Incipient Growth Processes with Competing Mechanisms

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This Demonstration depicts the evolution of peaked processes such as microbial growth and mortality, where the initial number or concentration is a measurable quantity. Other examples are chemical reactions such as acrylamide or peroxide formation and degradation.

Contributed by: Mark D. Normand, Maria G. Corradini, and Micha Peleg (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshot 1: no observed peak throughout the experiment's duration

Snapshot 2: a prominent peak appears after a lag with final concentration approaching zero

Snapshot 3: a peak with no lag and final concentration approaching zero

Snapshot 4: logistic decay

This Demonstration depicts processes or chemical reactions starting at a measurable initial concentration, . The process or reaction is governed by two competing mechanisms, one of growth or generation and the other of mortality or degradation. The concentration, , is the product of the growth component, , representing the system's potential for uninhibited growth, and a decay factor, , , which represents the decay component. Each has a characteristic time scale, and , and "rate parameter", and , whose values along with can be modified using sliders. The Demonstration plots the functions and together in blue and the corresponding in dark red. The maxima of the , , and axes can also be adjusted with sliders. The equations for , , and appear above the plots.



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