Scenarios of Self-Organization in Ideally Homogeneous One-Dimensional Systems

Autosolitons ◽  
1994 ◽  
pp. 552-557
Author(s):  
B. S. Kerner ◽  
V. V. Osipov
2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Makoto Tadokoro ◽  
Kyosuke Isoda ◽  
Yasuko Tanaka ◽  
Yuko Kaneko ◽  
Syoko Yamamoto ◽  
...  

Anionic tris (biimidazolate) nickelate (II) ([Ni(Hbim)3]−), which is a hydrogen-bonding (H-bonding) molecular building block, undergoes self-organization into honeycomb-sheet superstructures connected by complementary intermolecular H-bonds. The crystal obtained from the stacking of these sheets is assembled into channel frameworks, approximately 2 nm wide, that clathrate two cationic K+-crown ether derivatives organised into one-dimensional (1D) double-columnar arrays. In this study, we have shown that all five cationic guest-included crystals form nanochannel structures that clathrate the 1-D double-columnar arrays of one of the four types of K+-crown ether derivatives, one of which induces a polymorph. This is accomplished by adaptably fitting two types of anionic [Ni(Hbim)3]−host arrays. One is a network with H-bonded linkages alternating between the two different optical isomers of the and types with flexible H-bonded [Ni(Hbim)3]−. The other is a network of a racemate with 1-D H-bonded arrays of the same optical isomer for each type. Thus, [Ni(Hbim)3]−can assemble large cations such as K+crown-ether derivatives into double-columnar arrays by highly recognizing flexible H-bonding arrangements with two host networks of and .


1995 ◽  
Vol 51 (6) ◽  
pp. 6177-6187 ◽  
Author(s):  
Farhang Radjai ◽  
Stéphane Roux

2003 ◽  
Vol 10 (1) ◽  
pp. 69-75 ◽  
Author(s):  
H. Kosonen ◽  
S. Valkama ◽  
J. Ruokolainen ◽  
M. Torkkeli ◽  
R. Serimaa ◽  
...  

1999 ◽  
Vol 54 (2) ◽  
pp. 179-186 ◽  
Author(s):  
Rolf W. Saalfrank ◽  
Jochen Nachtrab ◽  
Stephan Reck

Reaction of dimethyl 1,3-acetonedicarboxylate 8 with oxalylchloride 2 and magnesium chloride as catalyst yielded 2,3-dioxo-2,3-dihydrofuran 9, which is in equilibrium with tautomer 10 (9:10 = 1:2). Addition of thionyl chloride to a mixture of 9/10 afforded 3-chloro-2(5H)-furanone 11. The structure of 11 was unequivocally established by X-ray diffraction, which indirectly proved the structure of 10 as well. Ring opening of 11 by nucleophilic attack with benzylamine 14 in C2-position and subsequent recyclization led to racemic 3-chloro-5-hydroxy-2-oxo-2,5-dihydropyrrole 15. According to a single crystal X-ray analysis, 15 aggregates via stereospecific self selection through hydrogen bonds to give chiroselectively the one-dimensional strands ∞1[(S)-15] and ∞1[( R)-15]


2003 ◽  
Vol 775 ◽  
Author(s):  
Harri Kosonen ◽  
Sami Valkama ◽  
Janne Ruokolainen ◽  
Gerrit ten Brinke ◽  
Olli Ikkala

AbstractPolystyrene-block-poly(4-vinylpyridine) (PS-block-P4VP) diblock copolymer was complexed with dodecylbenzenesulfonic acid (DBSA), leading to comb-coil polymeric supramolecules PS-block-P4VP(DBSA)y (y = 1.0, 1.5, and 2.0). Complexes formed hierarchical lamellar structure with long period of ca. 1400 Å. Due to periodicity and refractive index contrast between the layers, transmission and reflectance measurements showed a relatively narrow incomplete bandgap at ca. 460 nm. The angular dependence of the bandgap was also studied using different angles (ø) relative to the surface normal. The mid-gap was blue-shifted when the incident angle was increased indicating that the lamellar structure was partly oriented by the surfaces of quartz glasses.


1998 ◽  
Vol 30 (03) ◽  
pp. 850-869 ◽  
Author(s):  
Michel Benaïm ◽  
Jean-Claude Fort ◽  
Gilles Pagès

We show in a very general framework the a.s. convergence of the one-dimensional Kohonen algorithm–after self-organization–to its unique equilibrium when the learning rate decreases to 0 in a suitable way. The main requirement is a log-concavity assumption on the stimuli distribution which includes all the usual (truncated) probability distributions (uniform, exponential, gamma distribution with parameter ≥ 1, etc.). For the constant step algorithm, the weak convergence of the invariant distributions towards equilibrium as the step goes to 0 is established too. The main ingredients of the proof are the Poincaré-Hopf Theorem and a result of Hirsch on the convergence of cooperative dynamical systems.


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