Kinematic Moments Research Articles

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.

The VIRUS-dE Survey. I. Stars in Dwarf Elliptical Galaxies—3D Dynamics and Radially Resolved Stellar Initial Mass Functions

We analyze the stellar structure of a sample of dwarf ellipticals (dEs) inhabiting various environments within the Virgo cluster. Integral-field observations with a high spectral resolution allow us to robustly determine their low-velocity dispersions (∼25 km s−1) and higher-order kinematic moments out to the half-light radius. We find the dEs exhibit a diversity in ages, with the younger dEs being less enhanced than the older, suggesting a complex star formation history for those dEs that recently entered Virgo, while others have been quenched shortly after reionization. Orbit-superposition modeling allowed us to recover viewing angles, stellar mass-to-light ratios (with gradients), as well as the intrinsic orbit structure. We find that the angular momentum of the dEs is strongly suppressed compared to ordinary early-type galaxies and correlates with the environment. Flattened dEs are so because of a suppressed kinetic energy perpendicular to their equatorial plane. Combining population and dynamical modeling results, we find an age-dependent stellar initial mass function or, alternatively, evidence for a more extended star formation history for those galaxies that have had higher initial mass and/or inhabited lower-density environments. dEs appear to have a spatially homogeneous stellar structure, but the state they were “frozen” in as they stopped forming stars varies dramatically according to their initial conditions.

A novel four parameter formula for the rotational spectra of even-even nuclei

In this article, the authors presents a novel four parameter formula based on developing an expression for the moment of inertia in terms of Bohr-Mottelson Geometric Collective Model (GCM). The formula provides an excellent agreement with the experimental data for all nuclei under consideration. Some key quantities will also be derived such as the rotational frequency, the kinematic and dynamical moment of inertia, and their variation with spin will be investigated. A comparison between our proposed four parameter model with both the variable moment of inertia model, and the recently proposed β-stretching model is also presented. Various ΔI=1 and ΔI=2 energy staggering indices will be presented and compared to the experimental counterpart in the paper.

Emergence of High-Order Deformation in Rotating Transfermium Nuclei: A Microscopic Understanding.

The rotational properties of the transfermium nuclei are investigated in the full deformation space by implementing a shell-model-like approach in the cranking covariant density functional theory on a three-dimensional lattice, where the pairing correlations, deformations, and moments of inertia are treated in a microscopic and self-consistent way. The kinematic and dynamic moments of inertia of the rotational bands observed in the transfermium nuclei ^{252}No, ^{254}No, ^{254}Rf, and ^{256}Rf are well reproduced without any adjustable parameters using a well-determined universal density functional. It is found for the first time that the emergence of the octupole deformation should be responsible for the significantly different rotational behavior observed in ^{252}No and ^{254}No. The present results provide a microscopic solution to the long-standing puzzle on the rotational behavior in No isotopes, and highlight the risk of investigating only the hexacontetrapole (β_{60}) deformation effects in rotating transfermium nuclei without considering the octupole deformation.

Systematic study of the superdeformed bands in the framework of the asymmetric rotor model in A≈ 130–150 mass region

The superdeformed (SD) nuclei in the [Formula: see text]–150 mass region are examined for the first time within the Asymmetric Rotor Model (ARM) context. The asymmetry parameter [Formula: see text] is obtained by using the ARM expressions for the energy levels of nonaxially deformed nuclei (triaxial nuclei). The variation of kinematic moment of inertia [Formula: see text] and dynamic moment of inertia [Formula: see text] with [Formula: see text] is examined. Both appear to decline as [Formula: see text] increases. In addition, the variation of [Formula: see text] and the [Formula: see text] product with [Formula: see text] are also examined.

Description of moment of inertia and the interplay between anti-pairing and pairing correlations in 244Pu and 248Cm* *Xiao-Tao He Supported by the the National Key R and D Program of China (2023YFA1606503)

A variable moment of inertia (VMI) inspired interacting boson model (IBM), which includes many-body interactions and a perturbation possessing (5) (or (5)) symmetry, is used to investigate the rotational bands of the mass region. A novel modification is introduced, extending the Arima coefficient to the third order. This study is dedicated to the quantitative analysis of evolving trends in intraband γ-transition energy as well as the kinematic and dynamic moments of inertia (MoIs) within the rotational bands of Pu and Cm. The computed outcomes exhibit an exceptional degree of agreement with experimental observations across various conditions. The significance of including a higher-order Arima coefficient is further examined by contrasting it with the previously proposed model. The calculated results demonstrate the significance of both the anti-pairing and pairing effects in the evolution of the dynamic MoI. Additionally, these insights reveal the importance of a newly introduced parameter in accurately depicting complex nuclear behaviors, such as back-bending, up-bending, and downturn in the MoI.

Comparison of kinematics and joint moments calculations for lower limbs during gait using markerless and marker-based motion capture.

Objective: This study aimed at quantifying the difference in kinematic and joint moments calculation for lower limbs during gait utilizing a markerless motion system (TsingVA Technology, Beijing, China) in comparison to values estimated using a marker-based motion capture system (Nokov Motion Capture System, Beijing, China). Methods: Sixteen healthy participants were recruited for the study. The kinematic data of the lower limb during walking were acquired simultaneously based on the markerless motion capture system (120Hz) and the marker-based motion capture system (120Hz). The ground reaction force was recorded synchronously using a force platform (1,200Hz). The kinematic and force data were input into Visual3D for inverse dynamics calculations. Results: The difference in the lower limb joint center position between the two systems was the least at the ankle joint in the posterior/anterior direction, with the mean absolute deviation (MAD) of 0.74cm. The least difference in measuring lower limb angles between the two systems was found in flexion/extension movement, and the greatest difference was found in internal/external rotation movement. The coefficient of multiple correlations (CMC) of the lower limb three joint moments for both systems exceeded or equaled 0.75, except for the ad/abduction of the knee and ankle. All the Root Mean Squared Deviation (RMSD) of the lower limb joint moment are below 18N·m. Conclusion: The markerless motion capture system and marker-based motion capture system showed a high similarity in kinematics and inverse dynamic calculation for lower limbs during gait in the sagittal plane. However, it should be noted that there is a notable deviation in ad/abduction moments at the knee and ankle.

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Inclusive semileptonic B→Xcℓν¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ B\ o {X}_c\\ell \\overline{\ u} $$\\end{document} decays can be described in the Heavy Quark Expansion (HQE) and allow for a precision determination of the CKM element |Vcb|. We calculate the terms of 1/mb5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 1/{m}_b^5 $$\\end{document} and derive a “trace formula” which allows for the computation of the decay rate and kinematic moments of the spectrum up to this order in the HQE. We focus specifically on the reparametrization invariant (RPI) dilepton invariant mass q2 moments of the spectrum, which depend on a reduced set of HQE parameters. At this order, “intrinsic charm” (IC) contributions proportional to 1/mb3mc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 1/\\left({m}_b^3{m}_c^2\\right) $$\\end{document} enter, which are numerically expected to be sizeable. Using the “lowest-lying state saturation ansatz” (LLSA), we estimate the size of these contributions. Within this approximation, we observe a partial cancellation between the IC and the “genuine” 1/mb5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 1/{m}_b^5 $$\\end{document} contributions, resulting in a small overall contribution.

Comparison between patients with COPD and healthy subjects on spatiotemporal, moment and kinematic parameters: A quasi-experimental study.

Chronic obstructive respiratory diseases (COPD) not only cause damage to the respiratory system as well as the heart and blood vessels of the patient but also have a direct effect on the condition of the musculoskeletal system. The risk of falling is increasing due to dysfunction of the joints as well as aging, which occurs frequently in this population. Gait deficits are known as an important risk factor for falls. This research aimed to investigate the gait of COPD patients compared to healthy people to gain a better understanding of the reasons for falls. Twenty patients with COPD and 20 age and BMI-matched healthy individuals were included in this study. Sixteen markers were applied to the lower body of the subjects. Spatio-temporal, kinematic, and maximum moment parameters were measured in different phases in three lower body joints, including the hip, knee, and ankle. The results showed that all spatio-temporal parameters in patients were significantly lower than in healthy people. The ankle angle in the sagittal plane at initial contact was significantly difference (p = 0.03). As well as, in the frontal plane the hip angle in the mid-stance showed a significant difference (p = 0.02). There was also a significant difference in maximum hip moment in the sagittal plane between the two groups (p = 0.01). The larger hip angle of the patients can be related to the balance problems in the mediolateral direction. The moment showed a significant difference in the hip joint. Since the hip muscles are directly in a synergistic relationship with the trunk muscles, it seems the performance of these muscles is likely to be seriously damaged due to respiratory diseases.

Shell model based description of single-particle and collective excitations in 66Zn

Shell model calculations have been performed in f5/2pg9/2 model space using two different interactions viz., jj44bpn and jun45pn to explore the observed band like structure in 66Zn. Calculated energy values of the excited states are compared with the experimental values and a good agreement is found at low excitation energies. The experimental kinematic moment of inertia and the calculated values using shell model are compared and similar trend is observed. Also, the plotted values of the observed and theoretical alignment suggest very similar gain in the angular momentum of 66Zn. The nature of the variation of calculated energy with spin is very similar to the observation and shows a rotational like behaviour. Observed band crossing phenomenon is also reproduced from the plots of theoretical data points. Thus, these two effective interactions, without any modification, are quite efficient in producing the trend of the observed collectivity in even-even 66Zn nucleus. Configurations and occupation numbers for different states are obtained using the two aforementioned interactions and suggests substantial contribution of 1g9/2 orbital in generating the angular momentum of the high spin states.

Parity-doublet bands in the odd- A isotones U237 and Pu239 investigated by a particle-number-conserving method based on the cranked shell model

Based on the reflection-asymmetric Nilsson potential, the parity-doublet rotational bands in odd-$A$ isotones \element{237}U and \element{239}Pu have been investigated by using the particle-number-conserving (PNC) method in the framework of the cranked shell model (CSM). The experimental kinematic moments of inertia (MOIs) and angular momentum alignments are reproduced very well by the PNC-CSM calculations. The significant differences of rotational properties between \element{237}U and \element{239}Pu are explained with the contribution of nucleons occupying proton octupole-correlation pairs of $\pi ^{2} i_{13/2}f_{7/2}$. The upbendings of moments of inertia of the parity-doublet bands in \element{237}U are due to the interference terms of alignments of protons occupying $\pi f_{7/2}$ (${1/2}$) and the high-$j$ intruder $\pi i_{13/2}$ $(1/2, 3/2)$ orbitals. The splittings between the simplex partner bands of the parity-doublet bands in both \element{237}U and \element{239}Pu result from the contribution of alignment of neutron occupying the $\nu d_{5/2}$ ($1/2$) orbital.

Investigation of the high-spin yrast band structure of Pu236–246 isotopes

The available data on some actinide nuclei point to certain significant features of the rotational yrast band and other excited bands. The rotational properties of plutonium isotopes ($^{236--346}\mathrm{Pu}$) were studied via projected shell model (PSM). Calculations are based on the Hamiltonian of the PSM which includes the formed part of a single particle, the $Q\ensuremath{-}Q$ force, and the residual interaction of monopole and quadrupole pairings. The results of the calculated energy levels of the yrast band are then compared with available experimental data and a good agreement has been found. The crossing between two-quasiparticle (2qp) excited bands and the ground state band (g band) in the high-spin regions has been analyzed in terms of band diagrams. The upbendings observed in the kinematic moments of inertia (${j}^{(1)}$ MOI) curves for $^{236--346}\mathrm{Pu}$ isotopes are due to the effect of two aligning nucleons that occupy excited bands and the $\ensuremath{\nu}({j}_{15/2}$), $\ensuremath{\pi}({i}_{13/2}$) high-$j$ intruder orbits. The PSM successfully reproduces the observed upbending in ${j}^{(1)}$ as well as the upturning and downturning in ${j}^{(2)}$. For the $^{240}\mathrm{Pu}$ isotope, the PSM predicts a simultaneous alignment of neutrons ${\ensuremath{\nu}}^{2} [1/2,\ensuremath{-}7/2] {K}^{\ensuremath{\pi}}$ = ${4}^{+}$ and protons ${\ensuremath{\pi}}^{2} [\ensuremath{-}3/2,5/2] {K}^{\ensuremath{\pi}}$ = ${1}^{+}$ bands cross the g band at spin $I=22$. We expect it to be mainly responsible for the disagreement at $I=22$. Furthermore, electric quadrupole transition probabilities $B(E2)$ and the gyromagnetic factor ($g$ factor) for the yrast band energy levels are also studied.

A first glance to the kinematic moments of B → Xcℓν at third order

We study the impact of third-order QCD corrections for several kinematic moments of the inclusive semileptonic B decays, to first order in the 1/mb expansion. We consider the first four moments of the charged-lepton energy ER spectrum, the total leptonic invariant mass q2 and the hadronic invariant mass {M}_X^2 . No experimental cuts are applied. Our analytic results are obtained via an asymptotic expansion around the limit mb ~ mc. After converting the scheme for the bottom mass to the kinetic scheme we compare the size of higher QCD corrections to the contributions from 1/ {m}_b^2 and 1/ {m}_b^3 power corrections and to the relative uncertainties.

Merger histories of brightest group galaxies from MUSE stellar kinematics

ABSTRACT Using Multi-Unit Spectroscopic Explorer (MUSE) spectroscopy, we analyse the stellar kinematics of 18 brightest group early-type (BGEs) galaxies, selected from the Complete Local-Volume Groups Sample (CLoGS). We analyse the kinematic maps for distinct features, and measure specific stellar angular momentum within one effective radius (λe). We classify the BGEs as fast (10/18) or slow (8/18) rotators, suggesting at least two different evolution paths. We quantify the anticorrelation between higher order kinematic moment h3 and V/σ (using the ξ3 parameter), and the kinematic misalignment angle between the photometric and kinematic position angles (using the Ψ parameter), and note clear differences between these parameter distributions of the fast and slow rotating BGEs. We find that all 10 of our fast rotators are aligned between the morphological and kinematical axis, consistent with an oblate galaxy shape, whereas the slow rotators are spread over all three classes: oblate (1/8), triaxial (4/8), and prolate (3/8). We place the results into context using known radio properties, X-ray properties, and observations of molecular gas. We find consistent merger histories inferred from observations for the fast-rotating BGEs, indicating that they experienced gas-rich mergers or interactions, and these are very likely the origin of the cold gas. Observational evidence for the slow rotators is consistent with gas-poor mergers. For the slow rotators with cold gas, all evidence point to cold gas cooling from the intragroup medium.

Four pseudo-mirror nuclei in the left-lower part of the nuclear chart

In the present work, we have reported four new pseudo-mirror nuclei 64Fe–70Zn and 60Cr–74Ge. We have discussed the symmetry in their ground state energy band and kinematic moment of inertia. Further, we have discussed the pseudo-spin coupling in the view of pseudo-mirror nuclei.

Novice Female Exercisers Exhibited Different Biomechanical Loading Profiles during Full-Squat and Half-Squat Practice.

Simple SummaryThis study adapted a customized OpenSim model aiming to analyze the loadings difference between full-squat and half-squat in novice females. The joint moment and joint angle of the hip, knee, and ankle increase significantly in the full-squat, which might increase the risks of potential injury. In the case of training, the cohort of young females could perform half-squat practice when muscle strength is insufficient. This study may present implications for the design of novice strength training programs and the formulation of rehabilitation plans.Background: Females with different practice experience may show different body postures and movement patterns while squatting in different depths, which may lead to changes of biomechanical loadings and increase the risks of injuries. Methods: Sixteen novice female participants without squat training experience participated in this study. A 3D motion capture system was used to collect the marker trajectory and ground reaction force data during bodyweight squatting in different depths. The participants’ kinematic data and joint moment were calculated using OpenSim’s inverse kinematics and inverse dynamics algorithm. In this study, authors adapted a model especially developed for squatting and customized the knee joint with extra Degree-of-Freedom (DoF) in the coronal and horizontal plane with adduction/abduction and internal/external rotation. A paired-sample t-test was used to analyze the difference of joint range of motions (ROM) and peak moments between full-squat (F-SQ) and half-squat (H-SQ). One-Dimensional Statistical Parametric Mapping (SPM1D) is used to analyze the difference of joint angle and moment between the process of squatting F-SQ and H-SQ. Results: (1) Compared with H-SQ, F-SQ showed larger ROM in sagittal, coronal, and transverse planes (p < 0.05). (2) SPM1D found that the difference in joint angles and joint moments between F-SQ and H-SQ was mainly concentrated in the mid-stance during squatting, which suggested the difference is greatly pronounced during deeper squat. (3) Peak hip extension moment, knee extension moment, hip adduction moment, and plantar flexion moment of F-SQ were significantly higher than H-SQ (p < 0.05). (4) Difference of hip and knee extension moments and rotation moments between the F-SQ and H-SQ were exhibited during descending and ascending. Conclusions: The study found that novice women had larger range of joint motion during the F-SQ than H-SQ group, and knee valgus was observed during squatting to the deepest point. Greater joint moment was found during F-SQ and reached a peak during ascending after squatting to the deepest point. Novice women may have better movement control during H-SQ. The findings may provide implications for the selection of lower limb strength training programs, assist the scientific development of training movements, and provide reference for squat movement correction, thus reducing the risk of injury for novice women in squatting practice.

Cosmic Flow Measurement and Mock Sampling Algorithm of Cosmicflows-4 Tully−Fisher Catalog

Abstract Measurements of cosmic flows enable us to test whether cosmological models can accurately describe the evolution of the density field in the nearby universe. In this paper, we measure the low-order kinematic moments of the cosmic flow field, namely bulk flow and shear moments, using the Cosmicflows-4 Tully−Fisher catalog (CF4TF). To make accurate cosmological inferences with the CF4TF sample, it is important to make realistic mock catalogs. We present the mock sampling algorithm of CF4TF. These mocks can accurately realize the survey geometry and luminosity selection function, enabling researchers to explore how these systematics affect the measurements. These mocks can also be further used to estimate the covariance matrix and errors of the power spectrum and two-point correlation function in future work. In this paper, we use the mocks to test the cosmic flow estimator and find that the measurements are unbiased. The measured bulk flow in the local universe is 376 ± 23 (error) ± 183 (cosmic variance) km s−1 at depth d MLE = 35 Mpc h −1, to the Galactic direction of (l, b) = (298° ± 3°, −6° ± 3°). Both the measured bulk and shear moments are consistent with the concordance Λ Cold Dark Matter cosmological model predictions.

Influence of the sloping ground conditions and the subsequent shaking events on the pile group response subjected to kinematic interactions for a liquefiable sloping ground

The soil-pile kinematic interaction under large nonlinearity, including soil liquefaction, represents a complex phenomenon that depends on many unforeseen factors. This paper presents the results of dynamic centrifuge tests carried out considering varying sloping inclination angles for a liquefiable ground subjected to four successive earthquake shakings having an increasing amplitude of acceleration. The results indicated the ground surface sloping inclinations to have a significant influence on the kinematic bending moment response of the piles. The significantly larger kinematic moments were generated on the downslope pile compared to the upslope pile highlighting the non-existence of shadowing effects during the lateral spreading for a liquefiable sloping ground. The kinematic moments generated during the first shaking, having predominant lateral spreading were substantially larger than the following three shakings, indicating the complex kinematic interaction to depend not only on the amplitude of base excitation; but mostly on the magnitude of lateral spreading. Moreover, the influences of the generated E.P.W.P on the pile response was studied and it was found that the piles may receive maximum kinematic moments around the occurrence of liquefaction to the time of initiation of dissipation phase of the generated E.P.W.P.

Possible antimagnetic rotation bands in 100Pd: A particle-number conserving investigation

The particle-number conserving method based on the cranked shell model is adopted to investigate the possible antimagnetic rotation bands in 100Pd. The experimental kinematic and dynamic moments of inertia, together with the B(E2) values are reproduced quite well. The occupation probability of each neutron and proton orbital in the observed antimagnetic rotation band is analyzed and its configuration is confirmed. The contribution of each major shell to the total angular momentum alignment with rotational frequency in the lowest-lying positive and negative parity bands is analyzed. The level crossing mechanism of these bands is understood clearly. The possible antimagnetic rotation in the negative parity α=0 branch is predicted, which sensitively depends on the alignment of the neutron (1g7/2, 2d5/2) pseudo-spin partners. The two-shears-like mechanism for this antimagnetic rotation is investigated by examining the closing of the proton hole angular momentum vector towards the neutron angular momentum vector.

Pseudo-mirror nuclei in A∼80 mass region

In the present work, an investigation of pseudo-mirror nuclei is extended to A~80 mass region. Within the limits of NpNn approximation, nuclei 72Ge–84Sr, 76Se–80Kr, 74Se–82Sr, and 76Kr–80Sr are identified as pseudo-mirror nuclei. A systematic comparison of their ground-state energy spectra, kinematic moment of inertia, and reduced transition probability B(E2) is presented. Furthermore, we have discussed the purview of the permitted range of NpNn approximation for pseudo-mirror nuclei.