In this paper, we perform a classification of Lie point symmetries of a (3+1)-dimensional model describing tumour cells, extracellular matrix (ECM), and matrix-degrading enzymes (MDEs). From the symmetries, we were able to find new exact solutions for the model. One of the solutions we found has haptotaxis effect. We explore these solutions, analysing the invasion of tumour cells, the evolution of the ECM degradation by MDEs and the diffusion of the MDEs. We also obtain three conserved currents and from them we explore the time variation of certain biological quantities.
The compositional heterogeneity of agro-industrial byproducts presents a significant challenge for engineering high-performance bio-based materials without resource-intensive macromolecular separation. Here, an eco-efficient strategy is proposed for the comprehensive valorization of whole mango byproducts (MBPs), including peels and finisher pulp (PeP), seed tegument (SeT), and kernel (SeK), into functional bioplastics intended for food packaging. To disrupt the organized biomass structure for subsequent assembly into films, MBPs were subjected to mild hydrothermal pretreatment (HTP) or dilute alkaline pretreatment (DALP), which selectively partitioned amorphous biomass components and induced distinct structural responses according to the mango byproduct. While HTP better preserved solubilized carbohydrates, DALP promoted more extensive pectin saponification and hemicellulose solubilization. Bioplastic films were then prepared using pretreated PeP, SeK, or a mixture of all byproducts (PePSe). The incorporation of only 10% carboxymethyl cellulose (CMC) improved film mechanical performance, yielding tensile strength values of up to 11 MPa. The SeK-based films exhibited the lowest water vapor permeability (2.3 g mm kPa−1 h−1 m−2), and all CMC-containing films displayed hydrophobic surfaces (water contact angle > 90°). All bioplastics provided near-total UVA and UVB shielding (>97%), while the PeP-based films exhibited the highest transparency (>43%). Although the antioxidant activity of the bioplastics decreased compared to that of the corresponding raw MBPs, the PeP-DALP-CMC film retained at least 50% of it. By demonstrating that biomass heterogeneity can be harnessed, rather than eliminated, to tailor functional bioplastics, this simple and effective approach emerges as a potentially scalable strategy for producing sustainable active packaging materials.
Additive manufacturing (AM) offers significant potential for fabricating microchannel heat exchangers (MCHEs) by overcoming the geometric limitations and material waste associated with conventional manufacturing methods. While laser powder bed fusion (L-PBF) enables high-resolution features, it remains constrained in scalability, particularly for large or multi-material structures. In contrast, laser powder directed energy deposition (LP-DED) provides greater flexibility but faces challenges in achieving thin walls with surface quality comparable to L-PBF. This study investigates the feasibility of fabricating Inconel 718 microchannels using a small laser spot size (0.8 mm) in LP-DED, with particular emphasis on the influence of deposition strategy and process parameters. Thin walls with thicknesses ranging from 0.579 mm to 0.674 mm were successfully produced using previously optimized conditions. The results demonstrate that deposition strategy plays a decisive role in geometric fidelity. A continuous scanning path without a U-path resulted in severe defects, including material accumulation, wall tearing, and height inconsistencies. In contrast, the implementation of a U-path strategy significantly improved dimensional uniformity. The non-continuous strategy (300 W, 1500 mm/min, 4 g/min) minimized height variation and ensured corner stability, albeit with slightly increased surface roughness and waviness. Conversely, higher scan speeds (2000 mm/min) combined with a continuous U-path reduced internal roughness and waviness. Dimensional analysis confirmed high reproducibility across larger channels, while smaller channels (0.3 × 2 mm2) were prone to partial blockage due to powder adhesion, necessitating post-processing. Micro-milling was successfully applied, reducing the average surface roughness (Ra) from 11.16 µm to 0.75 µm. Furthermore, detailed surface characterization revealed intrinsic waviness, with Wsm ranging from 919 µm to 3180 µm and Wz from 29 µm to 76 µm. This inherent topography, characteristic of the LP-DED process, presents a promising opportunity for future research, as it may be leveraged to enhance thermal–hydraulic performance similarly to intentionally created through other manufacturing methods.
CuO was synthesized using various metal precursors as Cu2+ sources via a combined coprecipitation and microwave-assisted hydrothermal method, and its gas-sensing performance was systematically evaluated in relation to its structural, electronic, and morphological properties. This study systematically investigates the role of precursor chemistry as a key parameter in controlling the nucleation and growth of CuO nanostructures under identical synthesis conditions. X-ray diffraction (XRD) confirmed the formation of monoclinic CuO, and the crystallite sizes calculated using the Williamson–Hall method decreased in the order CuO-Chloride > CuO-Nitrate > CuO-Sulfate. Scanning and transmission electron microscopy (SEM and TEM) analyses revealed that all samples were composed mainly of CuO nanorods, with slight differences in thickness and dimensions. The Cu2+ oxidation state was further confirmed by X-ray photoelectron spectroscopy (XPS). The three sensors exhibited excellent NO2 detection at 200 °C, with the CuO-N sensor showing the highest response. The limit of detection (LOD) for CuO-N was 0.12 ppm, well below the safety threshold of 1 ppm, demonstrating its capability to detect low NO2 concentrations. Furthermore, the CuO-N sensor maintained stable responses over four consecutive cycles of 1 ppm NO2, indicating good operational stability without degradation of its sensing performance. The sensor produced using a metallic nitrate precursor showed the best NO2 detection response (58
Primate populations isolated in forest fragments within urban areas often face critical survival challenges due to the negative effects of habitat degradation on genetic diversity, evolutionary potential, and ecological dynamics. The Arc of Deforestation has the highest deforestation rates in the Brazilian Amazon, driven primarily by growth of monocultures, ranching, and urbanisation. However, there are no published studies on urban primate demography and genetic diversity in this region. The range of the white-cheeked spider monkey (Ateles marginatus) overlaps significantly with the Arc of Deforestation, where anthropogenic pressures threaten its long-term survival. We assessed the genetic diversity and structure of A. marginatus from five urban forest fragments in Sinop, Mato Grosso, Brazil, by analysing the mitochondrial control region (D-loop). We also compared our data with publicly available Ateles D-loop sequences. Results showed that the study population has high levels of genetic diversity and no signs of spatial substructuring. The haplotype network and phylogenetic tree showed one individual identified as A. marginatus clustered with Genbank sequences of A. chamek, a congeneric species expected only on the opposite bank of the Teles Pires-Tapajós River. Historical demographic analysis showed population expansion between 22–20 kybp, followed by population decline at 10–2 kybp. Recent population fragmentation was probably accompanied by local haplotype extinctions in the study area. Our findings show that urban primate populations can retain genetic diversity and significant evolutionary potential for conservation management and suggest that Amazonian rivers may be more a filter than barrier for Atelid species, allowing the sporadic crossing of individuals.
