Transmitted sound field due to an impulsive line acoustic source bounded by a plate followed by a vortex sheet

The propagation of sound due to a line acoustic source in the moving stream across a semiinfinite vortex sheet which trails from a rigid plate is examined in a linear theory for the subsonic case. A solution for the transmitted sound field is obtained with the aid of multiple integral transforms and the Wiener-Hopf technique for both the steady state (time harmonic) and initial value (impulsive source) situations. The contour of inverse transform and hence the decomposition of the functions are determined through causality and radiation conditions. The solution obtained satisfies causality and the full Kutta conditions. The transmitted sound field is composed of two waves in both the stady state and initial value problems. One is the wave scattered from the edge of the plate which is associated with the bow wave and the instability wave. These waves exist in the downstream sectors. The other is the wave transmitted through the vortex sheet which is also associated with the instability wave. Regional divisions of the transmitted sound field are identified

The MHD Kelvin-Helmholtz Instability III: The Role of Sheared Magnetic Field in Planar Flows

We have carried out simulations of the nonlinear evolution of the magnetohydrodynamic (MHD) Kelvin-Helmholtz (KH) instability for compressible fluids in $2\frac{1}{2}$-dimensions, extending our previous work by Frank et al (1996) and Jones \etal (1997). In the present work we have simulated flows in the x-y plane in which a ``sheared'' magnetic field of uniform strength ``smoothly'' rotates across a thin velocity shear layer from the z direction to the x direction, aligned with the flow field. We focus on dynamical evolution of fluid features, kinetic energy dissipation, and mixing of the fluid between the two layers, considering their dependence on magnetic field strength for this geometry. The introduction of magnetic shear can allow a Cat's Eye-like vortex to form, even when the field is stronger than the nominal linear instability limit given above. For strong fields that vortex is asymmetric with respect to the preliminary shear layer, however, so the subsequent dissipation is enhanced over the uniform field cases of comparable field strength. In fact, so long as the magnetic field achieves some level of dynamical importance during an eddy turnover time, the asymmetries introduced through the magnetic shear will increase flow complexity, and, with that, dissipation and mixing. The degree of the fluid mixing between the two layers is strongly influenced by the magnetic field strength. Mixing of the fluid is most effective when the vortex is disrupted by magnetic tension during transient reconnection, through local chaotic behavior that follows.Comment: 14 pages including 9 figures (4 figures in degraded jpg format), full paper with original quality figures available via anonymous ftp at ftp://canopus.chungnam.ac.kr/ryu/mhdkh2d.uu, to appear in The Astrophysical Journa

The Magnetohydrodynamic Kelvin-Helmholtz Instability: A Three-Dimensional Study of Nonlinear Evolution

We investigate through high resolution 3D simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. We confirm in 3D flows the conclusion from our 2D work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in 3D by this work, because it shows how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of two over the 2D effect. If, by these developments, the Alfv\'en Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memory of the original shear. For our flow configurations the regime in 3D for such reorganization is $4\lesssim M_{Ax} \lesssim 50$, expressed in terms of the Alfv\'en Mach number of the original velocity transition and the initial Alfv\'en speed projected to the flow plan. For weaker fields the instability remains essentially hydrodynamic in early stages, and the Cat's Eye is destroyed by the hydrodynamic secondary instabilities of a 3D nature. Then, the flows evolve into chaotic structures that approach decaying isotropic turbulence. In this stage, there is considerable enhancement to the magnetic energy due to stretching, twisting, and turbulent amplification, which is retained long afterwards. The magnetic energy eventually catches up to the kinetic energy, and the nature of flows become magnetohydrodynamic.Comment: 11 pages, 12 figures in degraded jpg format (2 in color), paper with original quality figures available via ftp at ftp://ftp.msi.umn.edu/pub/users/twj/mhdkh3dd.ps.gz or ftp://canopus.chungnam.ac.kr/ryu/mhdkh3dd.ps.gz, to appear in The Astrophysical Journa

Slowly modulated oscillations in nonlinear diffusion processes

It is shown here that certain systems of nonlinear (parabolic) reaction-diffusion equations have solutions which are approximated by oscillatory functions in the form R(ξ - cτ)P(t^*) where P(t^*) represents a sinusoidal oscillation on a fast time scale t* and R(ξ - cτ) represents a slowly-varying modulating amplitude on slow space (ξ) and slow time (τ) scales. Such solutions describe phenomena in chemical reactors, chemical and biological reactions, and in other media where a stable oscillation at each point (or site) undergoes a slow amplitude change due to diffusion

Discovery and Assessment of New Target Sites for Anti-HIV Therapies

Human immunodeficiency virus (HIV) infects cells by endocytosis and takes over parts of the cell’s reaction pathways in order to reproduce itself and spread the infection. One such pathway taken over by HIV becomes the inflammatory pathway which uses Nuclear Factor κB (NF-κB) as the principal transcription factor. Therefore, knocking out the NF-κB pathway would prevent HIV from reproducing itself. In this report, our goal is to produce a simple model for this pathway with which we can identify potential targets for anti-HIV therapies and test out various hypotheses. We present a very simple model with four coupled first-order ODEs and see what happens if we treat IκK concentration as a parameter that can be controlled (by some unspecified means). In Section 3, we augment this model to account for activation and deactivation of IκK, which is controlled (again, by some unspecified means) by TNF

On the multispacecraft determination of periodic surface wave phase speeds and wavelengths

Observations of surface waves on the magnetopause indicate a wide range of phase velocities and wavelengths. Their multispacecraft analysis allows a more precise determination of wave characteristics than ever before and reveal shortcomings of approximations to the phase speed that take a predetermined fraction of the magnetosheath speed or the average flow velocity in the boundary layer. We show that time lags between two or more spacecraft can give a qualitative upper estimate, and we confirm the unreliability of flow approximations often used by analyzing a few cases. Using two‐point distant magnetic field observations and spectral analysis of the tailward magnetic field component, we propose an alternative method to estimate the wavelength and phase speed at a single spacecraft from a statistical fit to the data at the other site