Research Catalog

Title

Growth and diffusion phenomena : mathematical frameworks and applications / Robert B. Banks.

Author

Banks, Robert B.

Publication

Berlin ; New York : Springer-Verlag, [1994], ©1994.

Items in the Library & Off-site

Holdings

Details

Description

xix, 455 pages : illustrations; 24 cm.

Summary

• Diffusion and growth phenomena abound in the real world surrounding us. Some examples are 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 of agricultural innovations, and spreading of epidemics and migration of insects.
• These and numerous other phenomena are illustrations of typical growth and diffusion problems confronted in many branches of the physical, biological and social sciences as well as in various areas of agriculture, business, education, engineering, medicine and public health.
• The book presents a large number of mathematical models to provide frameworks for the analysis and display of many of these. The models developed and utilized commence with relatively simple exponential, logistic and normal distribution functions. Considerable attention is given to time dependent growth coefficients and carrying capacities. The topics of discrete and distributed time delays, spatial-temporal diffusion and diffusion with reaction are examined.
• Throughout the book there are a great many numerical examples. In addition and most importantly, there are more than 50 in-depth "illustrations" of the application of a particular framework or model based on real world problems. These examples provide the reader with an appreciation of the intrinsic nature of the phenomena involved. They address mainly readers from the physical, biological, and social sciences, as the only mathematical background assumed is elementary calculus.
• Methods are developed as required, and the reader can thus acquire useful tools for planning, analyzing, designing, and evaluating studies of growth, transfer and diffusion phenomena. The book draws on the author's own extensive experience in problems of environmental diffusion and dispersion, as well as in technology transfer and innovation diffusion

Series Statement

Texts in applied mathematics ; 14

Uniform Title

Texts in applied mathematics ; 14.

Subjects

• Growth > Mathematical models
• Diffusion processes

Bibliography (note)

• Includes bibliographical references (p. [429]-443) and indexes.

Contents

• 1. Introduction -- 2. Some Basic Frameworks. 2.1. Exponential Function. 2.2. Logistic Distribution. 2.3. Confined Exponential Distribution. 2.4. Combination of the Logistic Distribution and the Confined Exponential Distribution. 2.5. Normal Probability Distribution. 2.6. Power Law Logistic Distribution. 2.7. Logistic Growth with Migration. 2.8. Epidemics and Technology Transfer. 2.9. Some Modifications of the Logistic Distribution -- 3. Some Additional Frameworks. 3.1. Gompertz Distribution. 3.2. Weibull Distribution. 3.3. A Generalized Distribution. 3.4. Hyperlogistic Distribution. 3.5. Various Other Distributions -- 4. Phenomena with Variable Growth Coefficients. 4.1. Linearly Variable Growth Coefficient. 4.2. Hyperbolically Variable Growth Coefficient. 4.3. Exponentially Variable Growth Coefficient. 4.4. Sinusoidally Variable Growth Coefficient -- 5. Phenomena with Variable Carrying Capacities. 5.1. Exponentially Variable Carrying Capacity. 5.2. Logistically Variable Carrying Capacity.
• 5.3. Linearly Variable Carrying Capacity. 5.4. Hyperbolically Variable Carrying Capacity. 5.5. Sinusoidally Variable Carrying Capacity. 5.6. Power Law Logistic with a Power Law Logistically Variable Carrying Capacity -- 6. Phenomena with Time Delays. 6.1. Discrete Time Delay in the Exponential Equation. 6.2. Discrete Time Delay in the Logistic Equation. 6.3. Distributed Time Delay: Delay Integral in the Crowding Term. 6.4. Distributed Time Delay: Delay Integral in a Pollution Term -- 7. Phenomena with Spatial Diffusion. 7.1. Diffusion from Instantaneous Sources. 7.2. Diffusion from Continuous Source. 7.3. Diffusion with Reaction in a Finite Region. 7.4. Diffusion with Convection and Reaction. 7.5. Diffusion with Confined Exponential Growth. 7.6. Diffusion with Logistic Growth -- 8. Conclusion.

ISBN

• 3540555072 (Berlin : acid-free) :
• 0387555072 (New York : acid-free) :

LCCN

93037076

OCLC

• 28964630
• ocm28964630

Owning Institutions

Columbia University Libraries