Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation

We are interested in the nonlinear stability of the Eckhaus-stable equilibria of the Swift-Hohenberg equation on the infinite line with respect to small integrable perturbations. The difficulty in showing stability for these stationary solutions comes from the fact that their linearizations possess continuous spectrum up to zero. The nonlinear stability problem is treated with renormalization theory which allows us to show that the nonlinear terms are irrelevant, i.e. that the fully nonlinear problem behaves asymptotically as the linearized one which is under a diffusive regime.     

Wavelet filtering to study mixing in 2D isotropic turbulence

This paper presents the application of coherent vortex simulation (CVS) filtering, based on an orthogonal wavelet decomposition of vorticity, to study mixing in 2D homogeneous isotropic turbulent flows. The Eulerian and Lagrangian dynamics of the flow are studied by comparing the evolution of a passive scalar and of particles advected by the coherent and incoherent velocity fields, respectively. The former is responsible for strong mixing and produces the same anomalous diffusion as the total flow, due to transport by the coherent vortices, while mixing in the latter is much weaker and corresponds to classical diffusion.     

Unusual mesomorphic behaviour of new bent-core mesogens derived from 4-cyanoresorcinol

New five-ring bent-core mesogens derived from 4-cyanoresorcinol as the central core have been synthesized. The mesophases were assigned by polarizing microscopy, X-ray diffraction and electro-optical measurements. It was found that the mesophase behaviour clearly depends on the direction of the carboxyl linking groups between the aromatic rings. If the outer and inner ester linking groups of a wing are in the same direction then nematic phases and, for long chain members, SmC and SmCP_A phases are observed. If the outer and inner linking groups are in opposing directions a dimorphism, SmA-SmAP_A, is observed and the clearing temperatures are increased by about 55 K. It is remarkable that in the SmCP_A phases of the first series, polar switching preferably takes place through a collective rotation of the molecules around their long axes which is accompanied by the inversion of the chirality of the smectic layers.     

Combinatorial approximation algorithms: a comparative review

This paper is a comparative review of three related books:Giorgio Ausiello, Pierluigi Crescenzi, Giorgio Gambosi, Viggo Kann, Alberto Marchetti-Spaccamela, Marco Protasi, Complexity and Approximation (Combinatorial Optimization Problems and Their Approximability Properties), second printing, Springer, Berlin, 2003, ISBN 3-540-65431-3, 524 pp., €53.45 (first printing 1999).Juraj Hromkovi?, Algorithmics for Hard Problems (Introduction to Combinatorial Optimization, Randomization, Approximation, and Heuristics), second edition, Springer, Berlin, 2003, ISBN 3-540-44134-4, 544 pp., €53.45 (first printing 2001).Vijay Vazirani, Approximation Algorithms, second printing, Springer, Berlin, 2002, ISBN 3-540-65367-8, 380 pp., €37.40 (first printing 2001).     

Squares of regular languages

The square of a language L is the set of all words pp where p ∈ L. The square of a regular language may be regular too or context‐free or none of both. We give characterizations for each of these cases and show that it is decidable whether a regular language has one of these properties. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stereoselective Ring Opening of Electronically Excited Cyclohexa-2, 4-dienones: Cause and effect

The two conformers of a cyclohexa-2, 4-dienone with different substituents at C(6) on irradiation are believed to undergo ring opening stereospecifically affording a mixture of two configurationally isomeric diene-ketenes (and descendents thereof)- Exceptions are generally found for those dienones with one C and one O substituent or even with two C substituents, if one of them carries a polar group at a site able to interact through space with the ring C?O group. In these cases, only one of the two anticipated diene-ketenes (and descendents thereof) is produced. A thorough investigation of the photochemistry of a series of structurally different cyclohexa-2, 4-dienones on analytical as well as on preparative scale extends our mechanistic knowledge of the various routes from diene-ketenes into a variety of compound classes. Novel compound classes accessible to diene-ketenes are seven-membered carbocycles (by intramolecular aldolization of the zwitterion of appropriately substituted, transiently formed diene-(N, O)-ketene acetals) and β-lactams (by Staudinger reaction).     

Electronic excitation and singlet-triplet coupling in uracil tautomers and uracil-water complexes

Electronic spectra of uracil in its diketo (lactam) form and five enol (lactim) tautomeric forms have been investigated by means of combined density functional and configuration interaction methods. We have simulated the effects of hydrogen bonding with a protic solvent by recomputing the spectrum of uracil in the presence of two, four, or six water molecules. Geometries of the electronic ground state and several low-lying excited states have been optimized. Spin-orbit coupling has been determined for correlated wavefunctions employing a non-empirical spin-orbit mean-field approach. In accord with experiment, we find the diketo tautomer to be the most stable one. The calculations confirm that the first absorption band arises from the ¹( π↦π^*) S ₀↦S ₂ excitation. The experimentally observed vibrational structure in this band originates from a breathing mode of the six ring. Complexation with water molecules is seen to cause a significant blue shift of n↦π^* excitations while leaving π↦π^* excitations nearly uninfluenced. Computed radiative lifetimes are presented for the experimentally known weak phosphorescence from the π↦π^* excited T₁ state. Among the uracil lactim tautomers, one is particularly interesting from a spectroscopic point of view. In this tautomer, the π↦π^* excitation gives rise to the S₁ state. Received 18 February 2002 / Received in final form 5 June 2002 Published online 13 September 2002