Three-dimensional finite-element models provide a method to study the relationship between human scalp potentials and neural current sources inside the brain. A new formulation of dipole-like current sources is developed here. Finite-element analyses based on this formulation are carried out for both a three-concentric-spheres model and a human-head model. Differences in calculated scalp potentials between these two models are studied in the context of the forward and inverse problems in EEG. The effects of the eye orbit structure on surface potential distribution are also studied.

We present the necessary conditions for the existence of the Kolwankar-Gangal local fractional derivatives (KG-LFD) and introduce more general but weaker notions of LFDs by using limits of certain integral averages of the difference-quotient. By applying classical results due to Stein and Zygmund (1965) [16] we show that the KG-LFD is almost everywhere zero in any given intervals. We generalize some of our results to higher dimensional cases and use integral approximation formulas obtained to design numerical schemes for detecting fractional dimensional edges in signal processing.

This paper presents some results of a numerical micromagnetic calculation for ferromagnetic fine particles. Two basic shapes are discussed: elongated parallelopipeds and parallelopipeds with pointed ends. The variation of coercivity, switching field, and reversal modes with particle size, orientation, and material parameters are discussed. Equilibrium magnetization structures suggest that particles may have remanent states that are substantially nonuniform. The flipping mode, in which the magnetization reversal starts from the longitudinal ends of the particles, is found to be the energetically favorable switching mechanism. Small particles are switched by the quasi-coherent flipping mode, while large particles are reversed by the quasi-curling flipping mode. The angular dependence of the coercive and switching fields for three particle sizes is found to agree qualitatively with classical results, but both fields are quantitatively smaller. The nucleation field is compared with the Stoner–Wohlfarth model as well as with the curling mode, and is found to be about half of their value.

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Numerical micromagnetic modeling of a single particle and small numbers of particles has recently greatly increased our understanding of fine particle magnetizing processes, but the behavior of a large number of such interacting particles is not yet completely understood. The analysis presented here shows that the moving-model Preisach approach, as a framework for explaining the behavior of such a distribution, is plausible; however, the proportionality factor is considerably different from the one that had been previously calculated.