scholarly journals Lorentzian spacetimes with constant curvature invariants in three dimensions

2007 ◽  
Vol 25 (2) ◽  
pp. 025008 ◽  
Author(s):  
Alan Coley ◽  
Sigbjørn Hervik ◽  
Nicos Pelavas
Keyword(s):  
Constant Curvature ◽  
Three Dimensions ◽  
Curvature Invariants

scholarly journals Kinematic formula and tube formula in space of constant curvature

1990 ◽  
Vol 33 (1) ◽  
pp. 79-88
Author(s):  
Sungyun Lee
Keyword(s):  
Euclidean Space ◽  
Euler Characteristic ◽  
Constant Curvature ◽  
Kinematic Formula ◽  
Curvature Invariants ◽  
Space Of Constant Curvature

The Euler characteristic of an even dimensional submanifold in a space of constant curvature is given in terms of Weyl's curvature invariants. A derivation of Chern's kinematic formula in non-Euclidean space is completed. As an application of above results Weyl's tube formula about an odd-dimensional submanifold in a space of constant curvature is obtained.

scholarly journals Basis for scalar curvature invariants in three dimensions

2014 ◽  
Vol 31 (23) ◽  
pp. 235010 ◽  
Author(s):  
A A Coley ◽  
A MacDougall ◽  
D D McNutt
Keyword(s):  
Scalar Curvature ◽  
Three Dimensions ◽  
Curvature Invariants

Lorentzian spacetimes with constant curvature invariants in four dimensions

2009 ◽  
Vol 26 (12) ◽  
pp. 125011 ◽  
Author(s):  
Alan Coley ◽  
Sigbjørn Hervik ◽  
Nicos Pelavas
Keyword(s):  
Constant Curvature ◽  
Four Dimensions ◽  
Curvature Invariants

scholarly journals Geometric curve flows in low dimensional Cayley–Klein geometries

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Joseph Benson ◽  
Francis Valiquette
Keyword(s):  
Evolution Equations ◽  
Three Dimensions ◽  
Geometric Flows ◽  
Moving Frames ◽  
Arc Length ◽  
Recursion Operators ◽  
Curvature Invariants ◽  
Curve Flows ◽  
Low Dimensional ◽  
Equivariant Moving Frames

Abstract Using the method of equivariant moving frames, we derive the evolution equations for the curvature invariants of arc-length parametrized curves under arc-length preserving geometric flows in two-, three- and four-dimensional Cayley–Klein geometries. In two and three dimensions, we obtain recursion operators, which show that the curvature evolution equations obtained are completely integrable.

scholarly journals Curvature Invariants for the Alcubierre and Natário Warp Drives

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 21 ◽  
Author(s):  
Brandon Mattingly ◽  
Abinash Kar ◽  
Matthew Gorban ◽  
William Julius ◽  
Cooper K. Watson ◽  
...  
Keyword(s):  
Constant Curvature ◽  
Constant Velocity ◽  
Shape Function ◽  
Skin Depth ◽  
Safe Harbor ◽  
Field Equations ◽  
Curvature Invariants ◽  
Unique Effect ◽  
Coordinate Mapping ◽  
Faster Than Light

A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natário warp drives at a constant velocity. Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes, such as warp drives. Warp drives are the theoretical solutions to Einstein’s field equations that allow for the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter’s unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natário warp drive do not contain a wake or a constant curvature, indicating that these are unique features of the accelerating Natário warp drive.

scholarly journals STATIC SPHERICALLY SYMMETRIC SOLUTIONS FOR CONFORMAL GRAVITY IN THREE DIMENSIONS

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1588-1592 ◽  
Author(s):  
JULIO OLIVA ◽  
DAVID TEMPO ◽  
RICARDO TRONCOSO
Keyword(s):  
Black Holes ◽  
Constant Curvature ◽  
Conformal Transformation ◽  
Three Dimensions ◽  
Spherically Symmetric ◽  
Conformal Gravity ◽  
Spatial Curvature ◽  
Static Universe ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

Static spherically symmetric solutions for conformal gravity in three dimensions are found. Black holes and wormholes are included within this class. Asymptotically the black holes are spacetimes of arbitrary constant curvature, and they are conformally related to the matching of different solutions of constant curvature by means of an improper conformal transformation. The wormholes can be constructed from suitable identifications of a static universe of negative spatial curvature, and it is shown that they correspond to the conformal matching of two black hole solutions with the same mass.

Hypothetical graphite structures with negative gaussian curvature

1993 ◽  
Vol 343 (1667) ◽  
pp. 113-127 ◽  
Keyword(s):  
Constant Curvature ◽  
Gaussian Curvature ◽  
Minimal Surfaces ◽  
Hyperbolic Plane ◽  
Negative Curvature ◽  
Positive Curvature ◽  
Three Dimensions ◽  
Ring Size ◽  
Two Dimensional ◽  
Planar Lattice

We consider the geometries of hypothetical structures, derived from a graphite net by the inclusion of rings of seven or eight bonds, which may be periodic in three dimensions. Just as the positive curvature of fullerene sheets is produced by the presence of pentagons, so negative curvature appears with a mean ring size of more than six. These structures are based on coverings of periodic minimal surfaces, and surfaces parallel to these, which are known as exactly defined mathematical objects. In the same way that the cylindrical and conical structures can be generated (geometrically) by curving flat sheets so that the perimeter of a ring can be identified with a vector in the two-dimensional planar lattice, so these structures can be related to tessellations of the hyperbolic plane. The geometry of transformations at constant curvature relates various surfaces. Some of the proposed structures, which are reviewed here, promise to have lower energies than those of the convex fullerenes

High-resolution scanning electron microscopy (HRSEM) of mitochondria from various rat tissues

1988 ◽  
Vol 46 ◽  
pp. 14-15
Author(s):  
P.J. Lea ◽  
M.J. Hollenberg
Keyword(s):  
Electron Microscopy ◽  
Pigment Epithelium ◽  
Retinal Pigment ◽  
Rat Hepatocytes ◽  
Three Dimensions ◽  
Objective Lens ◽  
Rat Tissues ◽  
Thin Sections ◽  
Reconstruction Methods ◽  
Scanning Electron

Our current understanding of mitochondrial ultrastructure has been derived primarily from thin sections using transmission electron microscopy (TEM). This information has been extrapolated into three dimensions by artist's impressions (1) or serial sectioning techniques in combination with computer processing (2). The resolution of serial reconstruction methods is limited by section thickness whereas artist's impressions have obvious disadvantages.In contrast, the new techniques of HRSEM used in this study (3) offer the opportunity to view simultaneously both the internal and external structure of mitochondria directly in three dimensions and in detail.The tridimensional ultrastructure of mitochondria from rat hepatocytes, retinal (retinal pigment epithelium), renal (proximal convoluted tubule) and adrenal cortex cells were studied by HRSEM. The specimens were prepared by aldehyde-osmium fixation in combination with freeze cleavage followed by partial extraction of cytosol with a weak solution of osmium tetroxide (4). The specimens were examined with a Hitachi S-570 scanning electron microscope, resolution better than 30 nm, where the secondary electron detector is located in the column directly above the specimen inserted within the objective lens.

Inelastic Electron Scattering from Valence Electrons in Aluminum

1976 ◽  
Vol 34 ◽  
pp. 462-463
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
Electron Scattering ◽  
Single Scattering ◽  
Three Dimensions ◽  
Inelastic Electron ◽  
Weak Beam ◽  
Scattering Spectrum ◽  
Valence Electrons ◽  
Diffraction Patterns ◽  
Electronic Scattering

We wish to report in this paper measurements of the inelastic scattering component due to the collective excitations (plasmons) and single particlehole excitations of the valence electrons in Al. Such scattering contributes to the diffuse electronic scattering seen in electron diffraction patterns and has recently been considered of significance in weak-beam images (see Gai and Howie) . A major problem in the determination of such scattering is the proper correction for multiple scattering. We outline here a procedure which we believe suitably deals with such problems and report the observed single scattering spectrum.In principle, one can use the procedure of Misell and Jones—suitably generalized to three dimensions (qx, qy and #x2206;E)--to derive single scattering profiles. However, such a computation becomes prohibitively large if applied in a brute force fashion since the quasi-elastic scattering (and associated multiple electronic scattering) extends to much larger angles than the multiple electronic scattering on its own.

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