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单词 mathematical model
释义
mathematical model

Mathematics
  • A mathematical model is a mathematical description of a real world problem, which may be deterministic or stochastic. Typically the model makes simplifying assumptions about the problem so that the mathematical equations describing the model may be solved or more easily analysed. For example, the two-body problem of the Earth going around the Sun treats both as particles and ignores other celestial bodies. But these are reasonable assumptions to make in light of the characteristics and strength of the gravitational field (see gravity). It may be reasonable to consider viscosity negligible in a fluid but not within a boundary layer of an object; so, in such cases different simplifications are made in different parts of the model.


Chemical Engineering
  • A mathematic description of a process or system used to understand or predict its behaviour. It can also be used to aid understanding of the influences on a process as well as to control the process or system itself. A model may take the form of a set of differential equations and describe both steady-state behaviour and dynamic behaviour, and may be combined with experimental data for validation purposes or for leading to new theories and hypothesises. Unstructured models, such as Monod kinetics, are used to describe the time variation of a component such as accumulation of biomass or depletion of a limiting substrate in which the environmental changes are ignored. Although mathematically simple, they are frequently useful for design, control, and optimization purposes. Structured models are more complex in nature, and endeavour to describe and predict the influence of the environment on the internal mechanisms of a living organism.


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