*Baltazar D. Aguda and Avner Friedman*

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198570912
- eISBN:
- 9780191718717
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570912.003.0003
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary ...
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This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary differential equations; but coupling of chemical reactions to physical processes such as diffusion requires the formulation of partial differential equations to describe the spatiotemporal evolution of the system. Mathematical analysis of the dynamical models involves basic concepts from ordinary and partial differential equations. Computational methods, including stochastic simulations and sources of computer software programs available free on the internet are also summarized.Less

This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary differential equations; but coupling of chemical reactions to physical processes such as diffusion requires the formulation of partial differential equations to describe the spatiotemporal evolution of the system. Mathematical analysis of the dynamical models involves basic concepts from ordinary and partial differential equations. Computational methods, including stochastic simulations and sources of computer software programs available free on the internet are also summarized.

*Chun Wa Wong*

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199641390
- eISBN:
- 9780191747786
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199641390.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Ordinary and partial differential equations appear in physics as equations of motion or of state. They are often linear differential equations for which a sum of solutions remains a solution. The ...
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Ordinary and partial differential equations appear in physics as equations of motion or of state. They are often linear differential equations for which a sum of solutions remains a solution. The solution of first- and second-order linear differential equations are obtained. The specification of linearly independent solutions using suitable boundary/initial conditions is discussed. Special methods of solution using Green's functions, separation of variables and eigenfunction expansions are described.Less

Ordinary and partial differential equations appear in physics as equations of motion or of state. They are often linear differential equations for which a sum of solutions remains a solution. The solution of first- and second-order linear differential equations are obtained. The specification of linearly independent solutions using suitable boundary/initial conditions is discussed. Special methods of solution using Green's functions, separation of variables and eigenfunction expansions are described.

*Christophe Godin, Eugenio Azpeitia, and Etienne Farcot*

- Published in print:
- 2016
- Published Online:
- March 2016
- ISBN:
- 9780198752950
- eISBN:
- 9780191814426
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198752950.003.0009
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter presents models of processes involved in the initiation and development of a flower. Models of hormonal transport are briefly described, focusing on two key aspects of floral ...
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This chapter presents models of processes involved in the initiation and development of a flower. Models of hormonal transport are briefly described, focusing on two key aspects of floral development: initiation, due to the periodic local accumulation of auxin near the plant apex, and the genetic regulation of its development. Gene regulatory networks (GRNs) that control the initial steps of floral development and differentiation are investigated. In a simplified form, this network contains dozens of actors interacting with each other in space and time. The understanding of such a complex system requires a modeling approach in order to quantify these interactions and analyze their properties. The two main formalisms used to model GRNs are presented: the Boolean and ordinary differential equation formalisms. Throughout the chapter, specific mathematical topics of particular interest to the development of the ideas developed in the different sections are highlighted.Less

This chapter presents models of processes involved in the initiation and development of a flower. Models of hormonal transport are briefly described, focusing on two key aspects of floral development: initiation, due to the periodic local accumulation of auxin near the plant apex, and the genetic regulation of its development. Gene regulatory networks (GRNs) that control the initial steps of floral development and differentiation are investigated. In a simplified form, this network contains dozens of actors interacting with each other in space and time. The understanding of such a complex system requires a modeling approach in order to quantify these interactions and analyze their properties. The two main formalisms used to model GRNs are presented: the Boolean and ordinary differential equation formalisms. Throughout the chapter, specific mathematical topics of particular interest to the development of the ideas developed in the different sections are highlighted.