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Modeling Complex Living SystemsFrom Scaling and Determinism to Kinetic Theory Representation

Modeling Complex Living Systems: From Scaling and Determinism to Kinetic Theory Representation From Scaling and Determinism to Kinetic Theory Representation 1.1 Scaling and Determinism Systems of the real world are generally composed of several interacting elements. This implies that mathematical models can be designed at various observation and representation scales. The microscopic scale corresponds to modeling, by mathematical equations, the evolution of a variable suitable to describe the physical state of each single object. An alternative to this approach can be developed if the system is constituted by a large number of elements and it is possible to obtain suitable local in space averages of their state in an elementary space volume ideally tending to zero. In this case, the modeling can be developed at a macroscopic scale, which refers to the evolution of locally averaged quantities, called macroscopic variables. Different classes of equations correspond to these scalings. Generally, models designed at the microscopic scale are stated in terms of ordinary differential equations, while models at the macroscopic scale are generally stated in terms of partial differential equations. The modeling is developed within the framework of deterministic causality principles unless some ex- ternal noise is added. This means that once a cause is given, the effect is deterministically identified. Motivations to http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Modeling Complex Living SystemsFrom Scaling and Determinism to Kinetic Theory Representation

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Publisher
Birkhäuser Boston
Copyright
© Birkhäuser Boston 2008
ISBN
978-0-8176-4510-6
Pages
1 –25
DOI
10.1007/978-0-8176-4600-4_1
Publisher site
See Chapter on Publisher Site

Abstract

From Scaling and Determinism to Kinetic Theory Representation 1.1 Scaling and Determinism Systems of the real world are generally composed of several interacting elements. This implies that mathematical models can be designed at various observation and representation scales. The microscopic scale corresponds to modeling, by mathematical equations, the evolution of a variable suitable to describe the physical state of each single object. An alternative to this approach can be developed if the system is constituted by a large number of elements and it is possible to obtain suitable local in space averages of their state in an elementary space volume ideally tending to zero. In this case, the modeling can be developed at a macroscopic scale, which refers to the evolution of locally averaged quantities, called macroscopic variables. Different classes of equations correspond to these scalings. Generally, models designed at the microscopic scale are stated in terms of ordinary differential equations, while models at the macroscopic scale are generally stated in terms of partial differential equations. The modeling is developed within the framework of deterministic causality principles unless some ex- ternal noise is added. This means that once a cause is given, the effect is deterministically identified. Motivations to

Published: Jan 1, 2008

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