Micromagnetic simulation of domain walls in iron films

The micromagnetic structure and energy of 180° domain walls spanning laminar crystals of iron having (100) or (110) surfaces and ranging in thickness from 145 to 580 nm have been investigated by numerical integration of the Landau-Lifshitz-Gilbert equation. Stable equilibrium structures with two flux symmetries were obtained for both crystal orientations at all thicknesses studied.

Two-stage open shop scheduling with a bottleneck machine

It is known that for the open shop scheduling problem to minimize the makespan there exists no polynomial-time heuristic algorithm that guarantees a worst-case performance ratio better than 5/4, unless P6≠NP. However, this result holds only if the instance of the problem contains jobs consisting of at least three operations. This paper considers the open shop scheduling problem, provided that each job consists of at most two operations, one of which is to be processed on one of the m⩾2 machines, while the other operation must be performed on the bottleneck machine, the same for all jobs. For this NP-hard problem we present a heuristic algorithm and show that its worst-case performance ratio is 5/4.