1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

纳秒脉冲等离子体合成射流激励器的流场特性分析

采用一台高重频、快上升沿纳秒脉冲电源作为激励源,对典型的双电极合成射流激励器进行放电,通过粒子图像测速法（particle image velocimetry,PIV）测量放电实验中激励器稳定流场特性以及发展速度.分析实验结果发现,随着重复频率的提高,合成射流的平均发展速度也随之增大,1 kHz时的平均速度最高达到28.28 m/s,并在单脉冲能量远低于微秒脉冲的情况下,实现了更快的稳态流场控制,表明高重复频率下,更多次数的脉冲放电可提高激励总能量,有效地弥补纳秒脉冲单脉冲输出能量不足的缺点.而且频率越高,流场发展速度越快,说明高重频工作模式会对输出总能量有补偿作用.      

High-speed imaging of ultrasonic emulsification using a water-gallium system

Aiming at elucidating ultrasonic emulsification mechanisms, the interaction between a single or multiple acoustic cavitation bubbles and gallium droplet interface was investigated using an high-speed imaging technique. To our best knowledge, the moment of emulsification and formation of fine droplets during ultrasound irradiation were observed for the first time. It was found that the detachment of fine gallium droplets occurs from the water-gallium interface during collapse of big cavitation bubbles. The results suggest that the maximum size of cavitation bubble before collapsing is of prime importance for emulsification phenomena. Previous numerical simulation revealed that the collapse of big cavitation bubble is followed by generation of high-velocity liquid jet directed toward the water-gallium interface. Such a jet is assumed to be the prime cause of liquid emulsification. The distance between cavitation bubbles and water-gallium interface was found to slightly affect the emulsification onset. The droplet fragmentation conditions are also discussed in terms of the balance between (1) interfacial and kinetic energies and (2) dynamic and Laplace pressure during droplet formation.     

纵磁作用下真空电弧单阴极斑点等离子体射流三维混合模拟

真空电弧的特性直接受到从阴极斑点喷射出的等离子体射流的影响,对等离子体射流进行数值仿真有助于我们深入了解真空电弧的内部物理机制.然而,磁流体动力学和粒子云网格仿真方法受限于计算精度和计算效率的原因,无法有效地应用于真空电弧等离子体射流仿真模拟.本文开发了一套三维等离子体混合模拟算法,并在此基础上建立了真空电弧单阴极斑点射流仿真模型,模型中将离子作宏粒子考虑,而电子作无质量流体处理,仿真计算了自生电磁场与外施纵向磁场作用下等离子体的分布运动状态.仿真结果表明,单个阴极斑点情况下真空等离子体射流在离开阴极斑点后扩散至极板间,其整体几何形状为圆锥形,离子密度从阴极到阳极快速下降.外施纵向磁场会压缩等离子体,使得等离子体射流径向的扩散减少并且轴线上的离子密度升高.随着外施纵向磁场的增大,其对等离子体射流的压缩效应增强,表现为等离子体射流的扩散角度逐渐减小.此外,外施纵向磁场对等离子体射流的影响也受到电弧电流大小的影响,压缩效应随电弧电流的增加而逐渐减弱.     

多化学组份反应气体流动的Godunov格式

本文将单介质气体流动的Goduoov方法推广到多化学组份气体流动的计算中,建立了多化学组份气体的间断分解公式以及任意四边形网格下的Godunov方法的差分格式,提出了处理自由边界的虚相法,应用第二类网格,计算了超音速射流及其冲击问题的几个算例,并且同实验结果进行了比较。     

Shock tunnel flow visualization using planar laser-induced fluorescence imaging of NO and OH

Temporal sequences of planar laser-induced fluorescence (PLIF) images of several high-speed, transient flowfields created in a reflection-type shock tunnel facility were acquired. In each case, the test gas contained either nitric oxide or the hydroxyl radical, the fluorescent species. The processes of shock reflection from an endwall with a converging nozzle and of underexpanded free jet formation were examined. A comparison was also made between PLIF imaging and shadow photography. The investigation demonstrated some of the capabilities of PLIF imaging diagnostics in complex, transient, hypersonic flowfields, including those with combustion.Nomenclature A spontaneous emission rate - A _las cross sectional area of laser sheet - B laser absorption rate - C _opt constant dependent on optical arrangement, collection efficiency, etc. - D nozzle throat diameter - E _p laser pulse energy - f _J Boltzmann fraction of absorbing state - g spectral convolution of laser and absorption lineshapes - k Boltzmann constant - M _s incident shock Mach number - N noise, root-mean-square signal fluctuation - P static pressure - P ₁ initial pressure of test gas in shock tube - P _a free jet ambient pressure - P _s stagnation pressure - Q electronic quenching rate of excited state - S PLIF signal - t time between shock reflection and image acquisition - T static temperature - T _s stagnation temperature - _a mole fraction of absorbing species     

Le jet libre immergé d'un fluide viscoélastique

Résumé Les auteurs étudient le jet libre laminaire bidimensionnel d'un fluide viscoélastique obéissant à une loi de comportement semiempirique. Ils appliquent la méthode de raccordement des développements asymptotiques afin de déterminer le profil de vitesses à l'intérieur du jet, et l'entraînement du fluide extérieur. Les résultats obtenus illustrent l'influence de l'élasticité sur le champ de vitesse et la présence d'un gradient de pression à l'intérieur du jet. Les lignes de courant obtenues montrent que le fluide externe est aspiré vers l'axe du jet.

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Summary A two-dimensional laminar free jet of a viscoelastic fluid following a semiempiric constitutive equation is studied. The method of matching asymptotic expansions is applied to determine the velocity profiles inside the jet and the entrainment of the external fluid. The results thus obtained highlight the influence of elasticity on the velocity field and the presence of a pressure gradient inside the jet. The streamlines obtained show that the external fluid is sucked in towards the axis of the jet.

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Zusammenfassung Es wird der laminare zweidimensionale Freistrahl einer viskoelastischen Flüssigkeit, die einem halbempirischen Stoffgesetz folgt, untersucht. Asymptotische Entwicklungen werden aneinandergefügt, um die Geschwindigkeitsverteilung in der Strahlströmung und die Ansaugkraft der äußeren Flüssigkeit zu bestimmen. Die erzielten Ergebnisse zeigen den Einfluß der Elastizität auf die Geschwindigkeitsverteilung und das Bestehen eines Druckgradienten innerhalb der Strahlströmung. Die abgeleiteten Stromlinien zeigen weiter, daß die äußere Flüssigkeit zur Strahlachse hin angesaugt wird.

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A ₁;A ₂;A ₃ tenseurs de Rivlin-Ericksen - A constante définie par [27] - D domaine d'écoulement - f ₁();f ₀() fonctions définies par la transformation [20] - I tenseur unité - J nombre adimensionnel [12] - L longueur de référence - M flux total d'impulsion [19]m: µ/ - N _Re nombre de Reynolds - N _w nombre de Weissenberg - n indice de comportement - p pression - s indice de comportement «élastique» - T tenseur des contraintes - U ₀ vitesse de référence - u, v composantes du vecteur vitesse - x, y coordonnées cartésiennes - Y coordonnée de «couche limite» [9] - Z variable complexe - angle entre les parois de la fente - paramètre de perturbation - variable affine [20] - () fonction définie par [2c] - coefficient d'élasticité - fonction de viscosité [2a] - µ indice de consistance - masse volumique - ; fonctions de courant - fonction définie par [2b] - 2ème invariant principal du tenseurA ₁ Avec 7 figures     

The stick-slip problem for a round jet

Summary The stick-slip problem for a round jet studied in Part I gives a good approximation for the swell of a low speed jet when the surface tension is large but it fails when the surface tension is small. In this paper a new stick-slip problem (II) is defined and solved using matched eigenfunction expansions. The new problem reduces to that solved in Part I when the surface tension is large and gives good results in the case of zero and small surface tension.With 18 figures