The Devil is in the details: Spectrum and eigenvalue distribution of the discrete Preisach memory model
Autor: | Dmitrii Rachinskii, Tamás Kalmár-Nagy, Daniel Kim, Andreas Amann |
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Rok vydání: | 2019 |
Předmět: |
Numerical Analysis
Chebyshev polynomials Applied Mathematics FOS: Physical sciences Mathematical Physics (math-ph) 01 natural sciences 010305 fluids & plasmas Inventory management Eigenvalue distribution Modeling and Simulation 0103 physical sciences Density of states Applied mathematics Adjacency matrix Memory model 010306 general physics Mathematical Physics Eigenvalues and eigenvectors Mathematics Characteristic polynomial |
Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 77:1-17 |
ISSN: | 1007-5704 |
Popis: | We consider the adjacency matrix associated with a graph that describes transitions between the states of the discrete Preisach memory model. This matrix can also be associated with the “last-in-first-out” inventory management rule. We present an explicit solution for the spectrum by showing that the characteristic polynomial is the product of Chebyshev polynomials. The eigenvalue distribution (density of states) is explicitly calculated and is shown to approach a scaled Devil’s staircase. The eigenvectors of the adjacency matrix are also expressed analytically. |
Databáze: | OpenAIRE |
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