Extended hierarchy equation of motion for the spin-boson model

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

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Particle motion with air resistance

Progress in Agricultural Engineering Sciences ◽

10.1556/progress.8.2012.1 ◽

2012 ◽

Vol 8 (1) ◽

pp. 1-15

Author(s):

Gy. Sitkei

Keyword(s):

Basic Equation ◽

Initial Conditions ◽

Equation Of Motion ◽

Terminal Velocity ◽

Dimensionless Form ◽

Wood Industry ◽

Acceptable Error ◽

General Validity ◽

Practical Applications ◽

Air Resistance

Motion of particles with air resistance (e.g. horizontal and inclined throwing) plays an important role in many technological processes in agriculture, wood industry and several other fields. Although, the basic equation of motion of this problem is well known, however, the solutions for practical applications are not sufficient. In this article working diagrams were developed for quick estimation of the throwing distance and the terminal velocity. Approximate solution procedures are presented in closed form with acceptable error. The working diagrams provide with arbitrary initial conditions in dimensionless form of general validity.

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Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i1.6950 ◽

2015 ◽

Vol 11 (1) ◽

pp. 2960-2971

Author(s):

M.Abdel Wahab

Keyword(s):

Velocity Field ◽

Angular Velocity ◽

Finite Difference ◽

Numerical Study ◽

Outer Sphere ◽

Equation Of Motion ◽

Annular Region ◽

Surface Traction ◽

Angular Velocities ◽

Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1 ï— and the outer sphererotate with angular velocity 2 ï— about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (ï¡,ï¢ ,ïª) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

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On the Harmonic Oscillations for the Motion of a Dynamical System

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v13i2.5754 ◽

2017 ◽

Vol 13 (2) ◽

pp. 4657-4670

Author(s):

W. S. Amer

Keyword(s):

Dynamical System ◽

Numerical Solutions ◽

Equation Of Motion ◽

Parameter Method ◽

Kutta Method ◽

Small Parameter Method ◽

Harmonic Oscillations ◽

Pivot Point ◽

Runge Kutta Method ◽

High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

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A Multi-Layer Approach to the Equation of Motion Coupled-Cluster Method for the Electron Affinity

10.26434/chemrxiv.11853399 ◽

2020 ◽

Author(s):

Soumi Haldar ◽

Achintya Kumar Dutta

Keyword(s):

Electron Affinity ◽

Electron Attachment ◽

Equation Of Motion ◽

Cluster Method ◽

Coupled Cluster ◽

Coupled Cluster Method ◽

Large Molecules ◽

Layer Method ◽

Speed Up ◽

Attachment Process

We have presented a multi-layer implementation of the equation of motion coupled-cluster method for the electron affinity, based on local and pair natural orbitals. The method gives consistent accuracy for both localized and delocalized anionic states. It results in many fold speedup in computational timing as compared to the canonical and DLPNO based implementation of the EA-EOM-CCSD method. We have also developed an explicit fragment-based approach which can lead to even higher speed-up with little loss in accuracy. The multi-layer method can be used to treat the environmental effect of both bonded and non-bonded nature on the electron attachment process in large molecules.<br>

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Nonequilibrium Green’s Functions

10.1093/oso/9780198797241.003.0007 ◽

2018 ◽

Author(s):

Klaus Morawetz

Keyword(s):

Green’S Function ◽

Quantum Transport ◽

Green's Function ◽

Green's Functions ◽

Green’S Functions ◽

Equation Of Motion ◽

Diagrammatic Technique ◽

Initial Correlations ◽

Nonequilibrium Green’S Functions ◽

Nonequilibrium Green's Functions

The method of the equation of motion is used to derive the Martin–Schwinger hierarchy for the nonequilibrium Green’s functions. The formal closure of the hierarchy is reached by using the selfenergy which provides a recipe for how to construct selfenergies from approximations of the two-particle Green’s function. The Langreth–Wilkins rules for a diagrammatic technique are shown to be equivalent to the weakening of initial correlations. The quantum transport equations are derived in the general form of Kadanoff and Baym equations. The information contained in the Green’s function is discussed. In equilibrium this leads to the Matsubara diagrammatic technique.

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A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; General ◽

10.1115/94-gt-107 ◽

1994 ◽

Cited By ~ 1

Author(s):

Wen Zhang ◽

Wenliang Wang ◽

Hao Wang ◽

Jiong Tang

Keyword(s):

Finite Element ◽

Degrees Of Freedom ◽

Coupled System ◽

Equation Of Motion ◽

Coupled Systems ◽

The Finite Element Method ◽

Bladed Disk ◽

Modal Synthesis ◽

Element Approach ◽

Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

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