Moment Of Inertia Model Research Articles

Studying the nuclear structure of the () deformed nucleus by using (IBM-1) and (VAVM) Models

In this paper, the nuclear structure of the deformed even-even nucleus was studied using the first interacting boson model (IBM-1) to calculate the energy levels E(L) and the transitional energy (Eγ ). The energy bands, as well as the quadrupole moment (QL ) can be calculated to know the shape of the nucleus and the moment of inertia model, energy levels E(L), transitional energy (Eγ ) and the bands intersection. The current study showed that at dynamic symmetry SU (3), there is no effect of inertia moment on the shape of the rotational nuclei due to the absence of the phenomenon of back bending that belongs to this dynamic symmetry, through calculating the energy levels ratios found that nucleus belongs to the rotational dynamic symmetry SU (3). A comparison of the available practical results with the results calculated by (VAVM) and (IBM-1) showed that the (VAVM) model are better than the results calculated by (IBM-1).

Effect of Tension Stiffening on the Deflection of a Tapered Reinforced Concrete Cantilever Under a Concentrated Load

Tapered cantilever concrete beams are widely used in various types of applications. However, deflections for these types of beams are usually estimated using numerical techniques. In this research, an analytical solution is obtained for a non-prismatic tapered cantilever concrete beam that has a varying depth along the length when subjected to a concentrated load at its end. The dependence of the solution on the steel reinforcement ratio is simplified in order to obtain the solution. An effective moment of inertia model with tension stiffening is used in the formulation to obtain a better prediction for deflection. The obtained equation of deflection has the advantage of practicality and ease of use for designers and engineers. The finite element method is used to verify the analytical solution. A smeared cracking model with a tension softening effect was incorporated in the finite element model in order to obtain better simulation results. Despite the fact that the model predicted deflection well, the model lacks the ability to accurately predict the location of the neutral axis.

A new perspective of ground band energy formulae

A host of alternative energy formulae for the ground bands of even Z even N nuclei are available in the literature. The usual approach is to compare the relative numerical accuracy of the predictions of the level energies by these formulae, for varying deformations of the nuclear core and for high spins. The soft rotor formula and variable moment of inertia model, the ab and pq formulae, the rotation vibration interaction and power index formulae are illustrated. Here, a new perspective is presented, with emphasis on the limitation of the region of their physical validity and on deriving useful meaning of their parameters.

Guest–host systems containing anthraquinone dyes with multiple visible transitions giving positive and negative dichroic order parameters: an assessment of principal molecular axes and computational methods

ABSTRACTThree 1,4-disubstituted anthraquinone dyes with bis(4-n-butylphenyl) substituents connected via amine or amide linking groups have been studied as guest molecules dissolved in the nematic host E7. UV-visible absorption spectroscopy has shown each of the dyes to exhibit multiple absorption bands in the visible region, and dichroic order parameters obtained from polarised spectra of aligned guest–host samples were shown to differ significantly between the bands for each dye, and between the dyes. Time-dependent density functional theory calculations indicated that each dye exhibits several transitions, giving transition dipole moment vectors with a range of orientations, and fully atomistic molecular dynamics simulations of the guest–host mixtures showed differences in the calculated molecular alignments of the dyes. Combining the results from these two sets of calculations enabled a comparison of molecular alignment models based on the moments of inertia and the surface tensors of the dyes. The match between calculated and experimental values was improved significantly when using the surface tensor rather than the moment of inertia model, indicating that the shapes of the molecular surfaces of these dyes are crucial to their alignment. A novel method of calculating polarised UV-visible absorption spectra of dyes in liquid crystal hosts is also presented.

Explaining the riddle of effective moment of inertia models for FRP concrete beams

The current provisions in ACI Committee 440 for calculating deflections of flexural structures reinforced with fibre reinforced polymer (FRP) bars or reinforcements require the use of an effective moment of inertia. Many equations giving its expression have been developed over the past years and show significant difference between them among the CEB-FIP and Benmokrane formula, largely used in literature are selected. The discrepancy of response curves shows that the variation between them can be explained by the bond character and tension stiffening effect. The comparison between responses of various FRP reinforced concrete (RC) beams shows a relative accuracy via the experimental data. For this object, an analytical expression is proposed to quantify the effective moment of inertia and accurately results are shown. Obtained results show a favourite accuracy using the novel expression of the effective moment of inertia model of an in-service FRP bars RC beam subjected to a monotonic loading.

Multi-view face identification and pose estimation using B-spline interpolation

The available face views in the training set are mostly limited. In this paper, we present a view interpolation method using nonlinear B-spline on face manifolds. Two models, the inner–outer ellipse model and the moment of inertia model, are developed to estimate the pose orientation. We use the limited view-pose face images to form the pose eigen space. Then, based on these nonlinear manifolds we form a B-spline for each individual. Identification is to compute the shortest Euclidean distance from a given test view to the nearest point within one of these B-splines. Once the test view is classified as a familiar individual in the training set, not only can the individual be identified, but also the pose angle can be estimated. Experimental results show that B-spline interpolation can achieve a recognition rate of 95%.

Reexamination of the variable moment of inertia nuclear softness model

The three parameter variable moment of inertia (VMI) nuclear softness model named VMINS3 is shown to be adequate in reproducing the main features of the VMI model. Its failure for deformed nuclei reported by earlier workers is shown to be the result of a wrong approach in the calculation. The variation of the softness parameter \ensuremath{\sigma} and of the stretching parameter $K=(\frac{1}{2})C{\ensuremath{\theta}}_{0}^{2}$ with increasing deformation of the nuclear core is now consistent with results of the variable moment of inertia model.

ERRATA: THE VMI-MODEL REVISITED IN THE ODD-ODD RARE-EARTH NUCLEI

A rather complete formulation of the variable moment of inertia model is presented for odd-odd nuclei and relationship obtained between the energy ratios and the parameters of the model. Range of validity of the model is defined and Mallmann-like curves are obtained for the odd-odd nuclei. An application is made to the rare-earth region and results are presented for the K+=(Ωp+Ωn) bands and those K−=|Ωp−Ωn| bands which remain reasonably free from Coriolis mixing. The parameters obtained from the fitting show excellent agreement with the predictions of the model. An interesting correlation between the variation of the moment of inertia of the odd-odd rotational bands with those of the neighboring odd-A nuclei involving either the same neutron or same proton configuration is also presented.

THE VMI-MODEL REVISITED IN THE ODD-ODD RARE-EARTH NUCLEI

A rather complete formulation of the variable moment of inertia model is presented for odd-odd nuclei and relationship obtained between the energy ratios and the parameters of the model. Range of validity of the model is defined and Mallmann-like curves are obtained for the odd-odd nuclei. An application is made to the rare-earth region and results are presented for the K+=(Ωp+Ωn) bands and those K−=|Ωp−Ωn| bands which remain reasonably free from Coriolis mixing. The parameters obtained from the fitting show excellent agreement with the predictions of the model. An interesting correlation between the variation of the moment of inertia of the odd-odd rotational bands with those of the neighboring odd-A nuclei involving either the same neutron or same proton configuration is also presented.

Model of superfluid liquid with triplet pairing, cranking model and model of variable moment of inertia in superdeformed bands inA?190 region

The triplet pairing model, which has been shown, in some cases, to be equivalent to the cranking and/or variable moment of inertia models, is used to describe the superdeformed bands inA∼190 region. The two-parameter expression for theγ-transition energiesEγ(I), common to these three models, allows a good description of experimental data and an unambiguous spin assignment for the states of these superdeformed bands.

Reformulation of the variable moment of inertia model in terms of nuclear softness.

The ground-state bands in even-even nuclei are studied by treating the variation of moment of inertia with angular momentum in terms of the relative increase of moment of inertia with angular momentum, called the softness parameter. Such a reformulation of the variable moment of inertia (VMI) model in terms of the various orders of softness of the nuclear softness (NS) model extends the range of validity of the new model, called VMINS, to 2.0\ensuremath{\le}${\mathit{R}}_{42}$\ensuremath{\le}3.33. This gradual softening of the rigid rotator throughout the Periodic Table requires softness parameter to, at least, second order, with the vibrational energy also becoming important for very soft nuclei.

APPLICATION OF THE VARIABLE MOMENT OF INERTIA MODEL TO BANDS IN ODD-ODD NUCLEI

The variable moment of inertia model is extended to rotational bands in odd-odd rare-earth nuclei. Results are presented for the K> = (Ωp + Ωn) bands which remain reasonably free from Coriolis mixing effects. The moment of inertia parameter exhibits significant variation with angular momentum which is strikingly similar to one of the odd-A rotational bands based on either the neutron or the proton configuration also involved in the odd-odd rotational band.

Variable moment of inertia models in the NpNnscheme

The two parameters of the variable moment of inertia model and the three parameters of the variable anharmonic vibrator model have been studied as functions on the valence proton-neutron product NpNn in several regions of the periodic table. All the quantities studied show simple systematic behaviour as functions of NpNn, paving the way for a unified description of a wide range of nuclei in the variable moment of inertia framework in terms of few parameters, and allowing for reliable predictions of properties of nuclei far from stability to be made by interpolation rather than extrapolation. The few exceptions observed serve to clarify the underlying differences between the two models.

Softness and shape coexistence in the light platinum isotopes

Data have recently been presented that were interpreted as evidence for shape coexistence in platinum-176. The authors re-examine these data using the dynamic deformation model of Kumar (1984) to calculate the potential energy surfaces (PES). These indicate that all the platinum isotopes are gamma soft and some are also beta soft. The PES show platinum-176 to be a transitional nucleus for both the Z=78 isotopes and the N=98 isotones, with an extremely flat minimum with respect to both beta and gamma deformations. This softness may account for its anomalous experimental level spacing in the yrast band. The interpretation of softness is supported by interacting boson approximation calculations made for this region, and by results obtained from the variational moment of inertia model. Differences between this interpretation and that of shape coexistence are discussed.

Nuclear rotation for low and high spin values

It is shown that a rigorous application of the Peierls-Yoccoz angular momentum projection method leads, in the case ofK=0 rotational bands, to a simple exact expression for the projected energyEI, which may be especially suitable for numerical calculations. On the basis of this energy law and without making any assumption for the overlapsn(Β) andh(Β), a finite expansion ofEI in powers ofI(I +1) is obtained and discussed. Using this finite series a microscopical variable moment of inertia model is presented.

Treatment of centrifugal elastic stresses in nuclear rotation

A treatment of elastic stresses in nuclear rotation with the nucleus considered as an incompressible elastic body with a stationary spherical core surrounded by a circulating mass is presented. Centrifugal stresses acting in directions perpendicular to the axis of rotation introduce variations in the moment of inertia. The variable moment of inertia model, so successful in predicting the rotational spectrum of even-even nuclei, is explained. (AIP)

Microscopic study of the macroscopic rotational parameters

A systematic procedure, based on the theory of probability, is described to calculate the collective parameters of the variable moment of inertia models. Its advantages over the generalized Skyrme procedure are discussed. The numerical calculations on the nucleus 20Ne using Ripka's (1968) deformed Hartree-Fock wavefunctions show that the values of the energies EJ using the method of moments are as good as those calculated using Skyrme's procedure, where one has to handle much higher-rank particle operators. An approximate scheme is described to evaluate the matrix elements of the square root and other complicated functions of J2 with respect to the intrinsic wavefunction mod Phi ) which are generated by large-scale Hartree-Fock calculations.

A study of the variable moment of inertia models

The variable moment of inertia (VMI) model proposed by Holmberg and Lipas has been shown to be a special case of the VMI model of Mariscottiet al. The solution of Mariscotti’s model is expressed in terms of hypergeometric functions, which directly give the rotational energies or their expansions in terms of the quantityF(F+1), whereF is the total angular momentum. The present way of looking at the VMI model also tells us how to write the general dependence of the vibrational energy and the moment of inertia on the energyEJ.