Efficient three-material PLIC interface positioning on unstructured polyhedral meshes

This paper introduces an efficient algorithm for the sequential positioning (or nested dissection) of two planar interfaces in an arbitrary polyhedron, such that, after each truncation, the respectively remaining polyhedron admits a prescribed volume. This task, among others, is frequently encountered in the numerical simulation of three-phase flows when resorting to the geometric Volume-of-Fluid method. For two-phase flows, the recent work of Kromer & Bothe (doi.org/10.1016/j.jcp.2021.110776) addresses the positioning of a single plane by combining an implicit bracketing of the sought position with up to third-order derivatives of the volume fraction. An analogous application of their highly efficient root-finding scheme to three-material configurations requires computing the volume of a twice truncated arbitrary polyhedron. The present manuscript achieves this by recursive application of the Gaussian divergence theorem in appropriate form, which allows to compute the volume as a sum of quantities associated to the faces of the original polyhedron. With a suitable choice of the coordinate origin, accounting for the sequential character of the truncation, the volume parametrization becomes co-moving with respect to the planes. This eliminates the necessity to establish topological connectivity and tetrahedron decomposition after each truncation. After a detailed mathematical description of the concept, we conduct a series of carefully designed numerical experiments to assess the performance in terms of polyhedron truncations. The high efficiency of the two-phase positioning persists for sequential application, thereby being robust with respect to input data and possible intersection topologies. In comparison to an existing decomposition-based approach, the number of truncations was reduced by up to an order of magnitude

Detection of metastable electronic states by Penning trap mass spectrometry

State-of-the-art optical clocks achieve fractional precisions of $10^{-18}$ and below using ensembles of atoms in optical lattices or individual ions in radio-frequency traps. Promising candidates for novel clocks are highly charged ions (HCIs) and nuclear transitions, which are largely insensitive to external perturbations and reach wavelengths beyond the optical range, now becoming accessible to frequency combs. However, insufficiently accurate atomic structure calculations still hinder the identification of suitable transitions in HCIs. Here, we report on the discovery of a long-lived metastable electronic state in a HCI by measuring the mass difference of the ground and the excited state in Re, the first non-destructive, direct determination of an electronic excitation energy. This result agrees with our advanced calculations, and we confirmed them with an Os ion with the same electronic configuration. We used the high-precision Penning-trap mass spectrometer PENTATRAP, unique in its synchronous use of five individual traps for simultaneous mass measurements. The cyclotron frequency ratio $R$ of the ion in the ground state to the metastable state could be determined to a precision of $\delta R=1\cdot 10^{-11}$, unprecedented in the heavy atom regime. With a lifetime of about 130 days, the potential soft x-ray frequency reference at $\nu=4.86\cdot 10^{16}\,\text{Hz}$ has a linewidth of only $\Delta \nu\approx 5\cdot 10^{-8}\,\text{Hz}$, and one of the highest electronic quality factor ($Q=\frac{\nu}{\Delta \nu}\approx 10^{24}$) ever seen in an experiment. Our low uncertainty enables searching for more HCI soft x-ray clock transitions, needed for promising precision studies of fundamental physics in a thus far unexplored frontier

Observation of a low-lying metastable electronic state in highly charged lead by Penning-trap mass spectrometry

Highly charged ions (HCIs) offer many opportunities for next-generation clock research due to the vast landscape of available electronic transitions in different charge states. The development of XUV frequency combs has enabled the search for clock transitions based on shorter wavelengths in HCIs. However, without initial knowledge of the energy of the clock states, these narrow transitions are difficult to be probed by lasers. In this Letter, we provide experimental observation and theoretical calculation of a long-lived electronic state in Nb-like Pb$^{41+}$ which could be used as a clock state. With the mass spectrometer Pentatrap, the excitation energy of this metastable state is directly determined as a mass difference at an energy of 31.2(8) eV, corresponding to one of the most precise relative mass determinations to date with a fractional uncertainty of $4\times10^{-12}$. This experimental result agrees within 1 $\sigma$ with two partially different \textit{ab initio} multi-configuration Dirac-Hartree-Fock calculations of 31.68(13) eV and 31.76(35) eV, respectively. With a calculated lifetime of 26.5(5.3) days, the transition from this metastable state to the ground state bears a quality factor of $1.1\times10^{23}$ and allows for the construction of a HCI clock with a fractional frequency instability of $<10^{-19}/\sqrt{\tau}$

The Electron Capture in 163^{163} Ho Experiment - a Short Update

The definition of the absolute neutrino mass scale is one of the main goals of the Particle Physics today. The study of the end-point regions of the β- and electron capture (EC) spectrum offers a possibility to determine the effective electron (anti-)neutrino mass in a completely model independent way, as it only relies on the energy and momentum conservation. The ECHo (Electron Capture in 163Ho) experiment has been designed in the attempt to measure the effective mass of the electron neutrino by performing high statistics and high energy resolution measurements of the 163 Ho electron capture spectrum. To achieve this goal, large arrays of low temperature metallic magnetic calorimeters (MMCs) implanted with with 163Ho are used. Here we report on the structure and the status of the experiment

High-precision mass measurement of doubly magic

The absolute atomic mass of $$^{208}$$Pb has been determined with a fractional uncertainty of $$7\times 10^{-11}$$ by measuring the cyclotron-frequency ratio R of $$^{208}$$Pb$$^{41+}$$ to $$^{132}$$Xe$$^{26+}$$ with the high-precision Penning-trap mass spectrometer Pentatra