Non-axisymmetric Modes Research Articles

New, Non-axisymmetric Modes of Deformation in Endocytosis

New, Non-axisymmetric Modes of Deformation in Endocytosis

Development of a compact ring type MDOF piezoelectric ultrasonic motor for humanoid eyeball orientation system

A ultrasonic motor (USM) has been developed to meet the specific demands for compact actuators, which can drive humanoid eyeball to realize multi-degree-of-freedom (MDOF) motions. This USM has a ring shape composite stator, and employs combinations of axial bending mode and in-plane nonaxisymmetric mode to generate three type ellipses at four driving feet, pushing the spherical rotor to rotate around x, y and z axes respectively. FEM was used in the design process, including tuning the mode frequencies by sensitivity analysis, as well as optimizing the stator dimensions by transient simulations, where the shapes and attitude angles of the driving ellipses were retracted and analyzed with the deduced method, together with the driving effects comparison of two feasible exciting methods, achieving uniform driving behavior among the four feet. A prototype has been fabricated to verify the working principles, designs and simulations. The mechanical performance around x, y and z axis were measured under different electrical excitements and preload conditions, and typical stall torque is 17.5 mN m and the no-load speed of 82 r/min in x, y rotation, meanwhile stall torque is 12.5 mN m and the maximum speed of 43 r/min in z rotation, which meet the presented requirements.

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor–Couette flow

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor–Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

Low Frequency Sloshing Analysis of Cylindrical Containers with Flat and Conical Baffles

This paper presents an analysis of low-frequency liquid vibrations in rigid partially filled containers with baffles. The liquid is supposed to be an ideal and incompressible one and its flow is irrotational. A compound shell of revolution is considered as the container model. For evaluating the velocity potential the system of singular boundary integral equations has been obtained. The single-domain and multi-domain reduced boundary element methods have been used for its numerical solution. The numerical simulation is performed to validate the proposed method and to estimate the sloshing frequencies and modes of fluid-filled cylindrical shells with baffles in the forms of circular plates and truncated cones. Both axisymmetric and non-axisymmetric modes of liquid vibrations in baffled and un-baffled tanks have been considered. The proposed method makes it possible to determine a suitable place with a proper height for installing baffles in tanks by using the numerical experiment.

Propagation of monopole source excited acoustic waves in a cylindrical high-density polyethylene pipeline.

Acoustic wave propagation (up to 50 kHz) within a water-filled high-density polyethylene (HDPE) pipeline is studied using laboratory experiments and theoretical analysis. Experiments were carried out in a 15 m length of cylindrical HDPE pipeline using acoustic transducers to acquire signals uniformly spaced along the axis of the pipe. By proposing the use of the iterative quadratic maximum likelihood algorithm to this experimental configuration, wavenumbers, attenuations, and mode amplitudes could be accurately extracted from the measurement data. To allow comparisons with theoretical analysis, dispersion curves of the wavenumbers, attenuations, and acoustic power characteristics of the axisymmetric and nonaxisymmetric modes are predicted by extending an existing waveguide model. The model extensions included the introduction of a monopole acoustic source into the water medium so that amplitude variations with respect to individual modes and frequencies could be investigated in detail. In addition, stiffness coefficients of HDPE material are carefully used to account for viscoelastic effects. The comparisons between the theoretical predictions and experimental results demonstrate a very good match and are a validation of the theoretical model.

Temporal analysis of breakup for a power law liquid jet in a swirling gas

The breakup mechanism and instability of a power law liquid jet are investigated in this study. The power law model is used to account for the non-Newtonian behavior of the liquid fluid. A new theoretical model is established to explain the breakup of a power law liquid jet with axisymmetric and asymmetric disturbances, which moves in a swirling gas. The corresponding dispersion relation is derived by a linear approximation, and it is applicable for both shear-thinning and shear-thickening liquid jets. Analysis results are calculated based on the temporal mode. The analysis includes the effects of the generalized Reynolds number, the Weber number, the power law exponent, and the air swirl strength on the breakup of the jet. Results show that the shear-thickening liquid jet is more unstable than its Newtonian and shear-thinning counterparts when the effect of the air swirl is taken into account. The axisymmetric mode can be the dominant mode on the power law jet breakup when the air swirl strength is strong enough, while the non-axisymmetric mode is the domination on the instability of the power liquid jet with a high We and a low Re n . It is also found that the air swirl is a stabilizing factor on the breakup of the power law liquid jet. Furthermore, the instability characteristics are different for different power law exponents. The amplitude of the power law liquid jet surface on the temporal mode is also discussed under different air swirl strengths.

Numerical simulation of circular Couette flow under a radial thermo-electric body force

The transition from circular Couette flow of a dielectric fluid with a radial temperature gradient and an alternating electric voltage has been investigated by a direct numerical simulation. The inner cylinder is rotating while the outer one is fixed. The radial temperature gradient and the electric voltage acting on a dielectric fluid generate a radial dielectrophoretic (DEP) force which can induce thermal convection. The flow is controlled by the Taylor number Ta that measures the intensity of the centrifugal force and the electric Rayleigh number L that indicates the intensity of the DEP force. For each value of L, the instability threshold (Tac) is determined and compared with that predicted by the linear stability analysis. Nonlinear coefficients of the Landau equation are computed to reveal the nature of the transition: oscillatory axisymmetric modes occur via a subcritical transition, while steady axisymmetric and oscillatory non-axisymmetric modes occur via supercritical bifurcations. The momentum and heat transfer coefficients are computed to evaluate the efficiency of the flow induced by the DEP force in the momentum and energy transfer.

Axisymmetric and Nonaxisymmetric Oscillations of Sessile Compound Droplets in an Open Digital Microfluidic Platform.

Manipulating droplets of biological fluids in an electrowetting on dielectric (EWOD)-based digital microfluidic platform is a significant challenge because of biofouling and surface contamination. This problem is often addressed by operating in an oil environment. We study an alternate configuration of sessile compound droplets having an aqueous core surrounded by a smaller oil shell. In contrast to the conventional EWOD platform, an open digital microfluidic platform enabled by the core-shell configuration will allow electrical, mechanical, or optical probes to get unrestricted access to the droplet, thus enabling highly flexible and dynamically reconfigurable lab-on-chip systems. Understanding droplet oscillations is essential as they are known to enhance mixing. To our knowledge, this is the first study of axisymmetric and nonaxisymmetric oscillations of compound droplets actuated using EWOD platforms. Mode shapes for both axisymmetric and nonaxisymmetric oscillations were studied and explained. Enhancement in the axisymmetric oscillation of the core by decreasing the shell volume was obtained experimentally and modeled theoretically. Smaller shell volumes reduce the damping losses, allowing the appearance of nonaxisymmetric modes over a larger range of operating parameters. The oscillation frequency regime for obtaining prominent nonaxisymmetric oscillations for different shell volumes was identified. Compound droplets provide a mechanism to reduce biofouling, sample contamination, and evaporation. We demonstrate axisymmetric and nonaxisymmetric oscillations of compound droplets with the biological core of red blood cells, providing crucial first steps for promoting applications such as rapid efficient assays, mixing of biological fluids, and fluidic photonics on hysteresis-free surfaces.

External versus internal triggers of bar formation in cosmological zoom-in simulations

The emergence of a large-scale stellar bar is one of the most striking features in disc galaxies. By means of state-of-the-art cosmological zoom-in simulations, we study the formation and evolution of bars in Milky Way-like galaxies in a fully cosmological context, including the physics of gas dissipation, star formation, and supernova feedback. Our goal is to characterise the actual trigger of the non-axisymmetric perturbation that leads to the strong bar observable in the simulations at z=0, discriminating between an internal/secular versus an external/tidal origin. To this aim, we run a suite of cosmological zoom-in simulations altering the original history of galaxy-satellite interactions at a time when the main galaxy, though already bar-unstable, does not feature any non-axisymmetric structure yet. We find that the main effect of a late minor merger and of a close fly-by is to delay the time of bar formation and those two dynamical events are not directly responsible for the development of the bar and do not alter significantly its global properties (e.g. its final extension). We conclude that, once the disc has grown to a mass large enough to sustain global non-axisymmetric modes, then bar formation is inevitable.

Dynamic response of internally nested hemispherical shell system to impact loading

The dynamic deformation behaviors of the internally nested hemispherical shell system (INHSS), were explored experimentally and computationally. Two specimens with different ratios of inner shell thickness δ to outer shell thickness Δ were tested in a drop weight machine. For the specimen with smaller δ/Δ, non-axisymmetric deformation mode occurred with a stable force platform and longer loading history, while for the specimen with larger δ/Δ, axisymmetric deformation was exhibited. Meanwhile, experimentally validated finite element model was employed to study the deformation mechanism after the critical point when the outer shell contacts with the inner shell based on the ratio of square of shell thickness to radius. Subsequently, parametric studies are conducted by varying governing factors, including thickness, radius and offset distance of the inner shell. Results show that the dynamic deformation process and energy absorption capability of the INHSS depends on the thickness and radius of the inner shell.

Axisymmetric and non-axisymmetric instability of a charged viscoelastic jet under an axial magnetic field

This paper investigates the axisymmetric and the first non-axisymmetric linear instability of a charged viscoelastic jet under an applied axial magnetic field. The Oldroyd-B model is employed to account for the viscoelastic effect. Viscoelastic fluid is considered to be a leaky dielectric, and the surrounding inviscid gas a perfect dielectric. Results suggest that increasing the axial magnetic field suppresses both the axisymmetric and non-axisymmetric instabilities, and moves the main unstable range of the non-axisymmetric instability to small wavenumber regions. The magnetic field is coupled with the electric field by increasing the critical electric intensity of the dual effects on the axisymmetric mode; it also favors the transition from axisymmetric mode (jetting-dripping motion) to non-axisymmetric mode (jetting-whipping motion). It is also discovered that the magnetic field weakens the effects of fluid elasticity and deformation retardation time, but has little influence on the role played by the ambient gas.

Gray-box modeling of resistive wall modes with vacuum-plasma separation and optimal control design for EXTRAP T2R

This paper presents a graybox methodology to model the resistive wall mode instability by combining first principle approach and system identification technique. In particular we propose a separate vacuum and plasma modeling with cascade interconnection. The shell is modeled using CARIDDI code which solves the 3D integral formulation of eddy current problem, whereas the plasma response is obtained empirically by system identification. Furthermore the resulting model is used to design an optimal feedback control. The model and feedback control is validated experimentally in EXTRAP T2R reversed-field pinch, where RWMs stabilization and non-axisymmetric mode sustainment is considered.

Marangoni effects on a thin liquid film coating a sphere with axial or radial thermal gradients

We study the time evolution of a thin liquid film coating the outer surface of a sphere in the presence of gravity, surface tension, and thermal gradients. We derive the fourth-order nonlinear partial differential equation that models the thin film dynamics, including Marangoni terms arising from the dependence of surface tension σ on temperature T. We consider two different imposed temperature distributions with axial or radial thermal gradients. We analyze the stability of a uniform coating under small perturbations and carry out numerical simulations in COMSOL for a range of parameter values. In the case of an axial temperature gradient, we find steady states either with uniform film thickness or with the fluid accumulating at the bottom or near the top of the sphere, depending on the total volume of liquid in the film, dictating whether gravity or Marangoni effects dominate. This suggests a potential method for the indirect measurement of dσ/dT by monitoring the thickness profile of the thin film. In the case of a radial temperature gradient, a stability analysis reveals the most unstable non-axisymmetric modes on an initially uniform coating film.

Efficient 58-GHz relativistic orotron with combined mode selection

This article presents time-dependent numerical modeling of V-band relativistic orotron: a high-power microwave generator with a TM03 oscillation mode in an oversized (D/λ ∼ 2.7) electrodynamic structure and diffractive output in the TM02 mode. Single-mode operation of the oscillator is ensured by the cyclotron selection of the working axisymmetric mode, with simultaneous depression of competing non-axisymmetric modes by means of cutting longitudinal slits in the wall of the slow-wave structure. The simulated output microwave power is 350 MW with a power conversion efficiency of 31% when using a 3.6 kA, 310 keV electron beam transported in the 3.9 T magnetic field. The simulation employed 2.5D axisymmetric and 3D Cartesian versions of the KARAT code.

The scattering of torsional guided waves from Gaussian rough surfaces in pipework.

In older sections of industrial pipework there are often regions of general corrosion that typically have a Gaussian thickness distribution. During guided wave inspection this corrosion causes an increase in the background noise and a significant attenuation of the inspection wave. These effects are investigated in this paper through finite element modelling of the interaction of torsional guided waves with rough surfaces in pipes. Pipes of different diameter and rough surface profile are modelled and it is found that the attenuation of waves is explained by significant mode conversion and scattering within the rough surface. This mode conversion is greatest when the non-axisymmetric modes to which energy is scattered are close to the cutoff frequency or when the ratio of surface correlation length to wavelength is around 0.2-0.25. Mode conversion increases with increasing surface roughness and is a strong function of frequency-diameter product, with larger pipes causing more mode conversion. When this mode conversion occurs the energy is lost mostly to those waves with a displacement profile closest to the original torsional inspection wave. Resulting attenuation of the inspection signal can be severe; for example a mean wall thickness loss of 28% can cause 2.7 dB/m attenuation in a pulse-echo configuration.

Period spacing of gravity modes strongly affected by rotation

Context. As of today, asteroseismology mainly allows us to probe the internal rotation of stars when modes are only weakly affected by rotation using perturbative methods. Such methods cannot be applied to rapidly rotating stars, which exhibit complex oscillation spectra. In this context, the so-called traditional approximation, which neglects the terms associated with the latitudinal component of the rotation vector, describes modes that are strongly affected by rotation. This approximation is sometimes used for interpreting asteroseismic data, however, its domain of validity is not established yet. Aims. We aim at deriving analytical prescriptions for period spacings of low-frequency gravity modes strongly affected by rotation through the full Coriolis acceleration (i.e. without neglecting any component of the rotation vector), which can be used to probe stellar internal structure and rotation. Methods. We approximated the asymptotic theory of gravito-inertial waves in uniformly rotating stars using ray theory described in a previous paper in the low-frequency regime, where waves are trapped near the equatorial plane. We put the equations of ray dynamics into a separable form and used the Einstein-Brillouin-Keller (EBK) quantisation method to compute modes frequencies from rays. Results. Two spectral patterns that depend on stratification and rotation are predicted within this new approximation: one for axisymmetric modes and one for non-axisymmetric modes. Conclusions. The detection of the predicted patterns in observed oscillation spectra would give constraints on internal rotation and chemical stratification of rapidly rotating stars exhibiting gravity modes, such as γ Doradus, SPB, or Be stars. The obtained results have a mathematical form that is similar to that of the traditional approximation, but the new approximation takes the full Coriolis, which allows for propagation near the centre, and centrifugal accelerations into account.

Excitation and reception of single torsional wave T(0,1) mode in pipes using face-shear d24 piezoelectric ring array

Excitation of single fundamental torsional wave T(0, 1) mode is of practical importance in inspecting or monitoring the structural integrity of pipelines, as T(0, 1) wave is the only non-dispersive mode in pipe-like structures. This work presents a piezoelectric ring array to excite and receive single T(0, 1) mode which is made up of a series of equally-spaced face-shear d24 PZT elements around the pipe. Firstly, we proposed that single T(0, 1) mode can be excited by the piezoelectric ring, when the number of d24 PZT elements is slightly greater than n, where F(n, 2) is the highest circumferential order flexural torsional mode within the frequency bandwidth of the drive signal. Then this proposed principle was confirmed by finite element simulations. Later, experimental testing was conducted on a 100 mm outer diameter, 3 mm thick aluminum pipe. Results show that the ring of 24 face-shear d24 PZT elements can suppress all the non-axisymmetric flexural modes at the excitation frequency of 150 kHz so that single T(0, 1) mode is generated. Moreover, such a piezoelectric ring transducer can also filter flexural modes and receive the T(0, 1) mode only at 150 kHz. Note that here the highest circumferential order flexural torsional mode within the frequency bandwidth is F(20, 2), so the experimental results are in good agreement with the proposed principle. The presented ring of face-shear d24 PZT elements is very suitable for severing as the T(0, 1) wave transducer in structural health monitoring system, as it is cost-effective and no external load is required for operation.

Three-dimensional dynamics of thin liquid films on vertical cylinders with Marangoni effect

The effects of thermocapillary force on the three dimensional dynamics of thin liquid films flowing down a uniformly heated vertical cylinder are investigated using a thin film model. Linear and nonlinear analyses predict the existence of a non-axisymmetric mode due to the Marangoni effect. Symmetry-breaking of axisymmetric steady traveling waves is observed when the Marangoni number exceeds a critical value. Linear stability analysis demonstrates that the steady traveling wave can be unstable to azimuthal disturbances due to the Marangoni effect, leading to the formation of non-axisymmetric patterns.

Non-linear regimes in mean-field full-sphere dynamo

The mean-field dynamo model is employed to study the non-linear dynamo regimes in a fully convective star of mass 0.3$M_{\odot}$ rotating with period of 10 days. For the intermediate value of the parameter of the turbulent magnetic Prandl number, $Pm_{T}=3$ we found the oscillating dynamo regimes with period about 40Yr. The higher $Pm_{T}$ results to longer dynamo periods. If the large-scale flows is fixed we find that the dynamo transits from axisymmetric to non-axisymmetric regimes for the overcritical parameter of the $\alpha$effect. The change of dynamo regime occurs because of the non-axisymmetric non-linear $\alpha$-effect. The situation persists in the fully non-linear dynamo models with regards of the magnetic feedback on the angular momentum balance and the heat transport in the star. It is found that the large-scale magnetic field quenches the latitudinal shear in the bulk of the star. However, the strong radial shear operates in the subsurface layer of the star. In the nonlinear case the profile of the angular velocity inside the star become close to the spherical surfaces. This supports the equator-ward migration of the axisymmetric magnetic field dynamo waves. It was found that, the magnetic configuration of the star dominates by the regular non-axisymmetric mode m=1, forming Yin Yang magnetic polarity pattern with the strong (>500 G) poloidal magnetic field in polar regions.

Discrete helical modes in imploding and exploding cylindrical, magnetized liners

Discrete helical modes have been experimentally observed from implosion to explosion in cylindrical, axially magnetized ultrathin foils (Bz = 0.2 – 2.0 T) using visible self-emission and laser shadowgraphy. The striation angle of the helices, ϕ, was found to increase during the implosion and decrease during the explosion, despite the large azimuthal magnetic field (>40 T). These helical striations are interpreted as discrete, non-axisymmetric eigenmodes that persist from implosion to explosion, obeying the simple relation ϕ = m/kR, where m, k, and R are the azimuthal mode number, axial wavenumber, and radius, respectively. Experimentally, we found that (a) there is only one, or at the most two, dominant unstable eigenmode, (b) there does not appear to be a sharp threshold on the axial magnetic field for the emergence of the non-axisymmetric helical modes, and (c) higher axial magnetic fields yield higher azimuthal modes.