82 research outputs found
STABILITY IN THE WEAK VARIATIONAL PRINCIPLE OF BAROTROPIC FLOWS
I find conditions under which the "Weak Energy Principle" of Katz, Inagaki
and Yahalom (1993) gives necessary and sufficient conditions. My conclusion is
that, necessary and sufficient conditions of stability are obtained when we
have only two mode coupling in the gyroscopic terms of the perturbed
Lagrangian. To illustrate the power of this new energy principle, I have
calculated the stability limits of two dimensional configurations such as
ordinary Maclaurin disk, an infinite self gravitating rotating sheet, and a two
dimensional Rayleigh flow which has well known sufficient conditions of
stability. All perturbations considered are in the same plane as the
configurations. The limits of stability are identical with those given by a
dynamical analysis when available, and with the results of the strong energy
principle analysis when given. Thus although the "Weak Energy" method is
mathematically more simple than the "Strong Energy" method of Katz, Inagaki and
Yahalom )1993) since it does not involve solving second order partial
differential equations, it is by no means less effective
A New Diffeomorphism Symmetry Group of Non-Barotropic Magnetohydrodynamics
The theorem of Noether dictates that for every continuous symmetry group of
an Action the system must possess a conservation law. In this paper we discuss
some subgroups of Arnold's labelling symmetry diffeomorphism related to
non-barotropic magnetohydrodynamics (MHD) and the conservations laws associated
with them. Those include but are not limited to the metage translation group
and the associated topological conservations law of non-barotropic cross
helicity.Comment: 10 pages, proceedings of Group 32 2018. arXiv admin note: text
overlap with arXiv:physics/0603115, arXiv:1703.08072, arXiv:1605.0253
A DLA model for Turbulence
A connection between fractal dimensions of "turbulent facets" and fractal
dimensions in diffusion-limited aggregation (DLA) is shown. The theoretical
correspondence is elucidated and an empirical support to the above claim is
given.Comment: 6 page
The Stability of Lorentzian Space-Time
It is stated in many text books that the any metric appearing in general
relativity should be locally Lorentzian i.e. of the type \eta_\mn = {\rm diag}
(1,-1,-1,-1) this is usually presented as an independent axiom of the theory,
which can not be deduced from other assumptions. In this work we show that the
above assertion is a consequence of a standard stability analysis of the
Einstein \eqs and need not be assumed.Comment: 8 page
Gravity and Faster than Light Particles
In this paper I discuss whether superluminal particles exist in the general
relativistic theory of gravity. It seems that the answer to this question is
negative. In truth the result may only represent a difficulty to {\bf special}
but not general relativity, the later allowing both Lorentzian and Euclidian
metrics. An Euclidian metric does not restrict speed. Although only the
Lorentzian metric is stable \cite{Yahaloma}, an Euclidian metric can be created
under special gravitational circumstances and persist in a limited region of
space-time causing possible superluminality.Comment: 10 page
Simplified Variational Principles for non-Barotropic Magnetohydrodynamics
Variational principles for magnetohydrodynamics were introduced by previous
authors both in Lagrangian and Eulerian form. In this paper we introduce
simpler Eulerian variational principles from which all the relevant equations
of non-barotropic magnetohydrodynamics can be derived. The variational
principle is given in terms of five independent functions for non-stationary
barotropic flows. This is less then the eight variables which appear in the
standard equations of barotropic magnetohydrodynamics which are the magnetic
field the velocity field , the entropy and the density
.Comment: 16 pages. arXiv admin note: substantial text overlap with
arXiv:physics/0603115, arXiv:0811.230
Variational Principles and Applications of Local Topological Constants of Motion for Non-Barotropic Magnetohydrodynamics
Variational principles for magnetohydrodynamics (MHD) were introduced by
previous authors both in Lagrangian and Eulerian form. In this paper we
introduce simpler Eulerian variational principles from which all the relevant
equations of non-barotropic MHD can be derived for certain field topologies.
The variational principle is given in terms of five independent functions for
non-stationary non-barotropic flows. This is less then the eight variables
which appear in the standard equations of barotropic MHD which are the magnetic
field the velocity field , the entropy and the density
.
The case of non-barotropic MHD in which the internal energy is a function of
both entropy and density was not discussed in previous works which were
concerned with the simplistic barotropic case. It is important to understand
the rule of entropy and temperature for the variational analysis of MHD. Thus
we introduce a variational principle of non-barotropic MHD and show that five
functions will suffice to describe this physical system.
We will also discuss the implications of the above analysis for topological
constants. It will be shown that while cross helicity is not conserved for
non-barotropic MHD a variant of this quantity is. The implications of this to
non-barotropic MHD stability is discussed.Comment: 27 pages, 7 figures. arXiv admin note: substantial text overlap with
arXiv:1510.00637, arXiv:physics/060311
A Simpler Eulerian Variational Principle for Barotropic Fluids
The variational principle of barotropic Eulerian fluid dynamics is known to
be quite cumbersome containing as much as eleven independent functions. This is
much more than the the four functions (density and velocity) appearing in the
Eulerian equations of motion. This fact may have discouraged applications of
the variational method. In this paper a four function Eulerian variational
principle is suggested and the implications are discussed briefly.Comment: 8 pages, submitted to physical review
Retardation Effects in Gravitation
Galaxies are huge physical systems having dimensions of many tens of
thousands of light years. Thus any change at the galactic center will be
noticed at the rim only tens of thousands of years later. Those retardation
effects seems to be neglected in present day galactic modelling used to
calculate rotational velocities of matter in the rims of the galaxy and
surrounding gas. The significant differences between the predictions of
Newtonian instantaneous action at a distance and observed velocities are
usually explained by either assuming dark matter or by modifying the laws of
gravity (MOND). In this paper we will show that taking general relativity
seriously without neglecting retardation effects one can explain the radial
velocities of galactic matter without postulating dark matter.Comment: 26 pages, 11 figure
Preliminary Energy Considerations in a Relativistic Engine
In a previous paper \cite{MTAY1} we have shown that Newton'n third law cannot
strictly hold in a distributed system of which the different parts are at a
finite distance from each other. This is due to the finite speed of signal
propagation which cannot exceed the speed of light at vacuum, which in turn
means that when summing the total force in the system the force does not add up
to zero. This was demonstrated in a specific example of two current loops with
time dependent currents, the above analysis led to suggestion of a relativistic
engine \cite{MTAY3,AY1}. Since the system is effected by a total force for a
finite period of time this means that the system acquires mechanical momentum
and energy, the question then arises if we need to abandon the law of momentum
and energy conservation. The subject of momentum conversation was discussed in
\cite{MTAY4}. Here some preliminary aspects of the exchange of energy between
the mechanical part of the relativistic engine and the electromagnetic field
are discussed. We also refer briefly to the material composition, structure and
properties of metals that should be used in a relativistic engine.Comment: 15 pages, 1 figur
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