An official website of the United States government
Abstract Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a convex entropy. We consider the family of smallBVfunctions which are global solutions of this equation. For any smallBVinitial data, such global solutions are known to exist. Moreover, they are known to be unique amongBVsolutions verifying either the so-called Tame Oscillation Condition, or the Bounded Variation Condition on space-like curves. In this paper, we show that these solutions are stable in a larger class of weak (and possibly not evenBV) solutions of the system. This result extends the classical weak-strong uniqueness results which allow comparison to a smooth solution. Indeed our result extends these results to a weak-BVuniqueness result, where only one of the solutions is supposed to be smallBV, and the other solution can come from a large class. As a consequence of our result, the Tame Oscillation Condition, and the Bounded Variation Condition on space-like curves are not necessary for the uniqueness of solutions in theBVtheory, in the case of systems with 2 unknowns. The method is$$L^2$$ based, and builds up from the theory of a-contraction with shifts, where suitable weight functionsaare generated via the front tracking method.
more »
« less
Exponential time‐decay for a one‐dimensional wave equation with coefficients of bounded variation
Abstract We consider the initial‐value problem for a one‐dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we prove that the local energy decays exponentially fast in time, and provide the explicit constant to which the solution converges. The key ingredient of the proof is a high‐frequency resolvent estimate for an associated Helmholtz operator with a BV potential.
more »
« less
- Award ID(s):
- 2204322
- PAR ID:
- 10444564
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Mathematische Nachrichten
- ISSN:
- 0025-584X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Bacterial vaginosis (BV) is the most prevalent vaginal condition among reproductive-age women presenting with vaginal complaints. Despite its significant impact on women’s health, limited knowledge exists regarding the microbial community composition and metabolic interactions associated with BV. In this study, we analyze metagenomic data obtained from human vaginal swabs to generate in silico predictions of BV-associated bacterial metabolic interactions via genome-scale metabolic network reconstructions (GENREs). While most efforts to characterize symptomatic BV (and thus guide therapeutic intervention by identifying responders and non-responders to treatment) are based on genomic profiling, our in silico simulations reveal functional metabolic relatedness between species as quite distinct from genetic relatedness. We grow several of the most common co-occurring bacteria (Prevotella amnii, Prevotella buccalis, Hoylesella timonensis, Lactobacillus iners, Fannyhessea vaginae, andAerrococcus christenssii) on the spent media ofGardnerellaspecies and perform metabolomics to identify potential mechanisms of metabolic interaction. Through these analyses, we identify BV-associated bacteria that produce caffeate, a compound implicated in estrogen receptor binding, when grown in the spent media of other BV-associated bacteria. These findings underscore the complex and diverse nature of BV-associated bacterial community structures and several of these mechanisms are of potential significance in understanding host-microbiome relationships.more » « less
-
Abstract The abundance and size distribution of marine particles control a range of biogeochemical and ecological processes in the ocean, including carbon sequestration. These quantities are the result of complex physical‐biological interactions that are difficult to observe, and their spatial and temporal patterns remain uncertain. Here, we present a novel analysis of particle size distributions (PSDs) from a global compilation of in situ Underwater Vision Profiler 5 (UVP5) optical measurements. Using a machine learning algorithm, we extrapolate sparse UVP5 observations to the global ocean from well‐sampled oceanographic variables. We reconstruct global maps of PSD parameters (biovolume [BV] and slope) for particles at the base of the euphotic zone. These reconstructions reveal consistent global patterns, with high chlorophyll regions generally characterized by high particle BV and flatter PSD slope, that is, a high relative abundance of large versus small particles. The resulting negative correlations between particle BV and slope further suggests synergistic effects on size‐dependent processes such as sinking particle fluxes. Our approach and estimates provide a baseline for an improved understanding of particle cycles in the ocean, and pave the way to global, three‐dimensional reconstructions of PSD and sinking particle fluxes from the growing body of UVP5 observations.more » « less
-
GaN-on-GaN vertical diode is a promising device for next-generation power electronics. Its breakdown voltage (BV) is limited by edge termination designs such as guard rings. The design space of guard rings is huge and it is difficult to optimize manually. In this paper, we propose an effective inverse design strategy to co-optimize BV and (V F Q) −1 , where BV, V F , and Q are the breakdown voltage, forward voltage, and reserve capacitive charge of the diode, respectively. Using rapid Technology Computer-Aided-Design (TCAD) simulations, neural network (NN), and Pareto front generation, a GaN-on-GaN diode is optimized within 24 hours. We can obtain structures with 200V higher BV at medium (V F Q) −1 or find a nearly ideal BV structure with 25% higher BV 2 /R on compared to the best randomly generated TCAD data.more » « less
-
Abstract Prion diseases are infectious neurodegenerative diseases that are capable of cross‐species transmission, thus arousing public health concerns. Seed‐templating propagation of prion protein is believed to underlie prion cross‐species transmission pathology. Understanding the molecular fundamentals of prion propagation is key to unravelling the pathology of prion diseases. In this study, we use coarse‐grained molecular dynamics to investigate the seeding and cross‐seeding aggregation of three prion protein fragments PrP(120–144) originating from human (Hu), bank vole (BV), and Syrian hamster (SHa). We find that the seed accelerates the aggregation of the monomer peptides by eliminating the lag phase. The monomer aggregation kinetics are mainly determined by the structure of the seed. The stronger the hydrophobic residues on the seed associate with each other, the higher the probability that the seed recruits monomer peptides to its surface/interface. For cross‐seeding aggregation, we show that Hu has a strong tendency to adopt the conformation of the BV seed and vice versa; the Hu and BV monomers have a weak tendency to adopt the conformation of the SHa seed. These two findings are consistent with Apostolet al.'s experimental findings on PrP(138–143) and partially consistent with Joneset al.'s finding on PrP(23–144). We also identify several conformational mismatches when SHa cross‐seeds BV and Hu peptides, indicating the existence of a cross‐seeding barrier between SHa and the other two sequences. This study sheds light on the molecular mechanism of seed‐templating aggregation of prion protein fragments underlying the sequence‐dependent transmission barrier in prion diseases.more » « less
