The evolution of numerical methods for predicting the distribution of surfactant in the bubble-scale dynamics of foams

Many numerical methods now exist to simulate the structure and dynamics of surface-tension-dominated aqueous foams at the level of the individual films and the liquid structures where they meet. We review these methods, focusing in particular on bubble-scale simulations of foam rheology. We highlight methods that allow the distribution of surfactant during flow to be taken into account.     

Time Discrete Approximation of Weak Solutions to Stochastic Equations of Geophysical Fluid Dynamics and Applications

As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and the oceans,the time discretization of these equations by an implicit Euler scheme is studied.From the deterministic point of view,the 3D primitive equations are studied in their full form on a general domain and with physically realistic boundary conditions.From the probabilistic viewpoint,this paper deals with a wide class of nonlinear,state dependent,white noise forcings which may be interpreted in either the It6 or the Stratonovich sense.The proof of convergence of the Euler scheme,which is carried out within an abstract framework,covers the equations for the oceans,the atmosphere,the coupled oceanic-atmospheric system as well as other related geophysical equations.The authors obtain the existence of solutions which are weak in both the PDE and probabilistic sense,a result which is new by itself to the best of our knowledge.     

波士顿矩阵法在河南承接产业转移中的应用

承接产业转移是加速区域经济发展的"助推器",提升产业集聚能力是提高区域产业竞争力的关键,如何科学地选择承接产业,并提升产业集聚能力是河南亟待解决的问题.选取2010年和2014年两个时点,运用产业梯度系数和产业动态集聚指数对工业进行分行业分析,并借鉴波士顿矩阵分析法将其划分为明星、金牛、问题、瘦狗和衰退等产业.根据河南的自然资源、劳动力、区位条件、市场需求等比较优势,并考虑产业集聚发展的能力,来确定河南承接产业转移的重点产业.     

Remarks on the Born approximation and the Factorization Method

In this paper, we compare the far-field operators for the full nonlinear inverse scattering problem with the Born approximation as its linearization. The Factorization Method shows that both operators share the same behavior with respect to illposedness of the inverse problem. The results are derived for acoustic and electromagnetic scattering problems and the corresponding problem in electrical impedance tomography.     

A comparative study of CE-SDS,SDS-PAGE,and Simple Western: Influences of sample preparation on molecular weight determination of proteins

The development of capillary electrophoresis, especially CE-SDS devices, has led CE-SDS to become an established tool in a wide range of applications in the analysis of biopharmaceuticals and is increasingly replacing its method of origin, SDS-PAGE. The goal of this study was to evaluate the comparability of molecular weight (MW) determination especially by CE-SDS and SDS-PAGE. For ensuring comparability, model proteins that have little or no posttranslational modifications and an IgG antibody were used. Only a minor influence of sample preparation conditions, including sample buffer, temperature conditions, and different reducing agents on the MW determination were found. In contrast, the selection of the MW marker plays a decisive role in determining the accurate apparent MW of a protein. When using different MW markers, the deviation in MW determination can exceed 10%. Interestingly, CE-SDS and 10% SDS-PAGE hardly differ in their trueness of MW determination. The trueness in relation to the reference MW for each protein was calculated. Although the trueness values for the model proteins considered range between 1.00 and 1.11 using CE-SDS, they range between 0.93 and 1.03 on SDS-PAGE, depending on the experimental conditions chosen.     

Electrokinetic actuation of an uncharged polarizable dielectric droplet in charged hydrogel medium

Electrokinetic transport of an uncharged nonconducting microsized liquid droplet in a charged hydrogel medium is studied. Dielectric polarization of the liquid drop under the action of an externally imposed electric field induces a non-homogeneous charge density at the droplet surface. The interactions of the induced surface charge of the droplet with the immobile charges of the hydrogel medium generates an electric force to the droplet, which actuates the drop through the charged hydrogel medium. A numerical study based on the first principle of electrokinetics is adopted. Dependence of the droplet velocity on its dielectric permittivity, bulk ionic concentration, and immobile charge density of the gel is analyzed. The surface conduction is significant in presence of charged gel, which creates a concentration polarization. The impact of the counterion saturation in the Debye layer due to the dielectric decrement of the medium is addressed. The modified Nernst–Planck equation for ion transport and the Poisson equation for the electric field is considered to take into account the dielectric polarization. A quadrupolar vortex around the uncharged droplet is observed when the gel medium is considered to be uncharged, which is similar to the induced charge electroosmosis around an uncharged dielectric colloid in free-solution. We find that the induced charge electrokinetic mechanism creates a strong recirculation of liquid within the droplet and the translational velocity of the droplet strongly depends on its size for the dielectric droplet embedded in a charged gel medium.     

Numerical simulations of viscoelastic particle migration in a microchannel with triangular cross-section

The migration of a spherical particle immersed in a viscoelastic liquid flowing in a microchannel with a triangular cross-section is investigated by direct numerical simulations under inertialess conditions. The viscoelastic fluid is modeled through two constitutive equations to investigate the effect of the second normal stress difference and the resulting secondary flows on the migration phenomenon. The results are presented in terms of trajectories followed by the particles released at different initial positions over the channel cross-section in a wide range of Weissenberg numbers and confinement ratios. Particles suspended in a fluid with a negligible second normal stress difference migrate toward the channel centerline or the closest wall, depending on their initial position. A much more complex dynamics is found for particles suspended in a fluid with a relevant second normal stress difference due to the appearance of secondary flows that compete with the migration phenomenon. Depending on the Weissenberg number and confinement ratio, additional equilibrium positions (points or closed orbits) may appear. In this case, the channel centerline becomes unstable and the particles are driven to the corners or “entrapped” in recirculation regions within the channel cross-section. The inversion of the centerline stability can be exploited to design efficient size-based separation devices.     

Controlled protein adsorption on a silica microparticle

In the present study, controlled protein adsorption on a rigid silica microparticle is investigated numerically using classical Langmuir and two-state models under electrokinetic flow conditions. The instantaneous particle locations are simulated along a straight microchannel using an arbitrary Lagrangian−Eulerian framework in the finite element method for the electrophoretic motion of the charged particle. Within the scope of the parametric study, the strength of the external electric field (E), particle diameter (D_p), the zeta potential of the particle (ζ_p), and the location of the microparticle away from the channel wall (H) are systematically varied. The results are also compared to the data of pressure-driven flow having a parabolic flow profile at the inlet whose maximum magnitude is set to the particle's electrophoretic velocity magnitude. The validation studies reveal that the code developed for the particle motion in the present simulations agrees well with the experimental results. It is observed that protein adsorption can be controlled using electrokinetic phenomena. The plug-like flow profile in electrokinetics is beneficial for a microparticle at every spatial location in the microchannel, whereas it is not valid for the pressure-driven flow. The electric field strength and the zeta potential of the particle accelerate the protein adsorption. The wall shear stress and shear rate are good indicators to predict the adsorption process for electrokinetic flow.     

Optimal Control for Multiscale Elliptic Equations with Rough Coefficients

This paper concerns the convex optimal control problem governed by multiscale elliptic equations with arbitrarily rough $L^\infty$ coefficients, which has not only complex coupling between nonseparable scales and nonlinearity, but also important applications in composite materials and geophysics. We use one of the recently developed numerical homogenization techniques, the so-called Rough Polyharmonic Splines (RPS) and its generalization (GRPS) for the efficient resolution of the elliptic operator on the coarse scale. Those methods have optimal convergence rate which do not rely on the regularity of the coefficients nor the concepts of scale-separation or periodicity. As the iterative solution of the nonlinearly coupled OCP-OPT formulation for the optimal control problem requires solving the corresponding (state and co-state) multiscale elliptic equations many times with different right hand sides, numerical homogenization approach only requires one-time pre-computation on the fine scale and the following iterations can be done with computational cost proportional to coarse degrees of freedom. Numerical experiments are presented to validate the theoretical analysis.     

B型套筒角焊缝缺陷相控阵超声检测定量方法

B型套筒修复作为油气管道修复的主要方式之一,在其修复的焊接过程中,该结构的环形角焊缝内部常常出现以气孔、夹渣为代表的孔型缺陷。这类缺陷由于角焊缝特殊的结构,在利用相控阵超声无损检测技术对其检测时,难以对其进行定量分析。通过数值模拟和实验,发现通过相控阵超声扇扫得到缺陷回波信号峰值与孔型缺陷直径呈正相关,为孔型缺陷的定量分析提供了一种可靠的手段。