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Rajendran, L.
- Approximate Analytical Solution of Non-linear Kinetic Equation in a Porous Pellet
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1 Department of Mathematics, The Madura College, Madurai-625011, Tamil Nadu, IN
1 Department of Mathematics, The Madura College, Madurai-625011, Tamil Nadu, IN
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Global Journal of Pure and Applied Mathematics, Vol 8, No 2 (2012), Pagination: 101-111Abstract
A mathematical model for immobilized enzyme system in porous spherical particles was developed. This model contains a non-linear term related to reversible Micahlies- Menten kinetics. Analytical expression pertaining to the substrate concentration was reported for all possible values of Thiele moduleφ , parameters c and k s . In this work, we report the theoretically evaluated steady-state concentration for immobilized enzyme systems in porous spherical particles for zero order, first order and second order reaction meacnisms. Herein we employ "Homotopy perturbation method" (HPM) to solve non-linear reaction /diffusion equation.Keywords
Mathematical Modelling, Non-linear Equations, Homotopy Perturbation Method, Reaction/diffusion Equation, Porous MediaReferences
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- Ghori, Q. K., Ahmed, M., Siddiqui, A. M., 2007, “Application of Homotopy perturbation method to squeezing flow of a Newtonian fluid”, International Journal of Nonlinear Science and Numerical Simulation, Vol. 8(2), pp. 179- 184.
- Ozis, T., Yildirim, A., 2007, “A comparative study of He’s homotopy perturbation method fordetermining frequency-amplitude relation of a nonlinear oscillater with discontinuities”, International Journal of Nonlinear Science and Numerical Simulation, Vol. 8(2), pp. 243-248.
- Li, S. J., and Liu, Y. X., 2006, “An improved approach to nonlinear dynamical system identification using PID neural networks”, International Journal of Nonlinear Science and Numerical Simulation, Vol. 7(2), pp. 177-182.
- Mousa, M. M., Ragab, S. F., 2008, “Application of the Homotopy Perturbation Method to Linear and Nonlinear Schrödinger Equations”, Zeitschrift fur Naturforschung, Vol. 63, pp. 140-144.
- He, J. H., 1999, “Homotopy perturbation technique”, Computer Methods in Applied Mechanics and Engineering, Vol. 178, pp. 257-262.
- He, J. H., 2003, “Homotopy perturbation method: a new nonlinear analytical Technique”, Applied Mathematics and Computation, Vol. 135, pp. 73-79.
- He, J. H., 2003, “A simple perturbation approach to Blasius equation”, Applied Mathematics and Computation, Vol. 140, pp. 217-222.
- He, J. H., 2006, “Homotopy perturbation method for solving boundary value problems”, Physics Letter A, Vol. 350, pp. 87-88.
- He, J. H., “Some asymptotic methods for strongly nonlinear equations, ” International Journal of Modern Physics B, Vol. 20, no. 10, pp. 1141-1199.
- Eswari, A., Rajendran, L., 2010, “Analytical solution of steady state current at a micro Disk biosensor”, Journal of Electroanalytical Chemistry, Vol. 641, pp. 35-44.
- Meena, A., Rajendran, L., 2010, “Mathematical modeling of amperometric and Potentiometric biosensors and system of non-linear equations-Homotopy perturbation approach”, Journal of Electroanalytical Chemistry, Vol. 644, pp. 50-59.
- Yan-Ping Sun, Shi-Bin Liu, Scott Keith, 2004, Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by the decomposition method, Chemical Engineering Journal 102, 1-10.
- Abbasbandy, S., 2008, “Approximate solution for the nonlinear model of diffusion and reaction in Porous catalysts by means of the homotopy analysis method”, Chemical Engineering Journal 136, 144-150.
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- Analytical Solution of the Concentration in a Packedbed Immobilized Enzyme Reactor Using Homotopy Perturbation Method
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Affiliations
1 Department of Mathematics, The Madura College, Madurai-625011, Tamil nadu, IN
1 Department of Mathematics, The Madura College, Madurai-625011, Tamil nadu, IN
Source
Global Journal of Theoretical and Applied Mathematics Sciences, Vol 2, No 1 (2012), Pagination: 21-33Abstract
A mathematical model of packed-bed immobilized enzyme (IME) reactor is presented. The model is based on system of reaction-diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reaction. A simple and closed approximate analytical expression of the steady-state concentrations and effectiveness factor in a Packed-bed immobilized enzyme reactor are derived for all values of the reaction diffusion parameters. In this paper, He's Homotopy perturbation method is implemented to give approximated and analytical expression of concentration of substrate and effectiveness factor for all values of the parameters.Keywords
Mathematical Model, Steady-state, Homotopy Perturbation Method, Packed-bed Reactor, Immobilized Enzyme, Michaelis -menten KineticReferences
- Roberts, D. Enzyme kinetics, Cambridge University Press, U. K, 1977.
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- Petre, D., Noel, C. and Thomas, D. A new method for cell immobilization, Biotechnol. Bioeng., 20: 127, 1978.
- Lee, S. B., Kim, S. M. and Ryu, D. Y. Effects of external diffusion and design geometry on the performance of immobilized glucose isomerase reactor system, Biotechnol. Bioeng., 21: 2023, 1979.
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- Shiraishi, F. Substrate concentration dependence of apparent maximum reaction rate and apparent Michaelis constant observed in immobilized enzyme reactions, Kagaku Kogaku, 16: 123, 1990.
- Shiraishi. F., Hasegawa, T., Kasai, S. and Makishita, N. Characteristics of apparent kinetic parameters in a packed-bed immobilized enzyme reactor, Chem. Eng. Sci., vol. 51, No. 11: 2847-2852, 1996.
- Li, S. J. and Liu,Y.X. An Improved Approach to Nonlinear Dynamical System Identification using PID Neural Networks, Int. J. Nonlinear. Sci. and Numer. Simulat, vol. 7, no. 2., 7(2): 177-182, 2006.
- Mousa, M. M., Ragab, S. F. and Nturforsch . Z. Application of the Homotopy Perturbation Method to Linear and Nonlinear Schrödinger Equations, Zeitschrift für Naturforschung, vol.63: 140-144, 2008.
- He, J.H, Homotopy perturbation technique, Comput. Meth. Appl. Mech. and Eng, vol. 178: 257-262, 1999.
- He, J.H, Homotopy perturbation method: a new nonlinear analytical Technique, Appl. Math and Comput. vol.135: 73-79, 2003.
- He, J.H, A Simple perturbation approach to Blasius equation, Appl. Math and Comput, vol 140: 217-222, (2003).
- He, J.H, Some asymptotic methods for strongly nonlinear equations, Int. J. Modern Phys. B, 20 (10): 1141–1199, 2006.
- He, J.H, Wu, G.C. Austin, F. The variational iteration method which should be followed, Nonlinear Sci. Lett. A 1: 1–30, 2010.
- He, J.H, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int. J. Nonlinear Mech. 35: 37–43, 2000.
- Ganji, D.D., Amini, M, and Kolahdooz, A, Analytical investigation of hyperbolic Equations via He’s methods, Am. J. Eng. Appl. Sci. 1 (4): 399–407, 2008.
- Concentration of Species in Two Species Oscillator Using Homotophy Peturbation Method
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Authors
Affiliations
1 Department of Mathematics, The Madura College, Madurai-625 011, Tamil Nadu
1 Department of Mathematics, The Madura College, Madurai-625 011, Tamil Nadu
Source
Global Journal of Theoretical and Applied Mathematics Sciences, Vol 2, No 2 (2012), Pagination: 99-108Abstract
The mathematical model of two-species oscillator is discussed. A simple approximate analytical expression of concentration profiles is derived in terms of all dimensionless parameters. Furthermore, in this work we employ the Homotopy perturbation method to solve the non-linear reaction equations. Moreover, the analytical results have been compared to the numerical simulation using Matlab program. The simulated results are agreed with the appropriate theories.Keywords
Mathematical Modelling, Homotopy Perturbation Method, Two- Species OscillatorReferences
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- Madzvamuse, A., Maini, P. K., and Wathen, A. J., 2005, “A moving grid finite element method for the simulation of pattern generation by Turing models on growing domains”, J. Sci. Comput., 24, 247–262.
- Madzvamuse, A., Wathen, A. J., and Maini, P. K., 2003, “ A moving grid finite element method applied to a model biological pattern generator”. J. Comput. Phys., 190, 478–500.
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- Ghori, Q. K., Ahmed, M., Siddiqui, and A. M., 2007, “Application of homotopy perturbation method to squeezing flow of a Newtonian fluid”, Int. J. Nonlinear Sci. Numer. Simulat., 8, 179-184.
- Ozis, T., Yildirim, A., 2007, “A Comparative Study of He’s Homotopy perturbation method for determining frequency-amplitude relation of a nonlinear oscillator with discontinuities”, Int. J. Nonlinear Sci. Numer. Simulat., 8, 243-248.
- Li, S. J., and Liu, Y. X., 2006, “An improved approach to nonlinear dynamical system identification using PID neural networks”, Int. J. Nonlinear Sci. Numer. Simulat., 7, 177-182.
- Mousa, M. M., Ragab, S. F., and Nturforsch . Z., 2008, “Application of the Homotopy. Perturbation Method to Linear and Nonlinear Schrödinger Equations“, Zeitschrift für Naturforschung., 63, 140-144.
- Loghambal, S., and Rajendran, L., 2010, “Mathematical modeling of diffusion and kinetics of amperometric immobilized enzyme electrodes”, Electrochim Acta., 55, 5230-5238.
- Meena, A., and Rajendran, L., 2010, ‘Mathematical modeling of amperometric and potentiometric biosensors and system of non-linear equations – Homotopy perturbation approach”, J .Electroanal Chem., 644, 50-59.
- Thiagarajan, S. Meena, A., Anitha, S., and Rajendran, L., 2011, “Analytical expression of the steady-state catalytic current of mediated bioelectrocatalysis and the application of He’s Homotopy perturbation method”, J Math Chem., 49, 1727–1740.
- Anitha, S., Subbiah, A., Subramaniam, S., and Rajendran, L., 2011,”Analytical solution of amperometric enzymatic reactions based on Homotopy perturbation method”, Electrochimica Acta., 56, 3345-3352.
- He. J. H., 1999, “Homotopy perturbation technique”, Comp Meth. Appl. Mech. Eng., 178, 257-262.
- He. J. H., 2003, “Homotopy perturbation method: a new non-linear analytical technique”, Appl. Math. Comput., 135, 73-79.
- He. J. H., 2003, “A simple perturbation approach to Blasius equation”, Appl. Math. Comput., 140, 217-222.
- Theoretical Analysis of Concentration of Oxygen in Aerobic Granule-based Reactors
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Authors
Affiliations
1 Department of Mathematics, The Madura College, Madurai-625 011, Tamilnadu, IN
1 Department of Mathematics, The Madura College, Madurai-625 011, Tamilnadu, IN
Source
Global Journal of Theoretical and Applied Mathematics Sciences, Vol 2, No 2 (2012), Pagination: 109-120Abstract
A mathematical model of bioreduction of acetophenone in an up-flow packed bed reactor is presented. This paper presents an approximate analytical method (Homotopy perturbation method) to solve the non-linear differential equations for Michaelis-Menten formalism that describe the concentrations of oxygen within the enzymatic layer. A simple and closed-form of expressions pertaining to oxygen concentration and effectiveness factor are presented for possible value of diffusion parameters. These analytical results are compared with numerical results and they are found to be in good agreement.Keywords
Mathematical Modeling, Michaelis-menten Kinetics, Homotopy Perturbation Method, Reaction/diffusion Equation, Effectiveness Factor, Gas HoldupReferences
- Beun, J.J., van Loosdrecht, M.C.M., Heijnen, J.J., Aerobic granulation in a sequencing batch airlift reactor, Water Res. 36: 702-712, 2002.
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- Su, K. Z., Yu, H. Q., Gas holdup and oxygen transfer in an aerobic granulebased sequencing batch reactor, Biochem. Eng. J. 25: 201-207, 2005.
- Weekman, V. W., Gorring, R. L., Influence of volume change on gas-phase reactions in porous catalysts, J. Catal. 4: 260-270, 1965.
- Gapes, D., Wilen, B. M., Keller, J., Mass transfer impacts in flocculent and granular biomass from SBR systems, Water Sci. Tech. 50: 203-212, 2004.
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- Ozis, T., Yildirim, A., Int. J. Nonlinear Sci. Numer. Simul. 8 (2): 243, 2007.
- Li, S.J., Liu, Y.X., Int. J. Nonlinear Sci. Numer. Simul. 7 (2): 177, 2006.
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- Meena, A., Rajendran, L., J. Electroanal. Chem. 644: 50, 2010.
- Eswari, A., Rajendran, L., J. Electroanal. Chem. 641: 35, 2010.
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- Indian Contribution to Pigeonpea (Cajanus cajan) Pulse Crop Research: A Scientometric Analysis
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Authors
Affiliations
1 Madras Veterinary College, TANUVAS, Chennai - 600007, Tamil Nadu, IN
1 Madras Veterinary College, TANUVAS, Chennai - 600007, Tamil Nadu, IN
Source
Journal of Information and Knowledge (Formerly SRELS Journal of Information Management), Vol 53, No 6 (2016), Pagination: 467-470Abstract
This paper attempts to quantitatively analyse the growth and development of Pigeonpea Pulse Crop research in India in terms of publication output as reflected in CAB Direct Online Database. During the period 1974-2014 scientists of India published a total of 3534 papers on the subject. The most preferred journals were the International Pigeonpea Newsletter with 272 papers (7.69%) followed by Indian Journal of Agronomy with 214 papers (6.05%). The study revealed that Indian Journal of Agricultural Sciences, Indian Journal of Pulses Research, Journal of Maharashtra Agricultural Universities contributed 415 papers (11.72%) of Indian research output on Pigeonpea Pulse Crop.Keywords
Agricultural Research, CAB Direct, Pigeonpea Pulse Crop, Research Journals, Scientometrics.References
- Ghosh, G. et al., (2014). Advances in genetic transformation of important pulse crop pigeonpea. OA Biotechnology. 3(1): 5.
- Rajendran, L. Indian contribution to global agricultural research: A scientometric profile. In: Proceedings of the UGCSAP National Seminar on Advancement of Science through Scientometrics, 2015. pp. 233–238.
- Rathinasabapathy, G. & Rajendran, L. (2013). Mapping of world-wide camel research publications: A scientometric analysis. Journal of Library, Information and Communication Technology. 5(1–2): 35–40.
- Rathinasabapathy, G., & Rajendran, L. (2010). A scientometric study on buffalo research in India and Pakistan: A profile based on CAB Direct Online. Asian Journal of Library and Information Science. 2(1–4): 58–67.
- Sachin, V.K. (2014). International journal of information science and technology: A scientometrics study. e-Library Science Research Journal. 2(5): 1–11.
- Priya, A.S. and Khaparde, V.S. (2012). Authorship pattern: Scientometric study on citation in journal documentation. Electronic International Interdisciplinary Research Journal (EIIRJ). 1(3): 53–64.
- Sekar, K. & Loganathan, G. (2014). Multidisciplinary citation databases for scientometric study. International Journal of Applied Engineering Reseach. 9(14): 2683–2689.