3,904 research outputs found
An inverse problem of the flux for minimal surfaces
For a complete minimal surface in the Euclidean 3-space, the so-called flux
vector corresponds to each end. The flux vectors are balanced, i.e., the sum of
those over all ends are zero. Consider the following inverse problem: For each
balanced n vectors, find an n-end catenoid which attains given vectors as flux.
Here, an n-end catenoid is a complete minimal surface of genus 0 with ends
asymptotic to the catenoids. In this paper, the problem is reduced to solving
algebraic equation. Using this reduction, it is shown that, when n=4, the
inverse problem for 4-end catenoid has solutions for almost all balanced 4
vectors. Further obstructions for n-end catenoids with parallel flux vectors
are also discussed.Comment: 28 pages, AMSLaTeX 1.1, with 8 figures, To appear in Indiana
University Mathematics Journa
Two-dimensional topological solitons in rectangular magnetic dots
A general approach allowing to find the analytical expressions for
equilibrium magnetic structures in small and flat magnetic nano-sized cylinders
of arbitrary shape made of soft magnetic material is presented. The resulting
magnetization distributions are two-dimensional topological solitons and have a
non-zero topological charge. The approach is illustrated here on an example of
a thin rectangular particle.Comment: 3 pages, 2 figures, RevTex, for SCM2001 (Seeheim, Germany, 2001),
satellite of JEMS'01 conferenc
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