A Conserved Cross Helicity for Non-Barotropic MHD

Cross helicity is not conserved in non-barotropic magnetohydrodynamics (MHD) (as opposed to barotropic or incompressible MHD). Here we show that variational analysis suggests a new kind of cross helicity which is conserved in the non barotropic case. The non barotropic cross helicity reduces to the standard cross helicity under barotropic assumptions. The new cross helicity is conserved even for topologies for which the variational principle does not apply.Comment: 3 pages. arXiv admin note: text overlap with arXiv:1510.0063

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

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 $\vec B$ the velocity field $\vec v$, the entropy $s$ and the density $\rho$. 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

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

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