A pde approach to small stochastic perturbations of Hamiltonian flows

In this note we present a unified approach, based on pde methods, for the study of averaging principles for (small) stochastic perturbations of Hamiltonian flows in two space dimensions. Such problems were introduced by Freidlin and Wentzell and have been the subject of extensive study in the last few years using probabilistic arguments. When the Hamiltonian flow has critical points, it exhibits complicated behavior near the critical points under a small stochastic perturbation. Asymptotically the slow (averaged) motion takes place on a graph. The issues are to identify both the equations on the sides and the boundary conditions at the vertices of the graph. Our approach is very general and applies also to degenerate anisotropic elliptic operators which could not be considered using the previous methodology.     

In vitro self-assembly of bacteriochlorophyll c derivatives monoesterified with α,ω-diols isolated from the green sulfur photosynthetic bacterium Chlorobaculum tepidum

Esterifying chains of chlorophyllous pigments play important roles in the formation of photosynthetic supramolecules, but their effects have not thoroughly been unraveled yet. Substitution of the esterifying chains in these pigments will be one possible strategy to elucidate this enigma. Recently, unnatural bacteriochlorophylls (BChls) c possessing a hydroxy group at the terminus of the esterifying chains were successfully biosynthesised in the green sulfur bacterium Chlorobaculum (Cba.) tepidum grown by supplementation of α,ω-diols. In this paper, in vitro assembling behaviours of unnatural BChls c isolated from Cba. tepidum grown with 1,8-octanediol, 1,12-dodecanediol and 1,16-hexadecanediol were characterised in aqueous Triton X-100 micelles to investigate the effects of the terminal hydroxy group in the esterifying chains of BChls c on self-aggregates such as chlorosomes, major antenna complexes in green photosynthetic bacteria. The bacteriochlorophyll (BChl) c derivatives monoesterified with α,ω-diols formed chlorosomal self-aggregates, but their formations were much slower than those of natural BChl c. The Q_y absorption bands of the residual monomers of these BChl c derivatives were larger than those of natural BChl c. These suggest that the esterifying α,ω-diols in these unnatural BChls c somewhat interfered with formation of chlorosome-like aggregates compared with the natural esterifying farnesol.     

Saving fourth generation and baryon number by living long

Recent studies of precision electroweak observables have led to the conclusion that a fourth generation is highly constrained. However, we point out that a long-lived fourth generation can reopen a large portion of the parameter space. In addition, it preserves baryon and lepton asymmetries against sphaleron erasure even if B−L=0. It opens up the possibility of exact B−L symmetry and hence Dirac neutrinos. The fourth generation can be observed at the LHC with unique signatures of long-lived particles in the near future.     

Lattice Dynamical Calculations of Trans and Cis Polyacetylene

Lattice dynamical calculations of the lattice modes for both trans and cis polyacetylene were performed. Using rigid body approximation for the chain we obtained all 8 lattice frequencies and modes of motion for both trans and cis polyacetylene. The frequencies concerned with Raman active lattice modes are presented for the first time. We also performed far infrared transmission measurements of undoped trans and cis polyacetylene and confirmed the results obtained by Bechtold et al. Comparison of the lattice frequencies obtained by lattice dynamical calculations with the results obtained by far infrared measurement and inelastic neutron scattering is discussed.