Relative equilibrium and collapse configurations of heterogeneous vortex triple rings

2007 ◽  
Vol 236 (2) ◽  
pp. 123-130 ◽  
Author(s):  
Kevin A. O’Neil
Keyword(s):  
Relative Equilibrium

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

scholarly journals Land area increase in Ukrainian part of the Danube delta

2021 ◽  
Author(s):  
V. M. Starodubtsev ◽  
◽  
M. M. Ladyka ◽  
Keyword(s):  
Land Cover ◽  
Satellite Images ◽  
Extreme Event ◽  
Relative Equilibrium ◽  
Danube River ◽  
Danube Delta ◽  
Land Area ◽  
Area Increase ◽  
Landsat Satellite ◽  
Quantitative Indicators

The quantitative indicators of land growth in the Ukrainian part of the Danube delta are considered. Comparison of Landsat satellite images in three key areas of the delta showed that for the period 1975-2020 the area of wetlands at the mouth of the Сhilia channel increased by 1448 hectares due to the accumulation of sediments between the Starostambul and Limba branches and their overgrowth with vegetation. In the area of the Bystroe channel, the area of new lands increased by 1037 hectares due to the artificial deepening of this channel for the Ukrainian ships passage into the Danube River and the deposition of sediments along the coast. A slightly smaller increase in land cover (797 ha) was found in the northern part of the coast of the Ukrainian part of the delta, where saline and carbonate soils are formed. In the future, active land growth is expected in the Musura bay between the mouths of the Starostambul and Sulina branches, ie at the contact of Ukraine and Romania. Some changes in these parameters are expected after a powerful flood in 2021, which will become known after the establishment of a relative equilibrium between the processes of accumulation and erosion after this extreme event.

scholarly journals Exact solution of the planar motion of three arbitrary point vortices

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1530017
Author(s):  
Robert Conte ◽  
Laurent de Seze
Keyword(s):  
Exact Solution ◽  
Equilibrium Configuration ◽  
Relative Equilibrium ◽  
Arbitrary Point ◽  
Triple Collision ◽  
Stability Conditions ◽  
Adiabatic Invariants ◽  
The Third ◽  
Elastic Diffusion ◽  
Equilateral Triangles

We give an exact quantitative solution for the motion of three vortices of any strength, which Poincaré showed to be integrable. The absolute motion of one vortex is generally biperiodic: in uniformly rotating axes, the motion is periodic. There are two kinds of relative equilibrium configuration: two equilateral triangles and one or three colinear configurations, their stability conditions split the strengths space into three domains in which the sets of trajectories are topologically distinct. According to the values of the strengths and the initial positions, all the possible motions are classified. Two sets of strengths lead to generic motions other than biperiodic. First, when the angular momentum vanishes, besides the biperiodic regime there exists an expansion spiral motion and even a triple collision in a finite time, but the latter motion is nongeneric. Second, when two strengths are opposite, the system also exhibits the elastic diffusion of a vortex doublet by the third vortex. For given values of the invariants, the volume of the phase space of this Hamiltonian system is proportional to the period of the reduced motion, a well known result of the theory of adiabatic invariants. We then formally examine the behaviour of the quantities that Onsager defined only for a large number of interacting vortices.

scholarly journals Double Pendulum Induced Stability

2015 ◽  
Vol 07 (06) ◽  
pp. 1550088
Author(s):  
Bezdenejnykh Nikolai ◽  
Andres Mateo Gabin ◽  
Raul Zazo Jimenez
Keyword(s):  
Theoretical Analysis ◽  
Potential Energy ◽  
High Frequency ◽  
Relative Equilibrium ◽  
Double Pendulum ◽  
Harmonic Vibrations ◽  
Hamilton Equations ◽  
High Frequency Harmonic ◽  
Good Agreement ◽  
Frequency Harmonic

In this work, a study of the relative equilibrium of a double pendulum whose point of suspension performs high frequency harmonic vibrations is presented. In order to determine the induced positions of equilibrium of the double pendulum at different gravity and vibration configurations, a set of experiments has been conducted. The theoretical analysis of the problem has been developed using Kapitsa’s method and numerical method. The method of Kapitsa allows to analyze the potential energy of a system in general and to find the values of the parameters of the problem that correspond to the relative extreme of energy — positions of stable or unstable equilibrium. The results of numerical and theoretical analysis of Hamilton equations are in good agreement with the results of the experiments.

scholarly journals The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. S. Amer
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Dynamical Behavior ◽  
Vertical Plane ◽  
The Body ◽  
Physical Parameters ◽  
Pendulum Model

In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.

An assessment of historic human impact on south-eastern Australian environmental systems, using late Holocene rates of environmental change

2002 ◽  
Vol 50 (4) ◽  
pp. 455 ◽  
Author(s):  
John R. Dodson ◽  
Stuart D. Mooney
Keyword(s):  
Human Impact ◽  
Late Holocene ◽  
Vegetation Change ◽  
Fire History ◽  
Relative Equilibrium ◽  
Rate Of Change ◽  
South Eastern ◽  
Environmental Systems ◽  
Eastern Australia ◽  
South Eastern Australia

The late Holocene of south-eastern Australia was typified by stable climate, vegetation and sedimentary regimes, in relative equilibrium with Aboriginal land use and fire management. The arrival of Europeans, with the associated vegetation clearance, introduction of exotic plants and animals, notably for grazing and agriculture and a change in fire regimes, resulted in changes in vegetation and sedimentary patterns. Impacts varied in type and magnitude through the region and evidence of impacts that is preserved varies with sedimentary setting. Here we take a number of proxy measures of vegetation change, fire history, erosion and weathering from six sediment sections across south-eastern Australia and use an index to measure overall rate of change. This shows that the vegetation and environmental systems of south-eastern Australia have been very sensitive to human impact following European settlement.

Study on the Time-Dependent Characteristics of Sandstone under Chemical Corrosion

2012 ◽  
Vol 256-259 ◽  
pp. 174-178
Author(s):  
Wu Xiu Ding
Keyword(s):  
Elastic Wave ◽  
Ph Value ◽  
Relative Equilibrium ◽  
Elastic Wave Velocity ◽  
Time Dependent ◽  
Test Results ◽  
Chemical Corrosion ◽  
Highly Sensitive ◽  
Chemical Solutions ◽  
The Masses

The masses, elastic wave velocities of sandstone specimens under chemical corrosion and pH values of solutions soaking specimens are tested in different soak time. It is indicated that elastic wave velocity can be utilized to perform time-dependent test research on the same specimen with the advantage of being highly sensitive to micro void and without damage on specimen in the testing process. The test results show that the relationships between the masses and the chemical solutions are small.The chemical erosion action on rock will reach a relative equilibrium status in a certain time in the closed chemical environment and pH value will reach ultimately one stable value which will be decided by the rock characteristics. The alkalescence of sandstone decides that the solutions of soaking specimen will turn to alkalescence.

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