Ferromagnetic elastic rods show a supercritical Hamiltonian Hopf pitchfork bifurcation for elastic and hard-magnetic cases but only for 0 < K_dM < 1/8 in soft-magnetic rods, with soft-rod localized buckles displaying non-collinear straight segments due to magnetoelastic coupling.
DOI 10.1007/978-1-4612-4066-2 10
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Low-rank structure in HBVM stage equations is exploited via Krylov projection for linear cases and Newton-Krylov with adaptive time-stepping for nonlinear cases, shown efficient on semi-discretized wave equations.
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Spatial deformation of a ferromagnetic elastic rod
Ferromagnetic elastic rods show a supercritical Hamiltonian Hopf pitchfork bifurcation for elastic and hard-magnetic cases but only for 0 < K_dM < 1/8 in soft-magnetic rods, with soft-rod localized buckles displaying non-collinear straight segments due to magnetoelastic coupling.
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Low-Rank Solvers for Energy-Conserving Hamiltonian Boundary Value Methods
Low-rank structure in HBVM stage equations is exploited via Krylov projection for linear cases and Newton-Krylov with adaptive time-stepping for nonlinear cases, shown efficient on semi-discretized wave equations.