Function Of Rotational Frequency Research Articles

Numerical modeling and design decisions for aerostatic bearings with relatively large nozzle sizes in Magic-Angle Spinning (MAS) systems

Numerical stability analysis for aerostatic bearings was performed to obtain optimized design parameters for small submillimeter to millimeter range diameter cylindrical rotors. Such rotors are used in nuclear magnetic resonance (NMR) application to rotate sample around an axis inclined by magic angle (54.74o) relative to the magnetic field direction at rotational frequencies of about 100 kHz (magic-angle spinning, MAS). The governing Reynolds equation for the fluid film between rotor and bearing was modified for small size aerostatic bearings with relatively large nozzle diameters. The modified Reynolds equation was solved using a finite-volume method to obtain pressure and film thickness around the rotor. This led to the solution of the maximum stable inertial force as a function of rotational frequency and design parameters. The comparison with aerostatic bearings with infinitesimal nozzle sizes was obtained for supported rotor weight and critical vibrational frequency of the rotor. The stable inertial force was found to correspond to a specific nozzle diameter and a specific rotor–bearing clearance. Numerical investigation also shows an enhancement of stable inertial force with decreasing nozzle number or increasing molecular mass of the impinging gas for a specific range of nozzle parameters. Experimental observations further confirmed the role of nozzle diameter, nozzle number and molecular weight of the gas in enhancing the rotor spinning frequency. Further, design decisions were made based on such analysis and were tested for varying rotor size and bearing properties. Using design optimization based on numerical simulation, the maximum frequency of rotation for a home-built 0.4mm MAS rotor could be enhanced from 25 kHz up to 110 kHz, still below the extrapolation from large rotors.

Effects of rotation and valence nucleons in molecular α -chain nuclei

Effects of rotation and valence nucleons in molecular linear $\ensuremath{\alpha}$-chain nuclei are analyzed using a three-dimensional lattice cranking model based on covariant density functional theory. The structure of the mirror nuclei $^{16}\mathrm{C}$ and $^{16}\mathrm{Ne}$ is investigated as a function of rotational frequency. The valence nucleons, with respect to the $3\ensuremath{\alpha}$ linear chain core of $^{12}\mathrm{C}$, at low frequency occupy the $\ensuremath{\pi}$ molecular orbital. With increasing rotational frequency these nucleons transition from the $\ensuremath{\pi}$ orbital to the $\ensuremath{\sigma}$ molecular orbital, thus stabilizing the $3\ensuremath{\alpha}$ linear chain structure. It is predicted that the valence protons in $^{16}\mathrm{Ne}$ change occupation from the $\ensuremath{\pi}$ to the $\ensuremath{\sigma}$ molecular orbital at $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}1.3$ MeV, a lower rotational frequency compared to $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}1.7$ MeV for the valence neutrons in $^{16}\mathrm{C}$. The same effects of valence protons are found in $^{20}\mathrm{Mg}$, compared to the four valence neutrons in $^{20}\mathrm{O}$. The model is also used to examine the effect of alignment of valence nucleons on the relative positions and size of the three $\ensuremath{\alpha}$ clusters in the mirror nuclei $^{16}\mathrm{C}$ and $^{16}\mathrm{Ne}$.

Impact of the Coriolis interaction on the potential landscape evolution across the nuclide chart: Systematic total-Routhian-surface calculations

Rotational structure properties along the yrast line for 766 observed even–even nuclei with Z ≥ 20 in the nuclide chart have been systematically studied by means of the approach of pairing-deformation self-consistent total Routhian surface calculations in three-dimensional deformation space (β 2, γ, β 4). Typical two-dimensional maps of the total nuclear energy are presented as functions of rotational frequency ℏ ω. Various types of physical quantities (including nuclear shapes, aligned angular momenta, pairing gaps and excitation energies) are presented in the (Z, N) plane, indicating the overall characteristics. The ground-state deformations are compared with experimental data and other theoretical results. The present investigation shows that the Coriolis coupling may affect the overall properties systematically, for instance, enforcing regular drifts of the different deformation ‘islands’. We believe that the synthetic presentation will be helpful when planning high-spin experiments, especially in the data-scarce drip-line or superheavy regions. Moreover, such systematic and large-scale calculation and analysis can help overcoming and eliminating the bias among different theoretical models and be useful for checking and developing them.

Investigation of instantaneous and local transmembrane pressure in rotating and vibrating filtration (RVF) module: Comparison of three impellers

The instantaneous and local pressure at membrane surface was experimentally investigated in a dynamic filtration module, named Rotating and Vibrating Filtration (RVF) module. The present paper focuses mainly on the pressure fluctuations in turbulent regime. To this end, the instantaneous pressure is decomposed into its time-averaged and fluctuating quantities using Statistical Analysis (SA), Probability Distribution Function (PDF) and Fast Fourier Transform (FFT). The effects of back pressure, flowrate, rotation frequency and radial position at the membrane on the magnitude of the pressure fluctuations are studied for three different impellers (Imp 1, 2 and 3). For mixing pressure, Imp 2 (6 blades) exhibits a larger core velocity coefficient than Imp 1 and Imp 3 (3 blades). For pressure fluctuation, the extracted variables from SA (standard deviations), PDF (peak-to-peak values) and FFT (amplitudes) confirm that the magnitude of Imp 1 > Imp 3 > Imp 2. Considering SA at 20 Hz, standard deviation of Imp 1 exceeds 100 mbar (up to 25% of TMP), while these values are negligible (<10%) for Imp 2 and 3. After FFT, the dominant frequency identified with Imp 1 is equal to 3 times the rotation frequency (3 N). Conversely, different frequencies (6 N, 3 N and N) exhibiting low amplitude are observed for Imp 2 and 3. Based on the PDF modelling, periodic and random contributions are extracted by deconvolution. Then, the empirical correlations are established to estimate their intensities as a function of rotation frequency and radial position. A “resonance frequency” of 21.1 Hz is clearly identified with Imp 1.

Description of Superdeformed Bands of the Isotones $$\boldsymbol{N=113}$$ for Nuclear Mass Region $$\boldsymbol{A\sim 190}$$

Electric quadrupole $$\gamma$$ -ray transition energies $$E_{\gamma}$$ , rotational frequencies $$\hbar\omega$$ and dynamic $$J^{(2)}$$ and kinematic $$J^{(1)}$$ moments of inertia have been calculated for yrast and excited superdeformed (SD) bands in Hg, Tl, Pb isotonic ( $$N=113$$ ) nuclei by using two-parameter power-law formula. The model parameters and the bandhead spins were determined using a $$\chi^{2}$$ fit by random minimization via Monte Carlo simulation technique with a uniform distribution of random numbers. The calculated results of $$E_{\gamma}$$ agreed with the experimental data published in National Nuclear Data Center (nndc) very well, and present assigned spins of the studied superdeformed rotational bands (SDRB’s) are consistent with the spins suggested by other previous formulae. The majority of the studied SD bands displayed the same large, smooth increase in $$J^{(2)}$$ by increasing $$\hbar\omega$$ . A saturation of $$J^{(2)}$$ at higher values of $$\hbar\omega$$ was observed for the two bands (1, 2) in $${}^{195}$$ Pb due to the Pauli blocking of the quasineutron alignment in the presence of quasiproton alignment. The studied SD bands exhibited staggering in their transition energies. Five pairs of signature partner SDRBs exhibited an $$\Delta I=1$$ staggering effect in their transition energies, namely $${}^{193}$$ Hg (SD1, SD2), $${}^{193}$$ Hg (SD3, SD4), $${}^{194}$$ Tl (SD1, SD2), $${}^{195}$$ Pb (SD1, SD2), and $${}^{195}$$ Pb (SD3, SD4). To investigate this $$\Delta I=1$$ staggering, we extracted the difference between the average transition $$I+2\to I$$ and $$I\to I-2$$ energies in one band and the transition $$I+1\to I-1$$ energies in the signature partner. Also, a $$\Delta I=2$$ staggering exists in three SD bands of odd–odd $${}^{194}$$ Tl. This $$\Delta I=2$$ staggering effect was determined by calculating the energy difference between two consecutive $$\gamma$$ -ray transitions as a function of rotational frequency after subtracting a smooth reference expressed in the notation of Cederwall.

Rotational excitations in rare-earth nuclei: A comparative study within three cranking models with different mean fields and treatments of pairing correlations

High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$) and Yb ($Z=70$) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground state rotational bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the features of band crossings, equilibrium deformations and pairing energies of even-even nuclei under study are discussed. These quantities are considered as a function of rotational frequency and proton and neutron numbers. The changes in the properties of the first band crossings with increasing neutron number in this mass region are investigated. On average, a comparable accuracy of the description of available experimental data is achieved in these models. However, the differences between model predictions become larger above the first band crossings. Because of time-consuming nature of numerical calculations in the CDFT-based models, a systematic study of the rotational properties of both ground state and excited state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in $^{165,167,169,171}$Tm are reproduced reasonably well.

“Stapler” mechanism for a dipole band in Se79

The spectroscopy of Se79 is studied via the Se82(α, α3n)Se79 fusion-evaporation reaction. A negative-parity magnetic dipole band in Se79 is established for the first time. Based on the calculations by the self-consistent tilted axis cranking covariant density functional theory, this new dipole band can be classified as a “stapler” band, which has a relatively stable symmetric prolate deformation as a function of rotational frequency. Hence, it is demonstrated that the stapler bands exist not only in the oblate and triaxial nuclei, but also in prolate nuclei. By examining the angular momentum coupling, it is found that the five valence nucleons in the high-j orbitals play a major role in the closing of the stapler.1 MoreReceived 6 June 2018Revised 16 September 2019DOI:https://doi.org/10.1103/PhysRevC.100.044318©2019 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsCollective modelsElectromagnetic transitionsNuclear density functional theoryNuclear spin & parityProperties59 ≤ A ≤ 89TechniquesNuclear structure & decaysNuclear Physics

Theoretical investigation of the antimagnetic rotation in 104Pd * * Supported by National Natural Science Foundation of China (11875027, 11505058, 11775112, 11775026, 11775099), Fundamental Research Funds for the Central Universities (2018MS058) and the program of China Scholarships Council (201850735020)

The particle-number-conserving method based on the cranked shell model is used to investigate the antimagnetic rotation band in 104Pd. The experimental moments of inertia and reduced B(E2) transition probabilities are reproduced well. The J(2)/B(E2) ratios are also discussed. The occupation probability of each orbital close to the Fermi surface and the contribution of each major shell to the total angular momentum alignment as function of rotational frequency are analyzed. The backbending mechanism of the ground state band in 104Pd is understood clearly and the configuration of the antimagnetic rotation after backbending is clarified. In addition, the crossing of a four quasiparticle state with this antimagnetic rotation band is also predicted. By examining the closing of the angular momenta of four proton holes towards the neutron angular momentum, the " two-shears-like” mechanism for this antimagnetic rotation is investigated and two stages of antimagnetic rotation in 104Pd are clearly seen.

Effect of optical lattice on rotating Bose–Einstein condensates in synthetic magnetic field

In this paper, we study the static and dynamic properties of vortices formation in a rotating Bose–Einstein condensate in synthetic magnetic field. The condensate is confined in a harmonic potential and an optical lattice potential. We numerically solve the time-dependent Gross–Pitaevskii equation in two dimensions and compare the vortices formation process with rotating frame method. We derive the two expressions about vortex number N[Formula: see text] and chemical potential [Formula: see text] as a function of rotational frequency [Formula: see text], which show that the number of vortices N[Formula: see text] increases linearly with [Formula: see text], while the chemical potential [Formula: see text] remains nearly unchanged with increasing [Formula: see text]. The analytical results are in qualitative agreement with the numerical ones. Moreover, we also investigate the vortex dynamics. Numerical results indicate that the time spent for the formation of steady state vortices is reduced drastically if the optical lattice is considered. Nevertheless, the synthetic magnetic field approach is still low efficient to generate more vortices.

Band structure inSn113

The structure of collective bands in $^{113}\mathrm{Sn}$, populated in the reaction $^{100}\mathrm{Mo}(^{19}\mathrm{F},\phantom{\rule{0.16em}{0ex}}p5n)$ at a beam energy of 105 MeV, has been studied. A new positive-parity sequence of eight states extending up to 7764.9 keV and spin $(39/{2}^{+})$ has been observed. The band is explained as arising from the coupling of the odd valence neutron in the ${g}_{7/2}$ or the ${d}_{5/2}$ orbital to the deformed 2p-2h proton configuration of the neighboring even-$A$ Sn isotope. Lifetimes of six states up to an excitation energy of 9934.9 keV and spin $47/{2}^{\ensuremath{-}}\mathrm{belonging}$ to a $\mathrm{\ensuremath{\Delta}}I=2$ intruder band have been measured for the first time, including an upper limit for the last state, from Doppler-shift-attenuation data. A moderate average quadrupole deformation ${\ensuremath{\beta}}_{2}=0.22\ifmmode\pm\else\textpm\fi{}0.02$ is deduced from these results for the five states up to spin $43/{2}^{\ensuremath{-}}$. The transition quadrupole moments decrease with increase in rotational frequency, indicating a reduction of collectivity with spin, a feature common for terminating bands. The behavior of the kinematic and dynamic moments of inertia as a function of rotational frequency has been studied and total Routhian surface calculations have been performed in an attempt to obtain an insight into the nature of the states near termination.

Evolving collective structures in the transitional nucleiW162andW164

Excited states in the neutron-deficient nuclides W8874162 and W9074164 were investigated by using the γ-ray spectrometer Jurogam. A change in structure is apparent from the first rotational alignments in W162 and W164, whose rotationally aligned bands are interpreted as ν(h9/2)2 and ν(i13/2)2 configurations, respectively. The level schemes have been extended using recoil (-decay) correlations with the observation of excited collective structures. Configuration assignments have been made on the basis of comparisons of the deduced aligned angular momentum, as a function of rotational frequency, with the predictions of the cranked shell model.1 MoreReceived 24 November 2015Revised 8 January 2016DOI:https://doi.org/10.1103/PhysRevC.93.024307©2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsElectromagnetic transitionsLow & intermediate energy heavy-ion reactionsProperties150 ≤ A ≤ 189Nuclear Physics

Structure of Superdeformed Rotational Bands in A ~ 150 Mass Region

The structure of superdeformed rotational bands (SDRB's) in A ~ 150 mass region are studied by using the Harris three – parameter expansion and the incremental alignment. The bandhead spins Io have been determined with best fit procedure in order to obtain a minimum root mean square deviation between the calculated and the experimental dynamical moments of inertia. The kinematic moment of inertia has been calculated as a function of rotational frequency and compared to the corresponding experimental ones by assuming three spin values Io - 2 , Io , Io + 2. The transition energies and the variation of the moments of inertia as a function of rotational frequency have been calculated. The agreement between theory and experiment are excellent. The identical bands of SDRB's with ΔI = 2 staggering in 148Gd (SD6) and 149Gd (SD1) are investigated. Also the presence of ΔI = 2 staggering effect in the yrast bands of 147Eu and 150Tb has been examined.

Theoretical Determination of Level Spins of Superdeformed Bands for Nuclei in the Mass Region A = 80 – 104

The bandhead spins of seventeen superdefomed bands in A = 80 – 104 region (38Sr, 39Y, 40Zr, 41Nb,42Mo, 43Tc, 46Pd) have assigned by an indirect method. The dynamical moment of inertia J(2) as a function of rotational frequency ђω are extracted from Harris expansion and fitted to the experimental values by using a computer simulated search program. The calculated dynamic moment of inertia with the best optimized parameters are integrated to give the spins. The intrinsic aligned angular momentum (the integration constant) is assumed to be zero. The values of the spins resulting from our approach are consistent with all spin assignments of other approaches, and have been used to determine the kinematic moment of inertia J(1). The systematic variation of J (2) and J (1) with rotational frequency ђω is investigated, which turns out to be helpful in the spin prediction. Most SD bands in this mass region exhibits decreasing in J(1) and J(2) with increasing ђω. The bandhead moment of inertia J0 which occur at J(2) = J (1) has been sensitive guideline parameter to spin proposition. The relationship between the Harris expansion three parameter model and the four parameter Bohr-Mottelson formula is derived.

Location of the vortex phase in the phase diagram of a rotating two-component Fermi gas

We determine the conditions under which superfluidity with and without quantized vortices appears in a weakly interacting two-component atomic Fermi gas that is trapped in a rotating cylindrical symmetric harmonic potential. We compute the phase diagram as a function of rotation frequency, scattering length, temperature, total number of trapped atoms, and population imbalance. Our analysis is based on solving the Bogoliubov--de Gennes equation.

Vortex formation of a Bose-Einstein condensate in a rotating deep optical lattice

We study the dynamics of vortex nucleation and lattice formation in a Bose--Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross--Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by Williams {\it et al.} [Phys. Rev. Lett. {\bf 104}, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.

Dynamics of contained liquids: A personal odyssey

Dynamics of contained liquids: A personal odyssey

Pairing Field and Moments of Inertia of Superdeformed Nuclei

We have systematically analysed the dynamic moments of inertia of theexperimental superdeformed (SD) bands observed in the A = 190, 150and 60-80 mass regions as functions of rotational frequency. Bycombining the different mass regions, the dramatic features of thedynamic moments of inertia were found and explained based on thecalculations of the pairing fields of SD nuclei with the anisotropicharmonic oscillator quadrupole pairing Hartree-Fock-Bogoliubovmodel.

High-spin excitations in158,159,160Hffrom recoil-decay tagging

The 270-MeV {sup 58}Ni+{sup A}Pd reaction was used for the first recoil-decay tagging measurement with Gammasphere coupled to the Fragment Mass Analyzer at Argonne National Laboratory. Level structures of {sup 158}Hf and {sup 159}Hf are identified for the first time, and that of {sup 160}Hf is extended. The systematical behavior of the energy levels in neighboring isotones and isotopes, as well as the aligned angular momenta as a function of rotational frequency, are examined. (c) 2000 The American Physical Society.

Nucleon-phonon coupling in hot, rapidly rotating nuclei (I)

The particle-vibration coupling formalism is generalized to deal with hot, strongly rotating nuclei. In this way the basis to carry out a microscopic description of the structure of compound nuclei has been developed, in particular the calculation of the effective mass of nucleons close to the Fermi energy. As a consequence, it will be possible to provide a realistic estimate of the nuclear level density as a function of rotational frequency and temperature, a quantity which is among the key ingredients needed in the study of the evolution of the cooling of the compound nucleus through nucleon and γ-decay.

Proton excitations across the Z = 64 gap in the doubly magic superdeformed nucleus 144Gd

Five superdeformed (SD) bands have been identified in 144Gd with the GASP array using the reaction 100Mo + 48Ti . The J (2) moments of inertia of the four excited SD bands are flat as a function of rotational frequency, indicating the blocking of the N = 6 proton crossing observed in the yrast SD band. According to cranked shell model calculations, the excited bands have two-quasiproton configurations with one proton in the N = 6 orbital and the other in each signature partner of the [404]9 2 + or [411]3 2 + orbitals, lying above the Z = 64 gap. The interpretation of the excited SD bands in terms of proton excitations points to the high stability of the N = 80 shell closure at SD shapes. The population of the yrast SD band as a function of the beam energy has been also investigated. Our data shows that the intensity of the yrast SD band is not configuration dependent, being comparable to that of yrast SD bands in the neighboring nuclei. By comparing experimental and theoretical alignments, spins and configurations are assigned to all observed SD bands in the A = 140–150 region.