The concept of equilibrium is a general tool to fill the gap between macroscopic and mesoscopic information, both within kinetic systems and kinetic schemes. This work explores the use of equilibria to devise numerical boundary conditions for multi-dimensional vectorial lattice Boltzmann schemes tackling systems of hyperbolic conservation laws. In the scalar case, we prove convergence for schemes with monotone relaxation to the weak entropy solution by Bardos, Leroux, and Nédelec [Comm. Partial Differential Equations 4 (1979), pp. 1017–1034], following the path by Crandall and Majda [Math. Comp. 34, (1980), pp. 1–21]. Numerical experiments are conducted both for scalar and vectorial problems, and demonstrate the effectiveness of equilibrium boundary conditions in capturing significant physical phenomena.
We study classes of graphs with bounded clique-width that are well-quasi-ordered by the induced subgraph relation, in the presence of labels on the vertices. We prove that, given a finite presentation of a class of graphs, one can decide whether the class is labelled-well-quasi-ordered. This solves an open problem raised by Daligault, Rao and Thomassé in 2010, and answers positively to two conjectures of Pouzet in the restricted case of bounded clique-width classes. Namely, we prove that being labelled-well-quasi-ordered by a set of size 2 or by a well-quasi-ordered infinite set are equivalent conditions, and that in such cases, one can freely assume that the graphs are equipped with a total ordering on their vertices. Finally, we provide a structural characterization of those classes as those that are of bounded clique-width and do not existentially transduce the class of all finite paths.
Developing affordable and stable electrode materials is crucial for advancing sustainable supercapacitor technologies. In this study, a lead-free Co(II)-halide hybrid material (CoTEA) was synthesized via slow evaporation and evaluated as an electrode for aqueous electrochemical energy storage. Single-crystal X-ray diffraction showed a zero-dimensional structure consisting of isolated tetrahedral units separated by tetraethylammonium cations. Morphological and spectroscopic analyses confirmed the crystalline nature and the Co(II) oxidation state of the material. Optical measurements indicated semiconducting behavior with a band gap of 3.64 eV. The electrochemical response of CoTEA was highly dependent on the electrolyte used. At 5 mV s-1, specific capacitances of 5.01, 22.24, and 21.37 F g-1 were recorded in 1 M H2SO4, 0.5 M Na2SO4, and 6 M KOH, respectively. While Na2SO4 yielded the highest capacitance at the lowest scan rate, KOH demonstrated better rate performance and lower charge-transfer resistance, suggesting more efficient interfacial kinetics. In 6 M KOH, CoTEA achieved a GCD-specific capacitance of 21.41 F g-1 at 0.5 A g-1 and maintained about 85% of its initial capacitance after 3000 cycles. These results underscore the significant impact of electrolyte composition on the charge-storage behavior of CoTEA and present it as a promising, tunable material for aqueous supercapacitor applications.strong influence of electrolyte composition on the charge-storage behavior of CoTEA and highlight it as a promising tunable material for aqueous supercapacitor applications.
Abstract To combat drug-resistant bacteria, antimicrobial agents with tunable and multi-modal mechanisms are urgently needed. While membrane-disrupting polymers have been widely explored, precisely regulating their membrane interactions and downstream metabolic effects remains challenging. Here, using naturally occurring lipoic acid, we designed cationic cyclic oligo(disulfide)s (CCOs) that induce targeted membrane depolarization and trigger distinct downstream metabolic responses. CCOs exhibit species-specific killing mechanisms: membrane depolarization in Staphylococcus aureus and reactive oxygen species induction in Escherichia coli. The cationic-to-hydrophilic ratio governs both membrane interactions and metabolic regulation. Coarse-grained molecular dynamics simulations revealed that fully cationic CCO1 adsorbs via electrostatic forces, whereas CCO2-64%, bearing partial hydrophilic groups, relies on a balance of electrostatic and van der Waals interactions, underlying its enhanced antibacterial selectivity. Transcriptomic analysis further showed that CCO1 disrupts ribosome assembly and sulfur-containing amino acid metabolism, while CCO2-64% downregulates oxidoreductase activity and nitrogen metabolism. With favorable biosafety and potent efficacy against methicillin-resistant S. aureus in a murine cutaneous abscess model, CCOs represent a tunable antimicrobial system with considerable clinical translation potential.
