Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 21, No. 4 (November 2008) 319-328   

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  MATHEMATICAL MODELING OF THE TEMPERATURE-DEPENDENT GROWTH OF LIVING SYSTEMS
 
 
M. Jain, G. C. Sharma and S. Kumar Sharma*

Department of Mathematics, Institute of Basic Science
Khandari, Agra-282002, India
madhujain@sancharnet.in - gokulchandra@sancharnet.in - sudheerbsaitm@rediffmail.com

* Corresponding Author
 
 
( Received: November 15, 2007 – Accepted in Revised Form: May 09, 2008 )
 
 

Abstract    In this investigation a non-equilibrium thermodynamic model of the temperature dependent biological growth of a living systems has been analyzed. The results are derived on the basis of Gompertzian growth equation. In this model, we have considered the temperature dependent growth rate and development parameter. The non-equilibrium thermodynamic model is also considered for exploring the variation of growth rate with temperature. The biological growth process of a living system near the threshold temperature has been studied. The growth rate has been taken as general function of temperature. The analytical solution has been obtained by solving differential equation governing the model. The solution of non linear equation provides an expression for biomass of the living systems at a time t, which is valid for a temperature near the threshold temperature. The numerical experiment has been conducted to exhibit the effects of various parameters on growth. The physical conditions of a living systems for different value of activated constant energy and gas, has been examined.

 

Keywords    Temperature Dependent Growth, Threshold Temperature, Gompertz Growth, Non-Equilibrium Thermodynamic Model, Living Systems.

 

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