58,081 research outputs found
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
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
Hamiltonian formulation of SL(3) Ur-KdV equation
We give a unified view of the relation between the 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
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
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