Viscous instability of a compressible round jet

The compressible linear stability equations are derived from the Navier Stokes equations in cylindrical polar coordinates. Numerical solutions for locally parallel flow are found using a direct matrix method. Discretization with compact finite difference is found to have better convergence properties than a Chebyshev spectral method for a round jet test case. The method is validated against previous results and convergence is tested for a range of jet profiles. Finally and en method is used to determine the dominant frequency of a Mach 0.9 jet

Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type

Recently was shown that standard odd and even-dimensional General Relativity can be obtained from a $(2n+1)$-dimensional Chern-Simons Lagrangian invariant under the $B_{2n+1}$ algebra and from a $(2n)$-dimensional Born-Infeld Lagrangian invariant under a subalgebra $\cal{L}^{B_{2n+1}}$ respectively. Very Recently, it was shown that the generalized In\"on\"u-Wigner contraction of the generalized AdS-Maxwell algebras provides Maxwell algebras types $\cal{M}_{m}$ which correspond to the so called $B_{m}$ Lie algebras. In this article we report on a simple model that suggests a mechanism by which standard odd-dimensional General Relativity may emerge as a weak coupling constant limit of a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the Maxwell algebra type $\cal{M}_{2m+1}$, if and only if $m\geq p$. Similarly, we show that standard even-dimensional General Relativity emerges as a weak coupling constant limit of a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under a subalgebra $\cal{L}^{\cal{M}_{2m}}$ of the Maxwell algebra type, if and only if $m\geq p$. It is shown that when $m<p$ this is not possible for a $(2p+1)$-dimensional Chern-Simons Lagrangian invariant under the $\cal{M}_{2m+1}$ and for a $(2p)$-dimensional Born-Infeld type Lagrangian invariant under $\cal{L}^{\cal{M}_{2m}}$ algebra.Comment: 30 pages, accepted for publication in Eur.Phys.J.C. arXiv admin note: text overlap with arXiv:1309.006

Generalized Poincare algebras and Lovelock-Cartan gravity theory

We show that the Lagrangian for Lovelock-Cartan gravity theory can be re-formulated as an action which leads to General Relativity in a certain limit. In odd dimensions the Lagrangian leads to a Chern-Simons theory invariant under the generalized Poincar\'{e} algebra $\mathfrak{B}_{2n+1},$ while in even dimensions the Lagrangian leads to a Born-Infeld theory invariant under a subalgebra of the $\mathfrak{B}_{2n+1}$ algebra. It is also shown that torsion may occur explicitly in the Lagrangian leading to new torsional Lagrangians, which are related to the Chern-Pontryagin character for the $B_{2n+1}$ group.Comment: v2: 18 pages, minor modification in the title, some clarifications in the abstract, introduction and section 2, section 4 has been rewritten, typos corrected, references added. Accepted for publication in Physic letters