We report on the electromagnetic properties of ‘focused doughnuts’ (FD), space-time localized solutions to Maxwell’s equations with toroidal topology. We show that light-matter interactions of FD pulses, include non-trivial field transformations and broadband modal excitations.

Pathwise non-uniqueness is established for non-negative solutions of the parabolic stochastic pde ∂X ∂t = ∆ 2 X +XẆ + ψ, X0 ≡ 0 where Ẇ is a white noise, ψ ≥ 0 is smooth, compactly supported and non-trivial, and 0 < p < 1/2. We further show that any solution spends positive time at the 0 function.

Non-uniform black strings in the two-brane system are investigated using the effective action approach. It is shown that the radion acts as a non-trivial hair of black strings. The stability of solutions is demonstrated using the catastrophe theory. The black strings are shown to be non-uniform.

Based on the non-abelian effective action for D1-branes, a new action for matrix string theory in non-trivial backgrounds is proposed. Once the background fields are included, new interactions bring the possibility of non-commutative solutions i.e. The Myers effect for “string bits” .