scholarly journals The oscillator spacing of nuclei as function of Ν and Ζ

2020 ◽  
Vol 6 ◽  
pp. 212
Author(s):  
G. A. Lalazissis ◽  
C. P. Panos
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Mean Square ◽  
Level Spacing ◽  
Neutron Excess ◽  
Asymptotic Formulae ◽  
The Mean ◽  
Isospin Dependence ◽  
Better Than

New improved expressions for the harmonic oscillator energy level spacing Κω as function of Ν and Ζ are derived. The isospin dependence is introduced by using new expressions for the mean square radius of nuclei, which fit the experimental mean square radii and the isotopie shifts of even-even nuclei much better than other frequently used relations. The effect of the neutron excess an hω is studied. Very accurate approximate asymptotic formulae for Ηω are also derived, which are suitable for practical use.

The dependence of the harmonic oscillator energy level spacing on the mass number of nuclei

1983 ◽  
Vol 121 (2-3) ◽  
pp. 91-95 ◽  
Author(s):  
C.B. Daskaloyannis ◽  
M.E. Grypeos ◽  
C.G. Koutroulos ◽  
S.E. Massen ◽  
D.S. Saloupis
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Mass Number ◽  
Level Spacing

scholarly journals Harmonic oscillator Brownian motion: Langevin approach revisited

2021 ◽  
Vol 18 (1) ◽  
pp. 97
Author(s):  
O. Contreras-Vergara ◽  
N. Lucero-Azuara ◽  
N. Sánchez-Salas ◽  
J. I. Jiménez-Aquino
Keyword(s):  
Harmonic Oscillator ◽  
Free Particle ◽  
Gaussian White Noise ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Brownian Movement ◽  
Deterministic Equation ◽  
Langevin Approach ◽  
The Mean ◽  
Movement Problem

The original strategy applied by Langevin to Brownian movement problem is used to solve the case of a free particle under a harmonic potential. Such straightforward strategy consists in separating the noise termin the Langevin equation in order to solve a deterministic equation associated with the Mean Square Displacement (MSD). In this work, to achieve our goal we first calculate the variance for the stochastic harmonic oscillator and then the MSD appears immediately. We study the problem in the damped and lightly damped cases and show that, for times greater than the relaxation time, Langevin's original strategy is quite consistent with the exact theoretical solutions reported by Chandrasekhar and Lemons, these latter obtained using the statistical properties of a Gaussian white noise. Our results for the MSDs are compared  with the exact theoretical solutions as well as with the numerical simulation.

scholarly journals Hybrid ANFIS-Rao algorithm for surface roughness modelling and optimization in electrical discharge machining

2021 ◽  
Vol 16 (2) ◽  
pp. 145-160
Author(s):  
N. Agarwal ◽  
N. Shrivastava ◽  
M.K. Pradhan
Keyword(s):  
Surface Roughness ◽  
Optimization Techniques ◽  
Training Data ◽  
Mean Square ◽  
Jaya Algorithm ◽  
Ann Model ◽  
Anfis Model ◽  
Data Set ◽  
The Mean ◽  
Better Than

Advanced modeling and optimization techniques are imperative today to deal with complex machining processes like electric discharge machining (EDM). In the present research, Titanium alloy has been machined by considering different electrical input parameters to evaluate one of the important surface integrity (SI) parameter that is surface roughness Ra. Firstly, the response surface methodology (RSM) has been adopted for experimental design and for generating training data set. The artificial neural network (ANN) model has been developed and optimized for Ra with the same training data set. Finally, an adaptive neuro-fuzzy inference system (ANFIS) model has been developed for Ra. Optimization of the developed ANFIS model has been done by applying the latest optimization techniques Rao algorithm and the Jaya algorithm. Different statistical parameters such as the mean square error (MSE), the mean absolute error (MAE), the root mean square error (RMSE), the mean bias error (MBE) and the mean absolute percentage error (MAPE) elucidate that the ANFIS model is better than the ANN model. Both the optimization algorithms results in considerable improvement in the SI of the machined surface. Comparing the Rao algorithm and Jaya algorithm for optimization, it has been found that the Rao algorithm performs better than the Jaya algorithm.

scholarly journals The variation of the Ηωwith the particle number and the appearance of "kinks" for atomic clusters

2020 ◽  
Vol 9 ◽  
pp. 306
Author(s):  
B. A. Kotsos ◽  
M. E. Grypeos
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Particle Number ◽  
Atomic Clusters ◽  
Level Spacing ◽  
Fermi Distribution ◽  
Sodium Clusters ◽  
Electronic Densities ◽  
Closed Shells

The dependence of the harmonic oscillator (HO) energy level spacing Ηω on the particle number Ν is studied analytically for atomic clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to "kinks", that is to "marked discontinuities in the slope" of Ηω at the closed shells. These discontinuities diminish as Ν increases.

scholarly journals On some mean value results for the zeta-function and a divisor problem

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2315-2327
Author(s):  
Aleksandar Ivic
Keyword(s):  
Zeta Function ◽  
Error Term ◽  
Mean Value ◽  
Divisor Problem ◽  
Mean Square ◽  
Asymptotic Formulae ◽  
Dirichlet Divisor Problem ◽  
The Mean

Let ?(x) denote the error term in the classical Dirichlet divisor problem, and let the modified error term in the divisor problem be ?*(x) = -?(x) + 2?(2x)-1/2?(4x). We show that ?T+H,T ?*(t/2?)|?(1/2+it)|2dt<< HT1/6log7/2 T (T2/3+? ? H = H(T) ? T), ?T,0 ?(t)|?(1/2+it)|2dt << T9/8(log T)5/2, and obtain asymptotic formulae for ?T,0 (?*(t/2?))2|?( 1/2+it)|2 dt, ?T0 (?*(t/2?))3|?(1/+it)|2 dt. The importance of the ?*-function comes from the fact that it is the analogue of E(T), the error term in the mean square formula for |?(1/2+it)|2. We also show, if E*(T) = E(T)-2??*(T/(2?)), ?T0 E*(t)Ej(t)|?(1/2+it)|2 dt << j,? T7/6+j/4+? (j=1,2,3).

scholarly journals The harmonic oscillator energy level spacing for neutrons and protons in nuclei

2019 ◽  
Vol 3 ◽  
pp. 76
Author(s):  
G. A. Lalazissis ◽  
C. P. Panos
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Density Distribution ◽  
Periodic Table ◽  
Neutron Number ◽  
Level Spacing ◽  
Proton Number ◽  
The Difference ◽  
Closed Shells ◽  
Approximate Expressions

Approximate expressions of hw for neutrons and protons separately, as functions of the neutron number Ν and the proton number Ζ respectively, are derived. The dependence of hωn{hωp) on N(Z) is established using a rather recently proposed semi-phenomenological density distribution based on the separation energies of the last neutron or proton. The corresponding curves of hω show "discontinuities in the slope" at the closed shells throughout the periodic table. The difference hωn — hωΛ is also discussed

scholarly journals The Performance of Some Restricted Estimators In Restricted Linear Regression Model

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Bader Aboud ◽  
Mustafa Ismaeel Naif
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Simulation Study ◽  
Linear Regression Model ◽  
Regression Estimator ◽  
Mean Square ◽  
Ridge Regression Estimator ◽  
The Mean ◽  
Biased Estimators ◽  
Better Than

In the linear regression model, the restricted biased estimation as one of important  methods to addressing the high variance and the  multicollinearity problems. In this paper, we make the simulation study of the some restricted biased estimators. The mean square error (MME) criteria are used to make a comparison  among them. According to the simulation study we observe that, the performance of the restricted modified unbiased  ridge regression estimator (RMUR) was proposed by  Bader and Alheety (2020)  is better than  of these estimators. Numerical example have been considered to illustrate the performance of the estimators.

Sign in / Sign up

Export Citation Format

Share Document