Symmetry

Pulse-like ground motions can cause severe damage to buried cast iron (CI) pipelines, which necessitates the selection of optimal seismic intensity measures (IMs) to estimate pipeline repair rates. Such a selection is essential for mitigating uncertainty in the seismic risk assessment of buried CI pipelines. For the first time, this study systematically screens the optimal scalar and vector IMs for buried cast iron pipelines with lead-caulked joints under pulse-like ground motions by a symmetrical evaluation based on the criteria of efficiency, sufficiency, and proficiency, providing a new method for reducing uncertainty in pipeline seismic risk assessment. We initiate the study by selecting 124 pulse-like ground motions from the NGA-West2 database and identifying 19 scalar and 171 vector IMs as potential candidates. A two-dimensional soil–pipe model is introduced, incorporating variability in the sealing capacity of lead-caulked joints along the axial direction. CI pipeline repair rates are calculated across various scaling factors and apparent wave velocities, yielding 1116 datasets pertinent to CI pipeline damage. The repair rate is adopted as the engineering demand parameter (EDP) to evaluate the efficiency, sufficiency, and proficiency of candidate IMs. Through comprehensive analysis, peak ground velocity (PGV) and the combination of PGV and the time interval between 5% and 75% of normalized Arias intensity ([PGV, Ds_5–75]) are determined as the optimal scalar- and vector-IMs, respectively, for assessing the repair rate of buried CI pipelines under pulse-like ground motions.

…“I’ll tell you all my ideas about Looking-glass House [...]

In quasi-Hermitian quantum mechanics (QHQM) of unitary systems, an optimal, calculation-friendly form of Hamiltonian is generally non-Hermitian, $H\ne H^{†}$. This makes its physical interpretation ambiguous. Without altering H, this ambiguity can be resolved either via a transformation of H into its isospectral Hermitian form via a so-called Dyson map , or via a (formally equivalent) specification of a nontrivial physical inner-product metric $\mathrm{\Theta }$ in Hilbert space. Here, we focus on the former strategy. Our present construction of the Hermitian isospectral twins $\mathfrak{h}$ of H is exhaustive. As a byproduct, it not only restores the conventional correspondence principle between quantum and classical physics, but it also provides a framework for a systematic classification of all of the admissible probabilistic interpretations of quantum systems using a preselected H in QHQM framework.