A three-dimensional renormalization group bubble merger model for Rayleigh-Taylor mixing

In this paper we formulate a model for the merger of bubbles at the edge of an unstable acceleration driven (Rayleigh-Taylor) mixing layer. Steady acceleration defines a self-similar mixing process, with a time-dependent inverse cascade of structures of increasing size. The time evolution is itself a renormalization group (RNG) evolution, and so the large time asymptotics define a RNG fixed point. We solve the model introduced here at this fixed point. The model predicts the growth rate of a Rayleigh-Taylor chaotic fluid mixing layer. The model has three main components: the velocity of a single bubble in this unstable flow regime, an envelope velocity, which describes collective excitations in the mixing region, and a merger process, which drives an inverse cascade, with a steady increase of bubble size. The present model differs from an earlier two-dimensional (2-D) merger model in several important ways. Beyond the extension of the model to three dimensions, the present model contains one phenomenological parameter, the variance of the bubble radii at fixed time. The model also predicts several experimental numbers: the bubble mixing rate, alpha(b)=h(b)/Agt(2) approximately 0.05-0.06, the mean bubble radius, and the bubble height separation at the time of merger. From these we also obtain the bubble height to the radius aspect ratio. Using the experimental results of Smeeton and Youngs (AWE Report No. O 35/87, 1987) to fix a value for the radius variance, we determine alpha(b) within the range of experimental uncertainty. We also obtain the experimental values for the bubble height to width aspect ratio in agreement with experimental values. (c) 2002 American Institute of Physics.     

Laser-induced bubble formation and collapse in a nonlinear Rayleigh-Taylor unstable interface in a thin layer of molten metal

Bubble formation and bubble collapse zones in a laser-induced nonlinear Rayleigh-Taylor (R-T) instability were shown to follow the contours of a series of R-T shock-fronts generated on an irregular planar (terrace-like) target surface. Bubble formation occurs in the regime of target planar vaporization. Spatial variation of the bubble density distribution, the bubble size, and the bubble-bubble distance, as a function of distance from the shock front envelope, were determined. Bubble collapse occurs in the regime of planar-to-volume boiling transition and proceeds by the so-called “chain reaction” collapse mechanism inside a 2D bubble array. The contours of bubble generation and of bubble collapse were simulated by using the analytical model of Ott with variable phase and variable amplitude of R-T modes.     

Magnetic field generation in Rayleigh-Taylor unstable inertial confinement fusion plasmas

Rayleigh-Taylor instabilities (RTI) in inertial confinement fusion implosions are expected to generate magnetic fields. A Hall-MHD model is used to study the field generation by 2D single-mode and multimode RTI in a stratified two-fluid plasma. Self-generated magnetic fields are predicted and these fields grow as the RTI progresses via the ?n(e)×?T(e) term in the generalized Ohm's law. Scaling studies are performed to determine the growth of the self-generated magnetic field as a function of density, acceleration, Atwood number, and perturbation wavelength.     

任意Atwood数Rayleigh-Taylor和 Richtmyer-Meshkov 不稳定性气泡速度研究

本文将Layzer气泡模型推广到任意界面Atwood数情形,得到了自洽的微分方程组.该模型描述了气泡从早期的指数增长阶段到气 泡以渐近速度上升的非线性阶段的发展过程,给出了Rayleigh-Taylor(RT)和Richtmyer-Meshkov(RM)不稳定性的二维和 三维气泡速度渐近解,还求出了二维和三维RT不稳定性气泡顶点附近速度的解析解.     

Stable and unstable vortices in multicomponent bose-einstein condensates

We study the stability and dynamics of vortices in two-species condensates as prepared in the recent JILA experiment [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)]. We find that of the two possible configurations, in which one species has vorticity m = 1 and the other one has m = 0, only one is linearly stable, which agrees with the experimental results. However, it is found that in the unstable case the vortex is not destroyed by the instability, but may be transferred from one species to the other or display complex spatiotemporal dynamics.     

A model for bimetallic interfaces

We have developed a theoretical model by considering the charge rearrangement in the region of a bimetallic interface. By using the density functional formalism we have calculated variationally interfacial energies due to pairs of semi-infinite jellia in contact. We infer that the electronic interaction has an important role in the bimetallic adhesion.     

Low-density expanison for unstable interactions and a model of crystallization

For a class of unstable pair interactions in classical continuous systems of identical particles the high-temperature thermodynamic behavior is shown to be normal by extending low-density theorems for the correlation functions. In an example we prove a transition between a translation-invariant phase at high temperatures and low densities and solid with long-range oder at low temperatures. The transition is catastropic in the sense that it is accompanied by the divergence of thermodynamic quantities. We also exhibit counterexamples of unstable interactions in any dimension which do not give rise to a low-temperature catastrophe.     

Monoenergetic electron parameters in a spheroid bubble model

A reliable analytical expression for the potential of plasma waves with phase velocities near the speed of light is derived.The presented spheroid cavity model is more consistent than the previous spherical and ellipsoidal models and it explains the mono-energetic electron trajectory more accurately,especially at the relativistic region.The maximum energy of electrons is calculated and it is shown that the maximum energy of the spheroid model is less than that of the spherical model.The electron energy spectrum is also calculated and it is found that the energy distribution ratio of electrons △E/E for the spheroid model under the conditions reported here is half that of the spherical model and it is in good agreement with the experimental value in the same conditions.As a result,the quasi-mono-energetic electron output beam interacting with the laser plasma can be more appropriately described with this model.     

Rayleigh-Taylor instability for immiscible fluids of arbitrary viscosities: a magnetic levitation investigation and theoretical model

A magnetic field gradient was used to draw down a low density paramagnetic fluid below a more dense fluid in a Hele-Shaw cell. On turning off the field a Rayleigh-Taylor instability was observed in situ, and the growth of the most unstable wave vector was measured versus time. A theory for the instability that permits different viscosities for two immiscible fluids was developed, and good agreement was found with the experimental results. The technique of magnetic levitation promises to broaden significantly the accessible parameter space of gravitational interfacial instability experiments.     

气泡室中"胚胎"气泡成长为可见气泡的模型建立及初步的理论计算

建立了气泡室中“胚胎”气泡成长为可见气泡模型.初步计算表明,“胚胎”气泡在成长为可见气泡的过程中,它不仅要从其周围吸收热量,而且还有分子进入到它的里面.理论上可以合理解释能量相同的中子和质子入射到气泡室所产生的径迹上的气泡半径是不同的,中子在气泡室中产生的径迹细长,而质子在气泡室中产生的径迹粗短;可以合理解释在同一径迹上某个区域内可以有半径大小相差不多的气泡存在;也可以合理解释电荷数较多的入射粒子较能量相同但电荷数不同的入射粒子,其在气泡室中径迹上气泡的半径要大;理论上预测入射粒子刚进入气泡室时,其径迹上有大气泡破裂现象发生.通过选择合适的工作物质可以提高气泡室的灵敏度和探测效率.     

Stable and unstable classical solutions in an effective gauge theory for low energy mesons

We study the stability of two related classical solutions in an effective gauge theory, which correctly describes the properties of π and ρ mesons at low energies. The first solution (sphaleron), which excites only the ρ field, with baryon numberB=0 and energyE≈1.5 GeV is unstable. The second (Skyrmion), which excites both the π and ρ fields, withB=1 andE≈1.0 GeV is perhaps stable locally. We show how to make this Skurmion absolutely stable without raising its energy too much, both of which properties are desirable for identification with the nucleon. We comment on the potential of heavy ion collision experiments to study configuration space. The Skyrmion solution may also have some relevance for the electroweak interactions (nowE≈10 TeV).     

Stability of hierarchical interfaces in a random field model

We study a hierarchical model for interfaces in a random-field ferromagnet. We prove that in dimensionD>3, at low temperatures and for weak disorder, such interfaces are rigid. Our proof uses renormalization group transformations for stochastic sequences.     

Stable and unstable manifolds of the Hénon mapping

By using a parametric representation of the stable and unstable manifolds, we prove that for some given values of the parameter (in particular in the case first investigated by Hénon) the Hénon mapping has a transversal homoclinic orbit.