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We investigate global solutions to the Euler-alignment system in |$d$| dimensions with unidirectional flows and strongly singular communication protocols |$\phi (x) = |x|^{-(d+\alpha)}$| for |$\alpha \in (0,2)$|⁠. Our paper establishes global regularity results in both the subcritical regime |$1<\alpha <2$| and the critical regime |$\alpha =1$|⁠. Notably, when |$\alpha =1$|⁠ , the system exhibits a critical scaling similar to the critical quasi-geostrophic equation. To achieve global well-posedness, we employ a novel method based on propagating the modulus of continuity. Our approach introduces the concept of simultaneously propagating multiple moduli of continuity, which allows us to effectively handle the system of two equations with critical scaling. Additionally, we improve the regularity criteria for solutions to this system in the supercritical regime |$0<\alpha <1$|⁠. [ABSTRACT FROM AUTHOR]

We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment system with measure-valued density, bounded velocity, and locally integrable communication protocol. A satisfactory understanding of the low-regularity theory is an issue of pressing interest, as smooth solutions may lose regularity in finite time. However, no such theory currently exists except for a very special class of alignment interactions. We show that the dynamics of the 1D Euler-alignment system can be effectively described by a nonlocal scalar balance law, the entropy conditions of which serves as an entropic selection principle that determines a unique weak solution of the Euler-alignment system. Moreover, the distinguished weak solution of the system can be approximated by the sticky particle Cucker–Smale dynamics. Our approach is inspired by the work of Brenier and Grenier on the pressureless Euler equations. [ABSTRACT FROM AUTHOR]

The spherical Au@Pt core–shell–satellite nanoparticles (NPs) are fabricated via a facile, efficient, and surfactant‐free method of seed‐mediated growth, and the electrocatalytic performance toward the methanol oxidation reaction (MOR) is systematically researched by cyclic voltammetry. Compared with commercial Pt/C, all the obtained Au@Pt NPs with such a core–shell–satellite structure exhibit greatly enhanced electrocatalytic activity and long‐term stability toward MOR. Among them, Au90@Pt10 NPs with less loading of Pt exhibit the most significantly enhanced electrocatalytic performance with a mass activity of 1.470 A mgPt−1, approximately 13 times that of commercial Pt/C (0.111 A mgPt−1) and specific activity (1.469 mA cm−2) approximately 9 times that of commercial Pt/C (0.157 mA cm−2). Au95@Pt5 NPs have the highest value of the oxidation current density (0.2615 mA cm−2), corresponding to 62.8% of its initial maximum value (0.4165 mA cm−2), showing higher stability at approximately 4000 s. Such a surfactant‐free synthesis technique of Au@Pt bimetallic NPs may be a simple method to prepare self‐supported bimetallic nanostructures, which is important to develop highly effective electrocatalysts for MORs. [ABSTRACT FROM AUTHOR]

We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong short-range alignment, and long-range misalignment. Compared with the well-studied Euler-alignment system, the presence of the misalignment brings different behaviors of the solutions, including the possible creation of vacuum at infinite time, which destabilizes the solutions. We show that with a strongly singular short-range alignment interaction, the solution is globally regular, despite the effect of misalignment. [ABSTRACT FROM AUTHOR]

Recently, direct formic acid fuel cells (DFAFCs) which possess superior advantages such as a low operating temperature, light environmental pollution and high energy density, have been considered as one of the power generation technologies with a bright prospect. Herein, bimetallic PdAg nanoparticles (NPs) with different particle sizes were successfully produced via an easy one‐pot solvothermal co‐reduction synthetic route and their electrocatalytic performance for formic acid oxidation (FAO) were further investigated. In our strategy, the size of PdAg NPs can be easily controlled by only varying the concentration of precursors. The larger sized PdAg alloy (9.5 nm, noted as PdAg−L) was obtained at a low concentration of precursors, while the smaller PdAg alloy (3.7 nm, named as PdAg−S) was separated from the reaction system with higher solubility by centrifugation. The electrocatalytic activity and stability of the obtained PdAg NPs could be well optimized when incorporated with carbon (C), which is owing to a synergetic effect. The PdAg−S/C exhibits the highest mass activity with around 1.6 times that of PdAg−L/C and 2 times that of commercial Pd/C, which can be attributed to its larger ECSA and lower adsorption energy of the intermediate to facilitate the direct oxidation of HCOOH molecule. [ABSTRACT FROM AUTHOR]

We study the pressureless Euler equations with nonlocal alignment interactions, which arises as a macroscopic representation of the Cucker–Smale model on animal flocks. For the Euler-alignment system with bounded interactions, a critical threshold phenomenon is proved in Tadmor and Tan (2014 Phil. Trans. R. Soc. A 372 20130401), where global regularity depends on initial data. With strongly singular interactions, global regularity is obtained in Do et al (2018 Arch. Ration. Mech. Anal. 228 1–37), for all initial data. We consider the remaining case when the interaction is weakly singular. We show a critical threshold, similar to the system with bounded interaction. However, different global behaviors may happen for critical initial data, which reveals the unique structure of the weakly singular alignment operator. [ABSTRACT FROM AUTHOR]

We propose a new class of asymptotic preserving schemes to solve kinetic equations with mono-kinetic singular limit. The main idea to deal with the singularity is to transform the equations by appropriate scalings in velocity. In particular, we study two biologically related kinetic systems. We derive the scaling factors, and prove that the rescaled solution does not have a singular limit, under appropriate spatial non-oscillatory assumptions, which can be verified numerically by a newly developed asymptotic preserving scheme. We set up a few numerical experiments to demonstrate the accuracy, stability, effeciency and asymptotic preserving property of the schemes. [ABSTRACT FROM AUTHOR]

We study a pressureless Euler system with a non-linear density-dependent alignment term, originating in the Cucker-Smale swarming models. The alignment term is dissipative in the sense that it tends to equilibrate the velocities. Its density dependence is natural: the alignment rate increases in the areas of high density due to species discomfort. The diffusive term has the order of a fractional Laplacian $${(-\partial _{xx})^{\alpha/2}, \alpha \in (0, 1)}$$ . The corresponding Burgers equation with a linear dissipation of this type develops shocks in a finite time. We show that the alignment nonlinearity enhances the dissipation, and the solutions are globally regular for all $${\alpha \in (0, 1)}$$ . To the best of our knowledge, this is the first example of such regularization due to the non-local nonlinear modulation of dissipation. [ABSTRACT FROM AUTHOR]

We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker-Smale [Emergent behaviors in flocks, IEEE Trans. Autom. Control. 52 (2007) 852-862] and Motsch-Tadmor [A new model for self-organized dynamics and its flocking behavior, J. Statist. Phys. 144 (2011) 923-947] models. We first establish a well-posedness theory and large-time flocking behavior for the kinetic systems, which indicates a concentration in velocity variable in infinite time. We then apply a discontinuous Galerkin method to treat the asymptotic -singularity, and construct high-order positive-preserving schemes to solve kinetic flocking systems. [ABSTRACT FROM AUTHOR]

We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in velocity in one dimension. We provide a complete description for the critical threshold to the system without interaction forces leading to a sharp dichotomy condition between global-in-time existence or finite-time blowup of strong solutions. When the interaction forces are considered, we also give a classification of the critical thresholds according to the different type of interaction forces. We also remark on global-in-time existence when the repulsion is modeled by the isothermal pressure law. [ABSTRACT FROM AUTHOR]

A novel strategy is first presented here to design and construct a good selective and highly sensitive dopamine (DA) biosensor based on single-crystalline CuPc nanowires with a reduced graphene oxide–Nafion film (rGON/CuPcNWs). Metal–organic semiconductor single-crystalline CuPc nanowires with excellent electronic properties and large surface-to-volume ratios were prepared using a physical vapor transport technique and modified onto a glassy carbon electrode (GCE), and exhibited high electrocatalytic activity for DA detection by immobilizing it onto a GCE with a film of the rGON composite. The introduction of a rGO–Nafion film can significantly improve the electrochemical signal of the CuPcNWs. The relevant detection limit toward dopamine is 0.3 nM with a wide linear range from 0.001 μM to 200 μM. The results of the demonstrated biosensor could provide important enlightenment for the design of more sensitive electrochemical biosensors. [ABSTRACT FROM AUTHOR]

A novel and general strategy for the synthesis of a monodispersed Au@CdS core-shell structure with uniform morphology and size through a self-assembly process is proposed here. The obtained negatively charged Au@CdS hybrid core-shell nanoparticles (NPs) are highly selective to dopamine (DA), in the presence of oxidation of ascorbic acid (AA) and uric acid (UA), based on electrostatic interaction. The fabricated biosensor shows a wide linear range from 0.002 to 800 μmol L-1, with a lower detection limit of 0.55 nmol (n = 5, S/N = 3), revealing the high-sensitivity properties. Electrostatic charge plays an important role in the selective electrocatalytic activity of Au@CdS hybrid core-shell nanoparticles, that is the formation of an electrostatic system between the negatively charged Au@CdS hybrid core- shell NPs and the DA cation. The modified electrode is used to achieve the real-time quantitative detection of DA for biological applications, and satisfactory results are obtained. Due to the advantages of the biosensor, its selectivity, sensitivity and stability, it will have a bright future in the field of medical diagnosis. [ABSTRACT FROM AUTHOR]

The coupling of the hydrogen evolution reaction (HER) and methanol oxidation reaction (MOR) to produce clean hydrogen energy with value-added chemicals has attracted substantial attention. However, achieving high selectivity for formate production in the MOR and high faradaic efficiency for H 2 evolution remain significant challenges. In light of this, this study constructs an Ru/Ni(OH) 2 /NF catalyst on nickel foam (NF) and evaluates its electrochemical performance in the MOR and HER under alkaline conditions. The results indicate that the synergistic effect of Ni(OH) 2 and Ru can promote the catalytic activity. At an overpotential of only 42 mV, the current density for the HER reaches 10 mA cm -2 . Moreover, in a KOH solution containing 1 M methanol, a potential of only 1.36 V vs. RHE is required to achieve an MOR current density of 10 mA cm -2 . Using Ru/Ni(OH) 2 /NF as a bifunctional catalyst, employed as both the anode and cathode, an MOR-coupled HER electrolysis cell can achieve a current density of 10 mA cm -2 with a voltage of only 1.45 V. Importantly, the faradaic efficiency (FE) for the hydrogen production at the cathode and formate (HCOO - ) production at the anode approaches 100%. Therefore, this study holds significant practical implications for the development of methanol electro-oxidation for formate-coupled water electrolysis hydrogen production technology., Competing Interests: The authors state that none of the work presented in this study may have been influenced by any known conflicting financial interests or personal ties., (This journal is © The Royal Society of Chemistry.)

The morphology of Pt-Au bimetal nanostructures plays an important role in enhancing the catalytic capability, catalytic stability and utilization efficiency of the platinum. We designed and successfully prepared Au@Pt nanoparticles (NPs) through an economical, surfactant-free and efficient method of seed-mediated growth. The Au@Pt NPs displayed electrochemical performances superior to those of commercial Pt/C catalysts because their agglomeration was prevented and exhibited better long-term stability with respect to methanol oxidation in acidic media by efficiently removing intermediates. Among the obtained Au@Pt NPs, Au 90 @Pt 10 NPs exhibited the most significantly enhanced catalytic performance for the methanol oxidation reaction (MOR). Their mass and electrochemically active surface area (ECSA)-normalized current densities are approximately 3.9 and 4.6 times higher than those of commercial Pt/C catalysts, respectively. The oxidation current densities of the Au 90 @Pt 10 NPs are approximately 1.8 times higher than those of commercial Pt/C catalysts after 4000 s of continuous measurement because the small Pt NPs grown on the surface of the Au 90 @Pt 10 NPs were effectively stabilized by the Au metal support. This approach may be a facile method for the synthesis of self-supported bimetallic nanostructures, which is of great significance for the development of high performance electrocatalysts and sensors.

A new silsesquioxane molecule was synthesized, in which triphenyl benzene was connected with three Si(OC2H5)3 groups using three urea groups as the bridge. The molecule could self-assemble through the intermolecular H-bonding among urea groups and pi-pi interaction of triphenyl benzene core in the solution and it could also be transferred into hybrid silicas by hydrolysis. When the non-preorganized silsesquioxane was hydrolyzed, isolated spherical hybrid silica was gained. However, when the silsesquioxane was preorganized before the hydrolyzation uniform interconnected spherical hybrid silica and intertwined nanofibrous one could be generated under acidic and basic conditions, respectively. The photoluminescence (PL) spectra of the obtained hybrid silicas showed that they still kept the emission properties of their precursor silsesquioxane, and the shift of the emission bands was due to the pi-pi interaction of triphenyl benzene in the course of polycondensation.

We report the synthesis and self-assembly of a new pi-conjugated dichalcone substituted carbazole-based low molecular mass organogelator. It could form stable gels in most halogen-aromatic solvents. The transmission electron microscopy (TEM) images revealed that the gel formed fibrous structures with diameter of 50-100 nm, which consisted of several thinner fibers. The FT-IR, UV-vis and XRD results suggested that the H-bonds and pi-pi interactions were the main driving forces for the formation of the self-assembled gel, in which the U-shaped molecules were stacked into lamellar structures. The fluorescent spectra showed that the emission of the xerogel red-shifted markedly compared with the sol state, which resulted from the aggregation of the molecules.

We report on the synthesis and self-assembly of a new series of discotic molecules containing triphenylbenzene as the core and alkoxy side chain with varying length. It was found that compounds 3 a-c, 4 b and 5 b could form stable gels in several apolar solvents. Transmission electron microscopy (TEM) images revealed that their morphologies were very different for the different alkoxy-substituted organogels. In toluene or hexane, 3 b and 3 c resulted in both left- and right-handed helical fibers, whereas 3 a resulted in straight rigid fibers; 4 b and 5 b resulted in most straight fibers with a few twisted fibers. The results from FT-IR and UV/Vis absorption spectroscopy indicated that the hydrogen bonding and pi-pi interactions were the main driving forces for the formation of the self-assembled gels. Further detailed analysis of their aggregation modes were conducted by UV-visible absorption spectra and X-ray diffraction (XRD) measurements. Based on these findings, the influence of these peripheral alkoxy substituents on the gel formation and the aggregation mode were discussed. The special enhanced fluorescent emissions, which resulted from aggregation, were also found in the gel phase.

A new hydrogel based on glucose-appended Schiff base derivative has been employed as the template to synthesize CdS and NiS nanostructures with different morphologies. The FT-IR and UV-vis results revealed that H-bonding and pi-pi interaction played important roles in the formation of original hydrogel fibers. The study of mineralization mechanism suggested that the inorganic ions were firstly adsorbed at the surface of the hydrogel fibers due to the hydrophilic affinity with the hydrophilic glucose groups. With the penetration of H2S gas, the preformed CdS or NiS nanoparticles on the surface of the fibers acted as the growing points for the continuous growth. And the different adsorption abilities of the metal ions at the hydrogel fibers resulted in the formation of CdS nano-necklaces and NiS nanotubes.

A new series of binary organogels, which showed good gelated capability and strongly enhanced fluorescence emission, were designed and prepared by simply mixing two components of L-tartaric acid and alkoxyl substituted stilbazoles. It was found that L-tartaric acid could not only introduce stilbazole with fluorescent property into the gel system, but also provided a main motif for the formation of the gel-phase via multiple hydrogen bonds. Meanwhile, pi-pi interactions between the complexes also played a key role in the gel formation. The decreased nonradiative process, suggested by the longer fluorescent lifetime of aggregates than that of monomers and the presence of the J-aggregation for the aggregated state, favored the enhanced fluorescence emission.

A new cholesterol organogelator 1 was synthesized, which was confirmed as an effective gelator for various organic solvents and could self-assemble into network fibers in some organic solvents. Moreover, gelator 1 could act as templates for the synthesis of various CuS nanofibers with different helical pitches. For example, when H(2)S was used as the sulfur source, straight and bending helical CuS nanofibers with a pitch of 100-200 nm could be fabricated in butyl acetate and benzene-butanol gel systems, respectively, while bending CuS nanofibers with a similar helical pitch (ca. 50 nm) could be obtained when thioacetamide was used as the sulfur source in both gel systems. It was first found that the morphologies of inorganic nanofibers could be controlled by the binding sites between the inorganic precursor and the organogel.

Hydrogels based on beta-D-glucopyranoside-substituent thiosemicarbazide derivatives were synthesized and used as template to fabricate netlike CdS nanofibers. The self-assembling properties of the hydrogels and their effect on the synthesis of CdS nanostructure were studied. Fourier transform infrared spectra, UV-visible absorption spectra and X-ray diffraction revealed that pi-pi stacking, hydrogen bonds and interdigitated interactions between hydrophobic chains had influence on the formation of self-assembled lamellar hydrogel. Transmission electron microscopic and electron diffraction observation showed the formation of hexagonal stacking nanofiber-based CdS semiconductor materials. The transmission electron microscopic pictures of the CdS nanostructure in difference growth stages revealed the growth mechanism of CdS nanofibers templated by hydrogel.

A new cholesterol organogelator 4 was synthesized and its gelation property was evaluated. It was confirmed that 4 was an effective gelator for various organic solvents and could self-assemble into network fibers with a bilayer of folded conformation in some organic solvents. Moreover, organogelator 4 could act as a template for the synthesis of novel pearl-necklace porous CdS nanofibers. The transcription process of organogel fibers into CdS nanofibers was investigated, and it was found that Cd2+ ions were coated on the organogel fibers by the interaction with ester groups of 4, which might lead to the change of the arrangement of the organogelator and seemed to serve as nucleation sites for metalization. The further growth of CdS began with these nucleation sites along the organogel fibers. Meanwhile, parts of 4 free from organogel fibers have an effect on the formation of the CdS nanofibers consisting of the network and wormlike CdS particles., (Copyright 2004 American Chemical Society)