The oscillator shell model with the state dependent frequencies

1981 ◽  
Vol 31 (1) ◽  
pp. 16-24 ◽  
Author(s):  
Nguyen tien Nguyen
Keyword(s):  
Shell Model ◽  
The State ◽  
State Dependent ◽  
Oscillator Shell

scholarly journals On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

2015 ◽  
Vol 22 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Alexey E. Rastegin
Keyword(s):  
The State ◽  
Uncertainty Relations ◽  
Trade Off ◽  
Entropic Uncertainty Relations ◽  
Finite Dimensional ◽  
State Dependent ◽  
Entanglement Detection

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

THE RESPONSE FUNCTION OF THE 4He, 16O AND 40Ca NUCLEI IN THE HARMONIC OSCILLATOR SHELL MODEL AND THE IMPULSE APPROXIMATIONS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350011
Author(s):  
M. MODARRES ◽  
Y. YOUNESIZADEH
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Momentum Distribution ◽  
Impulse Approximation ◽  
Distribution Functions ◽  
Heavy Nuclei ◽  
Momentum Distribution Function ◽  
Oscillator Shell ◽  
Nucleus Scattering ◽  
The One

In this work, the response functions (RFs) of the 4 He , 16 O and 40 Ca nuclei are calculated in the harmonic oscillator shell model (HOSM) and the impulse approximation (IA). First, the one-body momentum distribution and the one-body spectral functions for these nuclei are written in the HOSM configuration. Then, their RFs are calculated, in the two frameworks, namely the spectral and the momentum distribution functions, within the IA. Unlike our previous work, no further assumption is made to reduce the analytical complications. For each nucleus, it is shown that the (RF) evaluated using the corresponding spectral function has a sizable shift, with respect to the one calculated in terms of the momentum distribution function. It is concluded that for the heavier nuclei, this shift increases and reaches nearly to a constant value (approximately 62 MeV), i.e., similar to that of nuclear matter. It is discussed that in the nuclei with the few nucleons, the above shift can approximately be ignored. This result reduces the theoretical complication for the explanation of the ongoing deep inelastic scattering (DIS) experiments of 3 H or 3 H nucleus target in the Jefferson Laboratory. On the other hand, it is observed that in the heavier nuclei, the RF heights (width) decrease (increase), i.e., the comparison between the theoretical and the experimental electron nucleus scattering cross-section is more sensible for heavy nuclei rather than the light ones.

scholarly journals The Electro-Excitation Form Factors for Low-Lying States of 7Li Nucleus

2010 ◽  
Vol 7 (1) ◽  
pp. 105-112
Author(s):  
Baghdad Science Journal
Keyword(s):  
Shell Model ◽  
Electron Scattering ◽  
Form Factors ◽  
Model Space ◽  
Theoretical Models ◽  
Inelastic Electron ◽  
Oscillator Shell ◽  
21.60 Cs ◽  
Configuration Mixing ◽  
Transverse Electron

The transverse electron scattering form factors have been studied for low –lying excited states of 7Li nucleus. These states are specified by J? T= (0.478MeV), (4.63MeV) and (6.68MeV). The transitions to these states are taking place by both isoscalar and isovector components. These form factors have been analyzed in the framework of the multi-nucleon configuration mixing of harmonic oscillator shell model with size parameter brms=1.74fm. The universal two-body of Cohen-Kurath is used to generate the 1p-shell wave functions. The core polarization effects are included in the calculations through effective g-factors and resolved many discrepancies with experiments. A higher configuration effect outside the 1p-shell model space, such as the 2p-shell, enhances the form factors for q-values and reproduces the data. The present results are compared with other theoretical models. PACS: 25.30.Bf Elastic electron scattering - 25.30.Dh Inelastic electron scattering to specific states – 21.60.Cs Shell model – 27.20. +n 5? A ?19

scholarly journals Yaw Angle Tracking Control Design of Underactuated AUV By Using State Dependent Riccati Equations (SDRE)-LQT

2019 ◽  
Vol 3 (2) ◽  
pp. 325
Author(s):  
Muhammad Basri Hasan
Keyword(s):  
Tracking Control ◽  
Control Design ◽  
Riccati Equations ◽  
The State ◽  
Linear Quadratic ◽  
State Dependent ◽  
Linear Quadratic Tracking ◽  
Quadratic Tracking ◽  
Yaw Angle ◽  
Angle Tracking

In realizing yaw angle control tracking on AUV, the use of the State Dependent Riccati Equations method based on Linear Quadratic Tracking (SDRE-LQT) is realized. This algorithm calculates changes in yaw angle tracking problems through calculation of parameter changes from online AUV with Algebraic Riccati Equations.So that the control signal given to the plant can follow the changing conditions of the plant itself. 

scholarly journals Optimal Factorization of the State-Dependent Riccati Equation Technique in a Satellite Attitude and Orbit Control System

2021 ◽  
Vol 20 ◽  
pp. 98-107
Author(s):  
Alessandro Gerlinger Romero ◽  
Luiz Carlos Gadelha De Souza
Keyword(s):  
Control System ◽  
Riccati Equation ◽  
The State ◽  
Linear Control ◽  
Control Techniques ◽  
Orbit Control ◽  
Satellite Attitude ◽  
Modified Rodrigues Parameters ◽  
State Dependent ◽  
Attitude Maneuver

The satellite attitude and orbit control system (AOCS) can be designed with success by linear control theory if the satellite has slow angular motions and small attitude maneuver. However, for large and fast maneuvers, the linearized models are not able to represent all the perturbations due to the effects of the nonlinear terms present in the dynamics and in the actuators (e.g., saturation). Therefore, in such cases, it is expected that nonlinear control techniques yield better performance than the linear control techniques. One candidate technique for the design of AOCS control law under a large maneuver is the State-Dependent Riccati Equation (SDRE). SDRE entails factorization (that is, parameterization) of the nonlinear dynamics into the state vector and the product of a matrix-valued function that depends on the state itself. In doing so, SDRE brings the nonlinear system to a (nonunique) linear structure having state-dependent coefficient (SDC) matrices and then it minimizes a nonlinear performance index having a quadratic-like structure. The nonuniqueness of the SDC matrices creates extra degrees of freedom, which can be used to enhance controller performance, however, it poses challenges since not all SDC matrices fulfill the SDRE requirements. Moreover, regarding the satellite's kinematics, there is a plethora of options, e.g., Euler angles, Gibbs vector, modified Rodrigues parameters (MRPs), quaternions, etc. Once again, some kinematics formulation of the AOCS do not fulfill the SDRE requirements. In this paper, we evaluate the factorization options (SDC matrices) for the AOCS exploring the requirements of the SDRE technique. Considering a Brazilian National Institute for Space Research (INPE) typical mission, in which the AOCS must stabilize a satellite in three-axis, the application of the SDRE technique equipped with the optimal SDC matrices can yield gains in the missions. The initial results show that MRPs for kinematics provides an optimal SDC matrix.

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