Majorana-Oppenheimer approach to Maxwell electrodynamics in Riemannian space-time

The Riemann -- Silberstein -- Majorana -- Oppengeimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation under transformations of the complex rotation group SO(3.C) is demonstrated explicitly. In vacuum case, the matrix form includes four real $4 \times 4$ matrices $\alpha^{b}$. In presence of media matrix form requires two sets of $4 \times 4$ matrices, $\alpha^{b}$ and $\beta^{b}$ -- simple and symmetrical realization of which is given. Relation of $\alpha^{b}$ and $\beta^{b}$ to the Dirac matrices in spinor basis is found. Minkowski constitutive relations in case of any linear media are given in a short algebraic form based on the use of complex 3-vector fields and complex orthogonal rotations from SO(3.C) group. The matrix complex formulation in the Esposito's form, based on the use of two electromagnetic 4-vector, is studied and discussed. Extension of the 3-vector complex matrix formalism to arbitrary Riemannian space-time in accordance with tetrad method by Tetrode-Weyl-Fock-Ivanenko is performed.Comment: 32pages. Proccedings of the 14th Conference-School "Foundation & Advances in Nonlinear Science", Minsk, September 22-25, 2008. P. 20-49; ed. V.I. Kuvshinov, G.G. Krylov, Minsk, 200

Optimisation of biochar filter for handwashing wastewater treatment and potential treated water reuse for handwashing

Portable handwashing facilities help fight the transmission of water-borne diseases. However, in places lacking piped drainage systems, handwashing wastewater (HW) is commonly discarded into the ground. This harms the environment and public health and wastes reusable water. This study optimised the biochar filtration parameters such as particle size (0.5–2 mm), filter depth (15–30 cm) and flow rate (1–2.5 L/h) to remove colour, turbidity, phosphates and E. coli from HW using Response Surface Methodology. Fifteen configurations studied the impact of filtration parameters on pollutant removal. Quadratic models provided the best fit for pollution removal data. Optimal conditions were 1.25 mm particle size, 30 cm filter depth and 1 L/h flow rate, with predicted removals of 97.06, 97.50, 82.67 and 73.06 % for colour, turbidity, phosphates and E. coli, respectively. Biochar filter performance under optimal conditions validated the models. Actual removal efficiencies of 97.63, 99.85, 85.94 and 76.08 % for colour, turbidity, phosphates and E. coli, respectively, aligned closely with predicted values. Treated HW quality complied with several international water quality standards. Optimising biochar filtration is crucial for integrating this technology into portable handwashing facilities with potential water reuse, benefiting communities in developing countries with limited handwashing infrastructure and access to water