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Abstract Flocking cohesion is critical for maintaining a group’s aggregation and integrity. Designing a potential function to maintain flocking cohesion unaffected by social distance is challenging due to the uncertainty of real-world conditions and environments that cause changes in agents’ social distance. Previous flocking research based on potential functions has primarily focused on agents’ same social distance and the attraction–repulsion of the potential function, ignoring another property affecting flocking cohesion: well depth, as well as the effect of changes in agents’ social distance on well depth. This paper investigates the effect of potential function well depths and agent’s social distances on the multi-agent flocking cohesion. Through the analysis, proofs, and classification of these potential functions, we have found that the potential function well depth is proportional to the flocking cohesion. Moreover, we observe that the potential function well depth varies with the agents’ social distance changes. Therefore, we design a segmentation potential function and combine it with the flocking control algorithm in this paper. It enhances flocking cohesion significantly and has good robustness to ensure the flocking cohesion is unaffected by variations in the agents’ social distance. Meanwhile, it reduces the time required for flocking formation. Subsequently, the Lyapunov theorem and the LaSalle invariance principle prove the stability and convergence of the proposed control algorithm. Finally, this paper adopts two subgroups with different potential function well depths and social distances to encounter for simulation verification. The corresponding simulation results demonstrate and verify the effectiveness of the flocking control algorithm.

In this study, the problem of multi-agent flocking with partially informed agents is investigated, by considering the incomplete information factor in a flocking process. Incomplete information includes two aspects: receiver and sender. One is resisted or distorted information by the agents when they receive information from the virtual leader or others, and the other is passive loss of information sent by the virtual leader or others to the agents. In a flocking process with a fraction of informed agents, to make informed agents drive more uninformed agents to track the virtual leader, we first discuss the derivative of the potential function in the flocking algorithm: the force function. The relationship between repulsion and attraction among agents is directly shown. Subsequently, an improved flocking algorithm is proposed based on Morse potential function. The stability of the algorithm is proved by using the Lyapunov stability theorem and LaSalle’s invariance principle. Consider the initial distribution of agents with low connectivity and density, based on the above modified algorithm, a novel method of selecting informed agents as propagandists is presented. Propagandists are created in the vicinity of virtual leaders. Before flocking, propagandists move regularly within an arbitrarily distributed group, disseminating information to other uninformed agents. This approach can reduce the unfavorable effects caused by incomplete information. Eventually, the simulation results show that even though only one informed agent is selected as the propagandist, most agents can track the common objective.

Birnessite nanoflowers composed of layers have been proven to be the strongest adsorbent and oxidant in the surface environment. However, the current synthesis methods of birnessite nanoflowers are suffering from long reaction time and high reaction temperature. Based on these, this paper explores a new method for the rapid and controlled synthesis of layered manganese oxides. The method relies on the molar ratios of KMnO4 and H2O2 redox reacting species to drive the production of birnessite nanoflowers under acidic conditions. The molar ratios of KMnO4 and H2O2 are the key to the crystal structure of the as-prepared. It was found that when the molar ratios of KMnO4 and H2O2 is from 1:1.25 to 1:1.90, the sample is birnessite nanoflowers, and when the ratio is increased to 1:2.0, the sample is a mixture of birnessite nanoflowers and feitknechtite nanoplates. Among the as-prepared samples, BF-1.85 (molar ratios of KMnO4 and H2O2 is 1:1.85) shows the highest capacity for Pb2+ adsorption (2,955 mmol/kg) and greatest degradation efficiency of phenol and TOC. The method proposed herein is economical and controllable, and it yields products with high efficiency for the elimination of inorganic and organic pollutants.

Vernadite has excellent oxidation and adsorption performance, suggesting that it has good application prospects for the removal of phenolic substances and heavy metals from wastewater. In this study, after vernadite was synthesized by two different methods, the removal performance difference between the samples synthesized by the new and traditional methods (Ver-H and Ver-OH, respectively) was explored by sample characterization, phenol degradation, and Pb2+ adsorption experiments. The results show that, compared with Ver-OH, Ver-H has a larger particle size, specific surface areas, and total organic carbon (TOC) degradation capacity; the equilibrium degradation capacity of TOC of Ver-H was increased by 31.3%. The difference in the amount of TOC degradation may be attributed to more Mn(IV) oxygen vacancies in Ver-H, which facilitate the removal of intermediate products formed during phenol degradation. In addition, the larger specific surface areas provide the mineral surface with a larger number of active sites; Ver-H can therefore adsorb more intermediate products to promote their mineralization into CO2. The adsorptions of Pb2+ by Ver-H and Ver-OH are both consistent with Langmuir isothermal adsorption, and the maximum adsorption capacities are 569.79 g/kg and 623.10 g/kg, respectively. The lack of significant difference indicates that both vernadites have strong adsorption capacities for Pb2+.

With the intensification of human activities, arsenite (As(III)) pollutant from the soil and ground water has been a threat to human health, and the problem gradually becomes the focus of attention. In this study, the effects of several environment factors on As(III) removal ability of complex minerals are determined through the analysis of mineralogical characteristics of the complex synthesis of hematite and kaolin, using X-ray diffraction, Fourier transform infrared, and specific surface area. In the results, the XRD patterns of hematite and kaolin complexes indicate that the loading covers up some characteristic peaks of minerals in kaolin, which can be that hematite loading decrease the order of structure for some minerals. With increasing Fe content, the hydroxyl sites gradually increase, therefore strengthening the As(III) removal ability of complexes. With increasing the As(III) concentration, the removal ratios of kaolin on As(III) almost keep unchanged and that of complexes show no obvious regularity. However, with the pH increasing, the removal ratios of all samples keep increasing. Furthermore, the increasing of As(III) concentration and pH both improve As(III) removal amount significantly, especially for As(III) concentration. In addition, there is no forming of new mineral through it as observed by XRD. Therefore, hematite loading can promote the As(III) removal on kaolin through adsorption in different environments, which can provide a better method for the remediation of arsenic pollution.

Lead (Pb) chemical fixation is an important environmental aspect for human health. Phosphate rocks (PRs) were utilized as an adsorbent to remove Pb from aqueous solution. Raw PRs and oxalic acid-activated PRs (APRs) were used to investigate the effect of chemical modification on the Pb-binding capacity in the pH range 2.0-5.0. The Pb adsorption rate of all treatments above pH 3.0 reached 90%. The Pb binding on PRs and APRs was pH-independent, except at pH 2.0 in activated treatments. The X-ray diffraction analysis confirmed that the raw PRs formed cerussite after reacting with the Pb solution, whereas the APRs formed pyromorphite. The Fourier Transform Infrared spectroscopy analysis indicated that carbonate (CO2-3) in raw PRs and phosphate (PO3-4) groups in APRs played an important role in the Pb-binding process. After adsorption, anomalous block-shaped particles were observed by scanning electron microscopy with energy dispersive spectroscopy. The X-ray photoelectron spectroscopy data further indicated that both chemical and physical reactions occurred during the adsorption process according to the binding energy. Because of lower solubility of pyromorphite compared to cerussite, the APRs are more effective in immobilizing Pb than that of PR [ABSTRACT FROM AUTHOR]