Polynomial versus Exponential Time

2019 ◽  
pp. 25-52
1992 ◽  
Vol 57 (6) ◽  
pp. 1326-1334 ◽  
Author(s):  
Jaroslav Vojtěchovský ◽  
Jindřich Hašek ◽  
Stanislav Nešpůrek ◽  
Mojmír Adamec

2,4,4,6-Tetraphenyl-4H-thiopyran, C29H22S, orthorhombic, Pna21, a = 17.980(4), b = 6.956(2), c = 34.562(11) Å, V = 4323(2) Å3, Z = 8, Dx = 1.237 g cm-3, F(000) = 1696, λ(CuKα) = 1.54184 A, μ = 1.372 mm-2, T = 294 K. The final R was 0.050 for the unique set of 3103 observed reflections. The central 4H-thiopyran ring forms a boat conformation for both symmetrically independent molecules with average boat angles 4.4(3) and 6.8(3)° at S and C(sp3), respectively. The mean planes of phenyls at the position 2 and 6 are turned from the double plane of 4H-thiopyran by 42.5(5) and 35.8(3)°, respectively. The investigated material undergoes a photochromic change in the solid state after irradiation with UV light or X-rays. The maximum of the new absorption band is situated at 564 nm. The non-exponential time dependence of photochromic bleaching is analysed in terms of a dispersive first-order reaction.


2020 ◽  
Vol 31 (4) ◽  
pp. 703-711 ◽  
Author(s):  
Niu Liqiang ◽  
Xie Yongjun ◽  
Jiang Haolin ◽  
Wu Peiyu

2001 ◽  
Vol 12 (03) ◽  
pp. 377-385
Author(s):  
CHRISTIAN SCHULZE

The bifurcated, ordered Cayley tree with disorder and frustration as a model for relaxing granular media is examined numerically. Surprisingly, only exponential time dependencies are found despite frustration. Extensions to bidirectional models are discussed extensively and qualitatively new behavior is detected.


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