In the laboratory (upper figure) wave-packets emanating from two Gaussian slits spread in space x upon propagation in $$\tau$$ (in optics, distance; in quantum mechanics, time). The spreading wave packets give interference structures as they overlap. In a transformed ($$\bar{x}$$, $$\bar{\tau}$$) frame (lower figure), co-moving with the propagation of a Hermite-Gauss basis, the wave packets become non-spreading coherent oscillator states. The transformed $$\bar{\tau}$$, in both optics and quantum mechanics, is just the Gouy phase. The wave-packets move to coalesce at the origin and interfere only as the phase approaches $$\pi/2$$.

The discipline of catalysis arrived at China in 1860s. The country started immediately to employ catalytic technologies to produce traditional sulfuric acid, for example, the Cylinder-Tower Method during World WarII. Interestingly, the first Chinese term Cui Hua of catalysis appeared much late in 1930s. In recent years, however, China has become one of the global leaders in modern catalysis research by developing cutting-edge technologies in various fields, such as confinement catalysis, single-atom catalysis, chiral catalysis, the Sabatier principle of metal-support interaction, modern characterization methods, and clean energy catalysis.

In free propagation from a focus the Hermite–Gauss mode functions of optics, or the equivalent Harmonic Oscillator eigenfunctions of quantum mechanics spread in space. It is shown that a transformation to a frame travelling with the normals to the wave fronts gives the Gouy phase as proper position or time variable. In this frame Gaussian slit functions do not spread but coalesce when the Gouy phase reaches ninety degrees. This allows a

A space-time scaling is used to transform quantum wave packets describing free particle motion to packets moving in an effective harmonic oscillator potential that confines and directs the wave fronts along the classical phase space of the oscillator. The transformation is applied to multi-slit diffraction and shown to characterize diffraction features in both the near and far fields by the classical trajectories of the oscillator.

The most common cystic fibrosis-causing F508del mutation is located in the first nucleotide-binding domain (hNBD1) of the human cystic fibrosis transmembrane conductance regulator (hCFTR). The ATP-dependent weakest noncovalent bridge in isolated hNBD1 is found between two specific bold residues in the biggest thermo-ring (highlighted in red) at or near the ATP site. This bridge aligns the predicted melting temperature threshold of hNBD1 well with the experimental melting threshold and the systematic thermal instability (indicated by green labels).

Weather limits drone usability: precipitation (30%), wind (54%), and temperature (16%) constraints reduce operability to around 25% of days per year.