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Independent variable changes in dynamical systems and applications to systems regularization, giving canonical and Lagrangian motion equations with tensor notation
Coupled evolution of state and topology of dynamical networks is introduced. Due to the well organized tensor structure, the governing equations are presented in a canonical form, and required attractors as well as their basins can be easily implanted and controlled.
For a large class of quantum states, all local (pointwise) energy conditions widely used in relativity are violated by the renormalized stress-energy tensor of a quantum field.
If the restriction of incompressibility in the turbulence problem is relaxed, the phenomenon of energy radiation in the form of sound from the turbulent zone arises. In order to calculate this radiated energy, it is shown that new statistical quantities, such as time-space correlation tensors, have to be known within the turbulent zone in addition to the conventional quantities. For the particular case of the turbulent boundary layer, indications are that the intensity of radiation becomes significant only in supersonic flows. Under these conditions, the recent work of Phillips is examined together with some experimental findings of the author. It is shown that the qualitative features of the radiation field (intensity, directionality) as predicted by the theory are consistent with the measurements; however, even for the highest Mach number flow, some of the assumptions of the asymptotic theory are not yet satisfied in the experiments. Finally, the question of turbulence damping due to radiation is discussed, with the result that in the Mach number range covered by the experiments, the energy lost from the boundary layer due to radiation is a small percentage of the work done by the wall shearing stresses.
Acoustic radiation from supersonic compressible turbulent boundary layer calculated from space- time correlation tensors for sound field
Inertial sensors reviewing ring laser, electrostatic fluid sphere, magnetic resonance, superconductivity gyroscope, relativistic rotating tensor, vortex rate and quantum mechanical effect sensing
Superhyperfine structure tensors for 12 next- nearest ligands in manganese-doped CdTe expressed in terms of electron spin resonance and electron nuclear double resonance transition frequencies
Relationship of Riemannian space-times with metric tensors in solution of vacuum field equations
Energy from hydrogen molecule interaction with magnetic field and from hyperfine interaction expressed as products of irreducible spherical tensors
Dynamics of ionized stellar winds noting anisotropic effect of stress tensors and densities, velocities and electrostatic potentials distributions
Optimal coplanar orbit transfer treated by Contensou-Busemann approach with metric tensor completed by smallest possible convex hull
In a normal coordinate system { y 𝑎 } , the identity 𝜕 2 𝑥 𝑝 /∂y 𝑛 ∂y 𝑚 = ∂ 2 𝑥 𝑝 /∂y 𝑚 ∂y 𝑛 is used to obtain expressions, involving the components of the metric tensor in this coordinate system, for the derivatives of the unit tangent vectors to the parametric curves. An example is given for a normal coordinate system in the De Sitter universe.
Lorentzian scalar electrical conductivity as basis of mixture rules proposed for partially ionized gases in magnetic field to calculate tensor conductivity
Relativistic supernova model, discussing Einstein equation solution with two part stress- energy tensor
Molecular oxygen microwave spectrum application to mesospheric temperature profile determination, noting absorption matrix and tensor equation for microwave spectrum computation
Partially polarized waves in homogeneous dispersive medium with small anisotropy, deriving field solution for tensor permeability specified medium from Maxwell equations
Variable redundancy tensor product codes, discussing encoder modes implementation for adaptive coding and feedback transmission
Junction conditions across internal boundaries for Ricci rotation coefficients and Riemann tensor components in arbitrary reference tetrad frame