Growth and Diffusion Phenomena Mathematical Frameworks and Applicati
Diffusion and growth phenomena abound in the real world surrounding us. Someexamples: growth of the world's population, growth rates of humans, public interest in news events, growth and decline of central city populations, pollution of rivers, adoption o
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Editors F. John J. E. Marsdon L. Sirovich M. Golubitsky W. Jager
Texts in Applied Mathematics
1. Sirovich: Introduction to Applied Mathematics. 2. Wiggins: Introduction to Applied Nonlinear Dynamical Systems
and Chaos.
3. HaleIKOI;ak: Dynamics and Bifurcations. 4. ChoriniMarsden: A Mathematical Introduction to Fluid Mechanics, 3rd edition 5. HubbardIWest: Differential Equations: A Dynamical Systems Approch, Part I: Ordinary Differential Equations. 6. Sontag: Mathematical Control Theory: Deterministic Finite Dimensional Systems. 7. Perko: Differential Equations and Dynamical Systems. 8. Seaborn: Hypergeometric Functions and Their Applications. 9. Pipkin: A Course on Integral Equations. 10. HoppensteadtiPeskin: Mathematics in Medicine and the Life Sciences. 11. Braun: Differential Equations and Their Applications: An Introduction to Applied Mathematics, 4th edition 12. StoerlBulirsch: Introduction to Numerical Analysis, 2nd edition 13. RenardylRogers: A First Gradute Course in Partial Differential Equations. 14. Banks: Growth and Diffusion Phenomena: Mathematical Frameworks and Applications.
RobertB. Banks
Growth and Diffusion Phenomena Mathematical Frameworks and Applications With 216 Figures
Springer-Verlag Berlin Heidelberg GmbH
Robert B. Banks Former President and Professor of Environmental Engineering Asian Institute of Technology Bangkok 10501, Thailand
Editors F. John Courant Institute of Mathematical Sciences New York University New York, NY 10012 USA
J.E. Marsden Department of Mathematics University of California Berkeley, CA 94720 USA
M. Golubitsky Department of Mathematics University of Houston Houston, TX 77004 USA
W. Jiiger Department of Applied Mathematics Universitiit Heidelberg 1m Neuenheimer Feld 294 69120 Heidelberg, FRG
L. Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 USA
Cover figure. Among the many growth and diffusion models examined by the author is one relating to the temporal-spatial growth of cities. London is utilized as an illustration. The growth of London comensing 1840 is examined in detail in Section 7.5.6
Mathematical Subject Classification (1991): 60j60, 92-01, 90-01, 90AI6, 92D40, 92C30, 92HIO, 92H20, 94A05
ISBN 978-3-642-08140-8
Library of Congress Cataloging-in-Publication Data Banks, Robert B.: Growth and diffusion phenomena: mathematical frameworks and applications/Robert B. Banks. p. cm. - (Texts in applied mathematics; 14) Includes bibliographical references and indexes. ISBN 978-3-642-08140-8 ISBN 978-3-662-03052-3 (eBook) DOI 10.1007/978-3-662-03052-3 I. Diffusion processes. 2. Growth-Mathematical models. I. Title. II. Series. QA247.75.836 1994 003'.7-'
where l/J = 2(t - ti)/Llt.
(2.2.34)
2.2 Logistic Distribution
37
In the preceding equation we note that when ยข = -1, 0, and +1, we obtain, respectively, U = 0.10, 0.50, and 0.90 as we require. There is a reason for this "normalization" of the time coordinate. In their study, Fisher and Pry determined the values of the transfer coefficient, a, the inflection point
