LOW FREQUENCY FIELD OF AN EARTHING CONDUCTOR BY VARIATIONAL METHOD

A variational method using global approximation is extended to the analysis of the low-frequency field of exterior boundary value problems. The method is presented through the example of computing the current distribution of an earthing conductor. Using a T - Ω approach, an approximate solution of Helmholtz's equation is generated with the prescribed Dirichlet and Neumann boundary conditions, and also the approximate conditions at infinity are satisfied. The boundary surfaces of the region examined are assumed to be described or approximated by piecewise analytical functions. The satisfacion of the prescribed boundary conditions is ensured by means of R-functions

APPROXIMATE SOLUTION OF LAPLACE EQUATION IN UNBOUNDED REGIONS BY VARIATIONAL METHOD

The paper extends the global element variational method to the determination of the static and stationary electric and magnetic field in unbounded regions. An approximating solution of Laplace equation in the studied region is obtained with the aid of R-functions defined on the boundaries approximated by analytical functions with the solution satisfying the Dirichlet and Neumann boundary conditions on the boundaries and behaving appropriately in infinity. The application of the method is illustrated by an example

Reciprocity in Social Networks with Capacity Constraints

Directed links -- representing asymmetric social ties or interactions (e.g., "follower-followee") -- arise naturally in many social networks and other complex networks, giving rise to directed graphs (or digraphs) as basic topological models for these networks. Reciprocity, defined for a digraph as the percentage of edges with a reciprocal edge, is a key metric that has been used in the literature to compare different directed networks and provide "hints" about their structural properties: for example, are reciprocal edges generated randomly by chance or are there other processes driving their generation? In this paper we study the problem of maximizing achievable reciprocity for an ensemble of digraphs with the same prescribed in- and out-degree sequences. We show that the maximum reciprocity hinges crucially on the in- and out-degree sequences, which may be intuitively interpreted as constraints on some "social capacities" of nodes and impose fundamental limits on achievable reciprocity. We show that it is NP-complete to decide the achievability of a simple upper bound on maximum reciprocity, and provide conditions for achieving it. We demonstrate that many real networks exhibit reciprocities surprisingly close to the upper bound, which implies that users in these social networks are in a sense more "social" than suggested by the empirical reciprocity alone in that they are more willing to reciprocate, subject to their "social capacity" constraints. We find some surprising linear relationships between empirical reciprocity and the bound. We also show that a particular type of small network motifs that we call 3-paths are the major source of loss in reciprocity for real networks

MODELLING OF ELECTROMAGNETIC FIELD IN FERROMAGNETIC MATERIALS

The paper presents some results and ideas in the field of electromagnetic field calculation in the case of ferromagnetic materials and eddy currents. The hysteresis phenomenon is modelled by the classical Preisach model and the field is calculated with finite element method in time domain. A convergent and physically good scheme is given also for the solution

Deciding football sequences

An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential time exact algorithms which solve the problem