Symmetry breaking of infinitedimensional dynamic system Abstract   The relationship between the symmetry breaking and the energy dissipation of dynamic systems is the foundation of the geometric mechanics, the investigation of which will establish a bridge between the structurepreserving theory and the assessment approach of the structurepreserving property for the employed numerical scheme. In this letter, two typical factors inducing the symmetry breaking for the infinitedimensional dynamic system, including the symmetry breaking of the coefficient matrices and the spacexe2x80x93time dependence of the Hamiltonian function, are investigated in detail. Based on the multisymplectic theory, the local energy variations for dynamic systems with the mentioned symmetry breaking factors are deduced and the specific forms of which for a flexible cantilever with the variable bending rigidity under an external excitation are presented, which shows the local energy dissipation explicitly and provides the possibility of reproduction the local energy dissipation for the infinitedimensional dynamic system in the numerical simulation.

Approximation of stability radii for largescale dissipative Hamiltonian systems A linear timeinvariant dissipative Hamiltonian (DH) system dot x  (JR)Q x, with a skewHermitian J, a Hermitian positive semidefinite R, and a Hermitian positive definite Q, is always Lyapunov stable and under further weak conditions even asymptotically stable. By exploiting the characterizations from Mehl et al. (SIAM J. Matrix Anal. Appl. 37(4), 1625xe2x80x931654, 2016), we focus on the estimation of two stability radii for largescale DH systems, one with respect to nonHermitian perturbations of R in the form R  Bxcex94CH for given matrices B, C, and another with respect to Hermitian perturbations in the form R  Bxcex94BH,xcex94  xcex94H. We propose subspace frameworks for both stability radii that converge at a superlinear rate in theory. The one for the nonHermitian stability radius benefits from the DH structurepreserving model order reduction techniques, whereas for the Hermitian stability radius we derive subspaces yielding a Hermite interpolation property between the full and projected problems. With the proposed frameworks, we are able to estimate the two stability radii accurately and efficiently for largescale systems which include a finiteelement model of an industrial disk brake.