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

Suspended liquid particle disturbance on laser-induced blast wave and low density distribution

The impurity effect of suspended liquid particles on the laser-induced gas breakdown was experimentally investigated in quiescent gas. The focus of this study is the investigation of the influence of the impurities on the shock wave structure as well as the low density distribution. A 532 nm Nd:YAG laser beam with an 188 mJ/pulse was focused on the chamber filled with suspended liquid particles 0.9 ± 0.63 μm in diameter. Several shock waves are generated by multiple gas breakdowns along the beam path in the breakdown with particles. Four types of shock wave structures can be observed: (1) the dual blast waves with a similar shock radius, (2) the dual blast waves with a large shock radius at the lower breakdown, (3) the dual blast waves with a large shock radius at the upper breakdown, and (4) the triple blast waves. The independent blast waves interact with each other and enhance the shock strength behind the shock front in the lateral direction. The triple blast waves lead to the strongest shock wave in all cases. The shock wave front that propagates toward the opposite laser focal spot impinges on one another, and thereafter a transmitted shock wave (TSW) appears. The TSW interacts with the low density core called a kernel; the kernel then longitudinally expands quickly due to a Richtmyer-Meshkov-like instability. The laser-particle interaction causes an increase in the kernel volume which is approximately five times as large as that in the gas breakdown without particles. In addition, the laser-particle interaction can improve the laser energy efficiency

The relationship between CA/C ratio and individual differences in dynamic accommodative responses while viewing stereoscopic images

The oculomotor synergy as expressed by the CA/C and AC/A ratios was investigated to examine its influence on our previous observation that whereas convergence responses to stereoscopic images are generally stable, some individuals exhibit significant accommodative overshoot. Using a modified video refraction unit while viewing a stereoscopic LCD, accommodative and convergence responses to balanced and unbalanced vergence and focal stimuli (BVFS and UBVFS) were measured. Accommodative overshoot of at least 0.3 D was found in 3 out of 8 subjects for UBVFS. The accommodative response differential (RD) was taken to be the difference between the initial response and the subsequent mean static steady-state response. Without overshoot, RD was quantified by finding the initial response component. A mean RD of 0.11 +/- 0.27 D was found for the 1.0 D step UBVFS condition. The mean RD for the BVFS was 0.00 +/- 0.17 D. There was a significant positive correlation between CA/C ratio and RD (r = +0.75, n = 8, p <0.05) for only UBVFS. We propose that inter-subject variation in RD is influenced by the CA/C ratio as follows: an initial convergence response, induced by disparity of the image, generates convergence-driven accommodation commensurate with the CA/C ratio; the associated transient defocus subsequently decays to a balanced position between defocus-induced and convergence-induced accommodations

Dynamic measurement of accommodative responses while viewing stereoscopic images

Using video refraction accommodative and convergence dynamic responses were measured to stepped changes in convergence stimuli with unchanged accommodative stimuli (conflicting stereoscopic image) and compared with responses to non-conflicting target stimuli. Three targets were used that varied in their spatial frequency components. An accommodative transient overshoot was evident in four out of seven subjects for only conflicting stimuli. One showed accommodative and convergence oscillation probably due to difficulty in fusing the stereoscopic target when it had a higher spatial component, however, this oscillation diminished when the target was spatial low-pass filtered. We hypothesise that transient responses to step stimuli is initiated by convergence-driven accommodation and subsequently followed by slower fine-control of accommodation modulated by the amount of blur. Inter-subject differences in convergence-driven accommodation may also be a factor to consider. For stereoscopic stimuli, it is proposed that the increase in blur immediately after the onset of the accommodative response inhibits cessation of the response

On the speed of approach to equilibrium for a collisionless gas

We investigate the speed of approach to Maxwellian equilibrium for a collisionless gas enclosed in a vessel whose wall are kept at a uniform, constant temperature, assuming diffuse reflection of gas molecules on the vessel wall. We establish lower bounds for potential decay rates assuming uniform $L^p$ bounds on the initial distribution function. We also obtain a decay estimate in the spherically symmetric case. We discuss with particular care the influence of low-speed particles on thermalization by the wall.Comment: 22 pages, 1 figure; submitted to Kinetic and Related Model

Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel (Grad cut-off assumption). For this purpose we revisit the Kaniel--Shinbrot iteration technique to present an elementary proof of existence and uniqueness results that includes large data near a local Maxwellian regime with possibly infinite initial mass. We study the propagation of regularity using a recent estimate for the positive collision operator given in [3], by E. Carneiro and the authors, that permits to study such propagation without additional conditions on the collision kernel. Finally, an $L^{p}$-stability result (with $1\leq p\leq\infty$) is presented assuming the aforementioned condition.Comment: 19 page

Update of High Resolution (e,e'K^+) Hypernuclear Spectroscopy at Jefferson Lab's Hall A

Updated results of the experiment E94-107 hypernuclear spectroscopy in Hall A of the Thomas Jefferson National Accelerator Facility (Jefferson Lab), are presented. The experiment provides high resolution spectra of excitation energy for 12B_\Lambda, 16N_\Lambda, and 9Li_\Lambda hypernuclei obtained by electroproduction of strangeness. A new theoretical calculation for 12B_\Lambda, final results for 16N_\Lambda, and discussion of the preliminary results of 9Li_\Lambda are reported.Comment: 8 pages, 5 figures, submitted to the proceedings of Hyp-X Conferenc

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