On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals

Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.

Rayleigh theory of ultrasound scattering applied to liquid-filled contrast nanoparticles

We present a novel modified theory based upon Rayleigh scattering of ultrasound from composite nanoparticles with a liquid core and solid shell. We derive closed form solutions to the scattering cross-section and have applied this model to an ultrasound contrast agent consisting of a liquid-filled core (perfluorooctyl bromide, PFOB) encapsulated by a polymer shell (poly-caprolactone, PCL). Sensitivity analysis was performed to predict the dependence of the scattering cross-section upon material and dimensional parameters. A rapid increase in the scattering cross-section was achieved by increasing the compressibility of the core, validating the incorporation of high compressibility PFOB; the compressibility of the shell had little impact on the overall scattering cross-section although a more compressible shell is desirable. Changes in the density of the shell and the core result in predicted local minima in the scattering cross-section, approximately corresponding to the PFOB-PCL contrast agent considered; hence, incorporation of a lower shell density could potentially significantly improve the scattering cross-section. A 50% reduction in shell thickness relative to external radius increased the predicted scattering cross-section by 50%. Although it has often been considered that the shell has a negative effect on the echogeneity due to its low compressibility, we have shown that it can potentially play an important role in the echogeneity of the contrast agent. The challenge for the future is to identify suitable shell and core materials that meet the predicted characteristics in order to achieve optimal echogenity.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Numerical Partition of Energy Absorption of Foam-filled Top-Hat and Double-Hat Sections

The interaction effect, i.e., the contribution of each component to the total energy absorption of an axially crushed foam-filled hat section was investigated quantitatively via numerical simulation. The FE results were first verified by experimental work of aluminum foam-filled top-hat and double-hat sections, then the contribution of foam-fillers and that of hat sections to the overall energy absorption were quantitatively obtained, respectively. When foam-filled, increase in energy absorption was found both in hat section component and foam-filler component, whereas the latter contributes predominantly to the interaction effect.

Liquid-filled microstructured polymer fibers as monolithic liquid-core array fibers

Liquid-filled microstructured polymer optical fibers (MPOFs) as monolithic liquid-core array fiber are proposed and prepared by injecting high-refractive-index liquid into the holes array of the MPOFs. One example for potential applications is demonstrated as a new kind of coherent imaging fiber. It provides great potential for applications in chemical sensing, biosensors, and endoscopy, particularly in bifunctional detection. (C) 2009 Optical Society of America

Characterisation of a two-dimensional liquid-filled ion chamber detector array using flattened and unflattened beams for small fields, small MUs and high dose-rates

In this study, the PTW 1000SRS array with Octavius 4D phantom was characterised for FF and FFF beams. MU linearity, field size, dose rate, dose per pulse (DPP) response and dynamic conformal arc treatment accuracy of the 1000SRS array were assessed for 6MV, 6FFF and 10FFF beams using a Varian TrueBeam STx linac. The measurements were compared with a pinpoint IC, microdiamond IC and EBT3 Gafchromic film. Measured dose profiles and FWHMs were compared with film measurements. Verification of FFF volumetric modulated arc therapy (VMAT) clinical plans were assessed using gamma analysis with 3%/3 mm and 2%/2 mm tolerances (10% threshold). To assess the effect of cross calibration dose rate, clinical plans with different dose rates were delivered and analysed. Output factors agreed with film measurements to within 4.5% for fields between 0.5 and 1 cm and within 2.7% for field sizes between 1.5 and 10 cm and were highly correlated with the microdiamond IC detector. Field sizes measured with the 1000SRS array were within 0.5 mm of film measurements. A drop in response of up to 1.8%, 2.4% and 5.2% for 6MV, 6FFF and 10FFF beams respectively was observed with increasing nominal dose rate. With an increase in DPP, a drop of up to 1.7%, 2.4% and 4.2% was observed in 6MV, 6FFF and 10FFF respectively. The differences in dose following dynamic conformal arc deliveries were less than 1% (all energies) from calculated. Delivered VMAT plans showed an average pass percentage of 99.5(±0.8)% and 98.4(±3.4)% with 2%/2 mm criteria for 6FFF and 10FFF respectively. A drop to 97.7(±2.2)% and 88.4(±9.6)% were observed for 6FFF and 10FFF respectively when plans were delivered at the minimum dose rate and calibrated at the maximum dose rate. Calibration using a beam with the average dose rate of the plan may be an efficient method to overcome the dose rate effects observed by the 1000SRS array.

On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.

Novel Sealing Technique for Practical Liquid-Core Photonic Crystal Fibers

In this letter, we describe a simple and effective technique to prevent evaporation in liquid-core photonic crystal fibers (PCFs). The technique consists of using a micropipette to deploy a micro-droplet of an ultraviolet curable polymer adhesive in both core inputs. After it is cured, the adhesive creates sealing polymer plugs with quite satisfactory insertion loss (overall optical transmission of about 15%). Processed fibers remained liquid-filled for at least six weeks. From a practical point of view, we conducted a supercontinuum generation experiment in a water-core PCF to demonstrate a 120-minute spectral width stability and the ability to withstand at least 3-mW average power at the sealed fiber input. Similar experiments carried out with nonsealed fibers produced supercontinuum spectra lasting no longer than 10 minutes, with average powers kept below 0.5 mW to avoid thermally induced evaporation.

Simulation of Freight Trains Equipped with Partially Filled Tank Containers and Related Resonance Phenomenon

To study the fluid motion-vehicle dynamics interaction, a model of four, liquid filled two-axle container freight wagons was set up. The railway vehicle has been modelled as a multi-body system (MBS). To include fluid sloshing, an equivalent mechanical model has been developed and incorporated. The influence of several factors has been studied in computer simulations, such as track defects, curve negotiation, train velocity, wheel wear, liquid and solid wagonload, and container baffles. SIMPACK has been used for MBS analysis, and ANSYS for liquid sloshing modelling and equivalent mechanical systems validation. Acceleration and braking manoeuvres of the freight train set the liquid cargo into motion. This longitudinal sloshing motion of the fluid cargo inside the tanks initiated a swinging motion of some components of the coupling gear. The coupling gear consists of UIC standard traction hooks and coupling screws that are located between buffers. One of the coupling screws is placed in the traction hook of the opposite wagon thus joining the two wagons, whereas the unused coupling screw rests on a hanger. Simulation results showed that, for certain combinations of type of liquid, filling level and container dimensions, the liquid cargo could provoke an undesirable, although not hazardous, release of the unused coupling screw from its hanger. The coupling screw's release was especially obtained when a period of acceleration was followed by an abrupt braking manoeuvre at 1 m/s2. It was shown that a resonance effect between the liquid's oscillation and the coupling screw's rotary motion could be the reason for the coupling screw's undesired release. Possible solutions to avoid the phenomenon are given.Acceleration and braking manoeuvres of the freight train set the liquid cargo into motion. This longitudinal sloshing motion of the fluid cargo inside the tanks initiated a swinging motion of some components of the coupling gear. The coupling gear consists of UIC standard traction hooks and coupling screws that are located between buffers. One of the coupling screws is placed in the traction hook of the opposite wagon thus joining the two wagons, whereas the unused coupling screw rests on a hanger. This paper reports on a study of the fluid motion-train vehicle dynamics interaction. In the study, a model of four, liquid-filled two-axle container freight wagons was developed. The railway vehicle has been modeled as a multi-body system (MBS). To include fluid sloshing, an equivalent mechanical model has been developed and incorporated. The influence of several factors has been studied in computer simulations, such as track defects, curve negotiation, train velocity, wheel wear, liquid and solid wagonload, and container baffles. A simulation program was used for MBS analysis, and a finite element analysis program was used for liquid sloshing modeling and equivalent mechanical systems validation. Acceleration and braking maneuvers of the freight train set the liquid cargo into motion. This longitudinal sloshing motion of the fluid cargo inside the tanks initiated a swinging motion of some components of the coupling gear. Simulation results showed that, for certain combinations of type of liquid, filling level and container dimensions, the liquid cargo could provoke an undesirable, although not hazardous, release of an unused coupling screw from its hanger. It was shown that a resonance effect between the liquid's oscillation and the coupling screw's rotary motion could be the reason for the coupling screw's undesired release. Solutions are suggested to avoid the resonance problem, and directions for future research are given.

失重条件下对称充液陀螺的不稳定行为研究

对于质心固定的，充满粘性均匀液体的旋转对称陀螺在失重条件下绕对称长轴旋转态的小扰动不稳定及其极限行为进行了研究，所给出的定理3比以往的不稳定定理[4]为强，且反映的信息量多很多。关于初始大扰动后的渐近行为，对文[8]已给出但未严格证明的两条定理给出了严格证明，它由定理1和定理2所描述。

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

刚性充液容器内竖直激励表面波研究进展

受外激励的充液刚性容器中流体的波动问题有实际的工程应用背景.竖直方向的受周期性外激励的充液容器的自由表面波问题--Faraday波问题是流体力学三大不稳定性难题之一(另外两个不稳定性问题是RayleighBénard对流和Taylor-Couette流).本文综述了在理想流体中和弱粘性流体中Faraday波的研究成果;介绍了作者在底部垂直激励的圆柱形容器中流体表面波图谱的实验研究和理论分析的结果.最后提出有待进一步研究的问题.