Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization

2014 ◽  
Vol 744 ◽  
pp. 404-429 ◽  
Author(s):  
Anand U. Oza ◽  
Daniel M. Harris ◽  
Rodolfo R. Rosales ◽  
John W. M. Bush
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Stability Analysis ◽  
Rotation Rate ◽  
Wave Force ◽  
Rotating Frame ◽  
Wave Dynamics ◽  
Pilot Wave ◽  
Dynamic Constraint ◽  
The Stability

AbstractWe present the results of a theoretical investigation of droplets walking on a rotating vibrating fluid bath. The droplet’s trajectory is described in terms of an integro-differential equation that incorporates the influence of its propulsive wave force. Predictions for the dependence of the orbital radius on the bath’s rotation rate compare favourably with experimental data and capture the progression from continuous to quantized orbits as the vibrational acceleration is increased. The orbital quantization is rationalized by assessing the stability of the orbital solutions, and may be understood as resulting directly from the dynamic constraint imposed on the drop by its monochromatic guiding wave. The stability analysis also predicts the existence of wobbling orbital states reported in recent experiments, and the absence of stable orbits in the limit of large vibrational forcing.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

Nonlinear Effects on Coexistence Phenomenon in Parametric Excitation

2002 ◽  
Author(s):  
Leslie Ng ◽  
Richard Rand
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Perturbation Methods ◽  
Nonlinear Effects ◽  
Free Vibrations ◽  
The Stability ◽  
Parameter Values ◽  
Two Degree Of Freedom

We investigate the effect of nonlinearites on a parametrically excited ordinary differential equation whose linearization exhibits the phenomena of coexistence. The differential equation studied governs the stability mode of vibration in an unforced conservative two degree of freedom system used to model the free vibrations of a thin elastica. Using perturbation methods, we show that at parameter values corresponding to coexistence, nonlinear terms can cause the origin to become nonlinearly unstable, even though linear stability analysis predicts the origin to be stable. We also investigate the bifurcations associated with this instability.

Theoretical Prediction of Onset of Horizontal Slug Flow

1980 ◽  
Vol 102 (4) ◽  
pp. 441-445 ◽  
Author(s):  
Kaichiro Mishima ◽  
Mamoru Ishii
Keyword(s):  
Experimental Data ◽  
Stability Analysis ◽  
Slug Flow ◽  
Flow Analysis ◽  
Finite Amplitude ◽  
Empirical Correlations ◽  
Deformation Limit ◽  
Theoretical Criterion ◽  
The Stability ◽  
Good Agreement

A criterion for the onset of a slug flow in a horizontal duct is derived theoretically. A potential flow analysis is carried out by considering waves of finite amplitude. The stability criterion is obtained by introducing the wave deformation limit and the “most dangerous wave” concept in the stability analysis. The present theoretical criterion for slug formation shows very good agreement with a large number of experimental data and with some empirical correlations.

Lyapunov-Based Sufficient Conditions for Nonlinear Impulsive Systems

2011 ◽  
Vol 219-220 ◽  
pp. 508-512
Author(s):  
Yong Liang Gao ◽  
Xiao Wu Mu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Invariant Set ◽  
Positive Definite ◽  
Impulsive Systems ◽  
Stability Theorems ◽  
Sufficient Conditions For Convergence ◽  
The Stability

This paper focuses on the stability analysis and invariant set stability theorems for nonlinear impulsive systems. A set of Lyapunov-based sufficient conditions are established for these convergent properties. These results do not require the Lyapunov function to be positive definite. Inequalities relating the righthandside of the differential equation and the Lyapunov function derivative are involved for these results. These inequalities make it possible to deduce properties of the functions and thus leads to sufficient conditions for convergence and stability.

A Stability Algorithm for a Special Case of the Milling Process: Contribution to Machine Tool Chatter Research—6

1968 ◽  
Vol 90 (2) ◽  
pp. 325-329 ◽  
Author(s):  
R. E. Hohn ◽  
R. Sridhar ◽  
G. W. Long
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Machine Tool ◽  
Linear Differential Equation ◽  
Mathieu Equation ◽  
Milling Process ◽  
Machine Tool Chatter ◽  
Linear Differential ◽  
The Stability ◽  
Special Case

In an effort to determine the stability of the milling process, and due to the complexity of its describing equation, a special case of this equation is considered. In this way, it is possible to isolate and study its salient characteristics. Moreover, the simplified equation is representative of a machining operation on which experimental data can be obtained. This special case is described by a linear differential equation with periodic coefficients. A computer algorithm is developed for determining the stability of this equation. To demonstrate the use of the algorithm on an example whose solution is known, the classical Mathieu equation is studied. Also, experimental results on an actual machining operation described by this type of equation are compared to the results found using the stability algorithm. As a result of this work, some knowledge about the stability solution of the general milling process is obtained.

Stability of Ring-Stiffened Tubular Members Under External Pressure

1995 ◽  
Vol 117 (2) ◽  
pp. 150-155 ◽  
Author(s):  
S. A. Karamanos ◽  
J. L. Tassoulas
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Stability Analysis ◽  
External Pressure ◽  
Nonlinear Finite Element ◽  
Steel Tubes ◽  
Deformation Plasticity ◽  
The Stability ◽  
Element Technique ◽  
Stiffened Steel

This paper presents results of a rigorous nonlinear finite element technique for the stability analysis of ring-stiffened steel tubes under external pressure. Large deformation, plasticity, as well as residual stresses and imperfections, are taken into account. Both internal and external stiffeners are simulated. A study of various parameters which affect pressure capacity is summarized, along with a comparison with available experimental data.

Multi-Point Suspension Design and Stability Analysis of a Scaled Hoop Truss Antenna Structure

2021 ◽  
pp. 2150077
Author(s):  
Guoliang Ma ◽  
Minglong Xu ◽  
Longlei Dong ◽  
Zhuo Zhang
Keyword(s):  
Experimental Data ◽  
Stability Analysis ◽  
Transfer Function ◽  
Open Loop ◽  
Scaled Model ◽  
Antenna Structure ◽  
Loop Transfer Function ◽  
Before And After ◽  
Vibration Experiment ◽  
The Stability

This paper proposes a scaled model to investigate the dynamic characteristics and stability of a hoop truss antenna on the ground. First, the statically indeterminate equation for the multi-point suspension is established, along with the voltage of the suspension motor calculated. Then the transfer function of the system is theoretically established. The scaled model is established before and after suspension, and the static deformation and natural frequency of the system are obtained by calculation and measurement. There exist the shaking mode and nodding mode. Also, a vibration experiment is conducted for the system to obtain the vibration response. With this, the transfer function is identified by the system identification method, which appears to be of the second order, and the stability is analyzed through the zero pole diagram. The experiment results show that the first two frequencies are close before and after suspension. Moreover, the stability of the system can be judged by the open-loop transfer function. It is concluded that the vibration experimental data of the scaled model can be used as a reference for the large hoop truss antenna structure.

scholarly journals Libration-driven multipolar instabilities

2014 ◽  
Vol 739 ◽  
pp. 502-543 ◽  
Author(s):  
D. Cébron ◽  
S. Vantieghem ◽  
W. Herreman
Keyword(s):  
Stability Analysis ◽  
Rotation Rate ◽  
Basic Flow ◽  
Three Dimensions ◽  
Fluid Layers ◽  
Elliptical Instability ◽  
The Stability ◽  
Spherical Container ◽  
Boundary Deformation ◽  
Analytical Expressions

AbstractWe consider rotating flows in non-axisymmetric enclosures that are driven by libration, i.e. by a small periodic modulation of the rotation rate. Thanks to its simplicity, this model is relevant to various contexts, from industrial containers (with small oscillations of the rotation rate) to fluid layers of terrestrial planets (with length-of-day variations). Assuming a multipolar $n$-fold boundary deformation, we first obtain the two-dimensional basic flow. We then perform a short-wavelength local stability analysis of the basic flow, showing that an instability may occur in three dimensions. We christen it the libration-driven multipolar instability (LDMI). The growth rates of the LDMI are computed by a Floquet analysis in a systematic way, and compared to analytical expressions obtained by perturbation methods. We then focus on the simplest geometry allowing the LDMI, a librating deformed cylinder. To take into account viscous and confinement effects, we perform a global stability analysis, which shows that the LDMI results from a parametric resonance of inertial modes. Performing numerical simulations of this librating cylinder, we confirm that the basic flow is indeed established and report the first numerical evidence of the LDMI. Numerical results, in excellent agreement with the stability results, are used to explore the nonlinear regime of the instability (amplitude and viscous dissipation of the driven flow). We finally provide an example of LDMI in a deformed spherical container to show that the instability mechanism is generic. Our results show that the previously studied libration-driven elliptical instability simply corresponds to the particular case $n= 2$ of a wider class of instabilities. Summarizing, this work shows that any oscillating non-axisymmetric container in rotation may excite intermittent, space-filling LDMI flows, and this instability should thus be easy to observe experimentally.

A Decade of Wave Power Development in India—The Challenges

2002 ◽  
Vol 36 (4) ◽  
pp. 59-73 ◽  
Author(s):  
S. Neelamani
Keyword(s):  
Power Plant ◽  
Wave Energy ◽  
Research Effort ◽  
Wave Force ◽  
Wave Power ◽  
Nicobar Island ◽  
Model Studies ◽  
Pilot Wave ◽  
Kerala State ◽  
The Stability

Wave energy research in India started in 1984. Six years of research by the Indian wave energy group culminated in the installation of a 150 kW capacity pilot wave power plant in Vizhinjam, off Trivandrum in the Kerala state, in the Arabian Sea during 1990 (Figure 1). The problems encountered during the research, construction and installation directed the group to continue the research effort. The structural configuration of the caisson has changed considerably so that it has sufficient floating stability during towing, enough space for sand ballasting to increase the stability of the caisson against horizontal sliding and overturning and sufficient space at the rear of the caisson for berthing vessels (Figures 2 and 3). After the installation of a wave power caisson of 150 kW off Trivandrum, further attention was focused on a 1 to 2 MW wave power plant for sites, where new breakwaters for harbors is envisaged (Thangassery Harbour in the West Coast of India (Figure 4) and Mus Bay in Car Nicobar Islands (Figure 5) in Bay of Bengal). Optimum center to center spacing between the caissons was determined based on physical model studies. Further research was carried out to improve the wave to pneumatic efficiency by changing the harbor configuration. Techniques to reduce the wave force on the caisson were also simultaneously studied. The wave power economics is site specific. Two sites (Thangassery in Kerala and Mus bay in Car Nicobar Island) were selected to analyze the wave power economics. Wave power is not likely to become economical in the near future. A continued research effort in the research is very important in order to improve the efficiency of wave power conversion and reduce the cost of construction. A decade of experience (1986 to 1996) in wave power research is presented in this paper.

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