Convergence of the Self-Dual Ginzburg-Landau Gradient Flow

We prove convergence of the gradient flow of the Ginzburg-Landau energy functional on a Riemann surface in the self-dual Bogomolny case, in Coulomb gauge. The proof is direct and makes use of the associated nonlinear first order differential operators (the Bogomolny operators). One aim is to illustrate that the Bogomolny structure, which is known to be of great utility in the static elliptic case, can also be used effectively in evolution problems. We also identify the minimizers and minimum value of the energy when the Bogomolny bound is not achieved (below the Bradlow limit).     

Formation of the electron-hole droplet cloud in germanium

We describe luminescence imaging experiments that probe the nature of the phonon wind which transports electron-hole droplets in Ge. The participation of non-equilibrium phonons emanating near the excitation region is supported by: (a) sharp features in the droplet spatial distribution (b) a dependence of the average cloud density on the excitation photon energy, and (c) a rapid initial buildup of the cloud.     

Optimization of acoustic parameters for ultrasonic separation of emulsions with different physical properties

Ultrasound is an emerging and promising method for demulsification, which is highly affected by acoustic parameters and emulsion properties. Herein, a series of microscopic and dehydration experiments are carried out to investigate the parameter optimization of ultrasonic separation. The results show that the optimal acoustic parameters highly depend on the emulsion properties. For low frequency ultrasonic standing waves (USWs), mechanical vibrations not only facilitate droplet collision and coalescence, but also disperse the surfactant absorbed on the interface to decrease the interfacial strength. Therefore, low frequency ultrasound is suitable for separating emulsions with high viscosity and high interfacial strength. Increasing the energy density to produce moderate cavitation can increase demulsification efficiency. However, excessive cavitation results in secondary emulsification. In high frequency USWs, the droplets migrate directionally and form bandings, thereby promoting droplet coalescence. Therefore, high frequency ultrasound is favorable for separating emulsions with low dispersed phase content and small droplet size. Increasing the energy density can accelerate the aggregation of droplets, however, excessive energy density causes acoustic streaming that disturbs the aggregated droplets, resulting in reduced demulsification efficiency. This work presents rules for acoustic parameter optimization, further advancing industrial applications of ultrasonic separation.     

A Droplet Within the Spherical Model

Various substances in the liquid state tend to form droplets. In this paper the shape of such droplets is investigated within the spherical model of a lattice gas. We show that in this case the droplet boundary is always diffuse, as opposed to sharp, and find the corresponding density profiles (droplet shapes). The spatial location of a droplet is not fixed in translation-invariant models, hence, their natural states are described by mixed phases. To obtain pure macroscopic states (which describe localized droplets) one can use generalized quasi-averages. Conventional quasi-averaging deforms droplets and, hence, can not be used for this purpose. On the contrary, application of the generalized method of quasi-averages to the spherical model yields density profiles which do not depend on the magnitude of the applied external field.     

Collective nature of the reentrant integer quantum Hall states in the second Landau level

We report an unexpected sharp peak in the temperature dependence of the magnetoresistance of the reentrant integer quantum Hall states in the second Landau level. This peak defines the onset temperature of these states. We find that in different spin branches the onset temperatures of the reentrant states scale with the Coulomb energy. This scaling provides direct evidence that Coulomb interactions play an important role in the formation of these reentrant states evincing their collective nature.     

Small-angle light scattering symmetry breaking in polymer-dispersed liquid crystal films with inhomogeneous electrically controlled interface anchoring

We have described the method of analyzing and reporting on the results of calculation of the small-angle structure of radiation scattered by a polymer-dispersed liquid crystal film with electrically controlled interfacial anchoring. The method is based on the interference approximation of the wave scattering theory and the hard disk model. Scattering from an individual liquid crystal droplet has been described using the anomalous diffraction approximation extended to the case of droplets with uniform and nonuniform interface anchoring at the droplet–polymer boundary. The director field structure in an individual droplet is determined from the solution of the problem of minimizing the volume density of the free energy. The electrooptical effect of symmetry breaking in the angular distribution of scattered radiation has been analyzed. This effect means that the intensities of radiation scattered within angles +θ _s and–θ _s relative to the direction of illumination in the scattering plane can be different. The effect is of the interference origin and is associated with asymmetry of the phase shift of the wavefront of an incident wave from individual parts of the droplet, which appears due to asymmetry of the director field structure in the droplet, caused by nonuniform anchoring of liquid crystal molecules with the polymer on its surface. This effect is analyzed in the case of normal illumination of the film depending on the interfacial anchoring at the liquid crystal–polymer interface, the orientation of the optical axes of droplets, their concentration, sizes, anisometry, and polydispersity.     

Correlations to predict droplet size in ultrasonic atomisation.

In conventional two fluid nozzles, the high velocity air imparts its energy to the liquid and disrupts the liquid sheet into droplets. If the energy for liquid sheet fragmentation can be supplied by the use of ultrasonic energy, finer droplets with high sphericity and uniform size distribution can be achieved. The other advantage of ultrasound induced atomisation process is the lower momentum associated with ejected droplets compared to the momentum carried by the droplets formed using conventional nozzles. This has advantage in coating and granulation processes. An ultrasonic probe sonicator was designed with a facility for liquid feed arrangement and was used to atomise the liquid into droplets. An ingenious method of droplet measurement was attempted by capturing the droplets on a filter paper (size variation with regard to wicking was uniform in all cases) and these are subjected to image analysis to obtain the droplet sizes. This procedure was evaluated by high-speed photography of droplets ejected at one particular experimental condition and these were image analysed. The correlations proposed in the literature to predict droplet sizes using ultrasound do not take into account all the relevant parameters. In this work, a truly universal correlation is proposed which accounts for the effects of physico-chemical properties of the liquid (flow rate, viscosity, density and surface tension), and ultrasonic properties like amplitude, frequency and the area of vibrating surface. The significant contribution of this work is to define dimensionless numbers incorporating ultrasonic parameters, taking cue from the conventional numbers that define the significance of different forces involved in droplet formation. The universal correlations proposed are robust and can be used for designing ultrasonic atomisers for different applications. Among the correlations proposed here, those ones that are based on the dimensionless numbers and Davies approach predict droplet sizes within acceptable limits of deviation. Also, an empirical correlation from experimental data has been proposed in this work.     

Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges

We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.     

Coherent transmission and angular structure of light scattering by monolayer films of polymer dispersed liquid crystals with inhomogeneous boundary conditions

We consider monolayer polymer films with oriented droplets of a nematic liquid crystal (LC). Relations for the coherent transmission coefficients of a layer of oriented ellipsoidal droplets and for the intensity of light scattered by monolayers of spherical and spheroidal droplets have been obtained. The amplitude-phase screen model and the interference approximation of the theory of multiple wave scattering have been used. To describe light scattering by an individual ellipsoidal droplet with inhomogeneous surface binding, we have developed an anomalous diffraction approximation. For monolayers of spherical LC droplets, the coherent scattering coefficients and the angular scattering structure have been analyzed. The internal structure of nematic droplets have been calculated by the relaxation method based on the solution of the minimization problem of the free energy volume density. We have studied basic regular features of light scattering by a monolayer with homogeneous and inhomogeneous boundary conditions at the LC-polymer interface. We show that, for films that contain droplets with inhomogeneous boundary conditions of the tangentially normal type, the angular structure of the scattered light is asymmetric with respect to the polar scattering angle.     

纳米结构表面上部分润湿液滴合并诱导弹跳的理论研究

部分润湿液滴是适宜纳米结构表面上滴状冷凝传热的主要载体,研究纳米结构参数与部分润湿液滴合并弹跳之间的关系有重要意义,本文依据冷凝液滴生长过程中能量增加最小的原理来判断其是否为部分润湿状态,并根据液滴合并前后的体积和界面自由能守恒,确定了合并液滴的初始形状,进而对合并液滴变形过程的动力学方程进行了求解,结果表明:部分润湿冷凝液滴仅在纳米柱具有一定高度、直径间距比较大的表面上形成,而当纳米柱高度过低、直径间距比小于0.1时则形成完全润湿的冷凝液滴;液滴合并后能否弹跳与纳米结构参数紧密相关,仅在纳米柱较高、直径间距比适宜的表面上,部分润湿液滴合并后才能诱发弹跳;液滴尺度及待合并液滴间的尺度比对合并弹跳也有重要影响;多个部分润湿液滴合并后由于具有更多的过剩界面自由能而比两个液滴合并更容易诱发弹跳,本模型对纳米结构表面上冷凝液滴是否合并诱发弹跳的计算结果与绝大部分实测结果相一致,准确率达到95%。     

Generalized Ginzburg-Landau functional calculations of the structure and energy of the coherent interphase boundaries between austenite and martensite in iron

The earlier-developed methods and experimental data on the phonon spectra and thermodynamics of fcc and bcc iron are used to construct a generalized Ginzburg-Landau functional for microscopic investigations of the austenite-martensite phase transformations in iron. This functional is used to calculate the structure and properties of a plane austenite-martensite interface for arbitrary orientations of this interface at various temperatures. The transformation parameter profiles in the interface region are calculated. The interface width is found to substantially exceed the interatomic distances. The interfacial surface energy is 500?C800 erg/cm², depends strongly on the orientation, and has a sharp maximum when the interface is parallel to a close-packed plane.     

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.     

Stability of cellulose lyotropic liquid crystal emulsions

We studied a new kind of W/O emulsions based on a lyotropic liquid crystal as the aqueous droplet phase. The cholesteric phase, a solution hydroxypropyl cellulose in water was dispersed in the continuous oil matrix, paraffin oil or heptane. We made a specific choice of surfactant in order to impose director anchoring conditions at the oil-water interface and orient the liquid crystal inside the droplet. The strong anchoring conditions resulted in a topological defect inside the droplets of size above the critical value R^*. The defect elastic energy creates a barrier against droplet coalescence, the effect of topological size selection. We have studied the orientation of the director inside the droplets and their size distribution.     

Self-propelled droplets

Self-propelled droplets are a special kind of self-propelled matter that are easily fabricated by standard microfluidic tools and locomote for a certain time without external sources of energy. The typical driving mechanism is a Marangoni flow due to gradients in the interfacial energy on the droplet interface. In this article we review the hydrodynamic prerequisites for self-sustained locomotion and present two examples to realize those conditions for emulsion droplets, i.e. droplets stabilized by a surfactant layer in a surrounding immiscible liquid. One possibility to achieve self-propelled motion relies on chemical reactions affecting the surface active properties of the surfactant molecules. The other relies on micellar solubilization of the droplet phase into the surrounding liquid phase. Remarkable cruising ranges can be achieved in both cases and the relative insensitivity to their own ‘exhausts’ allows to additionally study collective phenomena.     

Numerical simulation of continuum models for fluid-fluid interface dynamics

This paper is concerned with numerical methods for two-phase incompressible flows assuming a sharp interface model for interfacial stresses. Standard continuum models for the fluid dynamics in the bulk phases, for mass transport of a solute between the phases and for surfactant transport on the interface are given. We review some recently developed finite element methods for the appropriate discretization of such models, e.?g., a pressure extended finite element (XFE) space which is suitable to represent the pressure jump, a space-time extended finite element discretization for the mass transport equation of a solute and a surface finite element method (SurFEM) for surfactant transport. Numerical experiments based on level set interface capturing and adaptive multilevel finite element discretization are presented for rising droplets with a clean interface model and a spherical droplet in a Poisseuille flow with a Boussinesq-Scriven interface model.     

Microcanonical determination of the interface tension of flat and curved interfaces from Monte Carlo simulations

The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed and, as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q?=?30) on L?×?L square lattices (40?≤?L?≤?100) are presented. It is shown that the microcanonical ensemble is well suited both to find the precise location of the first-order phase transition and to obtain an accurate estimate for the interfacial free energy between coexisting ordered and disordered phases. For this purpose, a microcanonical version of the heat bath algorithm is implemented. The finite size behaviour of the loop in the curve describing the inverse temperature versus energy density is discussed, emphasizing that the extrema do not have the meaning of van der Waals-like 'spinodal points' separating metastable from unstable states, but rather describe the onset of heterophase states: droplet/bubble evaporation/condensation transitions. Thus all parts of these loops, including the parts that correspond to a negative specific heat, describe phase coexistence in full thermal equilibrium. However, the estimates for the curvature-dependent interface tension of the droplets and bubbles suffer from unexpected and unexplained large finite size effects which need further study.     

Rayleigh instability of charged droplets in the presence of counterions

The classical instability of a charged spherical droplet is reconsidered in the presence of counterions. An ensemble of such droplets is studied within a simplified cell model. Screening of the electric field by the counterions is found to increase the equilibrium droplet size. Furthermore, if the ions can enter the droplet, a first-order phase transition occurs upon increasing Bjerrum length, surface tension or droplet density, leading to a phase separation. Simple scaling properties of the free energy give the shape of the phase boundary and show the system to be scale-invariant there. Pearl-necklace structures of hydrophobic polyelectrolytes are discussed as an application. Received 30 August 2001     

Observation of sharp resonances in the spontaneous Raman spectrum of a single optically levitated microdroplet

Sharp resonances have been observed in the spontaneous Raman spectra of single, optically levitated microdroplets. The droplets, 10 to 35 μm in diameter, were suspended by a CW argon laser beam which also served as the Raman excitation source. Experiments with dioctyl phthalate (DOP) and silicone oil confirmed that all Raman bands present in the bulk liquid spectra were also observable in the levitated droplet spectra, in agreement with previous micro-Raman studies of droplets on substrates. However, superimposed on the spectra of the levitated droplets was a series of sharp features not present in the bulk liquid spectra. Time-resolved experiments with growing DOP droplets showed that the sharp Raman features have the same origin as the elastic light scattering and flourescence resonances observed in previous studies of microspheres and fibers.     

Compressibility crossover and quantum opening of a gap for two-dimensional disordered clusters with Coulomb repulsion

Using Hartree-Fock orbitals with residual Coulomb repulsion, we study spinless fermions in a two-dimensional random potential. When we increase the system size L at fixed particle density, the size dependence of the average inverse compressibility exhibits a smooth crossover from a 1/L ² towards a 1/L decay when the Coulomb energy to Fermi energy ratio increases from 0 to 3. In contrast, the distribution of the first energy excitation displays a sharp Poisson-Wigner-like transition at . Received 13 March 2000