A paradox of hovering insects in two-dimensional space

2008 ◽  
Vol 617 ◽  
pp. 207-229 ◽  
Author(s):  
MAKOTO IIMA
Keyword(s):  
External Force ◽  
Stokes Equations ◽  
Hydrodynamic Force ◽  
Dimensional Space ◽  
Exact Formula ◽  
Uniform Flow ◽  
Far Field ◽  
Two Dimensional ◽  
Field Representation ◽  
Whole Space

A paradox concerning the flight of insects in two-dimensional space is identified: insects maintaining their bodies in a particular position (hovering) cannot, on average, generate hydrodynamic force if the induced flow is temporally periodic and converges to rest at infinity. This paradox is derived by using the far-field representation of periodic flow and the generalized Blasius formula, an exact formula for a force that acts on a moving body, based on the incompressible Navier–Stokes equations. Using this formula, the time-averaged force can be calculated solely in terms of the time-averaged far-field flow. A straightforward calculation represents the averaged force acting on an insect under a uniform flow, −〈V〉, determined by the balance between the hydrodynamic force and an external force such as gravity. The averaged force converges to zero in the limit 〈V〉 → 0, which implies that insects in two-dimensional space cannot hover under any finite external force if the direction of the uniform flow has a component parallel to the external force. This paradox provides insight into the effect of the singular behaviour of the flow around hovering insects: the far-field wake covers the whole space. On the basis of these assumptions, the relationship between this paradox and real insects that actually achieve hovering is discussed.

New Exact Axisymmetric Solutions to the Navier–Stokes Equations

2019 ◽  
Vol 75 (1) ◽  
pp. 29-42
Author(s):  
Oleg Bogoyavlenskij
Keyword(s):  
Exact Solutions ◽  
Stokes Equations ◽  
Dimensional Space ◽  
Phase Portraits ◽  
Navier Stokes ◽  
Elementary Functions ◽  
Navier Stokes Equations ◽  
New Exact Solutions ◽  
Whole Space ◽  
Dependent Viscosity

AbstractInfinite-dimensional space of axisymmetric exact solutions to the Navier–Stokes equations with time-dependent viscosity $\nu(t)$ is constructed. Inner transformations of the exact solutions are defined that produce an infinite sequence of new solutions from each known one. The solutions are analytic in the whole space ℝ3 and are described by elementary functions. The bifurcations of the instantaneous (for $t={t_{0}}$) phase portraits of the viscous fluid flows are studied for the new exact solutions. Backlund transforms between the axisymmetric Helmholtz equation and a linear case of the Grad–Shafranov equation are derived.

A diagram of the minimum necessary internal force required to resist external forces on two-point-grasped objects in two-dimensional space

Robotica ◽  
2011 ◽  
Vol 30 (5) ◽  
pp. 857-864
Author(s):  
Satoshi Ito ◽  
Kohta Tanaka ◽  
Minoru Sasaki
Keyword(s):  
External Force ◽  
Dimensional Space ◽  
Internal Force ◽  
Polar Coordinate System ◽  
Coordinate Frame ◽  
Two Dimensional ◽  
Force Diagram ◽  
Contact Points ◽  
Polar Coordinate ◽  
External Forces

SUMMARYThis paper considers the magnitude of the gripping power, i.e., the internal force that depends on the grasping posture or object orientation in a two-dimensional grasp by two contact points with friction. Expressing the effect of variations in the object posture as the direction of an external force, we propose an “internal force diagram.” The internal force necessary to create a statically stable grasp is depicted in the object coordinate frame. Then, a polar coordinate system is introduced in which the orientation represents the direction of the external force, while the distance from the origin represents the minimum necessary internal force. We demonstrate a method based on friction cone configurations to manually draw the internal force diagram, using only a ruler and a compass. The validity of this drawing method is confirmed by a comparison with computer-generated plots. Finally, the characteristics of the internal force diagram are discussed.

Locomotion inside a surfactant-laden drop at low surface Péclet numbers

2018 ◽  
Vol 851 ◽  
pp. 187-230 ◽  
Author(s):  
Vaseem A. Shaik ◽  
Vishwa Vasani ◽  
Arezoo M. Ardekani
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Stable Configuration ◽  
Far Field ◽  
Small Reynolds Number ◽  
Drop Surface ◽  
Field Representation ◽  
Small Surface ◽  
Bipolar Coordinates ◽  
Drag Forces

We investigate the dynamics of a swimming microorganism inside a surfactant-laden drop for axisymmetric configurations under the assumptions of small Reynolds number and small surface Péclet number $(Pe_{s})$. Expanding the variables in $Pe_{s}$, we solve the Stokes equations for the concentric configuration using Lamb’s general solution, while the dynamic equation for the stream function is solved in the bipolar coordinates for the eccentric configurations. For a two-mode squirmer inside a drop, the surfactant redistribution can either increase or decrease the magnitude of swimmer and drop velocities, depending on the value of the eccentricity. This was explained by analysing the influence of surfactant redistribution on the thrust and drag forces acting on the swimmer and the drop. The far-field representation of a surfactant-covered drop enclosing a pusher swimmer at its centre is a puller; the strength of this far field is reduced due to the surfactant redistribution. The advection of surfactant on the drop surface leads to a time-averaged propulsion of the drop and the time-reversible swimmer that it engulfs, thereby causing them to escape from the constraints of the scallop theorem. We quantified the range of parameters for which an eccentrically stable configuration can be achieved for a two-mode squirmer inside a clean drop. The surfactant redistribution shifts this eccentrically stable position towards the top surface of the drop, although this shift is small.

Numerical Analysis of Sound Generation by a Two-Dimensional Cylinder in a Uniform Flow

2003 ◽  
Author(s):  
Ayaka Imamura ◽  
Nozomu Hatakeyama ◽  
Osamu Inoue
Keyword(s):  
Sound Pressure ◽  
Stokes Equations ◽  
Sound Field ◽  
Uniform Flow ◽  
Navier Stokes ◽  
Pressure Waves ◽  
Two Dimensional ◽  
Sound Generation ◽  
Navier Stokes Equations ◽  
Characteristic Features

The sound generated by a squarer cylinder in a uniform flow is investigated by direct numerical simulation of the two-dimensional compressible Navier–Stokes equations. The characteristic features of the generated sound are investigated and compared for different configurations and angles of attack. Results show that sound pressure waves are generated by vortex shedding from the cylinder into its wake. The sound field is dominated by lift dipole. The effect of the angle of attack on the sound generation and propagation is also analyzed.

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

Political Cleavages and Political Parties

2018 ◽  
Author(s):  
Russell J. Dalton
Keyword(s):  
Political Parties ◽  
Dimensional Space ◽  
New Left ◽  
Party Systems ◽  
European Parliament ◽  
Two Dimensional ◽  
Far Right ◽  
Policy Positions ◽  
Cultural Policies ◽  
Policy Choices

This chapter uses the cleavage positions of Candidates to the European Parliament (CEPs) to as representative of their parties’ political positions. Three surveys of CEPs track the evolution of party supply in European party systems. In 1979 parties were primarily aligned along a Left–Right economic cleavage. Gradually new left and Green parties began to compete in elections and crystallized and represented liberal cultural policies. In recent decades new far-right parties arose to represent culturally conservative positions. The cross-cutting cultural cleavage has also prompted many of the established parties to alter their policy positions. In most multiparty systems, political parties now compete in a fully populated two-dimensional space. This increases the supply of policy choices for the voters. The analyses are based on the Candidates to the European Parliament Studies in 1979, 1994, and 2009.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

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