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Optimized Factor Approximants and Critical Index
- Source :
- Symmetry, Vol 13, Iss 903, p 903 (2021), Symmetry, Volume 13, Issue 5
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- Based on expansions with only two coefficients and known critical points, we consider a minimal model of critical phenomena. The method of analysis is both based on and inspired with the symmetry properties of functional self-similarity relation between the consecutive functional approximations. Factor approximants are applied together with various natural optimization conditions of non-perturbative nature. The role of control parameter is played by the critical index by itself. The minimal derivative condition imposed on critical amplitude appears to bring the most reasonable, uniquely defined results. The minimal difference condition also imposed on amplitudes produces upper and lower bound on the critical index. While one of the bounds is close to the result from the minimal difference condition, the second bound is determined by the non-optimized factor approximant. One would expect that for the minimal derivative condition to work well, the bounds determined by the minimal difference condition should be not too wide. In this sense the technique of optimization presented above is self-consistent, since it automatically supplies the solution and the bounds. In the case of effective viscosity of passive suspensions the bounds could be found that are too wide to make any sense from either of the solutions. Other optimization conditions imposed on the factor approximants, lead to better estimates for the critical index for the effective viscosity. The optimization is based on equating two explicit expressions following from two different definitions of the critical index, while optimization parameter is introduced as the trial third-order coefficient in the expansion.
- Subjects :
- Work (thermodynamics)
Physics and Astronomy (miscellaneous)
010308 nuclear & particles physics
General Mathematics
Critical phenomena
Sense (electronics)
Derivative
01 natural sciences
Upper and lower bounds
Symmetry (physics)
factor approximants
Minimal model
Amplitude
Chemistry (miscellaneous)
0103 physical sciences
Computer Science (miscellaneous)
critical index
QA1-939
Applied mathematics
010306 general physics
optimization
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 13
- Issue :
- 903
- Database :
- OpenAIRE
- Journal :
- Symmetry
- Accession number :
- edsair.doi.dedup.....d5828f4948b0e2170857ba2acb0273df