Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

ATEQ: Adaptive toroidal equilibrium code

A radially adaptive numerical scheme is developed to solve the Grad–Shafranov equation for axisymmetric magnetohydrodynamic equilibrium. Here, a decomposition with independent solutions is employed in the radial direction, and Fourier decomposition is used in the poloidal direction. The independent solutions are then obtained using an adaptive shooting scheme together with the multi-region matching technique in the radial direction. Accordingly, the adaptive toroidal equilibrium (ATEQ) code is constructed for axisymmetric equilibrium studies. The adaptive numerical scheme in the radial direction improves considerably the accuracy of the equilibrium solution. The decomposition with independent solutions effectively reduces the matrix size in solving the magnetohydrodynamic equilibrium problem. The reduction of the matrix size is about an order of magnitude as compared with the conventional radially grid-based numerical schemes. Also, in this ATEQ numerical scheme, no matter how accuracy in the radial direction is imposed, the size of matrices basically does not change. The small matrix size scheme gives ATEQ more flexibility to address the requirement of the number of Fourier components in the poloidal direction in tough equilibrium problems. These two unique features, the adaptive shooting and small matrix size, make ATEQ useful to improve tokamak equilibrium solutions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Porting fragmentation methods to GPUs using an OpenMP API: Offloading the resolution-of-the-identity second-order Møller–Plesset perturbation method

Here, using an OpenMP Application Programming Interface, the resolution-of-the-identity second-order Møller–Plesset perturbation (RI-MP2) method has been off-loaded onto graphical processing units (GPUs), both as a standalone method in the GAMESS electronic structure program and as an electron correlation energy component in the effective fragment molecular orbital (EFMO) framework. First, a new scheme has been proposed to maximize data digestion on GPUs that subsequently linearizes data transfer from central processing units (CPUs) to GPUs. Second, the GAMESS Fortran code has been interfaced with GPU numerical libraries (e.g., NVIDIA cuBLAS and cuSOLVER) for efficient matrix operations (e.g., matrix multiplication, matrix decomposition, and matrix inversion). The standalone GPU RI-MP2 code shows an increasing speedup of up to 7.5× using one NVIDIA V100 GPU with one IBM 42-core P9 CPU for calculations on fullerenes of increasing size from 40 to 260 carbon atoms using the 6-31G(d)/cc-pVDZ-RI basis sets. A single Summit node with six V100s can compute the RI-MP2 correlation energy of a cluster of 175 water molecules using the correlation consistent basis sets cc-pVDZ/cc-pVDZ-RI containing 4375 atomic orbitals and 14 700 auxiliary basis functions in ~0.85 h. In the EFMO framework, the GPU RI-MP2 component shows near linear scaling for a large number of V100s when computing the energy of an 1800-atom mesoporous silica nanoparticle in a bath of 4000 water molecules. The parallel efficiencies of the GPU RI-MP2 component with 2304 and 4608 V100s are 98.0% and 96.1%, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures

Quantum mechanical calculations for material modeling using Kohn–Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for N smallest eigenvector-eigenvalue pairs, with N proportional to the number of electrons in the material system. Here, these calculations are computationally demanding and have asymptotic cubic scaling complexity with the number of electrons. Large-scale matrix eigenvalue problems arising from the discretization of the Kohn–Sham DFT equations employing a systematically convergent basis traditionally rely on iterative orthogonal projection methods, which are shown to be computationally efficient and scalable on massively parallel computing architectures. However, as the size of the material system increases, these methods are known to incur dominant computational costs through the Rayleigh–Ritz projection step of the discretized Kohn–Sham Hamiltonian matrix and the subsequent subspace diagonalization of the projected matrix. This work explores the potential of polynomial expansion approaches based on recursive Fermi-operator expansion as an alternative to the subspace diagonalization of the projected Hamiltonian matrix to reduce the computational cost. Subsequently, we perform a detailed comparison of various recursive polynomial expansion approaches to the traditional approach of explicit diagonalization on both multi-node central processing unit and graphics processing unit architectures and assess their relative performance in terms of accuracy, computational efficiency, scaling behavior, and energy efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Graph network heterogeneity predicts interplant wake losses

Wind plants generate large-scale wakes, which can affect the performance of neighboring installations. Such wakes are challenging to estimate due to the inherent complexity in modeling wake interactions between large quantities of turbines at various distances. Weighted directed graph networks can inform complex models by linking turbine pairs into chains of upstream and downstream neighbors for a given wind direction. A novel interpretation of the graph network adjacency matrix is proposed where each element of the matrix represents the cumulative impact of upstream turbines on an individual. In this study, wake losses were estimated with an engineering wake model across a range of inflow conditions for nine parametric variations of a system containing two neighboring wind plants. The parametric nature of the study isolates turbine spacing within the plant, separation distance between plants, and wind direction as the main drivers of wake losses. Spatial heterogeneity is computed from the weighted average adjacency matrix of each plant arrangement. The proposed method is orders of magnitude faster than wake modeling and does not require detailed turbine information or atmospheric conditions. Furthermore, the weighted average adjacency matrix provides insight on the spatial organization of wake losses at various scales. Plant heterogeneity is correlated with wake losses within and among plants. Framing wind plant wake interaction in terms of graph network spatial heterogeneity provides an efficient approach for predicting wake losses within and among neighboring wind plants with applications to other complex systems where wake interactions are key factor.

17 WIND ENERGY↗
DOE OSTI2025

Influence of nanoscale interfaces on the dynamic deformation and spall failure of Cu–Fe alloy microstructures

Additively manufactured immiscible Cu–Fe alloys can exhibit a distribution of nanoscale interfaces due to the distribution of nanoscale clusters in the equilibrium and metastable phases. Molecular dynamics simulations investigate the role of such interfaces on the phase stability and transformation behavior during shock compression, as well as the mechanisms of damage nucleation during spall failure. The model multiphase Cu–Fe systems studied here comprise a distribution of Fe clusters in an FCC Cu matrix, as well as Cu clusters in a BCC Fe matrix. The length scales of the nanoscale clusters determine the energetics of the interfaces that can result in FCC/BCC (equilibrium) or FCC/FCC (metastable) interfaces in the Cu system matrix, and BCC/FCC (equilibrium) or BCC/BCC (metastable) interfaces in the Fe matrix. The MD simulations demonstrate that nanoscale metastable interface microstructures can induce plastic deformation and also stabilize phases or suppress phase transformations in metastable phase clusters. In contrast, equilibrium interfaces can influence phase transformation thresholds and serve as additional void nucleation sites during failure.

36 MATERIALS SCIENCE↗
DOE OSTI2022

The cosine-sine decomposition with different-orbitals-for-different-spins determinants

We report the spin decomposition of a spin-contaminated different-orbitals-for-different-spins (DODS) wave function is formulated in terms of the Krylov space of the $\hat{S}^2$ ||operator. The number of determinants that contribute to the various projected spin eigenfunctions vertical | $\psi ; S, M \rangle$ depends on the sparsity of the orbital overlap matrix X between the α and β spatial orbitals. The cosine-sine decomposition (CSD) procedure may be applied to this overlap matrix, and the resulting redundant orbital transformations may be applied to the α and β spatial orbitals. This produces a sparse X' matrix in the transformed basis in which each row or column has either one or two nonzero elements. This sparse X' matrix simplifies the spin-decomposition procedure in three ways:1) it reduces the number of contributing determinants within the Krylov basis functions and within the projected spin functions, 2) it reduces the effective orbital dimension through elimination of the frozen core and frozen virtual orbitals, and 3) it simplifies the spin-decomposition procedure in both the original and transformed bases by limiting the Krylov space dimension. These simplifications all reduce the computational effort for the spin-decomposition process. This procedure is implemented within a string-based DODS determinant formulation and applied to spin projection of unrestricted Hartree-Fock determinants.

unrestricted Hartree-Fock↗
DOE OSTI2021

Parametric Study of Used Nuclear Oxide Fuel Constituent Dissolution in Molten LiCl-KCl-UCl 3

Prior work identified dissolution of used nuclear oxide fuel constituents from a uranium oxide matrix into molten LiCl-KCl-UCl 3 at 500°C, prompting a subsequent series of three progressive studies (including an initial scoping study, an electrolytic dissolution study, and a chemical-seeded dissolution study) to further investigate associated parameters and mechanisms. Thermodynamic calculations were performed to identify possible reaction mechanisms and their propensities in used oxide fuel constituent dissolution. Used nuclear oxide fuels with varying preconditions from fast and thermal test reactors were separately immersed in the subject salt system to assess fuel constituent migration from the bulk fuel matrix to the salt phase in an initial scoping study. Dissolution of expected fuel constituents, including alkali, alkaline earth, lanthanide, and transuranium oxides, into the chloride salt phase varied widely, ranging from 12% to 99% in the initial study. Uranium isotope blending between the salt phase and bulk fuel matrix was also observed, which was attributed to reducing conditions in the fuel matrix. Electrolytic and chemical-seeded dissolution studies were subsequently performed to effect reducing conditions in the fuel. Other parameters, including temperature (at 500°C, 650°C, 725°C, and 800°C) and uranium trichloride concentrations (at 6, 9, and 19 wt% uranium), were investigated in the latter two studies, resulting in fuel constituent dissolution above 90%. Extents of dissolution were based on initial and final fuel constituent concentrations in the oxide fuels following operations in the salt and subsequent removal of the salt via distillation. Finally, in this series of progressive studies, oxide fuel preconditioning and in situ reducing conditions, along with elevated temperature and uranium trichloride concentrations, were the primary parameters promoting used nuclear oxide fuel constituent dissolution in accordance with identified reaction mechanisms.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initialization

Obtaining lightweight and accurate approximations of discretized objective functional Hessians in inverse problems governed by partial differential equations (PDEs) is essential to make both deterministic and Bayesian statistical large-scale inverse problems computationally tractable. The cubic computational complexity of dense linear algebraic tasks, such as Cholesky factorization, that provide a means to sample Gaussian distributions and determine solutions of Newton linear systems is a computational bottleneck at large-scale. These tasks can be reduced to log-linear complexity by utilizing hierarchical off-diagonal low-rank (HODLR) matrix approximations. In this work, we show that a class of Hessians that arise from inverse problems governed by PDEs are well approximated by the HODLR matrix format. In particular, we study inverse problems governed by PDEs that model the instantaneous viscous flow of ice sheets. In these problems, we seek a spatially distributed basal sliding parameter field such that the flow predicted by the ice sheet model is consistent with ice sheet surface velocity observations. Here, we demonstrate the use of HODLR Hessian approximation to efficiently sample the Laplace approximation of the posterior distribution with covariance further approximated by HODLR matrix compression. Computational studies are performed which illustrate ice sheet problem regimes for which the Gauss–Newton data-misfit Hessian is more efficiently approximated by the HODLR matrix format than the low-rank (LR) format. We then demonstrate that HODLR approximations can be favorable, when compared to global LR approximations, for large-scale problems by studying the data-misfit Hessian associated with inverse problems governed by the first-order Stokes flow model on the Humboldt glacier and Greenland ice sheet.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Analytical and EZmock covariance validation for the DESI 2024 results

The estimation of uncertainties in cosmological parameters is an important challenge in Large-Scale-Structure (LSS) analyses. For standard analyses such as Baryon Acoustic Oscillations (BAO) and Full-Shape two approaches are usually considered. First: analytical estimates of the covariance matrix use Gaussian approximations and (nonlinear) clustering measurements to estimate the matrix, which allows a relatively fast and computationally cheap way to generate matrices that adapt to an arbitrary clustering measurement. On the other hand, sample covariances are an empirical estimate of the matrix based on an ensemble of clustering measurements from fast and approximate simulations. While more computationally expensive due to the large amount of simulations and volume required, these allow us to take into account systematics that are impossible to model analytically. In this work we compare these two approaches in order to enable DESI's key analyses. We find that the configuration space analytical estimate performs satisfactorily in BAO analyses and its flexibility in terms of input clustering makes it the fiducial choice for DESI's 2024 BAO analysis. On the contrary, the analytical computation of the covariance matrix in Fourier space does not reproduce the expected measurements in terms of Full-Shape analyses, which motivates the use of a corrected mock covariance for DESI's 2024 Full Shape analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Aluminium composites prepared by laser cladding assisted by friction stir processing

Abstract A laser cladding and friction stir processing hybrid method was employed to produce an Al matrix composite layer. The microstructure, phase composition, microhardness and conductivity of the composites were investigated. A laser cladding layer with a thickness of approximately 200 μ m was prepared on a 1060 aluminium plate and it was broken up and distributed on the Al matrix after friction stir processing. The particle/Al interfaces exhibited extremely good interfacial integrity. Microstructural observations revealed that an obvious in situ reaction occurred at the particle/Al interfaces, which effectively improved the bonding between the reinforcement phase and the matrix. TEM analysis and selected area diffraction enabled the identification of the intermetallic compounds and confirmed them to be Al 5 Fe 2 and Al 3 Fe. The average microhardness values of the friction stir processed composites reached approximately 85 HV. The electrical resistivity of the friction stir processed composites is slightly higher than that of the aluminium matrix.

Wei, Yanni (ORCID:0000000244443642)↗
DOE OSTI2021

Mitigating baryonic effects with a theoretical error covariance

ABSTRACT One of the primary sources of uncertainties in modelling the cosmic-shear power spectrum on small scales is the effect of baryonic physics. Accurate cosmology for stage-IV surveys requires knowledge of the matter power spectrum deep in the non-linear regime at the per cent level. Therefore, it is important to develop reliable mitigation techniques to take into account baryonic uncertainties if information from small scales is to be considered in the cosmological analysis. In this work, we develop a new mitigation method for dealing with baryonic physics for the case of the shear angular power spectrum. The method is based on an augmented covariance matrix that incorporates baryonic uncertainties informed by hydrodynamical simulations. We use the results from 13 hydrodynamical simulations and the residual errors arising from a fit to a ΛCDM model using the extended halo model code HMCode to account for baryonic physics. These residual errors are used to model a so-called theoretical error covariance matrix that is added to the original covariance matrix. In order to assess the performance of the method, we use the 2D tomographic shear from four hydrodynamical simulations that have different extremes of baryonic parameters as mock data and run a likelihood analysis comparing the residual bias on Ωm and σ8 of our method and the HMCode for an LSST-like survey. We use different modelling of the theoretical error covariance matrix to test the robustness of the method. We show that it is possible to reduce the bias in the determination of the tested cosmological parameters at the price of a modest decrease in the precision.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Toward shell model interactions with credible uncertainties

Background: The nuclear shell model is a powerful framework for predicting nuclear structure observables, but relies on interaction matrix elements fit to experimental data as its inputs. Extending the shell model's applicability, particularly toward dripline nuclei, requires efficient fitting methods and credible uncertainty quantification. Traditional approaches face computational challenges and may underestimate uncertainties. Purpose: We develop and test a framework combining eigenvector continuation and Markov chain Monte Carlo to efficiently fit shell model interaction matrix elements and quantify their uncertainties. Methods: Eigenvector continuation is used to emulate shell model calculations, reducing computational costs. The emulator enables Markov chain Monte Carlo sampling to optimize interaction matrix elements and rigorously assess parametric uncertainties. Here, the framework is benchmarked using the USDB interaction in the 𝑠⁢𝑑 shell. Results: The emulator reproduces the USDB interaction with negligible error, validating its use in shell model fitting applications. However, we find that to obtain credible predictive intervals, the model defect of the shell model itself, rather than experimental or emulator error, must be taken into account in order to obtain credible uncertainties. Conclusions: The proposed framework provides an efficient and rigorous approach for fitting shell model interactions and quantifying uncertainties. Further, the normality assumption used in the past appears sufficient to describe the distribution of interaction matrix elements. However, it is crucial to account for model correlations to avoid underestimating uncertainties.

Nuclear forces↗
DOE OSTI2022

Entanglement perspective on the quantum approximate optimization algorithm

Many quantum algorithms seek to output a specific bitstring solving the problem of interest—or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial N -qubit product state | 0 〉 ⊗ N and the final one regarding entanglement? Here, we consider the QAOA algorithm for solving the paradigmatic MaxCut problem on different types of graphs. We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits and find that there is a volume-law entanglement barrier between the initial and final states. We also investigate the entanglement spectrum in connection with random matrix theory. In addition, we compare the entanglement production with a quantum annealing protocol aiming to solve the same MaxCut problems. Finally, we discuss the implications of our results for the simulation of QAOA circuits with tensor network-based methods relying on low-entanglement for efficiency, such as matrix product states.

Dupont, Maxime↗
DOE OSTI2023

Perturbative readout-error mitigation for near-term quantum computers

Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental response matrix that describes the error associated with the measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially with the number of qubits, n . In this work, we modify standard matrix inversion techniques using perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high-order bit-flip events is strongly suppressed. Given a characteristic error rate q , we discuss a method to recover the probability of the all-zeros bit string p 0 by sampling only a small subspace of the response matrix before inverting readout error, resulting in a relative speedup of poly [ 2 n / ( n w ) ] , which we motivate using a simplified error model for which the approximation incurs only O ( q w ) error for some integer w . We then provide a generalized technique to efficiently recover full output distributions with O ( q w ) error in the perturbative limit. These approximate techniques for readout-error correction may greatly accelerate near-term quantum computing applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems

Fully self-consistent GW (sc-GW) methods are now available to evaluate quasiparticle and spectral properties of various molecular and bulk systems. However, such techniques based on the full matrix of G and W are computationally demanding. Additionally, the routinely used single-shot GW approximation (G 0 W 0 ) has an undesirable dependency on the choice of initial exchange-correlation functional. In the literature, many so-called self-consistent GW methods are based on diagonal approximation of G and low-ranking approximation of W. It is thus worth checking how good such approximations are in comparison with the full matrix method. In this work, we consider AlAs, AlP, GaP, and ZnS as the prototype systems to perform sc-GW calculations by expressing the full G matrix using a plane-wave basis set. We compared our sc-GW results with the diagonal G and subspace W approximated sc-GW results (sc-GW-diagG and sc-GW-subW methods). In the sc-GW-diagG method, interacting G is expanded in the eigenvectors of noninteracting G such that only diagonal elements are retained, whereas the number of eigenmodes is truncated in sc-GW-subW calculations. A systematic analysis of the results obtained from the above techniques is presented. The differences in the quasiparticle band gap between the approximated and the full matrix sc-GW approaches are mostly less than 1.7%, which validates such widely adopted approximations, and also shows how such low-ranking approximation can be used to include higher-order terms such as the vertex correction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Impact of three-body forces on elastic nucleon-nucleus scattering observables

In a previous series of papers we investigated the domain of applicability of chiral potentials to the construction of a microscopic optical potential (OP) for elastic nucleon-nucleus scattering. The OP was derived at the first order of the spectator expansion of the Watson multiple scattering theory and its final expression was a folding integral between the nucleon-nucleon ( N N ) t matrix and the nuclear density of the target. In the calculations N N and three-nucleon ( 3 N ) chiral interactions were used for the target density and only the N N interaction for the N N t matrix. The purpose of this study is to achieve another step towards the calculation of a more consistent OP introducing the 3 N force also in the dynamic part of the OP. The full treatment of the 3 N interaction is beyond our present capabilities. Thus, here it is approximated with a density dependent N N interaction obtained after the averaging over the Fermi sphere. In practice, in our model the 3 N force acts as a medium correction of the bare N N interaction used to calculate the t matrix. Even if the 3 N force is treated in an approximate way, this method naturally extends our previous model of the OP and allows a direct comparison of our present and previous results. We consider as case studies the elastic scattering of nucleons off C 12 and O 16 . We present results for the differential cross section and the spin observables for different values of the projectile energy. From the comparison with the experimental data and with the results of our previous model we assess the importance of the 3 N interaction in the dynamic part of the OP. Conclusions: Our analysis indicates that the contribution of the 3 N force in the t matrix is small for the differential cross section and it is sizable for the spin observables, in particular, for the analyzing power. We find that the two-pion exchange term is the major contributor to the 3 N force. A chiral expansion order-by-order analysis of the scattering observables confirms the convergence of our results at the next-to-next-to-next-to-leading-order, as already established in our previous work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Entanglement and seniority

In quantum mechanics entanglement is the most striking phenomenon which has no counterpart in classical systems. Although, different approaches have already been developed to study correlations in the case of indistinguishable particles, the exploration of the so-called mode entanglement is still in its initial stage in nuclear physics. Study of mode-entanglement in the seniority model, derivation of analytic formulas for the one-body reduced density matrix of states with seniority $ν$ = 0, 1, 2, and $ν$ = 3, and also determination of the particle number dependence of the one-body reduced density matrix for arbitrary seniority. In addition, comparison of the predictions of the seniority model with the results of the shell model to gain insight into the structure and correlations of the ground and lowest yrast states. In the seniority model the analytic results are calculated using the quasi-spin formalism. The numerical shell model calculations are carried out in the standard shell model framework using an inert core. The applied realistic effective interactions are derived earlier using the $G$-matrix formalism. The density matrix renormalization group method is also applied in order to directly calculate the mode entropies. In the seniority model simple analytical expressions are given for the mode entropies. The peculiar behavior of the half-filled shells and the seniority-zero states are revealed. Numerical results are presented for the lightest stable calcium isotopes and for 94 Ru nucleus. For 94 Ru, the seniority model accounts for the 0$g$ 9/2 mode entropies, but seniority mixing is important for certain yrast states. Furthermore, interaction induced quantum fluctuations decrease the occupation of the 0$f$ 5/2 , 1$p$ 3/2 and 1$p$ 1/2 shells, and amount in non-negligible mode entropies on these shells, too, clearly outside the scope of the simple (0$g$ 9/2 ) 4 seniority model. The 0$f$ 7/2 shell-based seniority model is more accurate for the Ca isotopes, but seniority mixing is substantial for some 44 Ca yrast states, too. Mode and one-body entanglement entropies are useful tools to investigate the structure of quantum correlations in nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗