Permeability of the regular structure from spherical nanoparticles

This paper presents a theoretical study on permeability of a regular structure composed of twenty spherical nanoparticles of the same size. The numerical solution is constructed using turn-based schemes of higher-order accuracy. The interaction between structure elements and moving molecules is determined by the V.Y. Rudyak and S.L. Krasnolutsky potential. It was found, that the tested model structure has the helium permeability to four times more than for methane

``Smoke Rings'' in Ferromagnets

It is shown that bulk ferromagnets support propagating non-linear modes that are analogous to the vortex rings, or ``smoke rings'', of fluid dynamics. These are circular loops of {\it magnetic} vorticity which travel at constant velocity parallel to their axis of symmetry. The topological structure of the continuum theory has important consequences for the properties of these magnetic vortex rings. One finds that there exists a sequence of magnetic vortex rings that are distinguished by a topological invariant (the Hopf invariant). We present analytical and numerical results for the energies, velocities and structures of propagating magnetic vortex rings in ferromagnetic materials.Comment: 4 pages, 3 eps-figures, revtex with epsf.tex and multicol.sty. To appear in Physical Review Letters. (Postscript problem fixed.

Spectral analysis on infinite Sierpinski fractafolds

A fractafold, a space that is locally modeled on a specified fractal, is the fractal equivalent of a manifold. For compact fractafolds based on the Sierpinski gasket, it was shown by the first author how to compute the discrete spectrum of the Laplacian in terms of the spectrum of a finite graph Laplacian. A similar problem was solved by the second author for the case of infinite blowups of a Sierpinski gasket, where spectrum is pure point of infinite multiplicity. Both works used the method of spectral decimations to obtain explicit description of the eigenvalues and eigenfunctions. In this paper we combine the ideas from these earlier works to obtain a description of the spectral resolution of the Laplacian for noncompact fractafolds. Our main abstract results enable us to obtain a completely explicit description of the spectral resolution of the fractafold Laplacian. For some specific examples we turn the spectral resolution into a "Plancherel formula". We also present such a formula for the graph Laplacian on the 3-regular tree, which appears to be a new result of independent interest. In the end we discuss periodic fractafolds and fractal fields

Permeability of the regular structure from spherical nanoparticles

This paper presents a theoretical study on permeability of a regular structure composed of twenty spherical nanoparticles of the same size. The numerical solution is constructed using turn-based schemes of higher-order accuracy. The interaction between structure elements and moving molecules is determined by the V.Y. Rudyak and S.L. Krasnolutsky potential. It was found, that the tested model structure has the helium permeability to four times more than for methane