Bouncing phase variations in pilot-wave hydrodynamics and the stability of droplet pairs

2019 ◽  
Vol 871 ◽  
pp. 212-243 ◽  
Author(s):  
Miles M. P. Couchman ◽  
Sam E. Turton ◽  
John W. M. Bush
Keyword(s):  
Vertical Motion ◽  
Vibrational Acceleration ◽  
Pilot Wave ◽  
Theoretical Predictions ◽  
Phase Variations ◽  
The Stability ◽  
Impact Phase ◽  
Trajectory Equation ◽  
Variable Impact ◽  
Made In

We present the results of an integrated experimental and theoretical investigation of the vertical motion of millimetric droplets bouncing on a vibrating fluid bath. We characterize experimentally the dependence of the phase of impact and contact force between a drop and the bath on the drop’s size and the bath’s vibrational acceleration. This characterization guides the development of a new theoretical model for the coupling between a drop’s vertical and horizontal motion. Our model allows us to relax the assumption of constant impact phase made in models based on the time-averaged trajectory equation of Moláček and Bush (J. Fluid Mech., vol. 727, 2013b, pp. 612–647) and obtain a robust horizontal trajectory equation for a bouncing drop that accounts for modulations in the drop’s vertical dynamics as may arise when it interacts with boundaries or other drops. We demonstrate that such modulations have a critical influence on the stability and dynamics of interacting droplet pairs. As the bath’s vibrational acceleration is increased progressively, initially stationary pairs destabilize into a variety of dynamical states including rectilinear oscillations, circular orbits and side-by-side promenading motion. The theoretical predictions of our variable-impact-phase model rationalize our observations and underscore the critical importance of accounting for variability in the vertical motion when modelling droplet–droplet interactions.

scholarly journals A trajectory equation for walking droplets: hydrodynamic pilot-wave theory

2013 ◽  
Vol 737 ◽  
pp. 552-570 ◽  
Author(s):  
Anand U. Oza ◽  
Rodolfo R. Rosales ◽  
John W. M. Bush
Keyword(s):  
Chaotic Dynamics ◽  
Wave Theory ◽  
Pitchfork Bifurcation ◽  
Horizontal Motion ◽  
Straight Line ◽  
Pilot Wave ◽  
The Stability ◽  
Trajectory Equation ◽  
Insight Into ◽  
Pilot Wave Theory

AbstractWe present the results of a theoretical investigation of droplets bouncing on a vertically vibrating fluid bath. An integro-differential equation describing the horizontal motion of the drop is developed by approximating the drop as a continuous moving source of standing waves. Our model indicates that, as the forcing acceleration is increased, the bouncing state destabilizes into steady horizontal motion along a straight line, a walking state, via a supercritical pitchfork bifurcation. Predictions for the dependence of the walking threshold and drop speed on the system parameters compare favourably with experimental data. By considering the stability of the walking state, we show that the drop is stable to perturbations in the direction of motion and neutrally stable to lateral perturbations. This result lends insight into the possibility of chaotic dynamics emerging when droplets walk in complex geometries.

scholarly journals A NuSTAR confirmation of the 36 ks hard X-ray pulse-phase modulation in the magnetar 1E 1547.0 − 5408

2021 ◽  
Vol 502 (2) ◽  
pp. 2266-2284
Author(s):  
Kazuo Makishima ◽  
Teruaki Enoto ◽  
Hiroki Yoneda ◽  
Hirokazu Odaka
Keyword(s):  
Time Lapse ◽  
Phase Behaviour ◽  
Modulation Amplitude ◽  
Axial Deformation ◽  
Physical Processes ◽  
Arrival Times ◽  
Pulse Phase ◽  
Phase Variations ◽  
Complex Phenomena ◽  
Made In

ABSTRACT This paper describes an analysis of the NuSTAR data of the fastest-rotating magnetar 1E 1547 − 5408, acquired in 2016 April for a time lapse of 151 ks. The source was detected with a 1–60 keV flux of 1.7 × 10−11 erg s−1 cm−2, and its pulsation at a period of 2.086710(5) s. In 8–25 keV, the pulses were phase-modulated with a period of T = 36.0 ± 2.3 ks, and an amplitude of ∼0.2 s. This reconfirms the Suzaku discovery of the same effect at $T=36.0 ^{+4.5}_{-2.5}$ ks, made in the 2009 outburst. These results strengthen the view derived from the Suzaku data, that this magnetar performs free precession as a result of its axial deformation by ∼0.6 × 10−4, possibly caused by internal toroidal magneti fields (MFs) reaching ∼1016 G. Like in the Suzaku case, the modulation was not detected in energies below ∼8 keV. Above 10 keV, the pulse-phase behaviour, including the 36 ks modulation parameters, exhibited complex energy dependencies: at ∼22 keV, the modulation amplitude increased to ∼0.5 s, and the modulation phase changed by ∼65° over 10–27 keV, followed by a phase reversal. Although the pulse significance and pulsed fraction were originally very low in >10 keV, they both increased noticeably, when the arrival times of individual photons were corrected for these systematic pulse-phase variations. Possible origins of these complex phenomena are discussed, in terms of several physical processes that are specific to ultrastrong MFs.

Polydomain Structure of Epitaxial PbTiO3 films on MgO

1997 ◽  
Vol 493 ◽  
Author(s):  
S. P. Alpay ◽  
A. S. Prakash ◽  
S. Aggarwal ◽  
R. Ramesh ◽  
A. L. Roytburd ◽  
...  
Keyword(s):  
Domain Structure ◽  
Pulsed Laser ◽  
Laser Deposition ◽  
X Ray Diffraction ◽  
X Ray ◽  
Theoretical Predictions ◽  
The Stability ◽  
Increasing Temperature ◽  
Stable Domains ◽  
Domain Stability

ABSTRACTA PbTiO3(001) film grown on MgO(001) by pulsed laser deposition is examined as an example to demonstrate the applications of the domain stability map for epitaxial perovskite films which shows regions of stable domains and fractions of domains in a polydomain structure. X-ray diffraction studies indicate that the film has a …c/a/c/a… domain structure in a temperature range of °C to 400°C with the fraction of c-domains decreasing with increasing temperature. These experimental results are in excellent agreement with theoretical predictions based on the stability map.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

Observations on some basal failures in sheeted excavations

1970 ◽  
Vol 7 (2) ◽  
pp. 136-144 ◽  
Author(s):  
V. Milligan ◽  
K. Y. Lo
Keyword(s):  
Shear Strength ◽  
Ground Water ◽  
Groundwater Level ◽  
Soil Conditions ◽  
Remedial Measures ◽  
Factors Influencing ◽  
Water Head ◽  
The Stability ◽  
Made In

In excavations below groundwater level, instability of the base may result from the inflow of water into the excavation. The most important factors influencing the stability are the ground water and detailed soil conditions at the site.Construction problems encountered in excavations in clay strata, underlain by pervious water bearing layers, are described. The remedial measures adopted in each case are also discussed. From a study of the observations made in the case records, it is suggested that excavation in intact clays may be carried out to depths exceeding that limited by the ratio of t/h = 0.5, where t is the distance from the bottom of the excavation to the top of the water bearing stratum, and h is the water head at the top of the water bearing stratum, provided that the clay is not disturbed during construction so that the shear strength of the clay is preserved.

Stability of Water-Lubricated, Hydrostatic, Conical Bearings With Spiral Grooves for High-Speed Spindles

2001 ◽  
Vol 124 (2) ◽  
pp. 398-405 ◽  
Author(s):  
S. Yoshimoto ◽  
S. Oshima ◽  
S. Danbara ◽  
T. Shitara
Keyword(s):  
High Speed ◽  
Water Pressure ◽  
Rotating Shaft ◽  
Pressurized Water ◽  
High Speeds ◽  
Theoretical Predictions ◽  
The Stability ◽  
Stability Of Water ◽  
Spiral Grooves ◽  
Good Agreement

In this paper, the stability of water-lubricated, hydrostatic, conical bearings with spiral grooves for high-speed spindles is investigated theoretically and experimentally. In these bearing types, pressurized water is first fed to the inside of the rotating shaft and then introduced into spiral grooves through feeding holes located at one end of each spiral groove. Therefore, water pressure is increased due to the effect of the centrifugal force at the outlets of the feeding holes, which results from shaft rotation. In addition, water pressure is also increased by the viscous pumping effect of the spiral grooves. The stability of the proposed bearing is theoretically predicted using the perturbation method, and calculated results are compared with experimental results. It was consequently found that the proposed bearing is very stable at high speeds and theoretical predictions show good agreement with experimental data.

scholarly journals Kerukunan Umat Beragama: Relevansi Pasal 25 Piagam Madinah dan Pasal 29 UUD 1945

2019 ◽  
Vol 21 (2) ◽  
pp. 162
Author(s):  
Nurul Fajriah
Keyword(s):  
20Th Century ◽  
Religious Diversity ◽  
The State ◽  
Religious Communities ◽  
Modern Times ◽  
Indonesian Government ◽  
Important Concern ◽  
Similarities And Differences ◽  
The Stability ◽  
Made In

This article is a study of literature describing religious harmony: the relevance of Article 25 of the Medina Charter and Article 29 of the 1945 Constitution. The Medina Charter was made in the 7th century (classical century) and Article 29 of the 1945 Constitution was born in modern times, around the 20th century. Both have relevancy which states that every citizen is free to adhere to their respective religions. The plurality of society in Indonesia has similarities and differences from the plurality of society in Medina around 622 AD. The stability and harmony of religious communities in the Medina at that time was regulated in the Medina charter which is the constitution of the Medina state. Harmony among religious communities in Indonesia is also an important concern of the Indonesian government as stipulated in Article 29 of the 1945 Constitution. Freedom of religion is guaranteed by the state because the state believes that religious diversity is not a disintegrating factor for the Indonesian people.Abstrak: Artikel ini adalah kajian literatur yang mendeskripsikan kerukunan umat beragama: relevansi pasal 25 Piagam Madinah dan Pasal 29 UUD 1945. Piagam Madinah dibuat pada abad VII (abad klasik) dan pasal 29 UUD 1945 baru lahir pada zaman modern, sekitar abad XX. Keduanya memiliki relevansi yang menyatakan bahwa setiap warga negara bebas menganut agamanya masing-masing. Kemajemukan masyarakat di Indonesia mempunyai sisi-sisi persamaan dan perbedaan dengan kemajemukan masyarakat di Madinah sekitar tahun 622 M. Keberlangsungan dan keharmonisan umat beragama di negara Madinah pada waktu itu diatur dalam piagam Madinah yang merupakan konstitusi negara Madinah. Kerukunan antar umat beragama di Indonesia juga menjadi perhatian penting pemerintah dengan adanya kebijakan Negara Republik Indonesia dari segi agama yang tertuang dalam pasal 29 UUD 1945. Kebebasan beragama ini dijamin oleh negara karena keyakinan bahwa keberagaman agama tidak akan menjadi disentegrating factor bagi bangsa Indonesia

Annular Liquid Jet Experiments

1980 ◽  
Vol 102 (3) ◽  
pp. 344-349 ◽  
Author(s):  
M. A. Hoffman ◽  
R. K. Takahashi ◽  
R. D. Monson
Keyword(s):  
Dimensionless Parameter ◽  
Maximum Velocity ◽  
Reliable Data ◽  
Liquid Jet ◽  
External Disturbances ◽  
Annular Jet ◽  
Theoretical Predictions ◽  
Series Of Experiments ◽  
The Stability ◽  
Surface Tension Forces

Experiments have been performed to determine the length for convergence or closure of a vertical, hollow annular water jet due to the action of surface tension forces. The data agree well with theoretical predictions up to the maximum velocity where reliable data could be obtained (4.4 m/s). These experiments extend the range of confirmation of the theories in terms of the dimensionless parameter, Nc ≡ We/Fr2, from about 0.01 to over 100. The stability of the annular jet subjected to natural and external disturbances is also discussed briefly. Finally the results of a series of experiments on the flow spreading or splitting due to the presence of wedge-shaped obstacles in the path of the annular jet flow are presented.

On the Natural Modes and Their Stability in Nonlinear Two-Degree-of-Freedom Systems

1959 ◽  
Vol 26 (3) ◽  
pp. 377-385
Author(s):  
R. M. Rosenberg ◽  
C. P. Atkinson
Keyword(s):  
Free Vibrations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Natural Modes ◽  
Theoretical Predictions ◽  
Stability Chart ◽  
The Stability ◽  
Two Parameters ◽  
Two Degree Of Freedom

Abstract The natural modes of free vibrations of a symmetrical two-degree-of-freedom system are analyzed theoretically and experimentally. This system has two natural modes, one in-phase and the other out-of-phase. In contradistinction to the comparable single-degree-of-freedom system where the free vibrations are always orbitally stable, the natural modes of the symmetrical two-degree-of-freedom system are frequently unstable. The stability properties depend on two parameters and are easily deduced from a stability chart. For sufficiently small amplitudes both modes are, in general, stable. When the coupling spring is linear, both modes are always stable at all amplitudes. For other conditions, either mode may become unstable at certain amplitudes. In particular, if there is a single value of frequency and amplitude at which the system can vibrate in either mode, the out-of-phase mode experiences a change of stability. The experimental investigation has generally confirmed the theoretical predictions.

EFFECT OF ADDED TIP MASS ON THE NONLINEAR FLAPWISE AND CHORDWISE VIBRATION OF CANTILEVER COMPOSITE BEAM UNDER BASE EXCITATION

2012 ◽  
Vol 12 (02) ◽  
pp. 285-310 ◽  
Author(s):  
M. EFTEKHARI ◽  
M. MAHZOON ◽  
S. ZIAEI-RAD
Keyword(s):  
Cantilever Beam ◽  
Multiple Scales ◽  
Equilibrium Points ◽  
Laminated Composite ◽  
Base Excitation ◽  
System A ◽  
Autoparametric Resonance ◽  
The Stability ◽  
Tip Mass ◽  
Made In

In this paper, a comparative study is performed for a symmetrically laminated composite cantilever beam with and without a tip mass under harmonic base excitation. The base is subjected to both flapwise and chordwise excitations tuned to the primary resonances of the two directions and conditions of 2:1 autoparametric resonance. In the literature, the governing nonlinear equations of the same problem without tip mass have been derived using the extended Hamilton's principle. Extension is made in this study to include the effect of a tip mass on the response of the beam. The natural frequencies are obtained numerically using the diversity guided evolutionary algorithm (DGEA). Next, the multiple scales method is applied to determine the nonlinear response and stability of the system. A set of four first-order differential equations describing the modulation of the amplitudes and phases of interacting modes are derived for the perturbation analysis. For verification, the above equations are reduced to the special case of the cantilever beam without tip mass for comparison with existing results. Finally, the effect of the tip mass on the stability of the fixed points and on the amplitude of oscillation about the equilibrium points in both the frequency and force modulation responses is examined.

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