Instability In Rings Research Articles

Understanding Vortex Ring Instability During Droplet Impact Onto Thin Liquid Films Using High Speed PIV

This study investigates vortex ring instability during droplet impact on thin liquid films using high-speed Particle Image Velocimetry (PIV) and Laser-Induced Fluorescence (LIF). Experiments were conducted using two different setups, capturing the droplet impact from both bottom and side views. The study examines how different dimensionless parameters (Reynolds number, Weber number and dimentionless thickness) influence vortex ring behavior in thin liquid films. Vortices were analyzed by identifying the centers using Gamma_2 scalar and calculating the vortex circulation through a two superposed Lamb-Oseen vortex fitting. The effect of film thickness on vortex dynamics reveals that thinner films lead to greater instability due to higher energy at the moment of wall collision, facilitating the formation of additional vortex structures. Experimental phase mapping highlights the critical threshold of Reynolds number and dimensionless thickness for vortex ring instability. Moreover, the number of fingers formed due to vortex ring instabilities increases with higher Reynolds numbers and thinner films, providing a clear relationship between film thickness, impact energy, and the complexity of resulting fluid structures.

Stabilization of the bunch position during the control of the microbunching instability in storage rings

Stabilization of the bunch position during the control of the microbunching instability in storage rings

LIF-based quantification of the species transport during droplet impact onto thin liquid films

In the present study, laser-induced fluorescence (LIF) is used to investigate the mixing process of a droplet impacting onto a thin liquid film. A robust multidimensional calibration procedure is developed enabling the extraction of local instantaneous dye concentrations as well as film heights. A series of validation measurements are conducted confirming a low reconstruction error of 4.53%. The impact-induced mixing process is thoroughly investigated across various liquid film thicknesses to examine the propagation of the mixing zone and the instantaneous radial concentration gradients within it. It is shown that the maximum extent of the mixing zone scales inversely proportional with the thickness of the liquid film. Within our experiments, we discover the formation of wall-induced vortex ring instabilities subsequent to impact. The disintegration of vortex rings during droplet impact significantly enhances convection-driven mixing, as quantified by the coefficient of variation.Graphical abstract

Instabilities of thin black rings: closing the gap

We initiate the study of dynamical instabilities of higher-dimensional black holes using the blackfold approach, focusing on asymptotically flat boosted black strings and singly-spinning black rings in D ≥ 5. We derive novel analytic expressions for the growth rate of the Gregory-Laflamme instability for boosted black strings and its onset for arbitrary boost parameter. In the case of black rings, we study their stability properties in the region of parameter space that has so far remained inaccessible to numerical approaches. In particular, we show that very thin (ultraspinning) black rings exhibit a Gregory-Laflamme instability, giving strong evidence that black rings are unstable in the entire range of parameter space. For very thin rings, we show that the growth rate of the instability increases with increasing non-axisymmetric mode m while for thicker rings, there is competition between the different modes. However, up to second order in the blackfold approximation, we do not observe an elastic instability, in particular for large modes m ≫ 1, where this approximation has higher accuracy. This suggests that the Gregory-Laflamme instability is the dominant instability for very thin black rings. Additionally, we find a long-lived mode that describes a wiggly time-dependent deformation of a black ring. We comment on disagreements between our results and corresponding ones obtained from a large D analysis of black ring instabilities.

Minimally invasive stabilisation of posterior pelvic ring instabilities with pedicle screws connected to a transverse rod.

The goal was to evaluate the clinical outcomes, quality of reduction and complications of pelvic fractures treated by minimally invasive stabilisation of posterior pelvic ring instabilities with pedicle screws connected to a transverse rod. Retrospective analysis of prospectively collected data in a consecutive patient series with pelvic fractures treated by minimally invasive stabilisation of posterior pelvic ring instabilities with pedicle screws between January 2010 and January 2016. The functional outcomes evaluated by Majeed scores, and fracture reduction results were evaluated using the Tornetta and Matta standard. As well as recording the duration of the surgical procedure, intraoperative blood loss, the times of intra-operative fluoroscopy and complications. A total of 29 patients (15 men and 14 women; age range, 21-72years; mean, 40.8years) could be followed-up after an average of 38.2 ± 21.3months (range, 12-84months). According to the AO/OTA classification, there were 24 patients with B2 injury and five patients with C1 injury of the pelvic ring. For the sacral fractures, according to Denis classification, four cases were zone I fractures and 25 cases were zone II fractures. The duration of the surgical procedure, intra-operative blood loss and the times of intra-operative fluoroscopic of the posterior-ring surgical procedure was 28.2 ± 4.6minutes (range, 20-38minutes), 46.7 ± 4.9ml (range, 39-56ml), and 13.1 ± 1.6seconds (range, 10-17seconds) respectively. Posterior-ring fracture reduction was excellent in 11 patients and 15 were good, three cases were fair; the excellent and good rate was 89.7% (26/29). At the final follow-up, the function result was rated as excellent in ten cases, good in 16, fair in three, and poor in zero cases; the excellent and good rate was 89.7% (26/29). There was no incision infection, intra-operative neurovascular injury, pedicle screw loose or breakage, and non-union of the posterior arch did not occur. Two patients requested removal of the fixator: one patient with breakage of the anterior pelvic ring internal fixator, and the pedicle screw was also taken out in the same operative session; another one with moderate pain on the posterior pelvic ring. Minimally invasive stabilisation of posterior-pelvic-ring instabilities with pedicle screw connected to a transverse rod may be a good alternative to sacroiliac screw fixation because it is quick, safe and associated with a good functional outcome; thus being a useful option in patients who do not qualify for sacroiliac screw fixation.

Fragility Fractures of the Pelvis.

➢ Fragility fractures of the pelvis exhibit different morphological characteristics and occur as a result of different mechanisms than high-energy pelvic ring lesions. The degree of instability may increase over time.➢ A new comprehensive classification system distinguishes between different degrees of instability and different locations of the fractures in the posterior pelvic ring.➢ The majority of fragility fractures of the pelvis have nondisplaced components in the posterior part of the pelvic ring. These types of fragility fractures are treated nonoperatively with pain therapy and mobilization as tolerated. A multidisciplinary approach is needed to ameliorate the general condition of the patient and to treat underlying metabolic abnormalities.➢ Because one of the primary goals of treatment is functional recovery, restoring stability is more important than restoring perfect anatomy.➢ Less-invasive stabilization techniques are preferable to open reduction and internal fixation for the treatment of posterior and anterior pelvic ring instabilities.

Curvature instability of a curved Batchelor vortex

In this paper, we analyse the curvature instability of a curved Batchelor vortex. We consider this short-wavelength instability when the radius of curvature of the vortex centreline is large compared with the vortex core size. In this limit, the curvature instability can be interpreted as a resonant phenomenon. It results from the resonant coupling of two Kelvin modes of the underlying Batchelor vortex with the dipolar correction induced by curvature. The condition of resonance of the two modes is analysed in detail as a function of the axial jet strength of the Batchelor vortex. In contrast to the Rankine vortex, only a few configurations involving $m=0$ and $m=1$ modes are found to become the most unstable. The growth rate of the resonant configurations is systematically computed and used to determine the characteristics of the most unstable mode as a function of the curvature ratio, the Reynolds number and the axial flow parameter. The competition of the curvature instability with another short-wavelength instability, which was considered in a companion paper (Blanco-Rodríguez & Le Dizès, J. Fluid Mech., vol. 804, 2016, pp. 224–247), is analysed for a vortex ring. A numerical error found in this paper, which affects the relative strength of the elliptic instability, is also corrected. We show that the curvature instability becomes the dominant instability in large rings as soon as axial flow is present (vortex ring with swirl).

Elliptic instability of a curved Batchelor vortex

The occurrence of the elliptic instability in rings and helical vortices is analysed theoretically. The framework developed by Moore & Saffman (Proc. R. Soc. Lond. A, vol. 346, 1975, pp. 413–425), where the elliptic instability is interpreted as a resonance of two Kelvin modes with a strained induced correction, is used to obtain the general stability properties of a curved and strained Batchelor vortex. Explicit expressions for the characteristics of the three main unstable modes are obtained as a function of the axial flow parameter of the Batchelor vortex. We show that vortex curvature adds a contribution to the elliptic instability growth rate. The results are applied to a single vortex ring, an array of alternate vortex rings and a double helical vortex.

End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture

We produce the first concrete evidence that violation of the weak cosmic censorship conjecture can occur in asymptotically flat spaces of five dimensions by numerically evolving perturbed black rings. For certain thin rings, we identify a new, elastic-type instability dominating the evolution, causing the system to settle to a spherical black hole. However, for sufficiently thin rings the Gregory-Laflamme mode is dominant, and the instability unfolds similarly to that of black strings, where the horizon develops a structure of bulges connected by necks which become ever thinner over time.

MAGNETIC FIELD FLUCTUATIONS OBSERVED IN THE HELIOSHEATH AND INTERSTELLAR MAGNETIC FIELD BYVOYAGER 1AT 115.7-124.9 AU DURING 2011-2013

We discuss microscale fluctuations of the hour averages of the magnetic field B observed on a scale of one day by Voyager 1 (V1) from 2011.0 to 2012.3143 (when it was within the distant heliosheath, where the average magnetic field strength (B) = 0.17 nT) and during the interval from 2012.6503 to 2013.5855 (when it was within the interstellar plasma with (B) = 0.47 nT). In both regions, the fluctuations were primarily compressive fluctuations, varying along the average B (≈T direction in RTN coordinates). In the heliosheath, the average of the daily standard deviations (SDs) of the compressive and transverse components of B were (SD{sub c}) = 0.010 nT and (SD{sub t}) ≤ 0.005 nT (which is the limit of the measurement). In the distant heliosheath (SD{sub c})/(B) = 0.06, and the distributions of SD were skewed and highly kurtotic. The interstellar magnetic field (ISMF) strength was B = 0.48 nT, but the fluctuations were below the limit of measurement: (SD{sub c}) = 0.004 nT and (abs(SD{sub t})) = 0.004 nT. The distributions of these interstellar SDs have skewness and kurtosis consistent with a Gaussian noise distribution. We also discuss the fluctuations of 48 s averages of B on amore » scale of 1 day during a 30 day interval when V1 was observing the ISMF. For the fluctuations in all three components of B, SD = 0.010 nT, which gives an upper limit on the fluctuations of the ISMF on the scales observed by V1. This SD rules out the possibility that there is significant power in electromagnetic fluctuations generated by pickup ion ring instabilities at these scales, which strongly constrains models of the IBEX ribbon.« less

The ballistic transport instability in Saturn's rings - II. Non-linear wave dynamics

The ejecta discharged by impacting meteorites can redistribute a planetary ring's mass and angular momentum. This `ballistic transport' of ring properties instigates a linear instability that could generate the 100--1000-km undulations observed in Saturn's inner B-ring and in its C-ring. We present semi-analytic results demonstrating how the instability sustains steadily travelling nonlinear wavetrains. At low optical depths, the instability produces approximately sinusoidal waves of low amplitude, which we identify with those observed between radii 77,000 and 86,000 km in the C-ring. On the other hand, optical depths of 1 or more exhibit hysteresis, whereby the ring falls into multiple stable states: the homogeneous background equilibrium or large-amplitude wave states. Possibly the `flat zones' and `wave zones' between radii 93,000 and 98,000 km in the B-ring correspond to the stable homogeneous and wave states, respectively. In addition, we test the linear stability of the wavetrains and show that only a small subset are stable. In particular, stable solutions all possess wavelengths greater than the lengthscale of fastest linear growth. We supplement our calculations with a weakly nonlinear analysis that suggests the C-ring reproduces some of the dynamics of the complex Ginzburg--Landau equation. In the third paper in the series, these results will be tested and extended with numerical simulations.

The ballistic transport instability in Saturn's rings - III. Numerical simulations

Saturn's inner B-ring and its C-ring support wavetrains of contrasting amplitudes but with similar length scales, 100-1000 km. In addition, the inner B-ring is punctuated by two intriguing `flat' regions between radii 93,000 km and 98,000 km in which the waves die out, whereas the C-ring waves coexist with a forest of plateaus, narrow ringlets, and gaps. In both regions the waves are probably generated by a large-scale linear instability whose origin lies in the meteoritic bombardment of the rings: the ballistic transport instability. In this paper, the third in a series, we numerically simulate the long-term nonlinear evolution of this instability in a convenient local model. Our C-ring simulations confirm that the unstable system forms low-amplitude wavetrains possessing a preferred band of wavelengths. B-ring simulations, on the other hand, exhibit localised nonlinear wave `packets' separated by linearly stable flat zones. Wave packets travel slowly while spreading in time, a result that suggests the observed flat regions in Saturn's B-ring are shrinking. Finally, we present exploratory runs of the inner B-ring edge which reproduce earlier numerical results: ballistic transport can maintain the sharpness of a spreading edge while building a `ramp' structure at its base. Moreover, the ballistic transport instability can afflict the ramp region, but only in low-viscosity runs.

Technical and clinical outcome of percutaneous CT fluoroscopy-guided screw placement in unstable injuries of the posterior pelvic ring.

To evaluate technical success, complications, and effective dose in patients undergoing CT fluoroscopy-guided iliosacral screw placement for the fixation of unstable posterior pelvic ring injuries. Our retrospective analysis includes all consecutive patients with vertical sacral fractures and/or injury of the iliosacral joint treated with CT fluoroscopy-guided screw placement in our department from 11/2005 to 03/2013. Interventions were carried out under general anesthesia and CT fluoroscopy (10-20mAs; 120kV; 16- or 128-row scanner, Siemens Healthcare, Erlangen, Germany). Technical outcome, major and minor complications, and effective patient dose were analyzed. We treated 99 consecutive patients (mean age 53.1 ± 21.7years, 50 male, 49 female) with posterior pelvic ring instability with CT fluoroscopy-guided screw placement. Intervention was technically successful in all patients (n = 99). No major and one minor local complication occurred (1%, secondary screw dislocation). General complications included three cases of death (3%) due to pulmonary embolism (n = 1), hemorrhagic shock (n = 1), or cardiac event (n = 1) during a follow-up period of 30days. General complications were not related to the intervention. Mean effective patient radiation dose per intervention was 12.28mSv ± 7.25mSv. Mean procedural time was 72.1 ± 37.4min. CT fluoroscopy-guided screw placement for the treatment of posterior pelvic ring instabilities can be performed with high technical success and a low complication rate. This method provides excellent intrainterventional visualization of iliac and sacral bones, as well as the sacral neuroforamina for precise screw placement by applying an acceptable effective patient dose.

Microbunching instability in storage rings: Link between phase-space structure and terahertz coherent synchrotron radiation radio-frequency spectra

In storage rings, when the number of electrons in a bunch exceeds a threshold value, microstructures appear spontaneously in the bunch. Experimental observations of these microstructures and their evolution are indirect to obtain. In practice, most information is obtained from the terahertz coherent synchrotron radiation (THz CSR), since microstructures in the millimeter range radiate THz CSR. Here we show, thanks to a simple analytical formula associated to numerical simulations, that a frequency component in the THz CSR signal permits one to obtain information about the structure of the electron bunch longitudinal phase space during the microbunching instability. The proposed formula permits one also to link experimental information together, in particular the bunch length and the THz CSR spectrum.

The early phase of multiple proto-stellar system emerging from collapse of molecular cloud under various initial thermal states

An attempt is made here to revisit structure formation in a proto-stellar cloud during the early phase of evolution. Molecular cloud subjected to a set of various initial conditions in terms of initial temperature and amplitude of azimuthal density perturbation is investigated numerically. Special emphasis remained on the analysis of ring and spiral type instabilities that have shown dependence on certain initial conditions chosen for a rotating solar mass cloud of molecular hydrogen. Generally, a star forming hydrogen gas is considered to be initially at 10K. We have found that a possible oscillation around this typical value can affect the fate of a collapsing cloud in terms of its evolving structural properties leading to proto-star formation. We explored the initial temperature range of cloud between 8K to 12K and compared physical properties of each within the first phase of proto-star formation. We suggest that the spiral structures are more likely to form in strongly perturbed molecular cores that initiate their phase of collapse from temperatures below 10K. Whereas, cores with initial temperatures above 10K develop, instead of spiral, a ring type structure which subsequently experiences the fragmentation. A transition from spiral to ring instability can be observed at a typical initial temperature of 10K.

The ballistic transport instability in Saturn's rings – I. Formalism and linear theory

Planetary rings sustain a continual bombardment of hypervelocity meteoroids that erode the surfaces of ring particles on time scales of 10^5 - 10^7 years. The debris ejected from such impacts re-accretes on to the ring, though often at a slightly different orbital radius from the point of emission. This `ballistic transport' leads to a rearrangement of the disk's mass and angular momentum, and gives rise to a linear instability that generates structure on relatively large scales. It is likely that the 100-km undulations in Saturn's inner B-ring and the plateaus and 1000-km waves in Saturn's C-ring are connected to the nonlinear saturation of the instability. In this paper the physical problem is reformulated so as to apply to a local patch of disk (the shearing sheet). This new streamlined model helps facilitate our physical understanding of the instability, and also makes more tractable the analysis of its nonlinear dynamics. We concentrate on the linear theory in this paper, showing that the instability is restricted to a preferred range of intermediate wavenumbers and optical depths. We subsequently apply these general results to the inner B-ring and the C-ring and find that in both regions the ballistic transport instability should be near marginality, a fact that may have important consequences for its prevalence and nonlinear development. Owing to damping via self-gravity wakes, the instability should not be present in the A-ring. A following paper will explore the instability's nonlinear saturation and how it connects to the observed large-scale structure.

Feedback for suppression of single-bunch transverse instability in electron-positron storage rings

Transverse head-tail instability is a severe limitationof a single-bunch beam current in circular accelerators.Applicability and efficiency of feedbacks for suppression of theinstability is analyzed. Both chromatic and nonlinear effects havebeen taken into account to understand the processes of excitationand damping of the instability. Analytical estimations arecompared with the results of experiments and numericalsimulations. A feedback system has been developed, installed andcommissioned at the VEPP-4M electron-positron collider. Anoriginal scheme of the kicker powering has been developed toprovide the necessary performance with minimal expenses. Real-timedigital data processing performed by a code running in an FPGAmodule provides high efficiency and flexibility of the system.During the system commissioning, a more than threefold increase ofintensity of the VEPP-4M single-bunch beam has beenachieved.

Suppression of beam-ion instability in electron rings with multibunch train beam fillings

The ion-caused beam instability in the future light sources and electron damping rings can be serious due to the high beam current and ultrasmall emittance of picometer level. One simple and effective mitigation of the instability is a multibunch train beam filling pattern which can significantly reduce the ion density near the beam, and therefore reduce the instability growth rate up to 2 orders of magnitude. The suppression is more effective for high intensity beams with low emittance. The distribution and the electric field of trapped ions are benchmarked to validate the model used in the paper. The wakefield of ion cloud and the beam-ion instability is investigated both analytically and numerically. We derived a simple formula for the buildup of ion cloud and instability growth rate with the multibunch train filling pattern. The simulation in NSLSII, PEPX, SuperKEKB, and the observation in SPEAR3 are used to compare with our analyses. The analyses agree well with simulations and observations.

Linear theory of microwave instability in electron storage rings

The well-known Haissinski distribution provides a stable equilibrium of longitudinal beam distribution in electron storage rings below a threshold current. Yet, how to accurately determine this threshold, above which the Haissinski distribution becomes unstable, is not firmly established in theory. In this paper, we will show how to apply the Laguerre polynomials in an analysis of this stability that are associated with the potential-well distortion. Our approach provides an alternative to the discretization method proposed by Oide and Yokoya. Moreover, it reestablishes an essential connection to the theory of mode coupling originated by Sacherer. Our new and self-consistent method is applied to study the microwave instability driven by commonly known impedances, including coherent synchrotron radiation in free space.

Percutaneous iliosacral screw fixation in S1 and S2 for posterior pelvic ring injuries: technique and perioperative complications

Percutaneous iliosacral screw placement allows for minimally invasive fixation of posterior pelvic ring instabilities. The objective of this study was to describe the technique for screws in S1 and S2 using conventional C-arm and to evaluate perioperative complications. Thirty-eight consecutive patients after percutaneous pelvic ring fixation with cannulated screws in S1 and S2 using conventional C-arm fluoroscopy were analysed. Accuracy of screw placement, nerval lesions, need for second surgery, operation time, and time to full weight bearing were assessed postoperatively and during regular follow-up examinations. Twenty-one patients underwent unilateral screw fixation and 17 patients underwent bilateral screw fixation. In total, 83 screws were placed. Mean age of the patients was 52 ± 19 years. Mean operation time was 16 ± 7 min/screw. Mean follow-up was 5 ± 3 months. Time to full weight bearing in 28 patients was 9 ± 4 weeks. Eight patients were still not able to support full weight bearing, partially due to concomitant injuries. Patients without concomitant injuries that affected walking were able to bear full weight after 8 ± 4 weeks (n = 17). Two patients had persistent postoperative hypaesthesia. No motor weakness was apparent and no postoperative bleeding was observed. Secondary surgery due to screw malpositioning or loosening had to be performed in four patients. The presence of a screw in S2 was not indicated for perioperative complications. Percutaneous iliosacral screw fixation is a rapid and definitive treatment for posterior pelvic ring injuries with a low risk of secondary bleeding during posterior pelvic stabilization. The technique using standard C-arm fluoroscopy was also found to be safe for screws placed in S2.