Humans gather most of our information on the outside world

Chapter 14, Problem 14.1.44

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Humans gather most of our information on the outside world through sight and sound. But many creatures use chemical signals as their primary means of communication; for example, honeybees, when alarmed, emit a substance and fan their wings feverishly to relay the warning signal to the bees that attend to the queen. These molecular messages between members of the same species are called pheromones. The signals may be carried by moving air or water or by a diffusion process in which the random movement of gas molecules transports the chemical away from its source. Figure 14.2.4 shows an ant emitting an alarm chemical into the still air of a tunnel. If c(x, t) denotes the concentration of the chemical x centimeters from the source at time t, then c(x, t) satisfie k 2 c x2 c t , x 0, t 0and k is a positive constant. The emission of pheromones as a discrete pulse gives rise to a boundary condition of the form,where d(t) is the Dirac delta function.