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.

scholarly journals Pair-production of cusps on a string in AdS3

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
David Vegh
Keyword(s):  
Pair Production ◽  
Discrete System ◽  
Gordon Equation ◽  
Equation Of Motion ◽  
Pair Creation ◽  
Speed Of Light ◽  
Final State ◽  
Classical Motion ◽  
Direct Energy ◽  
The Moment

Abstract The classical motion of a Nambu-Goto string in AdS3 spacetime is governed by the generalized sinh-Gordon equation. It can locally be reduced to the sinh-Gordon (shG), cosh-Gordon (chG), or Liouville equation, depending on the value of the scalar curvature of the induced metric. In this paper, I examine solutions that contain both shG-type and chG-type regions. The boundary between these regions moves with the speed of light. I show that near such boundaries (generalized) solitons can be classically pair-produced. The solitons move subluminally (superluminally) in the shG (chG) region on the worldsheet, and they correspond to cusps on the string. A direct energy cascade is observed at the moment of pair-creation.For the calculations, I use an exact discretization of the equation of motion. The solutions are segmented strings. In this discrete system, pair-production leads to a complete evaporation of the shG region. The final state is a gas of cusps in a chG environment.

scholarly journals A Monolithic Approach of Fluid–Structure Interaction by Discrete Mechanics

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 95
Author(s):  
Stéphane Vincent ◽  
Jean-Paul Caltagirone
Keyword(s):  
Solid Mechanics ◽  
Mechanical Energy ◽  
Fluid Structure Interaction ◽  
Equation Of Motion ◽  
Discrete Equation ◽  
Discrete Mechanics ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Vector Potentials

The unification of the laws of fluid and solid mechanics is achieved on the basis of the concepts of discrete mechanics and the principles of equivalence and relativity, but also the Helmholtz–Hodge decomposition where a vector is written as the sum of divergence-free and curl-free components. The derived equation of motion translates the conservation of acceleration over a segment, that of the intrinsic acceleration of the material medium and the sum of the accelerations applied to it. The scalar and vector potentials of the acceleration, which are the compression and shear energies, give the discrete equation of motion the role of conservation law for total mechanical energy. Velocity and displacement are obtained using an incremental time process from acceleration. After a description of the main stages of the derivation of the equation of motion, unique for the fluid and the solid, the cases of couplings in simple shear and uniaxial compression of two media, fluid and solid, make it possible to show the role of discrete operators and to find the theoretical results. The application of the formulation is then extended to a classical validation case in fluid–structure interaction.

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