Mathematical theory of reduction of physical parameters and similarity analysis
- 37 Downloads
The method of similarity analysis in the study of differential equations is extended to study the variability of parameters in a physical system. The analysis provides an insight into the meaning of “physical” similarity, which usually means the possibility of a reduction in the number of physical parameters characterizing the system. Theorems relating similarities to groups of invariant transformations are proved and employed to show how the number of parameters can be reduced.
KeywordsDifferential Equation Field Theory Elementary Particle Quantum Field Theory Physical Parameter
Unable to display preview. Download preview PDF.
- Birkhoff, G. (1960).Hydrodynamics, 2nd ed., Chap. 5. Princeton University Press, Princeton, New Jersey.Google Scholar
- Birkhoff, G., and MacLane, S. (1965).A Survey of Modern Algebra. Macmillan, New York.Google Scholar
- Bluman, G. W., and Cole, J. D. (1974).Similarity Methods for Differential Equations. Springer-Verlag, New York.Google Scholar
- Chevalley, C. (1946).Theory of Lie Groups, Princeton University Press, Princeton, New Jersey.Google Scholar
- Schwarzschild, M. (1958).Structure and Evolution of Stars, Chap. 3. Princeton University Press, Princeton, New Jersey.Google Scholar
- Spivak, M. (1970).A Comprehensive Introduction to Differential Geometry, Vol. I, Chap. 16. Publish or Perish Inc., Boston, Massachusetts.Google Scholar