mold powders are fluxing agents used as raw materials in the steel industry, which play very important role inprocessing stability and final surface quality of a product. surface quality depends particularly on the viscosity and the heat transfer of infiltrated mold flux between the mold wall and the solidified steel shell. heat flux across the interfacial gap depends on thermal properties of s...

We derive a posteriori error estimates for the discretization of the heat equation in a unified and fully discrete setting comprising the discontinuous Galerkin, finite volume, mixed finite element, and conforming and nonconforming finite element methods in space and the backward Euler scheme in time. Our estimates are based on a H-conforming reconstruction of the potential, continuous and piec...

When a conductive material is subjected to a time-varying magnetic flux, eddy currents are generated in the conductor. These eddy currents circulate inside the conductor generating a magnetic field of opposite polarity as the applied magnetic field. The interaction of the two magnetic fields causes a force that resists the change in magnetic flux. However, due to the internal resistance of the ...

In a recent paper, Opasanon and Miller-Hooks study multicriteria adaptive paths in stochastic time-varying networks. They propose a label correcting algorithm for finding the full set of efficient strategies. In this note we show that their algorithm is not correct, since it is based on a property that does not hold in general. Opasanon and Miller-Hooks also propose an algorithm for solving a p...

Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of static networks, each aggregating all edges and nodes present in a time interval of size Δt. In this work we quantify the impact of an arbitrary Δt on the descrip...

Different graph generalizations have been recently used in an ad-hoc manner to represent multilayer networks, i.e. systems formed by distinct layers where each layer can be seen as a network. Similar constructions have also been used to represent time-varying networks. We introduce the concept of MultiAspect Graph (MAG) as a graph generalization that we prove to be isomorphic to a directed grap...