Shell Model Research Articles

Re-examination of the β-decay properties of As isotopes

Abstract The β-decay properties of 67−80As nuclei have been investigated within the framework of the proton–neutron quasi-particle random phase approximation (pn-QRPA) model. The nuclear deformation obtained from the finite range droplet model is used as an input parameter in the pn-QRPA model for the analysis of β-decay properties including Gamow–Teller strength distributions, log ft, β-decay half-lives and stellar β ± decay rates. The predicted log ft values were fairly consistent with the observed data. The computed β-decay half-lives matched the measured values by a factor of 10. The stellar rates were compared with the shell model outcomes. At high densities and temperatures, the β + and electron capture rates had a finite contribution. However, the β − and positron capture rates are only significant at high temperatures and low densities. The pn-QRPA rates outperformed the shell model rates by a factor of 22 or more.

The Behavior of Elbow Elements at Pure Bending Applications Compared to Beam and Shell Element Models

Abstract This paper studies the response of ELBOW31 and ELBOW31B element types under pure bending conditions, using shell and beam element models for benchmarking. Various model lengths are evaluated, showing that a model length of six pipe diameters exhibits a hardening effect when total strain exceeds 3.5%, though a strain up to 1% is deemed sufficient for pipeline design. The study examines the effects of ovality modes and boundary conditions such as NOWARP and NOOVAL on the bending response. ELBOW31 with one or two ovality modes yields accurate results, while additional ovality modes or zero ovality mode can lead to overprediction of the elastic bending moment capacity. The introduction of the NOWARP condition enhances the accuracy of the ELBOW31 model, while the NOOVAL condition alone produces unrealistic results. The simplified ELBOW31B model shows good agreement with the ELBOW31-NOWARP model but similarly overpredicts the bending moment when zero ovality mode is used. The study also finds that Poisson's ratio and model length have no significant impact on the bending response when no restrictions are applied. Additional analyses, as presented in Appendices A and B, highlight the importance of D/t ratios in pipeline performance. A D/t ratio of 20 offers a stiffer response with reduced ovalization, while a D/t ratio of 50 results in greater flexibility and increased ovalization. These findings provide valuable insights for the selection of element types, boundary conditions, and D/t ratios in robust pipeline design.

Comparing numerical simulation methods for evaluating hysteretic response of self-centering shear walls reinforced with SMA-ECC under cyclic loading

Under the action of earthquake, the traditional shear wall structure has the problems of excessive residual deformation and macroscopic cracks. The SMA-ECC composite material formed by the combination of smart materials such as shape memory alloy (SMA) and high ductility engineered cementitious composite (ECC) not only has good energy dissipation capacity, but also can obtain superior self-centering ability and damage self-healing ability, thereby improving the seismic performance and durability of shear wall structures. In this paper, in order to explore the nonlinear behavior of the self-centering shear wall under earthquake action and accurately simulate it, ECC and SMA material tests are carried out to establish the uniaxial constitutive relationship of the material. Using OpenSees finite element analysis platform, considering the micro and macro perspectives, a variety of finite element models are established, namely layered shell model, fiber model and multi-vertical rod model. Combined with the low-cycle reciprocating loading test of shear walls, the numerical simulation results are compared with the experimental data. By considering the parameters such as yield load, peak load and simulation time, the feasibility, stability and calculation efficiency of these models are evaluated. The results show that among the three models, the model based on fiber element can capture well the hysteretic response of new materials, and simulate the hysteretic performance, pinch effect and stiffness degradation of various shear wall members. The simulated values and experimental values can be well matched. Compared with the microscopic model, the computational efficiency of the fiber model is greatly improved, and the model has good feasibility, accuracy and efficiency.This work provides a basis for further research on the optimization of design parameters of SMA-ECC shear wall.

Assessment of water diffusion in epoxy composites: a novel approach towards holistic understanding

Performance of insulating polymers is seriously impacted by water absorption. Hence, its assessment using Fick’s law and 3-core water shell model are used for a holistic understanding of water diffusion. Epoxy with organically modified montmorillonite clay of 2, 5 and 7 weight percent (wt.%) are fabricated and water diffusion is carried out for 240 hours. The results are analysed by dielectric and gravimetric approaches. The weight gain in epoxy after 240 hours is 0.42% and 0.19% at 5 wt.% of the filler. The weight gain peaks after 120 hours in all the composites and the variations from 120 to 240 hours are minimal. The weight gain rate is lowest at 96 hours, and it peaks at 120 hours and is highest at 0.00033%/hour in epoxy, and reduces to 0.0023%/hour with filler of 7 wt.%. The weight gain and weight gain rate are characteristics of the epoxy and the filler controls the magnitude. Diffusion coefficient is lowest at 5 wt.% but the differences in the other composites are limited. The effect of fillers on free volume, free volume rate and fractional free volume are correlated to the dielectric parameters. Water uptake increases the DC conductivity from 10−14 to 10−12 S/m after 240 hours and the relative permittivity increases by 40%. The water shell model, diffusion parameters and the free volume parameters are correlated to the results of DC conductivity and relative permittivity. Subtle changes induced by absorbed water is identified by the method adopted.

Calculating some nuclear properties of chromium isotopes in the shell model

Calculating some nuclear properties of chromium isotopes in the shell model

An Investigation of the Stiffness Characteristics of a PWR Nuclear Fuel Spacer Grid by a 3D Shell Model

The structural integrity of fuel assemblies hinges significantly on the effectiveness of spacer grids. In this paper, we introduce a novel approach to assess the structural robustness of the mid-spacer grid (SG) of the PLUS7 fuel assembly (FA) using 3D shell elements. Any excessive external load from seismic activity can be broken down into two perpendicular components, namely normal load and shear load. The decomposition enables easy assessment of the structural integrity of the fuel spacer grid for any external loads. From the analysis, the reaction force of normal input displacement is around 440 times greater than that for shear input displacement for the same amount of displacement. This result highlights how vulnerable the spacer grid is to shear load and this should be considered in studies of fuel assembly integrity assessment. This study also highlights the need for improved and more robust spacer grids for safer operation of NPPs.

Interoperable information modelling leveraging asset administration shell and large language model for quality control toward zero defect manufacturing

In the era of Industry 4.0, Zero Defect Manufacturing (ZDM) has emerged as a prominent strategy for quality improvement, emphasizing data-driven approaches for defect prediction, prevention, and mitigation. The success of ZDM heavily depends on the availability and quality of data typically collected from diverse and heterogeneous sources during production and quality control, presenting challenges in data interoperability. Addressing this, we introduce a novel approach leveraging Asset Administration Shell (AAS) and Large Language Models (LLMs) for creating interoperable information models that incorporate semantic contextual information to enhance the interoperability of data integration in the quality control process. AAS, initiated by German industry stakeholders, shows a significant advancement in information modeling, blending ontology and digital twin concepts for the virtual representation of assets. In this work, we develop a systematic, use-case-driven methodology for AAS-based information modeling. This methodology guides the design and implementation of AAS models, ensuring model properties are presented in a unified structure and reference external standardized vocabularies to maintain consistency across different systems. To automate this referencing process, we propose a novel LLM-based algorithm to semantically search model properties within a standardized vocabulary repository. This algorithm significantly reduces manual intervention in model development. A case study in the injection molding domain demonstrates the practical application of our approach, showcasing the integration and linking of product quality and machine process data with the help of the developed AAS models. Statistical evaluation of our LLM-based semantic search algorithm confirms its efficacy in enhancing data interoperability. This methodology offers a scalable and adaptable solution for various industrial use cases, promoting widespread data interoperability in the context of Industry 4.0.

High-precision measurements of the atomic mass and electron-capture decay Q value of 95Tc

A direct measurement of the ground-state-to-ground-state electron-capture decay Q value of 95Tc has been performed utilizing the double Penning trap mass spectrometer JYFLTRAP. The Q value was determined to be 1695.92(13) keV by taking advantage of the high resolving power of the phase-imaging ion-cyclotron-resonance technique to resolve the low-lying isomeric state of 95Tc (excitation energy of 38.910(40) keV) from the ground state. The mass excess of 95Tc was measured to be −86015.95(18) keV/c2, exhibiting a precision of about 28 times higher and in agreement with the value from the newest Atomic Mass Evaluation (AME2020). Combined with the nuclear energy-level data for the decay-daughter 95Mo, two potential ultra-low Q-value transitions are identified for future long-term neutrino-mass determination experiments. The atomic self-consistent many-electron Dirac–Hartree–Fock–Slater method and the nuclear shell model have been used to predict the partial half-lives and energy-release distributions for the two transitions. The dominant correction terms related to those processes are considered, including the exchange and overlap corrections, and the shake-up and shake-off effects. The normalized distribution of the released energy in the electron-capture decay of 95Tc to excited states of 95Mo is compared to that of 163Ho currently being used for electron-neutrino-mass determination.

Bridging turbulent scales: A unified LES approach from low to high Reynolds numbers using TSDIA and GOY Shell models

Large Eddy Simulation (LES) has become a widely adopted method for modeling turbulence across various fields, such as aerospace, wind energy, and urban wind flow analysis. While traditional LES models are highly effective at high Reynolds numbers, they face challenges at low Reynolds numbers due to the absence of a clearly defined inertial subrange. This paper introduces an improved LES approach by integrating Yoshizawa's Two-Scale Direct Interaction Approximation (TSDIA) theory and the GOY shell model. This combined method extends the applicability of LES by capturing turbulence features across both inertial and dissipation ranges, overcoming limitations found in conventional models. By deriving model constants directly from the shell model, this approach avoids reliance on empirical values and enhances accuracy, particularly at low Reynolds numbers. Validation against DNS data demonstrates a significant improvement in prediction accuracy, offering a more comprehensive and adaptable solution for turbulent flow simulations across a wide range of practical applications. This method provides a more robust foundation for industrial fluid simulations and environmental modeling.

An essay on deformation measures in isotropic thin shell theories: Bending versus curvature

It has become commonplace for the stored energy function of any realistic shell model to align “within first order” with the classical Koiter membrane-bending (flexural) shell model. In this paper, we assess whether certain extended Cosserat shell models are consistent with the classical linear Koiter model. In doing this, we observe that there are numerous reasons why a modified version of the classical Koiter model should be considered, a consensus reached not only by Koiter himself but also by Sanders and Budiansky, who independently developed the same theory during the same period. To provide a comprehensive overview of the strain measures employed in our Cosserat shell models, this paper presents them in a unified manner and compares them with the strain measures previously utilized in the literature. We show that all our new strain tensors either generalize (in the case of nonlinear constrained or unconstrained models) or coincide (in the case of the linear constrained model) with the strain tensors recognized as the “best" or those possessing a well-defined geometric interpretation connected to bending or curvature.

Uncertainty quantification of collective nuclear observables from the chiral potential parametrization

We perform an uncertainty estimate of quadrupole moments and B(E2) transition rates that inform nuclear collectivity. In particular, we study the low-lying states of 6Li and 12C using the ab initio symmetry-adapted no-core–shell model. For a narrow standard deviation of approximately 1% on the low-energy constants which parametrize high-precision chiral potentials, we find output standard deviations in the collective observables ranging from approximately 3%–6%. The results mark the first step towards a rigorous uncertainty quantification of collectivity in nuclei that aims to account for all sources of uncertainty in ab initio descriptions of challenging collective and clustering observables.

High precision measurement of the Tc99β spectrum

Highly precise measurements of the Tc99β spectrum were performed in two laboratories using metallic magnetic calorimeters. Independent sample preparations, evaluation methods, and analyses yielded consistent results and the spectrum could be measured down to less than 1keV. Consistent β spectra were also obtained via cross evaluations of the experimental data sets. An additional independent measurement with silicon detectors in a 4π configuration confirms the spectrum shape above 25keV. Detailed theoretical calculations were performed using the nuclear shell model and including atomic effects. The spectrum shape was found to be sensitive to the effective value of the axial-vector coupling constant. Combining measurements and predictions, we extracted Qβ=295.82(16)keV, gVeff=0.376(5), and gAeff=0.574(36), which seems to solve an inconsistency of the quenched coupling constants between first and higher forbidden nonunique transitions. Furthermore, we derived the mean energy of the β spectrum, E¯β=98.51(23)keV, logf=−0.47660(22), and logft=12.3478(23). Published by the American Physical Society 2024

ON THE MODELING OF BOUNDARY CONDITIONS IN THE PROBLEM OF DETERMINING THE NATURAL FREQUENCIES OF A PIPE

The article discusses the issues of modeling boundary conditions for calculating the natural frequencies of a cylindrical straight pipe based on finite element models. For this purpose, various types of models were used, including rod (Pipe), shell (Shell) and solid (Solid). The study examines various options for implementing the conditions of hinged and rigid fastening: at two points, four points, along the middle surface of the pipe for the Shell model, along the end surface or along part of the outer surface of the pipe for the Solid model. The results of the study showed that the Pipe model provides a better approximation to the analytical solution. For the Shell and Solid models, when hinged, the best option for limit conditions to get closer to the analytical results is to fasten on each edge of the pipe at two points through which the neutral line of the cross-section of the pipe passes during bending. For rigid fastening, the results obtained from the Shell model are closest to the analytical solution if the fastening is carried out at four points or along the line of the middle surface of the pipe. For the Solid model, fastening along the end or part of the outer surface of the pipe is most effective. An analysis of the vibration modes showed that under different fastening conditions vibration modes arise that are associated with the deformation of the pipe as a shell. An assessment of the convergence of the obtained results was given, which confirmed the adequacy of the finite element models. The conclusions from the study made it possible to determine effective ways to set boundary conditions for the Shell and Solid models, which is also confirmed by the preliminary experimental studies of the authors. To obtain clearer results when determining the natural frequencies of pipeline systems, it is recommended to use experimental research methods along with numerical ones. The results obtained are of practical importance for solving problems of design and resource assessment of pipeline systems in various fields of industry.

Theoretical analysis and predictions for the two-neutrino double electron capture of 124Xe

Abstract We provide a complete theoretical description of the two-neutrino electron capture in 124Xe, improving both the nuclear and the atomic structure calculations. We improve the general formalism through the use of the Taylor expansion method, leading to higher-order terms in the decay rate of the process. The nuclear part is treated with pn-QRPA and interacting shell model (ISM) methods. The nuclear matrix elements (NMEs) are calculated with the pn-QRPA method with isospin restoration by fixing the input parameters so that the experimental decay rate is reproduced, resulting in values significantly lower than in previous calculations. The validity of the pn-QRPA NMEs is tested by showing their values to be comparable with the ones for double-beta decay with the emission of two antineutrinos of 128,130Te, which have similar pairing features. Within the ISM, we reproduce the total experimental half-life within a factor of two and predict the capture fraction to the KK channel of about 74%. We also predict the capture fractions to other decay channels and show that for the cumulative decay to the KL1–KO1 channels, a capture fraction of about 24% could be observed experimentally. On the atomic side, calculations are improved by accounting for the Pauli blocking of the decay of innermost nucleon states and by considering all s-wave electrons available for capture, expanding beyond the K and L1 orbitals considered in previous studies. We also provide improved atomic relaxation energies of the final atomic states of 124Te, which may be used as input for background modeling in liquid Xenon experiments.

Rotational properties and blocking effects in N = 152 isotones 254No, 255Lr, and 256Rf

Abstract The ground-state bands in the N = 152 isotones 254No, 255Lr, and 256Rf are investigated by using the cranked shell model (CSM) with pairing correlations treated by the particle-number-conserving (PNC) method. The experimentally kinematic moments of inertia are all reproduced quite well by the PNC-CSM calculations, and the contributions to J(1) from neutrons exhibit remarkable similarities. Compared to 254No, the observed identity of J(1) in 256Rf is due to the negligible contribution to J(1) from the two more protons partially occupying the π[514]7/2, π[521]1/2, and π[624]9/2 orbitals. The increase of J(1) observed in the odd-A nucleus 255Lr, compared to those of the neighboring even-even isotones 254No and 256Rf, is attributed to the contribution of proton j(1)([521]1/2) due to the blocking of nucleon on the proton π[521]1/2 orbital. Compared to the case in heavier isotones 255Lr and 256Rf, the different behavior of B(E2) value above hω ∼ 0.20 MeV in 254No is predicted due to the level π[514]7/2 crossing with π[521]1/2.

Acoustic analysis of a three-dimensional cylindrical shell model under electromagnetic vibration

This paper presents the acoustic analysis of a three-dimensional cylindrical shell model under electromagnetic vibration, a critical factor affecting the performance of electric motors in various applications such as automotive, aerospace, and industrial systems. The study provides a multidisciplinary approach that integrates electromagnetics, structural vibration, and acoustics, solved using the fast multipole boundary element method (FMBEM). The results summarize the validation of the analytical models and numerical simulations, offering insights into effective vibration reduction methods. The conclusions indicate that the 3-D numerical analysis using FMBEM aligns well with the analytical solution for the sound pressure in the exterior acoustic domain of the cylindrical shell model. The paper contributes valuable insights for the design of low-noise motors and the control of electromagnetic vibration and noise in electric motors.

Deciphering the evolution of thermodynamic properties and their connection to the global kinematics of high-speed coronal mass ejections using FRIS model

ABSTRACT Most earlier studies have been limited to estimating the kinematic evolution of coronal mass ejections (CMEs), and only limited efforts have been made to investigate their thermodynamic evolution. We focus on the interplay of the thermal properties of CMEs with their observed global kinematics. We implement the Flux rope Internal State model to estimate variations in the polytropic index, heating rate per unit mass, temperature, pressure, and various internal forces. The model incorporates inputs of 3D kinematics obtained from the Graduated Cylindrical Shell (GCS) model. In our study, we chose nine fast-speed CMEs from 2010 to 2012. Our investigation elucidates that the selected fast-speed CMEs show a heat-release phase at the beginning, followed by a heat-absorption phase with a near-isothermal state in their later propagation phase. The thermal state transition, from heat release to heat absorption, occurs at around 3($\pm$0.3) to 7($\pm$0.7) $R_\odot$ for different CMEs. We found that the CMEs with higher expansion speeds experience a less pronounced sharp temperature decrease before gaining a near-isothermal state. The differential emission measurement (DEM) analysis findings, using multiwavelength observation from Solar Dynamics Observatory/Atmospheric Imaging Assembly, also show a heat release state of CMEs at lower coronal heights. We also find the dominant internal forces influencing CME radial expansion at varying distances from the Sun. Our study shows the need to characterize the internal thermodynamic properties of CMEs better in both observational and modeling studies, offering insights for refining assumptions of a constant value of the polytropic index during the evolution of CMEs.

Preponderance of triaxial shapes in atomic nuclei predicted by the proxy-SU(3) symmetry

Abstract The proxy-SU(3) symmetry predicts, in a parameter-free way, based only on the Pauli principle and the short-range nature of the nucleon-nucleon interaction, non-vanishing values of the collective variable gamma almost everywhere across the nuclear chart. Substantial triaxiality with gamma between 15 and 45 degrees is proved to be expected along horizontal and vertical stripes on the nuclear chart, covering the nucleon numbers 22-26, 34-48, 74-80, 116-124, 172-182. Empirical support for these stripes is found by collecting all even-even nuclei for which the first two excited 2+ states are known, along with the B(E2)s connecting them, as well as the second 2+ state to the ground state. The stripes are related to regions in which oblate SU(3) irreducible representations appear, bearing similarity to the appearance of triaxiality within the SU(3)* dynamical symmetry of the interacting boson model-2. Detailed comparisons of the proxy-SU(3) predictions to the data and to predictions by state-of-the-art Monte Carlo shell model calculations for deformed N=94, 96, 98 isotones in the rare earth region show good overall agreement, with the exception of Z=70 and N=94, which correspond to fully symmetric proxy-SU(3) irreps, suggesting that the latter are an artifact of the method which can be amended by considering the influence of the neighboring irreps.

Computational Technology for Shell Models of Magnetohydrodynamic Turbulence Constructing

The paper discusses the computational technology for constructing one type of small-scale magnetohydrodynamic turbulence models – shell models. Any such model is a system of ordinary quadratic nonlinear differential equations with constant coefficients. Each phase variable is interpreted in absolute value as a measure of the intensity of one of the fields of the turbulent system in a certain range of spatial scales (scale shell). The equations of any shell model must have several quadratic invariants, which are analogues of conservation laws in ideal magnetohydrodynamics. The derivation of the model equations consists in obtaining such expressions for constant coefficients for which the predetermined quadratic expressions will indeed be invariants. Derivation of these expressions «manually» is quite cumbersome and the likelihood of errors in formula transformations is high. This is especially true for non-local models in which large-scale shells that are distant in size can interact. The novelty and originality of the work lie in the fact that the authors proposed a computational technology that allows one to automate the process of deriving equations for shell models. The technology was implemented using computer algebra methods, which made it possible to obtain parametric classes of models in which the invariance of given quadratic forms is carried out absolutely accurately – in formula form. The determination of the parameter values in the resulting parametric class of models is further carried out by agreement with the measures of the interaction of shells in the model with the probabilities of their interaction in a real physical system. The idea of the described technology and its implementation belong to the authors. Some of its elements were published by the authors earlier, but in this work, for the first time, its systematic description is given for models with complex phase variables and agreement of measures of interaction of shells with probabilities. There have been no similar works by other authors previously. The technology allows you to quickly and accurately generate equations for new non-local turbulence shell models and can be useful to researchers involved in modeling turbulent systems.

A 3D shell model for static and free vibration analysis of multilayered magneto-elastic structures

In this paper, an exact 3D coupled magneto-elastic shell model for static and free vibration analysis of multilayered piezomagnetic smart structures is presented. The introduction of the mixed curvilinear orthogonal reference system (α,β,z) allows investigations of plates, cylindrical shells, cylinders and spherical shells as actuators or sensors and also in free vibration conditions. The present exact 3D coupled shell model is composed of four second-order differential equations whose primary variables are the three displacements u, v and w and the magnetic potential ψ. Displacements, stresses, strains, magnetic potential, magnetic induction and circular frequency values are computed to understand the behaviour of piezomagnetic smart structures. The resolution method adopted for the present 3D magneto-elastic problem is based on harmonic forms in α and β in-plane directions and the exponential matrix method in the z direction. Simply supported one-layered/multilayered structures with 0° or 90° orthotropic angles have been analysed. The results section is divided into a first part related to the validation of the proposed 3D model and a second part where new benchmark cases are presented and discussed. Different lamination schemes, load boundary conditions, geometries and materials are studied. Magneto-elastic coupling, thickness and material layer effects are discussed for thin and thick structures. The main novelty of the present exact 3D coupled magneto-elastic shell model stands in the ability to analyse several geometries and multilayered configurations embedding piezomagnetic materials under the action of different boundary loads via a general mathematical formulation.