Differential invariants and conservation lows of granular activated carbon filter system
Keywords:
nonclassical symmetries, differential invariants, conservation laws, GAC filter systemAbstract
In this study, differential invariants of the granular activated carbon (GAC) filter system are investigated. Investigation of differential invariants offers a deeper understanding of the system's inherent properties that remain unchanged under specific transformations. Nonclassical symmetry method is applied to study the lifetime of (GAC) filter system. Finally, conservation laws of the GAC system are presented. The derivation of conservation laws further enhances the analysis by providing conserved quantities that remain constant over time.
Downloads
References
[1] Borsi, I., Fasano, A., Lenzini, L. (2011). Computing the lifetime of granular activated carbon
filters by means of travelling waves solutions. Applied Mathematical Modelling. vol. 35, p. 1868-1880.
[2] Bohart, G.S., Adams, E.Q. (1920). Some aspects of the behavior of charcoal with respect to chlorine. J. Am. Chem. Soc. vol. 42, no. 3, p. 523-544.
[3] Singh, T.S., Pant, K. (2006). Experimental and modelling studies on fixed bed adsorption of As(iii) ions from aqueous solution. Separ. Purif. Technol. Vol. 48, no. 3, p. 288-296.
[4] Shirvani, V., (2025). Group analysis for granular activated carbon filter system. Proceedings of Ninth International Conference on Physic, Mathematics and Development of Basic Science.
[5] Bluman, G.W., Cole, J.D. (1969). The general similarity solutions of heat equation. Journal of Mathematics and Mechanics. vol. 18, p. 1025-1042.
[6] Clarkson, P.A. (1995). Nonclassical symmetry reductions of the Boussinesq equation. Chaos, Solitons, Fractals. vol. 5, p. 2261-2301.
[7] Clarkson, P.A., Mansfield, E.L. (1994). Algorithms for the nonclassical method of symmetry reductions. SIAM Journal on Applied Mathematics. vol. 55, p. 1693-1719.
[8] Bila, N., Niesen, J. (2004) On a new procedure for finding nonclassical symmetries. Journal of Symbolic Computation. vol. 38, p. 1523-1533.
[9] Bluman, G.W. (2006). New conservation laws obtained directly from symmetry action on a known conservation law. J. Math. Anal. Appl. vol. 322, p. 233-250.
[10] Bluman, G.W., Cheviacov, A.F., Anco, S.C. (2010). Applications of Symmetry Methods to Partial Differential Equations. Applied Mathematical Sciences. 168 Springer, New York.
[11] Shirvani, V., Nadjafikhah, M. (2020). Symmetry analysis and conservation laws for higher order CamassaHolm equation. vol. 8, no. 2, p. 364-372.
[12] Olver, P.J., (1993). Applications of Lie Groups to Differential Equations, In: Graduate Texts in Mathematics. 107 Springer, New York.
[13] Poole, D., Hereman, W. (2010). The homotopy operator method for symbolic integration by parts and inversion of divergences with applications. Appl. Anal. vol. 87, p. 433-455
