25,213 research outputs found
An explanation of the Newman-Janis Algorithm
After the original discovery of the Kerr metric, Newman and Janis showed that
this solution could be ``derived'' by making an elementary complex
transformation to the Schwarzschild solution. The same method was then used to
obtain a new stationary axisymmetric solution to Einstein's field equations now
known as the Kerr-newman metric, representing a rotating massive charged black
hole. However no clear reason has ever been given as to why the Newman-Janis
algorithm works, many physicist considering it to be an ad hoc procedure or
``fluke'' and not worthy of further investigation. Contrary to this belief this
paper shows why the Newman-Janis algorithm is successful in obtaining the
Kerr-Newman metric by removing some of the ambiguities present in the original
derivation. Finally we show that the only perfect fluid generated by the
Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov
typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra
Two-fluid model of the solar corona
A simple model of the lower corona which allows for a possible difference in the electron and proton temperatures is analyzed. With the introduction of a phenomenological heating term, temperature and density profiles are calculated for several different cases. It is found that, under certain circumstances, the electron and proton temperatures may differ significantly
Stress-intensity factor calculations using the boundary force method
The Boundary Force Method (BFM) was formulated for the three fundamental problems of elasticity: the stress boundary value problem, the displacement boundary value problem, and the mixed boundary value problem. Because the BFM is a form of an indirect boundary element method, only the boundaries of the region of interest are modeled. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, unlike other boundary element methods, here the crack face need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing a center-cracked specimen subjected to mixed boundary conditions and a three-hole cracked configuration subjected to traction boundary conditions. The results obtained are in good agreement with accepted numerical solutions. The method is then used to generate stress-intensity solutions for two common cracked configurations: an edge crack emanating from a semi-elliptical notch, and an edge crack emanating from a V-notch. The BFM is a versatile technique that can be used to obtain very accurate stress intensity factors for complex crack configurations subjected to stress, displacement, or mixed boundary conditions. The method requires a minimal amount of modeling effort
Wall interference assessment and corrections
Wind tunnel wall interference assessment and correction (WIAC) concepts, applications, and typical results are discussed in terms of several nonlinear transonic codes and one panel method code developed for and being implemented at NASA-Langley. Contrasts between 2-D and 3-D transonic testing factors which affect WIAC procedures are illustrated using airfoil data from the 0.3 m Transonic Cryogenic Tunnel and Pathfinder 1 data from the National Transonic Facility. Initial results from the 3-D WIAC codes are encouraging; research on and implementation of WIAC concepts continue
Boundary force method for analyzing two-dimensional cracked bodies
The Boundary Force Method (BFM) was formulated for the two-dimensional stress analysis of complex crack configurations. In this method, only the boundaries of the region of interest are modeled. The boundaries are divided into a finite number of straight-line segments, and at the center of each segment, concentrated forces and a moment are applied. This set of unknown forces and moments is calculated to satisfy the prescribed boundary conditions of the problem. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate are used as the fundamental solution. Thus, the crack need not be modeled as part of the boundary. The formulation of the BFM is described and the accuracy of the method is established by analyzing several crack configurations for which accepted stress-intensity factor solutions are known. The crack configurations investigated include mode I and mixed mode (mode I and II) problems. The results obtained are, in general, within + or - 0.5 percent of accurate numerical solutions. The versatility of the method is demonstrated through the analysis of complex crack configurations for which limited or no solutions are known
Connectedness properties of the set where the iterates of an entire function are unbounded
We investigate the connectedness properties of the set I+(f) of points where the iterates of an entire function f are unbounded. In particular, we show that I+(f) is connected whenever iterates of the minimum modulus of f tend to ∞. For a general transcendental entire function f, we show that I+(f)∪ \{\infty\} is always connected and that, if I+(f) is disconnected, then it has uncountably many components, infinitely many of which are unbounded
Fast algorithm for detecting community structure in networks
It has been found that many networks display community structure -- groups of
vertices within which connections are dense but between which they are sparser
-- and highly sensitive computer algorithms have in recent years been developed
for detecting such structure. These algorithms however are computationally
demanding, which limits their application to small networks. Here we describe a
new algorithm which gives excellent results when tested on both
computer-generated and real-world networks and is much faster, typically
thousands of times faster than previous algorithms. We give several example
applications, including one to a collaboration network of more than 50000
physicists.Comment: 5 pages, 4 figure
Radiation Reaction fields for an accelerated dipole for scalar and electromagnetic radiation
The radiation reaction fields are calculated for an accelerated changing
dipole in scalar and electromagnetic radiation fields. The acceleration
reaction is shown to alter the damping of a time varying dipole in the EM case,
but not the scalar case. In the EM case, the dipole radiation reaction field
can exert a force on an accelerated monopole charge associated with the
accelerated dipole. The radiation reaction of an accelerated charge does not
exert a torque on an accelerated magnetic dipole, but an accelerated dipole
does exert a force on the charge. The technique used is that originally
developed by Penrose for non-singular fields and extended by the author for an
accelerated monopole charge.Comment: 11 page
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