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UID:20261113-applied-math-seminar@jiazhaomath.github.io
DTSTAMP:20261007T000000Z
DTSTART:20261113T170000Z
DTEND:20261113T175000Z
SUMMARY:Applied Mathematics Seminar: Vadim Zharnitsky — Optimal damping i
 n the mass-spring systems
DESCRIPTION:Vadim Zharnitsky\, Professor\, Department of Mathematics\, Univ
 ersity of Illinois Urbana-Champaign\nOptimal damping in the mass-spring sy
 stems\nIt is a well-known textbook example in classical mechanics that a s
 ingle-degree-of-freedom mass-spring harmonic oscillator achieves its faste
 st exponential decay when the damping is critical. We study the analogous 
 problem of designing optimal damping for a system of several coupled linea
 r oscillators. Using the Weyl–Horn theorem\, we construct an explicit da
 mping matrix that theoretically realizes the best possible exponential dec
 ay rate of the system\, which turns out to be the geometric mean of the na
 tural frequencies. We show that this damping strategy outperforms the clas
 sical Rayleigh (proportional) damping approach. We also characterize the p
 arameter regimes in which the optimal damping matrix necessarily ceases to
  be positive definite\, and discuss the implications of this phenomenon.\n
 \nThis is a joint work with M. Arnold (UT-Dallas\, USA) and O. Gendelman (
 Technion\, Israel).\nhttps://jiazhaomath.github.io/seminar/2026-2027.html#
 2026-11-13
URL:https://jiazhaomath.github.io/seminar/2026-2027.html#2026-11-13
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