Search

We develop an abstract theory of flows of geometric 퐻-structures, i.e., flows of tensor fields defining 퐻-reductions of the frame bundle, for a closed and connected subgroup H ⊂ SO ⁢ (n) , on any connected and oriented 푛-manifold with sufficient topology to admit such structures. The first part of the article sets up a unifying theoretical framework for deformations of 퐻-structures, by way of the natural infinitesimal action of GL ⁢ (n , R) on tensors combined with various bundle decompositions induced by 퐻-structures. We compute evolution equations for the intrinsic torsion under general flows of 퐻-structures and, as applications, we obtain general Bianchi-type identities for 퐻-structures, and, for closed manifolds, a general first variation formula for the L 2 -Dirichlet energy functional ℰ on the space of 퐻-structures. We then specialise the theory to the negative gradient flow of ℰ over isometric 퐻-structures, i.e., their harmonic flow. The core result is an almost-monotonocity formula along the flow for a scale-invariant localised energy, similar to the classical formulas by Chen–Struwe [M. Struwe, On the evolution of harmonic maps in higher dimensions, J. Differential Geom.28 (1988), 3, 485–502; Y. M. Chen and M. Struwe, Existence and partial regularity results for the heat flow for harmonic maps, Math. Z.201 (1989), 1, 83–103] for the harmonic map heat flow. This yields an 휀-regularity theorem and an energy gap result for harmonic structures, as well as long-time existence for the flow under small initial energy, relative to the L ∞ -norm of initial torsion, in the spirit of Chen–Ding [Y. M. Chen and W. Y. Ding, Blow-up and global existence for heat flows of harmonic maps, Invent. Math.99 (1990), 3, 567–578]. Moreover, below a certain energy level, the absence of a torsion-free isometric 퐻-structure in the initial homotopy class imposes the formation of finite-time singularities. These seemingly contrasting statements are illustrated by examples on flat 푛-tori, so long as the set [ S n , SO ⁢ (n) / H ] of homotopy classes of maps S n → SO ⁢ (n) / H contains more than one element and the universal cover of SO ⁢ (n) / H is a sphere, e.g. when n = 7 and H = G 2 , or n = 8 and H = Spin ⁢ (7) . [ABSTRACT FROM AUTHOR]

We describe the 10-dimensional space of Sp (2) -invariant G 2 -structures on the homogeneous 7-sphere S 7 = Sp (2) / Sp (1) as Ω + 3 (S 7) Sp (2) ≃ R + × Gl + (3 , R) . In those terms, we formulate a general Ansatz for G 2 -structures, which realises representatives in each of the 7 possible isometric classes of homogeneous G 2 -structures. Moreover, the well-known nearly parallel round and squashed metrics occur naturally as opposite poles in an S 3 -family, the equator of which is a new S 2 -family of coclosed G 2 -structures satisfying the harmonicity condition div T = 0 . We show general existence of harmonic representatives of G 2 -structures in each isometric class through explicit solutions of the associated flow and describe the qualitative behaviour of the flow. We study the stability of the Dirichlet gradient flow near these critical points, showing explicit examples of degenerate and nondegenerate local maxima and minima, at various regimes of the general Ansatz. Finally, for metrics outside of the Ansatz, we identify families of harmonic G 2 -structures, prove long-time existence of the flow and study the stability properties of some well-chosen examples. [ABSTRACT FROM AUTHOR]

Harmful algal blooms (HABs) in coastal areas similarly impact both ecosystems and human health. The translocation of phytoplankton species via maritime transport can potentially promote the growth of HABs in coastal systems. Accordingly, ballast water must be disinfected. The main goal of this study is to assess the effectiveness of different emerging biocides, including H 2 O 2 , peracetic acid (PAA), peroxymonosulfate (PMS), and peroxydisulfate (PDS). The effectiveness of these biocides is compared with that of conventional chlorination methods. Their effects on two ichthyotoxic microalgae with worldwide distribution, i.e., Prymnesium parvum and Heterosigma akashiwo, are examined. To ensure the prolonged effectiveness of the different reagents, their concentration-response curves for 14 days are constructed and examined. The results suggest a strong but shorter effect by PMS (EC50 = 0.40-1.99 mg·L -1 ) and PAA (EC50 = 0.32-2.70 mg·L -1 ), a maintained effect by H 2 O 2 (EC50 = 6.67-7.08 mg·L -1 ), and a negligible effect by PDS. H. akashiwo indicates higher resistance than P. parvum, except when H 2 O 2 is used. Based on the growth inhibition performance and consumption of the reagents as well as a review of important aspects regarding their application, using H 2 O 2 , PAA, or PMS can be a feasible alternative to chlorine-based reagents for inhibiting the growth of harmful phytoplankton., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 The Authors. Published by Elsevier B.V. All rights reserved.)

Ultraviolet (UV) radiation is a well-implemented process for water disinfection. The development of emergent UV sources, such as light-emitting diodes (LEDs), has afforded new possibilities for advanced oxidation processes. The emission wavelength is considered to be an important factor for photo-chemical processes in terms of both biological damage and energetic efficiency, as the inactivation mechanisms and mode-of-action may differ according to the wavelength that is applied. In addition, these processes merit exploration for inactivating emerging pathogens, such as marine vibrios, that are important bacteria to control in maritime activities. The main goal of this study was to compare the disinfection efficacy of several UV-LED driven processes with different modes of action. First, the effect of UV-LEDs was assessed at different UV ranges (UV-A, UV-B, or UV-C). Second, the possible enhancement of a combination with hydrogen peroxide (H 2 O 2 ) or peroxymonosulfate salt (HSO 5 - ) was investigated under two different application strategies, i.e. simultaneous or sequential. The results obtained indicate a high sensitivity of Vibrio alginolyticus to UV radiation, especially under UV-B (k obs  = 0.24 cm 2 /mJ) and UV-C (k obs  = 1.47 cm 2 /mJ) irradiation. The highest inactivation rate constants were obtained for UV/HSO 5 - (k obs (cm 2 /mJ)=0.0007 (UV-A); 0.39 (UV-B); 1.79 (UV-C)) with respect to UV/H 2 O 2 (k obs (cm 2 /mJ)=0.0006 (UV-A); 0.26 (UV-B); and 1.54 (UV-C)) processes, however, regrowth was avoided only with UV/H 2 O 2 . Additionally, the disinfection enhancement caused by a chemical addition was more evident in the order UV-A > UV-B > UV-C. By applying H 2 O 2 (10 mg/L) or HSO 5 - (2.5 mg/L) in a sequential mode before the UV, negligible effects were obtained in comparison with the simultaneous application. Finally, promising electrical energy per order (EE O ) values were obtained as follows: UV/HSO 5 - (EE O (kWh/m 3 )=1.68 (UV-A); 0.20 (UV-B); 0.04 (UV-C)) and UV/H 2 O 2 (EE O (kWh/m 3 )=2.15 (UV-A); 0.32 (UV-B); 0.04 (UV-C)), demonstrating the potential of UV-LEDs for disinfection in particular activities such as the aquaculture industry or maritime transport., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Harmful algal blooms in coastal areas can significantly impact a water source. Microorganisms such as cyanobacteria and associated pathogenic bacteria may endanger an ecosystem and human health by causing significant eco-hazards. This study assesses the efficacy of two different reagents, H2O2 and S2O82−, as (pre-)treatment options for algae-laden waters. Anabaena sp. and Vibrio alginolyticus have been selected as target microorganisms. With the objective of activating H2O2 or S2O82−, additional experiments have been performed with the presence of small amounts of iron (18 µmol/L). For the cyanobacterial case, H2O2-based processes demonstrate greater efficiency over that of S2O82−, as Anabaena sp. is particularly affected by H2O2, for which >90% of growth inhibition has been achieved with 0.088 mmol/L of H2O2 (at 72 h of exposure). The response of Anabaena sp. as a co-culture with V. alginolyticus implies the use of major H2O2 amounts for its inactivation (0.29 mmol/L of H2O2), while the effects of H2O2/Fe(II) suggests an improvement of ~60% compared to single H2O2. These H2O2 doses are not sufficient for preventing the regrowth of V. alginolyticus after 24 h. The effects of S2O82− (+ Fe(II)) are moderate, reaching maximum inhibition growth of ~50% for Anabaena sp. at seven days of exposure. Nevertheless, doses of 3 mmol/L of S2O82− can prevent the regrowth of V. alginolyticus. These findings have implications for the mitigation of HABs but also for the associated bacteria that threaten many coastal ecosystems.