Timeline for Optic fibers after Joseph O'Rourke
Current License: CC BY-SA 4.0
24 events
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| Nov 18, 2022 at 16:23 | comment | added | Anton Petrunin | @alesia I see counterexamples in dimension 2 (constructedd by Arseniy Akopyan) and in Riemannian case, but so far I do not see examples of 3-dimensional tubes (assuming that the walls are smooth). | |
| Nov 18, 2022 at 15:38 | comment | added | alesia | @AntonPetrunin yes, however my question was why is it true that your definition of optical fiber precludes the existence of such rays. What I understand from the comment on Riemannian manifolds suggests that you take it for granted or obvious, and I don't see why it is so | |
| Nov 18, 2022 at 12:11 | comment | added | Anton Petrunin | @alesia I changed the wording, hope it is clear now. But anyway look at the example with ellipses --- if you shoot a random geodesic from inside, then with positive probability it does not reach the boundary. For the Riemannian case, think of surface of revolution of a horizontal line with small bump on it (so it is almost cylinder). If you shoot a geodesic from the bump then with positive probability it will stay in the bump forever. | |
| Nov 18, 2022 at 12:07 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
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| Nov 17, 2022 at 21:47 | comment | added | alesia | @AntonPetrunin to clarify, I was thinking of both side infinite rays that stay in the optic fiber without ever reaching the ends of it. I'd imagine these would correspond to trapped geodesics in the manifold obtained by identifying two copies of the optic fiber along their common boundary tube. | |
| Nov 17, 2022 at 20:56 | comment | added | alesia | but such geodesics never hit the ends of the tube, so the assumptions don't preclude their existence do they? | |
| Nov 17, 2022 at 19:47 | comment | added | Anton Petrunin | @alesia here by trapped I mean both-side infinite geodesics that spend all time in the manifold --- actually I mean positive measure of initial data for such geodesics. | |
| Nov 17, 2022 at 17:41 | comment | added | alesia | You said there are counterexamples in the Riemaniann geometry framework but that those involve trapped rays. Why are your assumptions inconsistent with the existence of trapped rays? | |
| Nov 17, 2022 at 16:39 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Oct 30, 2014 at 4:07 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Oct 30, 2014 at 0:59 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Oct 30, 2014 at 0:20 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| May 20, 2012 at 15:45 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Apr 12, 2012 at 21:33 | answer | added | Marcos Cossarini | timeline score: 3 | |
| Mar 1, 2012 at 14:33 | comment | added | Cam McLeman | The title of this question always makes me think this would make for a fantastic sci-fi movie. | |
| Oct 13, 2011 at 18:04 | answer | added | Gerhard Paseman | timeline score: 2 | |
| Oct 11, 2011 at 0:50 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Oct 11, 2011 at 0:39 | comment | added | Anton Petrunin | No, I want optic fiber to be bidirectional (I will make it more clear). But you right, if you just want to send all rays from the first end to the second that you can get many more examples. | |
| Oct 10, 2011 at 5:35 | comment | added | Gerhard Paseman | Other than that they may not be bidirectional with respect to light transmission, why disallow frustrums (truncated cones)? Gerhard "Ask Me About System Design" Paseman, 2011.10.09 | |
| Oct 10, 2011 at 1:34 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Oct 8, 2011 at 19:58 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Oct 8, 2011 at 14:26 | answer | added | Joseph O'Rourke | timeline score: 2 | |
| Oct 8, 2011 at 5:53 | history | asked | Anton Petrunin | CC BY-SA 3.0 |