Mathematica® code for Stoner-Wohlfarth processes
A simple and robust numeric code written in Mathematica® is proposed in order to generate magnetic hysteresis loops and critical curves in the framework of the Stoner-Wohlfarth model, extended to take into account the effect on an external mechanical stress; a case study referring to the influence of the shear stress applied normal to the magnetic field direction is presented.
We consider the problem of finding the cheapest routing for a set of commodities over a directed graph, such that: i) each commodity flows through a single path, ii) the routing cost of each arc is given by a convex piecewise linear function of the load (i.e. the total flow) traversing it. We propose a new mixed-integer programming formulation for this problem. This formulation gives a complete description of the associated polyhedron for the single commodity case, and produces very tight linear programming bounds for the multi-commodity case.