地震纵横波时差耦合作用的斜坡崩滑效应研究

在燃烧室入口来流为Ma=2.64、T0=1483K、P0＝1.65MPa、T=724K、P=76.3kPa条件下,采用高速摄影和连续激光高速纹影对等截面型开窗燃烧室内氢气射流自燃过程、火花塞点燃氢气过程和引导氢气火焰点燃煤油过程进行了观测,获得了燃烧室内着火过程中火焰和流场波系结构的动态演化过程;观察到了初始火焰区首先起始于燃烧室下游,并逆流传播实现发动机着火的过程;分析表明燃料能否着火、以及着火位置与燃料着火时间、燃烧室流速和火焰稳定器安装情况相关,多火焰稳定区延长了燃料驻留时间,使燃料更容易着火。 关键词 超燃冲压发动机,点火过程,火焰传播,火焰稳定器     

Level set method for numerical simulation of a cavitation bubble,its growth,collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier–Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving interface is captured by the level set function, and the interface velocity is resolved by “one-side” velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the “shock wave”-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating. The project supported by the National Natural Science Foundation of China (10272032 and 10672043). The English text was polished by Keren Wang.     

An infinite series involving inverse tan

In this note we introduce an infinite series which represents an interesting challenge for students with the relevant background.     

Collapsing of connected sums and the eigenvalues of the Laplacian

We study the behavior of the eigenvalues of the Laplacian acting on functions when one side of a connected sum of two closed Riemannian manifolds collapses to a point. We prove that the eigenvalues converge to those of the limit space, by using the method of Anné and Colbois. From this, we obtain a gluing theorem for the eigenvalues.     

Interpreting the influence of liquid temperature on cavitation collapse intensity through bubble dynamic analysis

The violent collapse of inertial bubbles generates high temperature inside and emits strong impulsive pressure. Previous tests on sonoluminescence and cavitation erosion showed that the influence of liquid temperature on these two parameters is different. In this paper, we conducted a bubble dynamic analysis to explore the mechanism of the temperature effect and account for the above difference. The results show that the increase of vapor at higher liquid temperatures changes both the external compression pressure and the internal cushion and is responsible for the variation of bubble collapse intensity. The different trends of the collapsing temperature and emitted sound pressure are caused by the energy distribution during the bubble collapse. Moreover, a series of simulations are conducted to establish the distribution map of the optimum liquid temperature where the collapse intensity is maximized. The relationship between the collapse intensity and the radial dynamics of the bubble is discussed and the reliable indicator is identified. This study provides a clear picture of how the thermodynamic process changes cavitation aggressiveness and enriches the understanding of this complex thermal-hydrodynamic phenomenon.     

Linear colorings of simplicial complexes and collapsing

A vertex coloring of a simplicial complex Δ is called a linear coloring if it satisfies the property that for every pair of facets (F₁,F₂) of Δ, there exists no pair of vertices (v₁,v₂) with the same color such that v₁∈F₁?F₂ and v₂∈F₂?F₁. The linear chromatic numberlchr(Δ) of Δ is defined as the minimum integer k such that Δ has a linear coloring with k colors. We show that if Δ is a simplicial complex with lchr(Δ)=k, then it has a subcomplex Δ^′ with k vertices such that Δ is simple homotopy equivalent to Δ^′. As a corollary, we obtain that lchr(Δ)?Homdim(Δ)+2. We also show in the case of linearly colored simplicial complexes, the usual assignment of a simplicial complex to a multicomplex has an inverse. Finally, we show that the chromatic number of a simple graph is bounded from above by the linear chromatic number of its neighborhood complex.     

How to develop Proof-Theoretic Ordinal Functions on the basis of admissible ordinals

In ordinal analysis of impredicative theories so-called collapsing functions are of central importance. Unfortunately, the definition procedure of these functions makes essential use of uncountable cardinals whereas the notation system that they call into being corresponds to a recursive ordinal. It has long been claimed that, instead, one should manage to develop such functions directly on the basis of admissible ordinals. This paper is meant to show how this can be done. Interpreting the collapsing functions as operating directly on admissible sets also renders a new and perspicuous approach to well-ordering proofs possible. MSC: 03F15, 03F35.     

Limited damage of tissue mimic caused by a collapsing bubble under low-frequency ultrasound exposure

In this study, we investigated the bubble induced serious damage to tissue mimic exposed to 27-kHz ultrasound. The initial bubble radius ranged from 80 to 100 μm, which corresponded approximately to the experimentally-evaluated resonant radius of the given ultrasound frequency. The tissue mimic consisted of 10 wt% gelatine gel covered with cultured canine kidney epithelial cells. The collapsing bubble behaviour during the ultrasound exposure with negative peak pressures of several hundred kPa was captured by a high-speed camera system. After ultrasound exposure, a cell viability test was conducted based on microscopic bright-field images and fluorescence images for living and dead cells. In the viability test, cells played a role in indicating the damaged area. The bubble oscillations killed the cells, and on occasion detached layers of cultured cells from the gel. The damaged area was comparable or slightly larger than the initial bubble size, and smaller than the maximum bubble size. We concluded that only a small area in close proximity to the bubble could be damaged even above transient cavitation threshold.