| | 1 | Author
| Takashi Tsuchiya | Requires cookie* | | | Title
| The Critical Amplitude for Bifurcation Points of the Logistic Map  | | | | Abstract
| The phenomenon called critical slowing down is studied for some analytically tractable bifurca-tion points of the logistic map. The critical amplitude and the critical amplitude ratio are introduced to describe the critical behaviors more precisely when the critical exponents are identically unity for two critical behaviors which are to be compared. Since Hao predicted unity of the critical exponent for 1-d maps assuming exponential damping of the distance from the attractor, the assumption is checked. The result is that the shrinkage of the valid region of the assumption occurs as the adjustable parameter approaches one of the bifurcation points. | | | |
Reference
| Z. Naturforsch. 51a, 1170—1174 (1996); received September 25 1996 | | | |
Published
| 1996 | | | |
Keywords
| Bifurcation, Logistic map, Critical slowing down, Critical exponent, Critical amplitude | | | |
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| default:Reihe_A/51/ZNA-1996-51a-1170.pdf | | | | Identifier
| ZNA-1996-51a-1170 | | | | Volume
| 51 | |
| 2 | Author
| Ichi Suzuki, Shin'. Ichi, Ishimaru, Ryuichi Ikeda | Requires cookie* | | | Title
| Koh | | | | Abstract
| 133 Cs NMR spin-lattice relaxation times(Ti) in crystalline Cs 2 CdI 4 were measured at 225 -373 K. The critical exponent (of T\ observed near the normal-incommensurate transition in the normal phase was determined to be 0.62 ± 0.03, in good agreement with the predicted value for three-dimensional XK-model. The frequency dependent T\ in the incommensurate phase could be explained by the fluctuation of amplitudon and small gap phason. | | | |
Reference
| Z. Naturforsch. 55a, 339—342 (2000); received August 27 1999 | | | |
Published
| 2000 | | | |
Keywords
| l33 Cs NMR, T\ \ Incommensurate, Phase Transition, Critical Exponent | | | |
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| default:Reihe_A/55/ZNA-2000-55a-0339.pdf | | | | Identifier
| ZNA-2000-55a-0339 | | | | Volume
| 55 | |
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