Rankine-Hugoniot Relations in Relativistic Combustion Waves

As a foundational element describing relativistic reacting waves of relevance to astrophysical phenomena, the Rankine-Hugoniot relations classifying the various propagation modes of detonation and deflagration are analyzed in the relativistic regime, with the results properly degenerating to the non-relativistic and highlyrelativistic limits. The existence of negative-pressure downstream flows is noted for relativistic shocks, which could be of interest in the understanding of the nature of dark energy. Entropy analysis for relativistic shock waves are also performed for relativistic fluids with different equations of state (EoS), denoting the existence of rarefaction shocks in fluids with adiabatic index \Gamma < 1 in their EoS. The analysis further shows that weak detonations and strong deflagrations, which are rare phenomena in terrestrial environments, are expected to exist more commonly in astrophysical systems because of the various endothermic reactions present therein. Additional topics of relevance to astrophysical phenomena are also discussed.Comment: 34 pages, 9 figures, accepted for publication in Ap

Detonative Propagation and Accelerative Expansion of the Crab Nebula Shock Front

The accelerative expansion of the Crab nebula's outer envelope is a mystery in dynamics as a conventional expanding blast wave decelerates when bumping into the surrounding interstellar medium. Here we show that the strong relativistic pulsar wind bumping into its surrounding nebula induces energy-generating processes and initiates a detonation wave that propagates outward to form the current outer edge, namely the shock front, of the nebula. The resulting detonation wave, with a reactive downstream, then provides the needed power to maintain propagation of the shock front. Furthermore, relaxation of the curvature-induced reduction of the propagation velocity from the initial state of formation to the asymptotic, planar state of Chapman-Jouguet propagation explains the observed accelerative expansion. The essential role of detonative propagation in the structure and dynamics of the Crab nebula offers potential richness in incorporating reactive fronts in the description of various astronomical phenomena.Comment: 5 pages, 3 figures, accepted for publication in PR

Hamiltonian formulation of SL(3) Ur-KdV equation

We give a unified view of the relation between the $SL(2)$ KdV, the mKdV, and the Ur-KdV equations through the Fr\'{e}chet derivatives and their inverses. For this we introduce a new procedure of obtaining the Ur-KdV equation, where we require that it has no non-local operators. We extend this method to the $SL(3)$ KdV equation, i.e., Boussinesq(Bsq) equation and obtain the hamiltonian structure of Ur-Bsq equationin a simple form. In particular, we explicitly construct the hamiltonian operator of the Ur-Bsq system which defines the poisson structure of the system, through the Fr\'{e}chet derivative and its inverse.Comment: 12 pages, KHTP-93-03 SNUTP-93-2

Quantum criticality in a double quantum-dot system

We discuss the realization of the quantum-critical non-Fermi liquid state, originally discovered within the two-impurity Kondo model, in double quantum-dot systems. Contrary to the common belief, the corresponding fixed point is robust against particle-hole and various other asymmetries, and is only unstable to charge transfer between the two dots. We propose an experimental set-up where such charge transfer processes are suppressed, allowing a controlled approach to the quantum critical state. We also discuss transport and scaling properties in the vicinity of the critical point.Comment: 4 pages, 3 figs; (v2) final version as publishe

The double-edged sword of jurisdictional entrenchment: Explaining HR professionals’ failed strategic repositioning

To protect themselves against deskilling and obsolescence, professionals must periodically revise their claims to authority and expertise. Although we understand these dynamics in the broader system of professions, we have a less-complete understanding of how this process unfolds in specific organizational contexts. Yet given the ubiquity of embedded professionals, this context is where jurisdictional shifts increasingly take place. Drawing on a comparative ethnographic study of HR professionals in two engineering firms, we introduce the concept of jurisdictional entrenchment to explain the challenges embedded professionals face when they attempt to redefine their jurisdiction. Jurisdictional entrenchment describes a condition in which embedded professionals have accumulated tasks, tactics, and expertise that enable them to make jurisdictional claims in an organization. We show how such entrenchment is a double-edged sword: instrumental to the ability of professionals to withstand challenges to their authority, but detrimental when expertise and skills devalued by the professionals remain in high demand by clients, thus preventing the professionals’ shift to their aspirational jurisdiction. Overall, our study contributes to a better understanding of how embedded professionals renegotiate jurisdictional claims within the constraints of organizational employment