Structure-preserving finite-difference schemes for general nonlinear fourth-order parabolic equations on the one-dimensional torus are derived. Examples include thin-film and Derrida–Lebowitz–Speer–Spohn equations. The conserve mass dissipate entropy. scheme associated to logarithmic entropy also preserves positivity. idea of derivation is reformulate in such a way ...

We propose a mechanism ensuring (quasi)localization of massless gauge fields on a brane. The mechanism does not rely on BPS properties of the brane and can be realized in any theory where charged particles are confined to the world-volume. The localized matter fluctuations induce a gauge kinetic term on the brane. At short distances the resulting propagator for the gauge field is identical to t...