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1. A mathematical model for bedrock incision in near‐threshold gravel‐bed rivers

   https://doi.org/10.1002/esp.5957  

   Gabel, Vanessa; Tucker, Gregory E; Campforts, Benjamin (July 2025, Earth Surface Processes and Landforms)

   Gravel‐bed rivers that incise into bedrock are common worldwide. These systems have many similarities with other alluvial channels: they transport large amounts of sediment and adjust their forms in response to discharge and sediment supply. At the same time, the occurrence of bedrock incision implies behaviour that falls on a spectrum between fully detachment‐limited ‘bedrock channels’ and fully transport‐limited ‘alluvial channels’. Here, we present a mathematical model of river profile evolution that integrates bedrock erosion, gravel transport and the formation of channels whose hydraulic geometry is consistent with that of near‐threshold alluvial channels. We combine theory for five interrelated processes: bedload sediment transport in equilibrium gravel‐bed channels, channel width adjustment to flow and sediment characteristics, abrasion of bedrock by mobile sediment, plucking of bedrock and progressive loss of gravel‐sized sediment due to grain attrition. This model contributes to a growing class of models that seek to capture the dynamics of both bedrock incision and alluvial sediment transport. We demonstrate the model's ability to reproduce expected fluvial features such as inverse power law scaling between slope and area, and width and depth consistent with near‐threshold channel theory, and we discuss the role of sediment characteristics in influencing the mode of channel behaviour, erosional mechanism, channel steepness and profile concavity. 

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2. Unsolved problems: Mesoscale polar cap flow channels’ structure, propagation, and effects on space weather disturbances

   https://doi.org/10.3389/fspas.2023.1147531  

   Lyons, Larry R.; Nishimura, Yukitoshi; Liu, Jiang; Zou, Ying; Bristow, William A.; Yadav, Sneha; Donovan, Eric; Nishitani, Nozomu; Shiokawa, Kazuo; Hosokawa, Keisuke (April 2023, Frontiers in Astronomy and Space Sciences)

   Dynamic mesoscale flow structures move across the open field line regions of the polar caps and then enter the nightside plasma sheet where they can cause important space weather disturbances, such as streamers, substorms, and omega bands. The polar cap structures have long durations (apparently at least ∼1½ to 2 h), but their connections to disturbances have received little attention. Hence, it will be important to uncover what causes these flow enhancement channels, how they map to the magnetospheric and magnetosheath structures, and what controls their propagation across the polar cap and their dynamic effects after reaching the nightside auroral oval. The examples presented here use 630-nm auroral and radar observations and indicate that the motion of flow channels could be critical for determining when and where a particular disturbance within the nightside auroral oval will be triggered, and this could be included for full understanding of flow channel connections to disturbances. Also, it is important to determine how polar cap flow channels lead to flow channels within the auroral oval, i.e., the plasma sheet, and determine the conditions along nightside oval/plasma sheet field lines that interact with an incoming polar cap flow channel to cause a particular disturbance. It will also be interesting to consider the generality of geomagnetic disturbances being related to connections with incoming polar cap flow channels, including the location, time, and type of disturbances, and whether the duration and expansion of disturbances are related to flow channel duration and to multiple flow channels. 

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3. Out-of-Distribution Generalization for Learning Quantum Channels with Low-Energy Coherent States

   https://doi.org/10.1103/5m7p-kbf3  

   Pereira, Jason L; Zhuang, Quntao; Banchi, Leonardo (October 2025, PRX Quantum)

   When experimentally learning the action of a continuous-variable quantum process by probing it with inputs, there will often be some restriction on the input states used. One experimentally simple way to probe a quantum channel is to use low-energy coherent states. Learning a quantum channel in this way presents difficulties, due to the fact that two channels may act similarly on low-energy inputs but very differently for high-energy inputs. They may also act similarly on coherent-state inputs but differently on nonclassical inputs. Extrapolating the behavior of a channel for more general input states from its action on the far more limited set of low-energy coherent states is a case of out-of-distribution generalization. To be sure that such generalization gives meaningful results, one needs to relate error bounds for the training set to bounds that are valid for all inputs. We show that for any pair of channels that act sufficiently similarly on low-energy coherent-state inputs, one can bound how different the input-output relations are for any (high-energy or highly nonclassical) input. This proves that out-of-distribution generalization is always possible for learning quantum channels using low-energy coherent states, as long as enough samples are used. 

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4. Recoverability for Holevo's Just-as-Good Fidelity

   https://doi.org/10.1109/ISIT.2018.8437346  

   Wilde, Mark M. (June 2018, Proceedings of the 2018 International Symposium on Information Theory)

   Holevo's just-as-good fidelity is a similarity measure for quantum states that has found several applications. One of its critical properties is that it obeys a data processing inequality: the measure does not decrease under the action of a quantum channel on the underlying states. In this paper, I prove a refinement of this data processing inequality that includes an additional term related to recoverability. That is, if the increase in the measure is small after the action of a partial trace, then one of the states can be nearly recovered by the Petz recovery channel, while the other state is perfectly recovered by the same channel. The refinement is given in terms of the trace distance of one of the states to its recovered version and also depends on the minimum eigenvalue of the other state. As such, the refinement is universal, in the sense that the recovery channel depends only on one of the states, and it is explicit, given by the Petz recovery channel. The appendix contains a generalization of the aforementioned result to arbitrary quantum channels. 

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5. Islands in stable fluid equilibria

   https://doi.org/10.1090/proc/16951  

   Drivas, Theodore; Ginsberg, Daniel (November 2024, Proceedings of the American Mathematical Society)

   We prove that stable fluid equilibria with trivial homology on curved, reflection-symmetric periodic channels must posses “islands”, or cat’s eye vortices. In this way, arbitrarily small disturbances of a flat boundary cause a change of streamline topology of stable steady states. 

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