Figure 28.25. Solutions to the basic diffusion equation, dψ/dt = σ2d2ψ/dx2. (Left column) If the population starts concentrated at a point, it spreads out in a Gaussian distribution with variance σ2t. (Middle column) If the population starts out living only on the left side (x > 0), the step smooths out over time. (Right column) Fluctuations in density (~sin(ωt)) decay in amplitude, as exp(–σ2ω2t/2). The rate of diffusion is set to σ2 = 1.
|© 2007-2010 by Cold Spring Harbor Laboratory Press. All rights reserved.|
|The reproduction, modification, storage in a retrieval system, or retransmission, in any form or by any means, electronic, mechanical, or otherwise, for reasons other than personal, noncommercial use is strictly prohibited without prior written permission. You are authorized to download one copy of the material on this Web site for personal, noncommercial use only. The material made available on this Web site is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any of this material, as a whole or in parts (including on the World Wide Web), is not permitted. All users of these materials and visitors to this Web site are expected to abide by these restrictions. Requests for permission for other uses of this material should be directed to Cold Spring Harbor Laboratory Press, 1 Bungtown Road, Cold Spring Harbor, NY 11724 or submitted via our World Wide Web Site at http://www.cshlpress.com/.|