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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 Media
References
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- 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.
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- 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.
- Adomian, G., 1994, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Dordrecht.
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- Analytical Solution of the Concentration in a Packedbed Immobilized Enzyme Reactor Using Homotopy Perturbation Method
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Authors
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
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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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- 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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- Weekman, V. W., Gorring, R. L., Influence of volume change on gas-phase reactions in porous catalysts, J. Catal. 4: 260-270, 1965.
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- Ghori, Q.K., Ahmed, M., Siddiqui, A.M., Int. J. Nonlinear Sci. Numer. Simul. 8 (2): 2007.
- 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.
- Mousa, M.M., Ragab, S.F., Z. Naturforsch. 63: 140, 2008.
- He, J.H., Comput. Methods Appl. Mech. Eng. 178: 257, 1999.
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- He, J.H., Appl. Math. Comput. 140: 217, 2003.
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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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- Efficacy of Biological Control Agents for Management of Postharvest Black Rot Pathogen Aspergillus carbonarius in Grapes
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Authors
Affiliations
1 Department of Plant Pathology, Tamil Nadu Agricultural University, Coimbatore 641 003, Tamil Nadu, IN
1 Department of Plant Pathology, Tamil Nadu Agricultural University, Coimbatore 641 003, Tamil Nadu, IN
Source
Journal of Biological Control, Vol 26, No 3 (2012), Pagination: 266–271Abstract
Grape berries were treated with different biological agents to test their efficacy in reducing post harvest incidence of black mould rot and minimize the loss. The agents Pseudomonas, Bacillus, Trichoderma and yeast isolates were individually screened against the black rot pathogen Aspergillus carbonarius. B. subtilis strains EPC-8 and EPCO-16 and T. harzianum (Th Co) showed high mycelial growth suppression of A. carbonarius in vitro. The effective biological control agents were tested in pre, post and combined inoculation studies against A. carbonarius in grape berries. In the pre inoculation, B. subtilis (EPC-8) showed 57.80 per cent reduction in the incidence of A. carbonarius followed by T. harzianum (Th Co) (48.43 percent). The same trend of effectiveness was also found in the post-inoculation and combined inoculation tests under storage conditions at room temperature in grape berries.Keywords
Aspergillus carbonarius, Bacillus subtilis, Trichoderma harzianum.Full Text
References
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- Effect of Various Organic Substrates on the Mass Multiplication of Trichoderma viride
Abstract Views :202 |
PDF Views:128
Authors
Affiliations
1 Center for Plant Molecular Biology. Tamil Nadu Agricultural University, Coimbatore-641003, Tamil Nadu, IN
2 Department of Plant Pathology, Centre for Plant Protection Studies, Tamil Nadu Agricultural University, Coimbatore-641 003, Tamil Nadu, IN
1 Center for Plant Molecular Biology. Tamil Nadu Agricultural University, Coimbatore-641003, Tamil Nadu, IN
2 Department of Plant Pathology, Centre for Plant Protection Studies, Tamil Nadu Agricultural University, Coimbatore-641 003, Tamil Nadu, IN
Source
Journal of Biological Control, Vol 21, No 2 (2007), Pagination: 313-316Abstract
Four different organic substrates, viz., decomposed coir pith, dried cow dung, rice bran and tea waste, were tested tor the growth of Trichoderma viride (isolate t). The population (CFU) of T. viride on various substrates was estimated at 20th, 30th, 40th and 60th day after inoculation by serial dilution plate technique. The population of T. viride was highest on 20th day in sterilized tea waste (236.30 × 106 cfu), followed by rice bran (152 × 106 cfu), decomposed coir pith (44.35 × 106 cfu), talc (36 × 106 cfu) and dried cow dung (20 × 106 cfu). Sterilized substrate was favourable for the multiplication of T. viride except for dried cow dung. The population increased in all the substrates except talc on 30th day and declined from 40th day onwards.Keywords
Colony Forming Unit (CFU), Organic Substrates, Talc, Trichoderma viride (Isolate 1).Full Text
- Indian Contribution to Pigeonpea (Cajanus cajan) Pulse Crop Research: A Scientometric Analysis
Abstract Views :277 |
PDF Views:13
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.
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- Effect of TNAU-Pf1 Seed Biopriming and Foliar Spray of Newer Fungicides on the Incidence of Leaf Blight of Sunflower
Abstract Views :290 |
PDF Views:146
Authors
Affiliations
1 Plant Pathology, TNAU, Coimbatore – 3, Tamil Nadu, IN
2 Agronomy, TNAU, Coimbatore - 3, Tamil Nadu, IN
3 PBG, TNAU, Coimbatore - 3, Tamil Nadu, IN
4 Department of Oilseeds, TNAU, Coimbatore - 3, Tamil Nadu, IN
1 Plant Pathology, TNAU, Coimbatore – 3, Tamil Nadu, IN
2 Agronomy, TNAU, Coimbatore - 3, Tamil Nadu, IN
3 PBG, TNAU, Coimbatore - 3, Tamil Nadu, IN
4 Department of Oilseeds, TNAU, Coimbatore - 3, Tamil Nadu, IN
Source
Journal of Biological Control, Vol 31, No 2 (2017), Pagination: 114-118Abstract
Seed biopriming followed by foliar spray of different newer fungicide molecules to manage sunflower leaf spot under field conditions have been tried in Coimbatore, Tamil Nadu, India for three consecutive years (2014-2016). The result indicated that among the different treatments tested, seed biopriming with TNAU Pseudomonas fluorescens (Pf1) @ 10g/kg seeds followed by spray of Hexaconazole @ 0.1% at 45 days and P. fluorescens (Pf1) @ 1.0% at 60 DAS showed less severity of Alternaria leaf spot (25.7) with the highest yield of 1471kg/ha against the control (47.7) which recorded yield of 1111kg/ha. In addition, seed biopriming promoted higher and uniform seed germination under field conditions.Keywords
Newer Molecule, Leaf Spot/Blight, Seed Biopriming, Seed Yield, Sunflower.Full Text
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- Isolation and in vitro studies on indigenous fungi against ischolar_main-knot nematode, Meloidogyne incognita
Abstract Views :205 |
PDF Views:102
Authors
Affiliations
1 Department of Nematology, AC&RI, TNAU, Coimbatore – 641 003, Tamil Nadu, IN
2 Department of Plant Pathology, AC&RI, TNAU, Coimbatore – 641 003, Tamil Nadu, IN
1 Department of Nematology, AC&RI, TNAU, Coimbatore – 641 003, Tamil Nadu, IN
2 Department of Plant Pathology, AC&RI, TNAU, Coimbatore – 641 003, Tamil Nadu, IN
Source
Journal of Biological Control, Vol 35, No 3 (2021), Pagination: 153-160Abstract
The present study was carried out to evaluate the indigenous fungi from soil against the ischolar_main knot nematode, Meloidogyne incognita. Eleven isolates were isolated and screened for their efficacy against nematode under in vitro condition for egg hatching and juvenile mortality. The results revealed that the isolate F6 showed the highest egg hatching inhibition (88.5%) followed by F11 and F7 compared to control after incubation for 72 h. The highest juvenile mortality of 73% was recorded in isolate F6 followed by F11 and F9 after 72 h. Isolate F6 was morphologically and molecularly identified as Talaromyces pinophilus and F9 and F11 were identified as Aspergillus corrugates and Aspergillus nidulans. Among the fungi, T. pinophilus was found to be highly effective against ischolar_main knot nematode.
Keywords
Indigenous fungi, culture filtrate, in vitro, Meloidogyne incognita, Talaromyces pinophilusFull Text