Constraints in relativistic Hamiltonian mechanics

We propose a new scheme for the use of constraints in setting up classical, Hamiltonian, relativistic, interacting particle theories. We show that it possesses both Poincaré invariance and invariance of world lines. We discuss the transition to the physical phase space and the nonrelativistic limit.

Relativistic particle models with separable interactions

We present relativistic, classical particle models that possess Poincaré invariance, invariant world lines, particle interaction, and separability.

Separability in relativistic Hamiltonian particle dynamics

The problem of separability in recent models of classical relativistic interacting particles is examined. This physical requirement is shown to be more subtle than naive separability of all the constraints defining the system: it is adequate to be able to canonically transform the time-fixing constraints from an unseparated to a separated form when clusters emerge. Viewing separability in this way, and within a specific framework, we are led to a new no-interaction theorem which states the incompatibility of nontrivial interaction with relativistic invariance, separability, and invariant world lines for more than two particles.

Paraxial-wave optics and relativistic front description .1. The scalar theory

With the extension of the work of the preceding paper, the relativistic front form for Maxwell's equations for electromagnetism is developed and shown to be particularly suited to the description of paraxial waves. The generators of the Poincaré group in a form applicable directly to the electric and magnetic field vectors are derived. It is shown that the effect of a thin lens on a paraxial electromagnetic wave is given by a six-dimensional transformation matrix, constructed out of certain special generators of the Poincaré group. The method of construction guarantees that the free propagation of such waves as well as their transmission through ideal optical systems can be described in terms of the metaplectic group, exactly as found for scalar waves by Bacry and Cadilhac. An alternative formulation in terms of a vector potential is also constructed. It is chosen in a gauge suggested by the front form and by the requirement that the lens transformation matrix act locally in space. Pencils of light with accompanying polarization are defined for statistical states in terms of the two-point correlation function of the vector potential. Their propagation and transmission through lenses are briefly considered in the paraxial limit. This paper extends Fourier optics and completes it by formulating it for the Maxwell field. We stress that the derivations depend explicitly on the "henochromatic" idealization as well as the identification of the ideal lens with a quadratic phase shift and are heuristic to this extent.

Forms of relativistic dynamics with World Line Condition and separability

he Dirac generator formalism for relativistic Hamiltonian dynamics is reviewed along with its extension to constraint formalism. In these theories evolution is with respect to a dynamically defined parameter, and thus time evolution involves an eleventh generator. These formulations evade the No-Interaction Theorem. But the incorporation of separability reopens the question, and together with the World Line Condition leads to a second no-interaction theorem for systems of three or more particles. Proofs are omitted, but the results of recent research in this area is highlighted.

Note on the Similarity Solutions of Unsteady Jets in Rotating Fluids

The structure of time dependent jets in rotating fluids using similarity transformations is studied theoretically for which exact solutions are discussed. Approximate solution using a modified yon Mises transformation is also explored.

Film cooling at hypersonic Mach numbers using forward facing array of micro-jets

Experimental investigations are carried out in the IISc hypersonic shock tunnel on film cooling effectiveness of a single jet (diameter 2 mm and 0.9 mm), and an array forward facing of micro-jets (diameter 300 mu m each) of same effective area (corresponding to the respective single jet). The single jet and the corresponding micro-jets are injected from the stagnation zone of a blunt cone model (58, apex angle and nose radius of 35 mm). Nitrogen and Helium are injected as coolant gases. Experiments are performed at freestream Mach number 5.9, at 0 degrees angle of attack, with a stagnation enthalpy of 1.84 MJ/kg, with and without injections. The ratios of the jet stagnation pressure to the freestream pitot pressure used in the present study are 1.2 and 1.45. Up to 50% reduction in surface heat transfer rate was observed with the array of micro-jets, compared to that of the respective single jet with nitrogen as the coolant, while the corresponding eduction was up to 37% for helium injection, with the schlieren flow visualizations showing no major change in the shock standoff distance, and thus no major changes in other aerodynamic aspects such as drag.

Pressure shocks in relativistic viscous heat-conducting fluids

In this paper we have studied the propagation of pressure shocks in viscous, heat-conducting, relativistic fluids. Velocities of wave fronts and growth equations for the strength of the waves are obtained in the case of low and high temperatures with variable transport coefficients. On the basis of numerical integrations the growth equation results have been discussed. In the case of constant transport coefficients and for all admissible values of ratio of specific heats of the fluid, an analytical solution for the velocity of the wave as a function of distance along the normal trajectory to the wave front, has been obtained.

A note on mass transfer in turbulent wall jets

THE PROCESS of mass transfer from saturated porous surfaces virtual origin ; exposed to turbulent air streams finds many practical applitransverse coordinate; cations. In many cases, the air stream will be in the form of a height of nozzle above flat plate--radial wall jet; wall jet over the porous surface. The aerodynamics of both plane and radial wall jets have been investigated in detail and a vast amount of literature is available on the subject [l-3].

Spinorial relativistic rotator: The transformation from quasi-Newtonian to Minkowski coordinates

There exists a remarkably close relationship between the operator algebra of the Dirac equation and the corresponding operators of the spinorial relativistic rotator (an indecomposable object lying on a mass-spin Regge trajectory). The analog of the Foldy-Wouthuysen transformation (more generally, the transformation between quasi-Newtonian and Minkowski coordinates) is constructed and explicit results are discussed for the spin and position operators. Zitterbewegung is shown to exist for a system having only positive energies.

Turbulent Wall-Jets in Conical Diffusers

Abstract is not available.

Thermodynamic implication of the special relativistic postulate

Abstract is not available.

The jump in vorticity across a shock wave in relativistic hydrodynamics

Using the singular surface theory, an expression for the jump in vorticity across a shock wave of arbitrary shape propagating in a uniform, perfect fluid occupying the space-time of special relativity, has been derived. It has been shown that the jump in vorticity across a shock of given strength and curvature depends only on the velocity of the medium ahead of the shock.

Numerical Study of Heat Transfer From Pin-Fin Heat Sink Using Steady and Pulsated Impinging Jets

This paper investigates numerically the heat transfer characteristics of confined slot jet impingement on a pin-fin heat sink. A variety of pin-fin heat sinks is investigated, and the resulting enhancement of heat transfer studied. The distribution of heat transfer coefficient on the top surface of the base plate and that along the fin height are examined. Both steady and pulsated jets are studied. It is observed that for a steady jet impingement on a pin-fin heat sink, the effective heat transfer coefficient increases with fin height, leading to a corresponding decrease in base plate temperature for the same heat flux. In the case of pulsated jets, the influence of pulse frequency and the Reynolds number is examined, and their effect on the effective heat transfer coefficient is studied.

Force-free equilibria of magnetized jets

Force-free equilibrium configurations of magnetic-pressure-dominated magnetized supersonic jets confined by slowly varying external pressure are investigated analytically. For the case where internal dissipation mechanisms are active, the lowest-energy field configuration is found to be the superposition of an axisymmetric mode and a helical mode with a wavelength equal to 5 times the jet radius, and the pressure below which the nonaxisymmetric mode becomes energetically favorable is given as 2700 times the product of the 4th power of the magnetic helicity per unit length and the -6th power of the magnetic flux. A model of the total and polarized emission of such a configuration is developed and applied to the extended well-collimated astronomically resolved jet NGC 6251. The model is shown to reproduce significant features such as transverse oscillations of the ridge line, width oscillations and emission knots, the projected magnetic-field configuration, oscillations of the degree of polarization, and the distribution of the Faraday rotation measure.