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Mathematical Modeling of Earth's Dynamical Systems by Rudy Slingerland, Lee Kump

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CHAPTER4

One-Dimensional Diffusion Problems

 

There is a very large class of problems in the earth sciences in which a conservative property moves through space at a rate proportional to some gradient (i.e., it follows a first-order rate law). Here, “first order” refers to an equation that contains the first derivative but no higher derivatives. This is different from the use in chemistry where it denotes a reaction rate proportional to the first power of a concentration. The conservative property that flows can be the moles of ions in a solution, or the thermal energy of atoms in a material, or the mass of regolith on a hillside (table 4.1). In the study of transport phenomena, the amount of the property in question that flows per unit area ...

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