Interaction of the branes in the presence of the background fields: The dynamical, nonintersecting, perpendicular, wrapped-fractional configuration

We shall obtain the interaction of the [Formula: see text]- and [Formula: see text]-branes in the toroidal-orbifold space–time [Formula: see text]. The configuration of the branes is nonintersecting, perpendicular, moving-rotating, wrapped-fractional with background fields. For this, we calculate the bosonic boundary state corresponding to a dynamical fractional-wrapped [Formula: see text]-brane in the presence of the Kalb–Ramond field, a [Formula: see text] gauge potential and an open string tachyon field. The long-range behavior of the interaction amplitude will be extracted.

Interaction of dynamical fractional branes with background fields: Superstring calculations

We compute the boundary state corresponding to a fractional Dp-brane with transverse motion and internal background fields: Kalb–Ramond and a U(1) gauge field. The space–time has the orbifold structure [Formula: see text]. The calculations are in the superstring theory. Using this boundary state we shall obtain the interaction amplitude between two parallel moving fractional Dp-branes. We shall extract behavior of the interaction amplitude for large distances of the branes.

Stability and Bifurcation Analysis of a Forced Cylinder Wake

We present a study on the dynamics of a cylinder wake subjected to forced excitation. Williams et al. (1992) discovered that the spatial symmetry of the excitation plays a crucial role in determining the resulting wake dynamics. Reflection-symmetric forcing was found to affect the Karman wake much more strongly compared to Z2(κ, π) asymmetric forcing. For low forcing amplitudes, the existence of a nonlinear mode interaction mechanism was postulated to explain the observed “beating” phenomenon observed in the wake. Previous work by the authors (Mureithi et al. 2002, 2003) presented general forms of the modal interaction amplitude equations governing the dynamics of the periodically forced wake. In the present work, numerical CFD computations of the forced cylinder wake are presented. It is shown that the experimentally observed wake bifurcations can be reproduced by numerical simulations with reasonable accuracy. The CFD computations show that the forced wake first looses reflection symmetry followed by a bifurcation associated with vortex merging as the forcing amplitude is increased. A bifurcation analysis of a simplified amplitude equation shows that these two transitions are due to a pitchfork bifurcation and a period-doubling bifurcation of mixed mode solutions.