Symmetry in Self-Similarity in Space and Time—Short Time Transients and Power-Law Spatial Asymptotes
Abstract
1. Introduction
2. Symmetry Properties in the Family of Scaling Functions for the 1D Diffusion Process
2.1. Scaling Functions
2.2. Symmetry in the Family of Scaling Functions
3. Self-Similarity in Space and Time with Scaling Function Having Algebraic Tail
3.1. Late-Stage Self-Similarity in Space and Time of Gel Network
3.2. Self-Similarity in Space and Time in the Short-Time Limit of 1D Diffusion
3.3. Short-Time Self-Similarity in Space and Time of Capillary-Driven Thin-Film Equation
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Family of Scaling Functions for the Self-Similarity Solution of 1D Diffusion Equation
p | ||
---|---|---|
−3 | ||
−2 | ||
−1 | ||
0 | (*) | |
1 | (*) | |
2 | (*) |
Appendix B. Spacetime Self-Similarity Solution of Equation (7)
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Sekimoto, K.; Fujita, T. Symmetry in Self-Similarity in Space and Time—Short Time Transients and Power-Law Spatial Asymptotes. Symmetry 2019, 11, 1489. https://doi.org/10.3390/sym11121489
Sekimoto K, Fujita T. Symmetry in Self-Similarity in Space and Time—Short Time Transients and Power-Law Spatial Asymptotes. Symmetry. 2019; 11(12):1489. https://doi.org/10.3390/sym11121489
Chicago/Turabian StyleSekimoto, Ken, and Takahiko Fujita. 2019. "Symmetry in Self-Similarity in Space and Time—Short Time Transients and Power-Law Spatial Asymptotes" Symmetry 11, no. 12: 1489. https://doi.org/10.3390/sym11121489
APA StyleSekimoto, K., & Fujita, T. (2019). Symmetry in Self-Similarity in Space and Time—Short Time Transients and Power-Law Spatial Asymptotes. Symmetry, 11(12), 1489. https://doi.org/10.3390/sym11121489