External front instabilities induced by a shocked particle ring

Abstract

The dispersion of a cylindrical particle ring by a blast or shock wave induces the formation of coherent structures which take the form of particle jets. A blast wave, issuing from the discharge of a planar shock wave at the exit of a conventional shock tube, is generated in the center of a granular medium ring initially confined inside a Hele-Shaw cell. With the present experimental setup, under impulsive acceleration, a solid particle-jet formation is observed in a quasi-two-dimensional configuration. The aim of the present investigation is to observe in detail the formation of very thin perturbations created around the external surface of the dispersed particle layer. By means of fast flow visualization with an appropriate recording window, we focus solely on the first instants during which the external particle ring becomes unstable. We find that the critical area of the destabilization of the external ring surface is constant regardless of the acceleration of the initial layer. Moreover, we observe in detail the external front perturbation wavelength, rendered dimensionless by the initial ring perimeter, and follow its evolution with the initial particle layer acceleration. We report this quantity to be constant regardless of the evolution of the initial particle layer acceleration. Finally, we can reasonably assert that external front perturbations depend solely on the material of the particles.

Aging Wiener-Khinchin Theorem

“…We use Eqs. (4,5,7,8) and by comparison of coefficients of small argument expansion, we show that the time averaged correlation function has a similar expansion, with…”

“…However in recent years there is growing interest in the spectral properties of non-stationary processes, where the theorem is not valid [2][3][4][5][6][7][8][9][10]. In general, there seems no point to discuss and classify spectral properties of all possible non-stationary processes.…”

“…As mentioned in the introduction we have assumed a scaling form of the correlation function Eqs. (5,7), which works in the limit of t, τ → ∞. Information on the correlation function for short times is needed to estimate the very high frequency limit of the spectrum.…”

Dark Matter under the Microscope: Constraining Compact Dark Matter with Caustic Crossing Events

“…In this case, it is the magnification itself that is redistributed across the image plane, owing to the constraint that the total magnification (or observed flux) remains constant when integrating over long periods of time independent of the substructure in the lens plane. When F is large (PBH = 10%), the properties of the power spectrum resemble those of time series that fall in the categories of stationary fractals (Rodríguez 2014), which can be linked to renewal processes (a generalization of a Poissonian process) in which the time intervals between events are not correlated. This is the expected behavior for the separation between events when the distribution of projected microlenses is random.…”

Heterogeneous/particle-laden blast waves

“…A convenient arrangement for visualizing the instabilities that develop when a layer of particles is dispersed by a shock is the 2D Hele-Shaw apparatus used by Rodriguez et al [15,25,26], as well as, more recently, by Xue et al [27]. They attached an air shock tube perpendicular to the center of a Hele-Shaw cell containing a ring of fine powder.…”