On the levitation of a charged body in an electrostatic field

The possibility of levitation of a body bearing a point electric charge in the electric field of a fixed point charge of the same sign is demonstrated. Stabilization of the unstable equilibrium state of the body in which the body weight is balanced by the Coulomb force is provided by gyro forces due to body rotation. The conservative stability of the levitating body corresponds to a finite range of angular velocities. It is shown that dissipative and circulatory forces considered together can improve the stability of the system to asymptotic stability. The attraction domain of the stable equilibrium position is studied numerically as a function of system parameters.     

Stability of the equilibrium of a flat layer in a microconvection model

The stability of the equilibrium state of a flat layer bounded by rigid walls is studied using a microconvection model. The behavior of the complex decrement for longwave perturbations has an asymptotic character. Calculations of the full spectral problem were performed for melted silicon. Unlike in the classical Oberbeck–Boussinesq model, the perturbations in the microconvection model are not monotonic. It is shown that for small Boussinesq parameters, the spectrum of this problem approximates the spectra of the corresponding problems for a heatconducting viscous fluid or thermal gravitational convection when the Rayleigh number is finite.     

Validation of a numerical model for the simulation of an electrostatic powder coating process

Numerical modeling of a complete powder coating process is carried out to understand the gas-particle two-phase flow field inside a powder coating booth and results of the numerical simulations are compared with experimental data to validate the numerical results. The flow inside the coating booth is modeled as a three-dimensional turbulent continuous gas flow with solid powder particles as a discrete phase. The continuous gas flow is predicted by solving Navier–Stokes equations using a standard k–ε turbulence model with non-equilibrium wall functions. The discrete phase is modeled based on a Lagrangian approach. In the calculation of particle propagation, a particle size distribution obtained through experiments is applied. The electrostatic field, including the effect of space charge due to free ions, is calculated with the use of the user defined scalar transport equations and user defined scalar functions in the software package, FLUENT, for the electrostatic potential and charge density.     

Bifurcation points of the elastic-plastic equilibrium in a simple frame model

Summary This is a study of the characteristics of equilibrium bifurcation in a geometrically symmetric simple frame model in which the beam is loaded symmetrically and gradually. The deformability of the model is concentrated in two Shanley cells for whose elements a nonholonomic bilinear force-lengthening (or force-contraction) relation is adopted.The equilibrium bifurcation characteristics of this model are compared with those of Shanley's uniformly stressed column model. The characteristics of the two models coincide when instantaneous plasticisation of the deformable elements for the frame model are assumed, as occurs in the column model. But with a succession of different plastic states as the load increases, differences emerge. The most important being: in the frame model the borderline between the interval of unstable bifurcation points and the interval of stable bifurcation points is not necessarily, as it is in the column model, marked by a neutral (stationary load) bifurcation point.

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Sommario S'indagano i caratteri della biforcazione dell'equilibrio di un modello di portale, simmetrico nella geometria e simmetricamente caricato sul traverso in modo graduale. La deformabilità del modello è concentrata in due celle alla Shanley, per i cui elementi si adotta una relazione bilineare anolonoma tra forze ed allungamenti (od accorciamenti).Si confrontano tali caratteri con quelli della biforcazione dell'equilibrio del ben noto modello di asta caricata di punta studiato da Shanley.Quando si ipotizzi, per il modello di portale, una plasticizzazione istantanea degli elementi deformabili (proprio come avviene nel modello di asta), si ha perfetta coincidenza dei caratteri in esame.All'opposto, quando si ipotizzi un succedersi di diversi stati plastici al crescere del carico, si constatano delle differenze; in particolare, per il modello di portale esiste la possibilità, a differenza di quanto avviene nel modello di asta, che non sia un punto di biforcazione neutra (a carico stazionario) a segnare il confine tra l'intervallo dei punti di biforcazione instabile e quello dei punti di biforcazione stabile.

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Study supported by the Plasticity Group of the National Research Council.     

The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials

This investigation is concerned with the deformations and stresses in a slab of all-around infinite extent containing a traction-free plane crack, under conditions of plane strain. The analysis is carried out within the framework of the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids. For a fairly wide class of such materials and general loading conditions at infinity, assymptotic estimates appropriate to the various field quantities near the crack-tips are deduced. For a subclass of the materials considered, these results — in contrast to the analogous predictions of the linearized theory — lead to the conclusion that the crack opens up in the neighborhood of its tips even if the applied loading is antisymmetric about the plane of the crack, (e.g., Mode II loading). It is shown further that the non-linear global crack problem corresponding to such a loading in general cannot admit an antisymmetric solution.The results communicated in this paper were obtained in the course of an investigation supported in part by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C.     

Investigation of the velocity field in a full-scale model of a cerebral aneurysm

Due to improved and now widely used imaging methods in clinical surgery practise, detection of unruptured cerebral aneurysms becomes more and more frequent. For the selection and development of a low-risk and highly effective treatment option, the understanding of the involved hemodynamic mechanisms is of great importance. Computational Fluid Dynamics (CFD), in vivo angiographic imaging and in situ experimental investigations of flow behaviour are powerful tools which could deliver the needed information. Hence, the aim of this contribution is to experimentally characterise the flow in a full-scale phantom model of a realistic cerebral aneurysm. The acquired experimental data will then be used for a quantitative validation of companion numerical simulations. The experimental methodology relies on the large-field velocimetry technique PTV (Particle Tracking Velocimetry), processing high speed images of fluorescent tracer particles added to the flow of a blood-mimicking fluid.First, time-resolved planar PTV images were recorded at 4500 fps and processed by a complex, in-house algorithm. The resulting trajectories are used to identify Lagrangian flow structures, vortices and recirculation zones in two-dimensional measurement slices within the aneurysm sac. The instantaneous inlet velocity distribution, needed as boundary condition for the numerical simulations, has been measured with the same technique but using a higher frame rate of 20,000 fps in order to avoid ambiguous particle assignment. From this velocity distribution, the time-resolved volume flow rate has been also derived. In this manner, a direct comparison between numerical simulations and PTV measurements will be possible in the near future, opening the door for highly accurate computational predictions.     

The influence of the space charge in an electron beam accelerated in a constant electrostatic field up to energies of several MeV

Summary To realize a pulsed electron beam of high energy (2.5 MeV) and great intensity (ca 1 A) the influence of space charge has to be taken into account. A calculation in this article shows that at an average field strength in the acceleration tube of 10⁶ V/m the influence of the space charge begins to play a dominating part at a current density of 2A/cm².     

基于平稳过滤有色噪声地震动模型的MTMD性能评价

研究了由许多刚度和阻尼保持为常量且频率呈线性分布的TMDs形成的MTMD的地震特性。基于虚拟激励法和平稳过滤有色噪声地震动模型，建立了结构－MTMD系统的传递函数，进而导出了设置MTMD时结构的动力放大系数（DMF）明确表达式。于是MTMD的优化准则可定义为Min.Min.Max.DMF。通过最优搜寻可得MTMD的最优频率间隔、平均阻尼比、调谐频率比和相应的无量纲控制有效性指标。目前的论文通过考虑结构受控频率与地震加速度卓越频率比的不同取值和不同场地类型，研究地震卓越频率和场地类型对MTMD最优参数及有效性的影响。同时与基于Kanai-Tajimi平稳过滤白噪声地震动模型和不考虑地震加速度卓越频率(ωg=∝）两种情况的结果进行了比较。     

Critical evaluation of CFD codes for interfacial simulation of bubble‐train flow in a narrow channel

Computational fluid dynamics (CFD) codes that are able to describe in detail the dynamic evolution of the deformable interface in gas–liquid or liquid–liquid flows may be a valuable tool to explore the potential of multi‐fluid flow in narrow channels for process intensification. In the present paper, a computational exercise for co‐current bubble‐train flow in a square vertical mini‐channel is performed to investigate the performance of well‐known CFD codes for this type of flows. The computations are based on the volume‐of‐fluid method (VOF) where the transport equation for the liquid volumetric fraction is solved either by the methods involving a geometrical reconstruction of the interface or by the methods that use higher‐order difference schemes instead. The codes contributing to the present code‐to‐code comparison are an in‐house code and the commercial CFD packages CFX, FLUENT and STAR‐CD. Results are presented for two basic cases. In the first one, the flow is driven by buoyancy only, while in the second case the flow is additionally forced by an external pressure gradient. The results of the code‐to‐code comparison show that only the VOF method with interface reconstruction leads to physically sound and consistent results, whereas the use of difference schemes for the volume fraction equation shows some deficiencies. Copyright © 2007 John Wiley & Sons, Ltd.     

Stability of the equilibrium state in a convection model with nonlinear temperature and pressure dependences of density

The convection of a heat-conducting viscous liquid is considered. It is assumed that the liquid density depends quadratically on the temperature and pressure. The instability of the equilibrium state of a free-boundary horizontal layer with respect to small perturbations is studied using a linearization method. It is found that the state of mechanical equilibrium is unstable. Neutral curves are constructed and the critical Rayleigh numbers are found. The results are compared with the well-known solution of the same problem for the limiting case where the density is a quadratic function of temperature and does not depend on pressure. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 66–74, March–April, 2007.     

An empirically validated model of the pressure within a droplet confined between plates at equilibrium for low Bond numbers

An analytical model is presented that describes the equilibrium pressure within a confined droplet for small Bond numbers without prior knowledge of the interface shape. An explicit equation for the pressure was developed as a function of the gap height, surface tension, and contact angle. This equation was verified empirically. The shape of the interface was found based on the pressure predicted by both the proposed model and a model commonly used in electrowetting on dielectric (EWOD) investigations. These shapes were compared against experimentally observed interfaces for aspect ratios between 3.5 and 18. The pressures and shapes predicted by the proposed model were at least an order of magnitude more accurate than those predicted with a more commonly used model. At an aspect ratio of 3.5, the average error in the predicted shape was almost 4%, but decreased below the experimental error at an aspect ratio of 6. An aspect ratio of 15 is required for an EWOD device to split water droplets in air. The error in the model pressure and its predicted interface in this case were approximately 0.3%. The analytical pressure model proposed here can be used to increase the accuracy of models of practical EWOD devices. Better accuracy can be attained for small aspect ratios by iteratively calculating pressure using the model proposed here.     

A Numerical Study of the Critical Gas Saturation in a Porous Medium

We use porenetwork simulations to study the dependence of the critical gas saturation in solutiongas drive processes on the geometric parameters of the porous medium. We show that for a variety of growth regimes (including global and local percolation, instantaneous and sequential nucleation, and masstransfer driven processes), the critical gas saturation, Sgc, follows a powerlaw scaling with the final nucleation fraction (fraction of sites activated), fq. For 3D processes, this relation reads Sgcfq0.16, indicating a sensitive dependence of Sgc to fq at very small values of fq.     

Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack

The variational formulation of the equilibrium problem for a Timoshenko plate containing a vertical plane crack is considered. Nonpenetration conditions in the form of inequalities (Signorini type conditions) are specified on the crack faces. The behavior of the solution and the corresponding energy functional of the plate with variation in the crack length is analyzed. A formula for the derivative of the energy functional along the crack length is obtained. The solutions are found to continuously depend on the parameter characterizing the crack length.     

The influence of low-frequency varying magnetic field on the pulsatile flow in a rigid round tube

ProjcctsupportedbytheNatiol1alNaturalScienceFoundatio11ofChinaThemagnatictherapy,asaneffccti\'emedicaltreatment,hasabroadapp1icatiQn.lnrecentyears,plentyofanimalandclinicalresearcheshavebeendoneandprovedthatmagneticfieldhassuchpositivecurativeefttctsasant…     

Experimental evaluation of through-thickness stresses in a welded pipe using the consistent-splitting model

Experimental data for evaluating through-thickness residual stresses in a girth-welded pipe have been reanalyzed using an improvement in the analysis method. Data were obtained using a destructive experimental technique which involves three steps: parting-out, splitting, and layer removal. The improved analysis, called the consistent-splitting model, has been applied to the data in the splitting step. In addition to satisfying necessary equilibrium and compatibility conditions for the splitting step, the consistent-splitting model is easy to apply and requires no more data than are usually gathered for existing analysis models. Results from the consistent-splitting model show substantial corrections when compared to the originally computed residual-stress distributions. Comparisons of the results based on the consistent-splitting model with values from a finite-element computational model show generally good agreement. Questions about the assumptions embodied in analysis methods applied to the parting-out and layer-removal steps of the experimental procedure suggest future areas of potential improvement.