scholarly journals The Equation of Motion of a Spinning Particle in a Meson Field

1952 ◽  
Vol 8 (6) ◽  
pp. 670-672
Author(s):  
R. C. Majumdar ◽  
S. P. Pandya ◽  
S. Gupta
Keyword(s):  
Equation Of Motion ◽  
Meson Field ◽  
Spinning Particle

The Meson Field and the Equation of Motion of a Spinning Particle

Nature ◽  
1948 ◽  
Vol 161 (4089) ◽  
pp. 410-411 ◽  
Author(s):  
R. C. MAJUMDAR ◽  
S. GUPTA
Keyword(s):  
Equation Of Motion ◽  
Meson Field ◽  
Spinning Particle

scholarly journals Classical theory of spinning particles in a meson field

1941 ◽  
Vol 178 (974) ◽  
pp. 314-350 ◽  
Keyword(s):  
Cross Section ◽  
Classical Theory ◽  
Preceding Paper ◽  
Radiation Reaction ◽  
Meson Mass ◽  
Point Dipole ◽  
Meson Field ◽  
Spinning Particle ◽  
Neutral Mesons ◽  
Negative Moment

An exact classical theory of the motion of a point dipole in a meson field is given which takes into account the effects of the reaction of the emitted meson field. The meson field is characterized by a constant X = μ/h of the dimensions of a reciprocal length, μ being the meson mass, and as X -> 0 the theory of this paper goes over continuously into the theory of the preceding paper for the motion of a spinning particle in a Maxwell field. The mass of the particle and the spin angular momentum are arbitrary mechanical constants. The field contributes a small finite addition to the mass, and a negative moment of inertia about an axis perpendicular to the spin axis. A cross-section (formula (88a)) is given for the scattering of transversely polarized neutral mesons by the rotation of the spin of the neutron or proton which should be valid up to energies of 10 9 eV. For low energies E it agrees completely with the old quantum cross-section, having a dependence on energy proportional to p 4 / E 2 ( p being the meson momentum). At higher energies it deviates completely from the quantum cross-section, which it supersedes by taking into account the effects of radiation reaction on the rotation of the spin. The cross-section is a maximum at E ~ 3.5μ its value at this point being 3 x 10 -26 cm. 2 , after which it decreases rapidly, becoming proportional to E -2 at high energies. Thus the quantum theory of the interaction of neutrons with mesons goes wrong for E >3μ The scattering of longitudinally polarized mesons is due to the translational but not therotational motion of the dipole and is at least twenty thousand times smaller. With the assumption previously made by the present author that the heavy partilesc may exist in states of any integral charge, and in particular that protons of charge 2 e and — e may occur in nature, the above results can be applied to charged mesons; Thus transversely polarised mesons should undergo a very big scattering and consequent absorption at energies near 3 • 5μ. Hence the energy spectrum of transversely polarized mesons should fall off rapidly for energies below about 3μ Scattering plays a relatively unimportant part in the absorption of longitudinally polarized mesons, and they are therefore much more penetrating. The theory does not lead to Heisenberg explosions and multiple processes.

The Meson Fields and the Equation of Motion of a Spinning Particle

1949 ◽  
Vol 75 (12) ◽  
pp. 1788-1793 ◽  
Author(s):  
R. C. Majumdar ◽  
S. Gupta
Keyword(s):  
Equation Of Motion ◽  
Spinning Particle

Particle motion with air resistance

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.

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

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  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .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.

On the Harmonic Oscillations for the Motion of a Dynamical System

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.

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

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>

Nonequilibrium Green’s Functions

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.

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

1994 ◽  
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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