Propagation Speeds Of Perturbations Research Articles

Forced oscillation phenomenon of normal/oblique shock trains in a rectangular duct at Mach 2 and 3

The forced shock train oscillation is a common phenomenon in a practical working scramjet isolator. To evaluate the similarities and differences between the forced normal shock train oscillation and the forced oblique shock train oscillation, experiments were conducted in a rectangular duct at Mach 2 and 3. The normal/oblique shock trains were forced to oscillate for different back-pressure levels by changing the mechanical throttling ratio. High-frequency pressure measurements were mainly utilized for data acquisition and analysis. The frequency contents, the intermittency characteristics and the perturbation propagation of forced shock train oscillations were investigated in this work. Experimental results illustrate that the forced oscillation at Mach 3 is a composite pattern, which is dominated by the excited frequency and coupled with the inherent unsteadiness. This phenomenon is not obvious for the forced oscillation at Mach 2. For the forced oscillations at Mach 2 and 3, the maximum zero-crossing frequency is close to the downstream excitation frequency, and the whole intermittent region almost holds this value, which is very different from the self-excited oscillation pattern. By using the cross-spectral analysis, the frequency-dependent correlation was evaluated. It shows that the excitations and its harmonic contents can propagate upstream to affect the intermittent region and its downstream. Besides the excitation frequency and its harmonic contents, low-frequency contents (tens to more than a hundred Hz) can propagate nearby the separation region, and the propagation to downstream the separation bubble is very weak. Considering the time-lag between different transducers, the propagation speed of perturbations can be obtained. It implies that the propagation speed is independent of the magnitude of the back-pressure, but affected by the velocity of the incoming flow. Specifically, the higher the freestream Mach number is, the greater the propagation speed will be.

Stability of relativistic stars with scalar hairs

We study the stability of relativistic stars in scalar-tensor theories with a nonminimal coupling of the form $F(\phi)R$, where $F$ depends on a scalar field $\phi$ and $R$ is the Ricci scalar. On a spherically symmetric and static background, we incorporate a perfect fluid minimally coupled to gravity as a form of the Schutz-Sorkin action. The odd-parity perturbation for the multipoles $l \geq 2$ is ghost-free under the condition $F(\phi)>0$, with the speed of gravity equivalent to that of light. For even-parity perturbations with $l \geq 2$, there are three propagating degrees of freedom arising from the perfect-fluid, scalar-field, and gravity sectors. For $l=0, 1$, the dynamical degrees of freedom reduce to two modes. We derive no-ghost conditions and the propagation speeds of these perturbations and apply them to concrete theories of hairy relativistic stars with $F(\phi)>0$. As long as the perfect fluid satisfies a weak energy condition with a positive propagation speed squared $c_m^2$, there are neither ghost nor Laplacian instabilities for theories of spontaneous scalarization and Brans-Dicke (BD) theories with a BD parameter $\omega_{\rm BD}>-3/2$ (including $f(R)$ gravity). In these theories, provided $0<c_m^2 \le 1$, we show that all the propagation speeds of even-parity perturbations are sub-luminal inside the star, while the speeds of gravity outside the star are equivalent to that of light.

Viable cosmology in bimetric theory

We study cosmological perturbations in bimetric theory with two fluids each of which is coupled to one of the two metrics. Focusing on a healthy branch of background solutions, we clarify the stability of the cosmological perturbations. For this purpose, we extend the condition for the absence of the so-called Higuchi ghost, and show that the condition is guaranteed to be satisfied on the healthy branch. We also calculate the squared propagation speeds of perturbations and derive the conditions for the absence of the gradient instability. To avoid the gradient instability, we find that the model parameters are weakly constrained.