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13: Continuous Field Models I - Modeling
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- 13.1: Continuous Field Models with Partial Differential Equations
- Spatio-temporal dynamics of complex systems can also be modeled and analyzed using partial differential equations (PDEs), i.e., differential equations whose independent variables include not just time, but also space.
- 13.2: Fundamentals of Vector Calculus
- In order to develop continuous ﬁeld models, you need to know some basic mathematical concepts developed and used in vector calculus.
- 13.3: Visualizing Two-Dimensional Scalar and Vector Field
- Plotting scalar and vector ﬁelds in Python is straightforward, as long as the space is two-dimensional.
- 13.4: Modeling Spatial Movement
- Now we will discuss how to write a PDE-based mathematical model for a dynamical process that involves spatial movement of some stuff. There are many approaches to writing PDEs, but here in this textbook, we will use only one “template,” called the transport equation.
- 13.5: Simulation of Continuous Field Models
- 13.6: Reaction-Diffusion Systems
- Finally,I would like to introduce reaction-diffusion systems, a particular class of continuous ﬁeld models that have been studied extensively.