Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...

The contact of metal and semiconductor can lead to the formation of a junction with either Schottky or Ohmic behavior.
Schottky Barriers
Schottky barriers arise when a metal with a work function (Φm) contacts a semiconductor with a different work function (Φs). Initially, electrons transfer until the Fermi levels of the metal and semiconductor align at equilibrium. For instance, if Φm > Φs, the semiconductor Fermi level is higher than the metal's before contact. The...

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...

In hydraulic engineering, sluice gates are essential for managing water flow through channels, reservoirs, and irrigation systems. Sluice gates, acting as vertical barriers, regulate water by adjusting the gate's opening height, which changes the velocity and pressure of water flowing beneath the gate. Understanding the forces involved is crucial to designing sluice gates that can withstand dynamic pressure differences, especially when the gate is closed or partially open.
Key variables in...