ON THE EQUILIBRIUM CONFIGURATION OF TWO REISSNER-NORDSTROM OBJECTS AND REPULSIVE GRAVITY

2010 ◽  
Vol 57 (3(1)) ◽  
pp. 571-577
Author(s):  
George Alekseev ◽  
Vladimir Belinski
Keyword(s):  
Equilibrium Configuration ◽  
Repulsive Gravity

The Schwarzschild black hole

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Equilibrium Configuration ◽  
Original Form ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Schwarzschild Geometry

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.

scholarly journals The Vogt-Russell Theorem, and New Results on an Old Problem

1978 ◽  
Vol 80 ◽  
pp. 303-311
Author(s):  
Helmuth Kähler
Keyword(s):  
Existence And Uniqueness ◽  
Thermal Equilibrium ◽  
Equilibrium Configuration ◽  
Mathematical Proof ◽  
Stellar Structure

Half a centry ago Henry Norris Russell and Heinrich Vogt independently made a conjecture concerning the structure of spherical stars which are in hydrostatic and thermal equilibrium (Russell, 1927; Vogt, 1926). This conjecture has later come to be known as the Vogt-Russell theorem and is usually formulated as follows: The structure of a star is uniquely determined by the mass and the composition. In other words, the statement claims the existence and uniqueness of a stellar equilibrium configuration for given parameters mass and composition, and you may find what is called a mathematical proof in many textbooks on stellar structure.

scholarly journals Electric potential differences across auroral generator interfaces

2013 ◽  
Vol 31 (2) ◽  
pp. 251-261 ◽  
Author(s):  
J. De Keyser ◽  
M. Echim
Keyword(s):  
Electric Field ◽  
High Altitude ◽  
Electric Fields ◽  
Electric Potential ◽  
Equilibrium Configuration ◽  
Potential Difference ◽  
Field Profile ◽  
Electric Potential Difference ◽  
Electric Field Profile

Abstract. Strong localized high-altitude auroral electric fields, such as those observed by Cluster, are often associated with magnetospheric interfaces. The type of high-altitude electric field profile (monopolar, bipolar, or more complicated) depends on the properties of the plasmas on either side of the interface, as well as on the total electric potential difference across the structure. The present paper explores the role of this cross-field electric potential difference in the situation where the interface is a tangential discontinuity. A self-consistent Vlasov description is used to determine the equilibrium configuration for different values of the transverse potential difference. A major observation is that there exist limits to the potential difference, beyond which no equilibrium configuration of the interface can be sustained. It is further demonstrated how the plasma densities and temperatures affect the type of electric field profile in the transition, with monopolar electric fields appearing primarily when the temperature contrast is large. These findings strongly support the observed association of monopolar fields with the plasma sheet boundary. The role of shear flow tangent to the interface is also examined.

Atomistic Simulations of Nanoindentation on Cu (111) with a Void

2008 ◽  
Vol 33-37 ◽  
pp. 919-924
Author(s):  
Chung Ming Tan ◽  
Yeau Ren Jeng ◽  
Yung Chuan Chiou
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Indentation Depth ◽  
Equilibrium Configuration ◽  
Complete System ◽  
Internal Surface ◽  
Atomistic Simulations ◽  
Element Formulation ◽  
Variable Parameters ◽  
Deformed State

This paper employs static atomistic simulations to investigate the effect of a void on the nanoindentation of Cu(111). The simulations minimize the potential energy of the complete system via finite element formulation to identify the equilibrium configuration of any deformed state. The size and depth of the void are treated as two variable parameters. The numerical results reveal that the void disappears when the indentation depth is sufficiently large. A stress concentration is observed at the internal surface of the void in all simulations cases. The results indicate that the presence of a void has a significant influence on the nanohardness extracted from the nanoindentation tests.

The molecular orbital theory of chemical valency. V. The structure of water and similar molecules

1950 ◽  
Vol 202 (1070) ◽  
pp. 323-336 ◽  
Keyword(s):  
Spatial Distribution ◽  
Equilibrium Configuration ◽  
Bond Angle ◽  
Lone Pair ◽  
Orbital Theory ◽  
Hydrogen Atoms ◽  
Molecular Formation ◽  
Major Factors ◽  
Lone Pair Electrons ◽  
Electrostatic Repulsions

The theory of molecular and equivalent orbitals developed in previous papers of this series is used to discuss the spatial distribution of lone-pair electrons in molecules such as H 2 O and NH 3 and the part they play in determining the equilibrium configuration. Previous treatments of H 2 O have assumed that the lone pairs are essentially unaltered by molecular formation. It is shown here, on the other hand, that they will be displaced so as to be mainly concentrated on the side of the O-nucleus remote from the hydrogen atoms. An important consequence of this is that the lone-pair electrons will make a contribution to the total dipole moment. Comparison of the experimentally observed moment with an approximate quantitative treatment suggests that, as a result of this, transfer of electrons from the hydrogen atoms to the oxygen does not occur to the extent that has previously been believed. The variation of the spatial distribution of the orbitals of H 2 O with changes of nuclear configuration is examined and it is shown that, in the equilibrium position, the electronic structure can be described approximately by two sets of two equivalent orbitals pointing in nearly tetrahedral directions. The dependence of total energy on bond angle is discussed and it is shown that electrostatic repulsions between the equivalent orbitals are major factors in determining the equilibrium configuration. Similar considerations apply to NH 3 .

Equilibrium, Stability, and Robustness in Underactuated Grasping

2007 ◽  
Author(s):  
Gert A. Kragten ◽  
Just L. Herder
Keyword(s):  
Degrees Of Freedom ◽  
Equilibrium Configuration ◽  
Performance Measure ◽  
Equilibrium Stability ◽  
Equilibrium Conditions ◽  
Design Decisions ◽  
Grasp Stability ◽  
Movable Object ◽  
Passive Compliance ◽  
Freely Moving

This paper aims to develop a performance measure for underactuated grasping devices, which is useful in making design decisions to obtain an optimally performing device. Underactuated fingers, defined as having more degrees of freedom than degrees of actuation, intrinsically adapt their shape to the object. However, the equilibrium configuration and grasp forces of these fingers are not fully controllable, which may limit their performance. The grasp performance measure defined in this paper consists of three aspects: (1) the ability to grasp objects, which is limited by the equilibrium conditions and constraints of both the underactuated fingers and the freely movable object; (2) the grasp stability, which takes the passive compliance of the fingers into account; (3) the ability to oppose disturbance forces on the grasped object by passively adapting the frictional grasp forces. This measure was applied to optimize a planar grasping device with two underactuated fingers, each consisting of two phalanges, able to grasp freely moving circular objects.

Two-dimensional motion of a rolling non-circular cylinder on a flat horizontal surface

2018 ◽  
Vol 96 (6) ◽  
pp. 627-632
Author(s):  
Amir Aghamohammadi ◽  
Mohammad Khorrami
Keyword(s):  
Circular Cylinder ◽  
Energy Conservation ◽  
Cross Section ◽  
Equilibrium Configuration ◽  
Focal Point ◽  
Center Of Mass ◽  
Horizontal Surface ◽  
Two Dimensional ◽  
Small Oscillations ◽  
Equilibrium Configurations

The two dimensional motion of a generally non-circular non-uniform cylinder on a flat horizontal surface is investigated. Assuming that the cylinder does not slip, energy conservation is used to study the motion in general. Points of returns, and small oscillations around equilibrium configuration are studied. As examples, cylinders are studied for which the cross section is an ellipse, with the center of mass at the center of the ellipse or at a focal point, and the frequencies of small oscillations around their equilibrium configurations are found. The conditions for losing contact or sliding are also investigated. Finally, the motion is studied in more detail for the case of a nearly circular cylinder.

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.

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