scholarly journals Variation Principle in Relativistic Hydrodynamics

1955 ◽  
Vol 14 (5) ◽  
pp. 488-490 ◽  
Author(s):  
Ziro Koba
Keyword(s):  
Variation Principle ◽  
Relativistic Hydrodynamics

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

FIRST-ORDER APPROXIMATION OF THE NUMBER-PROJECTED SO(2N) TAMM-DANCOFF EQUATION AND ITS REDUCTION BY THE SCHUR FUNCTION

1999 ◽  
Vol 08 (05) ◽  
pp. 461-483
Author(s):  
SEIYA NISHIYAMA
Keyword(s):  
Wave Function ◽  
Order Approximation ◽  
Approximate Equation ◽  
Variation Principle ◽  
Schur Function ◽  
Soliton Theory ◽  
First Order ◽  
Fermion Systems ◽  
Group Manifold ◽  
First Order Approximation

First-order approximation of the number-projected (NP) SO(2N) Tamm-Dancoff (TD) equation is developed to describe ground and excited states of superconducting fermion systems. We start from an NP Hartree-Bogoliubov (HB) wave function. The NP SO(2N) TD expansion is generated by quasi-particle pair excitations from the degenerate geminals in the number-projected HB wave function. The Schrödinger equation is cast into the NP SO(2N) TD equation by the variation principle. We approximate it up to first order. This approximate equation is reduced to a simpler form by the Schur function of group characters which has a close connection with the soliton theory on the group manifold.

scholarly journals SPACE–TIME STRUCTURE AND SPINOR GEOMETRY

2008 ◽  
Vol 50 (2) ◽  
pp. 143-176 ◽  
Author(s):  
GEORGE SZEKERES ◽  
LINDSAY PETERS
Keyword(s):  
Cosmological Solution ◽  
Space Time ◽  
Time Structure ◽  
Variation Principle ◽  
Field Equations ◽  
Covering Group ◽  
Space Time Structure ◽  
Spinor Geometry ◽  
Complete Set ◽  
Particle Solution

AbstractThe structure of space–time is examined by extending the standard Lorentz connection group to its complex covering group, operating on a 16-dimensional “spinor” frame. A Hamiltonian variation principle is used to derive the field equations for the spinor connection. The result is a complete set of field equations which allow the sources of the gravitational and electromagnetic fields, and the intrinsic spin of a particle, to appear as a manifestation of the space–time structure. A cosmological solution and a simple particle solution are examined. Further extensions to the connection group are proposed.

scholarly journals Variation principle in calculating the flow of a two-phase mixture in the pipes of the cooling systems in high-rise buildings

2018 ◽  
Vol 33 ◽  
pp. 02063 ◽  
Author(s):  
Andrey Aksenov ◽  
Anna Malysheva
Keyword(s):  
Channel Cross Section ◽  
Variation Principle ◽  
Two Phase ◽  
Liquid Phases ◽  
Rate Of Increase ◽  
Annular Layer ◽  
Gas Liquid Flow ◽  
The Stability ◽  
Air Conditioning Systems ◽  
Physical Laws

The analytical solution of one of the urgent problems of modern hydromechanics and heat engineering about the distribution of gas and liquid phases along the channel cross-section, the thickness of the annular layer and their connection with the mass content of the gas phase in the gas-liquid flow is given in the paper.The analytical method is based on the fundamental laws of theoretical mechanics and thermophysics on the minimum of energy dissipation and the minimum rate of increase in the system entropy, which determine the stability of stationary states and processes. Obtained dependencies disclose the physical laws of the motion of two-phase media and can be used in hydraulic calculations during the design and operation of refrigeration and air conditioning systems.

Relativistic hydrodynamics in a global fashion

1993 ◽  
Vol 47 (4) ◽  
pp. 1738-1750 ◽  
Author(s):  
Ekkard Schnedermann ◽  
Ulrich Heinz
Keyword(s):  
Relativistic Hydrodynamics
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