Magnetic Sans of Nanoparticles and Complex Systems

2021 ◽  
pp. 172-222
Author(s):  
Andreas Michels
Keyword(s):  
Boundary Value Problem ◽  
Complex Systems ◽  
Spin Glasses ◽  
Boundary Value ◽  
Vortex State ◽  
Amorphous Magnets ◽  
Analytical Expressions ◽  
Complete Specification

This chapter provides an overview on the magnetic SANS of nanoparticles and complex systems, which include ferrofluids, magnetic steels, and spin glasses and amorphous magnets. The underlying assumptions of the conventional particle-matrix-based model of magnetic SANS, which assumes uniformly magnetized domains, characteristic e.g., for superparamagnets, are discussed and we provide a complete specification of the micromagnetic boundary-value problem. First attempts to provide analytical expressions for the vortex-state-related magnetic SANS of thin circular discs are considered.

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

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