Blowout bifurcation and spatial mode excitation in the bubbling transition to turbulence

The transition to turbulence (spatio-temporal chaos) in a wide class of spatially extended dynamical system is due to the loss of transversal stability of a chaotic attractor lying on a homogeneous manifold (in the Fourier phase space of the system) causing spatial mode excitation Since the latter manifests as intermittent spikes this has been called a bubbling transition We present numerical evidences that this transition occurs due to the so called blowout bifurcation whereby the attractor as a whole loses transversal stability and becomes a chaotic saddle We used a nonlinear three-wave interacting model with spatial diffusion as an example of this transition (C) 2010 Elsevier B V All rights reserved

Bubbling transition to spatial mode excitation in an extended dynamical system

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable. (C) 2008 Elsevier B.V. All rights reserved.

Stereochemical and electronic interaction studies of some N-methoxy-N-methyl-2-[(4 `-substituted)phenylsulfinyl]propanamides

The (1)H NMR spectra of N-methoxy-N-methyl-2-[(4`-substituted)phenylsulfinyl]-propanamides [Y-Ph-S(O)CH(Me)C(O)N(OMe)Me; Y = OMe 1, Me 2, H 3. Cl 4, NO(2) 5] along with the X-ray diffraction analysis of the nitro-derivative (5). have shown the existence of two pairs of diastereomers (racemic mixture) [C(R)S(S)/C(S)S(R) (diast(1)) and C(R)S(R)/C(S)S(S) (diast(2))] in the ratio of ca. 7:3. respectively. The v(CO) IR analysis of the title compounds supported by HF and B3LYP/6-31G** calculations of 3 and of the parent N-methoxy-N-methyl-propanamide (6) by HF, have shown that diast(1) exists in an equilibrium between the two more polar and more stable quasi-cis (q-c(1) and q-c(2)) conformers and the gauche(g) conformer. The population of the g conformer in the equilibrium increases with the increase in the solvent polarity, which is attributed to a larger solvation effect on the carbonyl and sulfinyl groups. Diast(2) of compound 3 occurs in the gas phase as an equilibrium between the most stable quasi-gauche (q-g) conformer and the quasi-cis (q-c) conformer, both presenting very similar dipole moments. The former is stabilized by electrostatic and charge transfer interactions, which results in a less solvated spatial arrangement. Moreover, all conformers of both diastereomers are stabilized by several intramolecular hydrogen bonds. X-ray single crystal analysis performed for diast(1) and for diast(2) of 5 indicates that both stereoisomers assume, in the solid state, the anti-clinal (gauche) conformation. For the crystal packing, diast(1) of 5 is made up of three molecules joined through two centro-symmetric H center dot center dot center dot O hydrogen bonds. (C) 2008 Elsevier B.V. All rights reserved.