LXXX.—The bromination of m-methoxycinnamic acid

Sherwood Number and Friction Factor Correlations for Electrodialysis Systems, with Application to Process Optimization

“…For subcritical Reynolds numbers (Re < 103) the data agree well with the Poiseuille flow result for truly two-dimensional channels (note that for channels with the cross-sectional aspect ratio of ours, the more correct correlation actually lies 2% above the correlation for truly twodimensional channels). The ,transition toward fully turbulent flow is similar to that found by Davies and White (1928). Also, although our data do not actually extend into the fully turbulent region, they do extrapolate toward the fully turbulent correlation of Davies and White.…”

Asymmetric, Helical, and Mirror-Symmetric Traveling Waves in Pipe Flow

“…This figure substantially lowers the current best estimate of 1251 for Re g -the Reynolds number at which the laminar state stops being a global attractor. The relative sizes of this new Re g and Re t for pipe flow are then more in line with plane Couette flow (Re t = 323 [16] and Re g = 127.7 [17,18]: Re based on half the velocity difference and half the channel width) than plane Poiseuille flow (Re t ≈ 1300 [19,20,21,22,23] and Re g = 860 [18]: Re based on the mean flow rate and the channel width). Beyond suggesting that Re g in plane Poiseuille flow can be significantly lowered, these latest discoveries highlight the substantial delay in Re between new solutions appearing in phase space and the emergence of sustained turbulent trajectories.…”

Long-lived resonant states in planetary atoms

“…Since the classical motion corresponding to the quantum states is stable (see figure 1) they are classically bound. However, in analogy to the (semiclassical) penetration through a "static" potential barrier these states can autoionize semiclassically by "dynamical" tunneling [22], but the decay widths for such processes decrease exponentially with the nodal excitation along the orbit [10].…”