The helicaliser : toroidal fractal, wiggleiser : string wiggles, and revolutioniser : curved traversable wormholes.

This research begins with the formulation of the helicaliser, which replaces a regular curve by another regular curve that winds around it. Modifying it into the revolutioniser generates a surface of revolution. We develop the 3-d and 4-d formalisms, generalise to n-d, before applying it to three ma...

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Main Author: Saw, Vee-Liem.
Other Authors: Chew Lock Yue
Format: Final Year Project
Language:English
Published: 2011
Subjects:
Online Access:http://hdl.handle.net/10356/44756
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Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-44756
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spelling sg-ntu-dr.10356-447562023-02-28T23:14:33Z The helicaliser : toroidal fractal, wiggleiser : string wiggles, and revolutioniser : curved traversable wormholes. Saw, Vee-Liem. Chew Lock Yue School of Physical and Mathematical Sciences DRNTU::Science::Physics::Atomic physics::Relativity physics DRNTU::Science::Astronomy DRNTU::Science::Mathematics::Geometry This research begins with the formulation of the helicaliser, which replaces a regular curve by another regular curve that winds around it. Modifying it into the revolutioniser generates a surface of revolution. We develop the 3-d and 4-d formalisms, generalise to n-d, before applying it to three major fields. Firstly, iterative helicalisations to a curve produce a set of helicalisations, with the in finite level being a fractal. These fractals are not self-similar, but we define a parameter d, and prove it reduces to the form of the self-similar dimension for self-similar fractals. We calculate the upper bound to d, preventing self-intersections. Next, we incorporate the crucial wiggling properties of strings from string theory to the toroidal helicalisations, generating the wiggleised toroidal helicalisations. We then derive analytically and provide numerical results to show that they share similar geometrical properties with strings. Finally, as revolutionised manifolds, such objects represent traversable wormholes satisfying the Einstein field equations. We study a class of (2+1)-d wormholes obtained by the revolutioniser and show explicitly that the helical wormhole must be supported by exotic matter. Since it is non-spherically (or non-axially) symmetric, it is significant as there are regions in the helical wormhole not requiring exotic matter, permitting safe human travel. Bachelor of Science in Physics 2011-06-03T07:23:09Z 2011-06-03T07:23:09Z 2011 2011 Final Year Project (FYP) http://hdl.handle.net/10356/44756 en 107 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Physics::Atomic physics::Relativity physics
DRNTU::Science::Astronomy
DRNTU::Science::Mathematics::Geometry
spellingShingle DRNTU::Science::Physics::Atomic physics::Relativity physics
DRNTU::Science::Astronomy
DRNTU::Science::Mathematics::Geometry
Saw, Vee-Liem.
The helicaliser : toroidal fractal, wiggleiser : string wiggles, and revolutioniser : curved traversable wormholes.
description This research begins with the formulation of the helicaliser, which replaces a regular curve by another regular curve that winds around it. Modifying it into the revolutioniser generates a surface of revolution. We develop the 3-d and 4-d formalisms, generalise to n-d, before applying it to three major fields. Firstly, iterative helicalisations to a curve produce a set of helicalisations, with the in finite level being a fractal. These fractals are not self-similar, but we define a parameter d, and prove it reduces to the form of the self-similar dimension for self-similar fractals. We calculate the upper bound to d, preventing self-intersections. Next, we incorporate the crucial wiggling properties of strings from string theory to the toroidal helicalisations, generating the wiggleised toroidal helicalisations. We then derive analytically and provide numerical results to show that they share similar geometrical properties with strings. Finally, as revolutionised manifolds, such objects represent traversable wormholes satisfying the Einstein field equations. We study a class of (2+1)-d wormholes obtained by the revolutioniser and show explicitly that the helical wormhole must be supported by exotic matter. Since it is non-spherically (or non-axially) symmetric, it is significant as there are regions in the helical wormhole not requiring exotic matter, permitting safe human travel.
author2 Chew Lock Yue
author_facet Chew Lock Yue
Saw, Vee-Liem.
format Final Year Project
author Saw, Vee-Liem.
author_sort Saw, Vee-Liem.
title The helicaliser : toroidal fractal, wiggleiser : string wiggles, and revolutioniser : curved traversable wormholes.
title_short The helicaliser : toroidal fractal, wiggleiser : string wiggles, and revolutioniser : curved traversable wormholes.
title_full The helicaliser : toroidal fractal, wiggleiser : string wiggles, and revolutioniser : curved traversable wormholes.
title_fullStr The helicaliser : toroidal fractal, wiggleiser : string wiggles, and revolutioniser : curved traversable wormholes.
title_full_unstemmed The helicaliser : toroidal fractal, wiggleiser : string wiggles, and revolutioniser : curved traversable wormholes.
title_sort helicaliser : toroidal fractal, wiggleiser : string wiggles, and revolutioniser : curved traversable wormholes.
publishDate 2011
url http://hdl.handle.net/10356/44756
_version_ 1759855397257084928