 # Point of View: Are theoretical results ‘Results’?

1. Raymond E Goldstein 1. University of Cambridge, United Kingdom
Feature Article
5 figures

## Figures

Figure 1 Experimental setup to study diffusion of the green alga Chlamydomonas. (a) A light sheet is used to gather the algae, which are swimming in a petri dish, into a narrow strip of cells along the y-axis. (b) After the light is turned off, the cells swim randomly and spread out. The concentration profile, C⁢(x,t), is then measured along a thin strip parallel to the x-axis; t is time.
Figure 2 Experimental results on diffusion in a population of the green alga Chlamydomonas. (a) Concentration profiles, C⁢(x,t), normalized to unity, at the following times: 1 second (red), 3 seconds (green), 7 seconds (blue) and 30 seconds (black). (b) The variance, ⟨x2⟩, of the data shown in (a) as a function of time; the dashed magenta line is a linear fit to the data. (c) The peak height, C⁢(0,t), of the data shown in (a) as a function of time.
Figure 3 A random walk in one dimension. (a) A cell at site m moves with probability 1/2 to the left or right. (b) Diagram illustrating the counting that underlies the evolution equation (Equation 1).
Figure 4 Flux and the diffusion equation. (a) Concentration profiles, C⁢(x,t), at times t=3 s and t=3.2 s . (b) The flux of cells past a given point, J (black; left axis), and the concentration gradient, ∂⁡C/∂⁡x (yellow; right axis), versus position, x. (c) Flux, J, versus concentration gradient, ∂⁡C/∂⁡x, for all the values of x and t shown in Figure 2a. The dashed magenta line has a slope D=0.1 mm2/s.
Figure 5 Rescaling the data. (a) The peak amplitude, C⁢(0,t), from Figure 2c plotted as a function time, t, on a log-log scale; the dashed magenta line has a slope of -1/2, which shows that C⁢(0,t)∼t-1/2. (b) When the data in Figure 2a are rescaled (see main text) and replotted, they collapse to a universal curve; the dashed magenta curve is the function exp⁡(-ξ2/2).