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Abstract Extending the work of Yang–Zumbrun for the hydrodynamically stable case of Froude number$$F<2$$ $F<2$, we categorize completely the existence and convective stability of hydraulic shock profiles of the Saint Venant equations of inclined thin film flow. Moreover, we confirm by numerical experiment that asymptotic dynamics for general Riemann data is given in the hydrodynamic instability regime by either stable hydraulic shock waves, or a pattern consisting of an invading roll wave front separated by a finite terminating Lax shock from a constant state at plus infinity. Notably, profiles, and existence and stability diagrams, are all rigorously obtained by mathematical analysis and explicit calculation. 

We study for the Richard-Gavrilyuk model of inclined shallow water flow, an extension of the classical Saint Venant equations incorporating vorticity, the new feature of convective-wave solutions analogous to contact discontinuitis in inviscid conservation laws. These are traveling waves for which fluid velocity is constant and equal to the speed of propagation of the wave, but fluid height and/or enstrophy (thus vorticity) varies. Together with hydraulic shocks, they play an important role in the structure of Riemann solutions. 

Neural Radiance Field (NeRF) based rendering has attracted growing attention thanks to its state-of-the-art (SOTA) rendering quality and wide applications in Augmented and Virtual Reality (AR/VR). However, immersive real-time (> 30 FPS) NeRF based rendering enabled interactions are still limited due to the low achievable throughput on AR/VR devices. To this end, we first profile SOTA efficient NeRF al- gorithms on commercial devices and identify two primary causes of the aforementioned inefficiency: (1) the uniform point sampling and (2) the dense accesses and computations of the required embeddings in NeRF. Furthermore, we propose RT-NeRF, which to the best of our knowledge is the first algorithm-hardware co-design acceleration of NeRF. Specifically, on the algorithm level, RT-NeRF integrates an efficient rendering pipeline for largely alleviating the inefficiency due to the commonly adopted uniform point sampling method in NeRF by directly computing the geometry of pre-existing points. Additionally, RT-NeRF leverages a coarse-grained view-dependent computing ordering scheme for eliminating the (unnecessary) pro- cessing of invisible points. On the hardware level, our proposed RT-NeRF accelerator (1) adopts a hybrid encoding scheme to adap- tively switch between a bitmap- or coordinate-based sparsity encoding format for NeRF’s sparse embeddings, aiming to maximize the storage savings and thus reduce the required DRAM accesses while supporting efficient NeRF decoding; and (2) integrates both a high-density sparse search unit and a dual-purpose bi-direction adder & search tree to coordinate the two aforementioned encod- ing formats. Extensive experiments on eight datasets consistently validate the effectiveness of RT-NeRF, achieving a large throughput improvement (e.g., 9.7×∼3,201×) while maintaining the rendering quality as compared with SOTA efficient NeRF solutions. 

For strong detonation waves of the inviscid Majda model, spectral stability was established by Jung and Yao for waves with step-type ignition functions, by a proof based largely on explicit knowledge of wave profiles. In the present work, we extend their stability results to strong detonation waves with more general ignition functions where explicit profiles are unknown. Our proof is based on reduction to a generalized Sturm-Liouville problem, similar to that used by Sukhtayev, Yang, and Zumbrun to study spectral stability of hydraulic shock profiles of the Saint-Venant equations. 

Volatile organic compounds (VOCs) are a group of aromatic or chlorinated organic chemicals commonly found in manufactured products that have high vapor pressure, and thus vaporize readily at room temperature. While airshed VOCs are well studied and have provided insights into public health issues, we suggest that belowground VOCs and the related vapor intrusion process could be equally or even more relevant to public health. The persistence, movement, remediation, and human health implications of subsurface VOCs in urban landscapes remain relatively understudied despite evidence of widespread contamination. This review explores the state of the science of subsurface movement and remediation of VOCs through groundwater and soils, the linkages between these poorly understood contaminant exposure pathways and health outcomes based on research in various animal models, and describes the role of these contaminants in human health, focusing on birth outcomes, notably low birth weight and preterm birth. Finally, this review provides recommendations for future research to address knowledge gaps that are essential for not only tackling health disparities and environmental injustice in post-industrial cities, but also protecting and preserving critical freshwater resources.