Kalmár-Nagy, Tamás
(BME GMK)
Devilish eigenvalues: hysteresis and
mechanistic turbulence
We consider the adjacency
matrix associated with a graph that describes transitions between 2^{N} 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. This is joint work with Andreas Amann,
Daniel Kim, and Dmitrii Rachinski.
We also examine a
mechanistic model of turbulence, a binary tree of masses connected
by springs. We analyze the
behavior of this linear model: a formula is presented for the analytical
calculation of the eigenvalues and the optimal damping - at which the decay of
the total mechanical energy is maximized. The discrete energy spectrum of the
mechanistic model (defined as the total
mechanical energy stored in
each level) can be tuned to display the features of the Kolmogorov-spectrum.
This is joint work with Bendegúz Dezső
Bak.
The talk is held in Hungarian!
Az előadás magyar nyelven lesz megtartva!
Date: Oct 17, Tuesday 4:15pm
Place: BME, Building „Q”, Room QBF13