Transverse jet-cavity interactions with the influence of an impinging shock

For high-speed air breathing engines, fuel injection and subsequent mixing with air is paramount for combustion. The high freestream velocity poses a great challenge to efficient mixing both in macroscale and microscale. Utilising cavities downstream of fuel injection locations, as a means to hold the flow and stabilise the combustion, is one mechanism which has attracted much attention, requiring further research to study the unsteady flow features and interactions occurring within the cavity. In this study we combine the transverse jet injection upstream of a cavity with an impinging shock to see how this interaction influences the cavity flow, since impinging shocks have been shown to enhance mixing of transverse jets. Utilising qualitative and quantitative methods: schlieren, oilflow, PIV, and PSP the induced flowfield is analysed. The impinging shock lifts the shear layer over the cavity and combined with the instabilities generated by the transverse jet creates a highly complicated flowfield with numerous vertical structures. The interaction between the oblique shock and the jet leads to a relatively uniform velocity distribution within the cavity

The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces for hard potential when the solution is a small perturbation of a global equilibrium

Anti-deuteron beam study at J-PARC HEF K1.8 beam line

We performed a $\overline{d}$ beam study at the K1.8 beam line of J-PARC Hadron Experimental Facility. 1.8 GeV/$c$ $\overline{d}$ beam yield was measured to be 0.30 $\pm$ 0.04 counts/spill for 30 GeV 70 $\times 10^{12}$ protons/spill irradiated on a 66 mm thick of gold target with the vertical slit opening widths of 2.2 mm, 5 mm and 5 mm for intermediate focus (IFV), mass slit 1 (MS1) and 2 (MS2), respectively. Corresponding $\overline{p}$ beam yield is roughly estimated to be $\sim$ 0.3 Mcounts/spill for the same slit condition. Then, the $\overline{d}/\overline{p}$ production ratio at extraction angle of 6 degrees is estimated to be $\sim 10^{-6}$. This is the first time measurement of the $\overline{d}$ beam yield and $\overline{d}/\overline{p}$ production ratio at J-PARC. Further beam line tuning may increase the $\overline{d}$ beam yield.Comment: 13 pages, 9 figures, J-PARC HEF K1.8 beam line group technical repor

Optimal time decay of the non cut-off Boltzmann equation in the whole space

In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space \threed_x with \DgE. We use the existence theory of global in time nearby Maxwellian solutions from \cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to determine the large time decay rates for the soft potential Boltzmann equation in the whole space, with or without the angular cut-off assumption \cite{MR677262,MR2847536}. For perturbative initial data, we prove that solutions converge to the global Maxwellian with the optimal large-time decay rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the L^2_\vel(L^r_x)-norm for any $2\leq r\leq \infty$.Comment: 31 pages, final version to appear in KR

Quantitative lower bounds for the full Boltzmann equation, Part I: Periodic boundary conditions

We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some uniform bounds on some hydrodynamic quantities. This lower bound is independent of time and space. When the collision kernel satisfies Grad's cutoff assumption, the lower bound is a global Maxwellian and its asymptotic behavior in velocity is optimal, whereas for non-cutoff collision kernels the lower bound we obtain decreases exponentially but faster than the Maxwellian. Our results cover solutions constructed in a spatially homogeneous setting, as well as small-time or close-to-equilibrium solutions to the full Boltzmann equation in the torus. The constants are explicit and depend on the a priori bounds on the solution.Comment: 37 page