Population increase and industrialization has resulted in high energy demand and consumptions, and presently, fossil fuels are the major source of staple energy, supplying 80% of the entire consumption. This has contributed immensely to the greenhouse gas emission and leading to global warming, and as a result of this, there is a tremendous urgency to investigate and improve fresh and renewable energy sources worldwide. One of such renewable energy sources is biogas that is generated by anaerobic fermentation that uses different wastes such as agricultural residues, animal manure, and other organic wastes. During anaerobic digestion, hydrolysis of substrates is regarded as the most crucial stage in the process of biogas generation. However, this process is not always efficient because of the domineering stableness of substrates to enzymatic or bacteria assaults, but substrates’ pretreatment before biogas production will enhance biogas production. The principal objective of pretreatments is to ease the accessibility of the enzymes to the lignin, cellulose, and hemicellulose which leads to degradation of the substrates. Hence, the use of pretreatment for catalysis of lignocellulose substrates is beneficial for the production of cost-efficient and eco-friendly process. In this review, we discussed different pretreatment technologies of hydrolysis and their restrictions. The review has shown that different pretreatments have varying effects on lignin, cellulose, and hemicellulose degradation and biogas yield of different substrate and the choice of pretreatment technique will devolve on the intending final products of the process.

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We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories z = ±2(x − x0), which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE.

Carbon nanomaterials such as graphene and carbon nanotubes possess great thermophysical properties which make them very good candidates for heat transfer application. However, the major challenge of these nanomaterials is their tendency to agglomerate and bundle together when dispersed in base fluids. This study reviews the homogeneous dispersion of these nanomaterials in aqueous solution with the aid of surfactants. The different surfactants and their characterization methods for stable dispersion of carbon nanomaterials have been examined. The influence of surfactants on the thermophysical and rheological properties of carbon-based nanofluids was also highlighted. The usefulness of noncovalent functionalization using surfactants is due to its ability to efficiently unbundle carbon nanomaterials and sustain homogeneity of the nanofluids without compromising the integrity of their structure. Sodium dodecyl sulfate (SDS), sodium dodecyl benzene sulfate (SDBS), Gum Arabic (GA), Triton X-100, and cetyltrimethylammonium bromide (CTAB) are the commonly used surfactants. Unlike SDS, SDBS, and CTAB, GA does not foam when agitated. Various authors have investigated the stability of carbon-based nanofluids. Both physical and chemical techniques have been used to stabilize nanofluids. Mixed surfactants were found to stably disperse nanomaterials at lower concentrations compared to individual surfactants. However, limited studies exist for long term stability of carbon-based nanofluids.

We suggest a real physical system — the honeycomb lattice — as a possible realization of the fractional Schrödinger equation (FSE) system, through utilization of the Dirac‐Weyl equation (DWE). The fractional Laplacian in FSE causes modulation of the dispersion relation of the system, which becomes linear in the limiting case. In the honeycomb lattice, the dispersion relation is already linear around the Dirac point, suggesting a possible connection with the FSE, since both models can be reduced to the one described by the DWE. Thus, we propagate Gaussian beams in three ways: according to FSE, honeycomb lattice around the Dirac point, and DWE, to discover universal behavior — the conical diffraction. However, if an additional potential is brought into the system, the similarity in behavior is broken, because the added potential serves as a perturbation that breaks the translational periodicity of honeycomb lattice and destroys Dirac cones in the dispersion relation.