and/or high energy density. In this review, we provide for the first time, comprehensive insights into the anion shuttling mechanisms of ASBs, including anion-based rocking-chair batteries (ARBs), dual-ion batteries (DIBs), including insertion-type, conversion-type, and conversion- insertion-type, and reverse dual-ion batteries (RDIBs). Thereafter, we review the latest progresses and challenges regarding electrode materials and electrolytes for ASBs. In addition, we summarize the existing dilemmas of ASBs and outline the perspective of ASB technology for future grid storage.

Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples.

In human pedagogy, teachers and students can interact adaptively to maximize communication efficiency. The teacher adjusts her teaching method for different students, and the student, after getting familiar with the teacher’s instruction mechanism, can infer the teacher’s intention to learn faster. Recently, the benefits of integrating this cooperative pedagogy into machine concept learning in discrete spaces have been proved by multiple works. However, how cooperative pedagogy can facilitate machine parameter learning hasn’t been thoroughly studied. In this paper, we propose a gradient optimization based teacher-aware learner who can incorporate teacher’s cooperative intention into the likelihood function and learn provably faster compared with the naive learning algorithms used in previous machine teaching works. We give theoretical proof that the iterative teacher-aware learning (ITAL) process leads to local and global improvements. We then validate our algorithms with extensive experiments on various tasks including regression, classification, and inverse reinforcement learning using synthetic and real data. We also show the advantage of modeling teacher-awareness when agents are learning from human teachers.

In this preliminary study, we consider the server allocation problem for edge computing system deployment. Our goal is to minimize the average turnaround time of application requests/tasks, generated by all mobile devices/users in a geographical region. We consider two approaches for edge cloud deployment: the flat deployment, where all edge clouds co-locate with the base stations, and the hierarchical deployment, where edge clouds can also co-locate with other system components besides the base stations. In the flat deployment, we demonstrate that the allocation of edge cloud servers should be balanced across all the base stations, if the application request arrival rates at the base stations are equal to each other. We also show that the hierarchical deployment approach has great potentials in minimizing the system’s average turnaround time. We conduct various simulation studies using the CloudSim Plus platform to verify our theoretical results. The collective findings trough theoretical analysis and simulation results will provide useful guidance in practical edge computing system deployment.