Figure 2

Communicating vessels as a physical model for a buffered system. Total fluid volume is taken as x, fluid volume inside vessel A ("transfer vessel", red) as the value of the transfer function τ(x), and aggregate fluid volumes in the other vessels ("buffering vessels", blue) represent the "buffering function" β(x). We can describe these systems in terms of our two measures of buffering action, namely the buffering coefficient b(x) = β'(x)/[τ'(x) + β'(x)] and the buffering ratio B(x) = β'(x)/τ'(x) (see main text for detailed explanation). A, Linear buffering, one buffering vessel. The volume changes in A are only half as big as the total volume changes in the system; the volume inside A is "buffered", or, more specifically, "moderated". The degree of moderation is the same at all fluid levels; b(x) = constant = 0.5 and B(x) = constant = 1. B, Zero buffering, or perfect transfer. Changing total volume in the system translates completely into identical volume changes in vessel A, without "moderation" or "amplification": b(x) = 0 B(x) = 0. C, Linear buffering, several buffering vessels. Increasing the number of buffering vessels increases buffering action. The four partitioning functions are replaced by a single buffering function β. Buffering parameters are b(x) = 0.8 and B(x) = 4. D, Linear buffering, general case. Same buffering behavior as in C, brought about by a single buffering vessel. E, Non-linear buffering, one buffering vessel. In this system, the individual volume changes are not linear functions of total volume. Consequently, the proportion between volume flow into or out of vessels A is not a constant, but a variable function of the system's filling state. F, Non-linear buffering, several buffering vessels. In most buffered systems, buffering is brought about by a multiplicity of buffers (as in C) that are non-linear in their individual ways (as in E). Buffering coefficient and buffering odds provide overall measures of buffering action that neither require nor deliver any knowledge about the individual components.