We study the fraction f of nucleotides involved in the formation of a cactuslike secondary structure of random heteropolymer RNA-like molecules. In the low-temperature limit, we study this fraction as a function of the number c of different nucleotide species. We show, that with changing c, the secondary structures of random RNAs undergo a morphological transition:f(c)→1 for c≤ccr as the chain length n goes to infinity, signaling the formation of a virtually perfect gapless secondary structure; while f(c)<1 for c>ccr, which means that a nonperfect structure with gaps is formed. The strict upper and lower bounds 2≤ccr≤4 are proven, and the numerical evidence for ccr is presented. The relevance of the transition from the evolutional point of view is discussed.
We demonstrate that waves excited on a fluid surface produce local surface rotation owing to hydrodynamic nonlinearity. We examine theoretically the effect and obtain an explicit formula for the vertical vorticity in terms of the surface elevation. Our theoretical predictions are confirmed by measurements of surface motion in a cell with water where surface waves are excited by vertical and harmonic shaking the cell. The experimental data are in good agreement with the theoretical predictions. We discuss physical consequences of the effect.
Using proton-proton collision data corresponding to an integrated luminosity of 3.0fb−1, recorded by the LHCb detector at centre-of-mass energies of 7 and 8TeV, the Bc+ → D0K+ decay is observed with a statistical significance of 5.1 standard deviations. By normalising to B+ → D0π+ decays, a measurement of the branching fraction multiplied by the production rates for Bc+ relative to B+ mesons in the LHCb acceptance is obtained,
R 0 =fc ×B(B+→D0K+)=(9.3+2.8±0.6)×10−7, DKfu c −2.5
where the first uncertainty is statistical and the second is systematic. This decay is expected to proceed predominantly through weak annihilation and penguin amplitudes, and is the first Bc+ decay of this nature to be observed.