Spectral bifurcations in dispersive wave turbulence

Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct stable spectra are observed—the direct and inverse cascades of weak turbulence (WT) theory, thermal equilibrium, and a fourth spectrum (MMT; Majda, McLaughlin, Tabak). Each spectrum can describe long-time behavior, and each can be only metastable (with quite diverse lifetimes)—depending on details of nonlinearity, forcing, and dissipation. Cases of a long-live MMT transient state dcaying to a state with WT spectra, and vice-versa, are displayed. In the case of freely decaying turbulence, without forcing, both cascades of weak turbulence are observed. These WT states constitute the clearest and most striking numerical observations of WT spectra to date—over four decades of energy, and three decades of spatial, scales. Numerical experiments that study details of the composition, coexistence, and transition between spectra are then discussed, including: (i) for deterministic forcing, sharp distinctions between focusing and defocusing nonlinearities, including the role of long wavelength instabilities, localized coherent structures, and chaotic behavior; (ii) the role of energy growth in time to monitor the selection of MMT or WT spectra; (iii) a second manifestation of the MMT spectrum as it describes a self-similar evolution of the wave, without temporal averaging; (iv) coherent structures and the evolution of the direct and inverse cascades; and (v) nonlocality (in k-space) in the transferral process.

Swi5 Controls a Novel Wave of Cyclin Synthesis in Late Mitosis

We have shown previously that the Swi5 transcription factor regulates the expression of the SIC1 Cdk inhibitor in late mitosis. This suggests that Swi5 might control other genes with roles in ending mitosis. We identified a gene with a Swi5-binding site in the promoter that encoded a protein with high homology to Pcl2, a cyclin-like protein that associates with the Cdk Pho85. This gene, PCL9, is indeed regulated by Swi5 in late M phase, the only cyclin known to be expressed at this point in the cell cycle. The Pcl9 protein is associated with a Pho85-dependent protein kinase activity, and the protein is unstable with peak levels occurring in late M phase. PCL2 is already known to be expressed in late G1 and we find that, in addition, it is also regulated by Swi5 in telophase. The expression of PCL2 and PCL9 at this stage of the cell cycle implies a role for the Pho85 Cdk at the end of mitosis. Consistent with this a synthetic interaction was observed between pho85Δ and strains deleted for SIC1, SWI5, and SPO12. These and other studies support the notion that the M/G1 switch is a major cell cycle transition.