scholarly journals On fractional Euler–Lagrange and Hamilton equations and the fractional generalization of total time derivative

2007 ◽  
Vol 53 (1-2) ◽  
pp. 67-74 ◽  
Author(s):  
Dumitru Baleanu ◽  
Sami I. Muslih ◽  
Eqab M. Rabei
Keyword(s):  
Time Derivative ◽  
Hamilton Equations ◽  
Total Time Derivative

scholarly journals Convection and its Stability in the Equatorial Regions of the Convection Zone

1990 ◽  
Vol 138 ◽  
pp. 325-328
Author(s):  
A.V. Klyachkin
Keyword(s):  
Convection Zone ◽  
Time Derivative ◽  
Equilibrium Temperature ◽  
Boussinesq Approximation ◽  
Gravitational Acceleration ◽  
Basic Equilibrium ◽  
Geophysical Hydrodynamics ◽  
Image Position ◽  
Total Time Derivative ◽  
Adiabatic Temperature Gradient

The problem of the existence, evolution, and stability of spatial structures in convection is of considerable importance to astrophysics as well as to geophysical hydrodynamics. The Boussinesq approximation will be used because the considered motions in stars are sufficiently slow. The system of hydrodynamic equations describing convection in a rotating inhomogeneous medium has the form: Here Dt is the total time derivative, U the velocity, P, T, and C the deviations of the pressure, temperature, and helium abundance (by mass) from the basic equilibrium values, ρm, νm, χm, and Dm the values averaged over the considered layer of the density, viscosity, thermal and helium diffusivities, βT and βc the averaged coefficients of the thermal and helium expansions, g and Ω the gravitational acceleration and angular velocity, ∇Tb, and ∇Cb the values of the basic equilibrium temperature and helium gradients, and ñTad the adiabatic temperature gradient.

Supersymmetric Quantum Mechanics and the Equivalent Classical Transformation

1997 ◽  
Vol 12 (13) ◽  
pp. 899-903 ◽  
Author(s):  
A. Agostinho Neto ◽  
E. Drigo Filho
Keyword(s):  
Quantum Mechanics ◽  
Time Derivative ◽  
Lagrangian Function ◽  
Supersymmetric Quantum Mechanics ◽  
Fermionic Sector ◽  
Classical Transformation ◽  
Total Time Derivative

In the usual supersymmetric quantum mechanics, the supercharges change the eigenfunction from the bosonic to fermionic sector and conversely. The classical correspondent of this transformation is shown to be the addition of a total time derivative of a purely imaginary function to the Lagrangian function of the system.

scholarly journals Noether symmetries, dynamical constants of motion, and spectrum generating algebras

2021 ◽  
Vol 36 (24) ◽  
pp. 2150166
Author(s):  
Daddy Balondo Iyela ◽  
Jan Govaerts
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Time Derivative ◽  
Hamiltonian Formulation ◽  
Lie Symmetry ◽  
Noether Symmetries ◽  
Time Dependency ◽  
Converse Statement ◽  
Constants Of Motion ◽  
Total Time Derivative

When discussing consequences of symmetries of dynamical systems based on Noether’s first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the existence of a time-independent conserved Noether charge which is the generator of the action on phase space of that symmetry, and which necessarily must as well commute with the Hamiltonian. However this need not be so, nor does that statement do justice to the complete scope and reach of Noether’s first theorem. Rather a much less restrictive statement applies, namely, that the corresponding Noether charge as an observable over phase space may in fact possess an explicit time dependency, and yet define a constant of the motion by having a commutator with the Hamiltonian which is nonvanishing, thus indeed defining a dynamical conserved quantity. Furthermore, and this certainly within the Hamiltonian formulation, the converse statement is valid as well, namely, that any dynamical constant of motion is necessarily the Noether charge of some symmetry leaving the system’s action invariant up to some total time derivative contribution. This contribution revisits these different points and their consequences, straightaway within the Hamiltonian formulation which is the most appropriate for such issues. Explicit illustrations are also provided through three general but simple enough classes of systems.

About a possible derivation of the London equations

2020 ◽  
Vol 33 (2) ◽  
pp. 208-210 ◽  
Author(s):  
Spiros Koutandos
Keyword(s):  
Hidden Variables ◽  
Time Derivative ◽  
Electric Energy ◽  
Open Access Journal ◽  
Point Particle ◽  
Small Ball ◽  
Energy Equivalence ◽  
Starting Point ◽  
Total Time Derivative ◽  
London Equations

In continuation of some previous work published by this author in an open access journal [S. Koutandos, IOSR J. Appl. Phys. 10, 26 (2018); 10, 35 (2018); 9, 47 (2017); 11, 72 (2019)], he now derives the London equations from an expansion of the rotation of vorticity. Vorticity is a vector quantity described in fluid mechanics which characterizes the angular motion of a point particle as it moves. A small ball, for example, found in a field of vorticity would turn around itself. This is in accordance with the existence of the spin of a particle. We claim that due to the dipolar nature of the electric charge, its rotation vortex effects appear. It is found that the total time derivative of the radius possibly due to Brownian motion is different from the velocity but is used as a starting point in describing a fluid-like flow for the electron where all the quantities behave accordingly. Finally, we ascribe the relativistic radius of the electron to a curvature of spacetime from the mass energy equivalence for the electric energy. This paper may also be looked at as one more discussion about the hidden variables quest in quantum mechanics, offering some progress in understanding them.

Optimized control over modes of hydraulic percussion cutting heads of mining machines

2020 ◽  
pp. 95-104
Author(s):  
Yu. M. Smirnov ◽  
B. M. Kenzhin ◽  
N. S. Smakova ◽  
M. A. Zhurunova
Keyword(s):  
Time Derivative ◽  
Operating Conditions ◽  
Control Action ◽  
Main Function ◽  
Output Data ◽  
Working Cycle ◽  
Control Units ◽  
Action Change ◽  
Function Element ◽  
Service Factors

The main cause of the disagreement between the actual and calculated output data of hydraulic percussion mining machines is the erroneous feed of manipulation signals by the control units. For the maximal fitting of the calculated and actual figures, the continuous method of control action using the third time derivative of the law of motion of the main function element is accepted, namely, the accuracy. The mathematical models of control using displacement, velocity and acceleration are developed. The service factors of mining machines are found. Based on the theory of control and the mathematical logic theory, the logical circuits of formation of manipulation signals in each phase of the working cycle are developed. The main elements are converters, integrators and accumulators ensuring decomposition of elements of the logical circuits and further generation of appropriate control action. It is found that the simplest way is to generate the control action for acceleration of the key function element. For the developed circuits, it is recommended to use general charts of the control action change, implementable for a certain design of hydraulic percussion cutting heads in certain operating conditions.

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