#curvature

2024-10-06

Now to sth completely different! After "why zebras don't have ulcers" was answered by Sapolsky, here is the next question: "how do zebras get their stripes" answered by a new maths research in @apsphysics :
journals.aps.org/pre/abstract/
Inspiring also for non-flat cosmologies... 😁

#mathematics #applied_mathematics #diffusion #curvature #scicomm #InterdisciplinaryMathematics

2024-08-08

On how membrane curvature allows our hearts to beat… 💓

#preLighter Barbora Knotkova highlights beautiful work from Yang Yang & colleagues #preprint

#preLight + author response ⬇️ 👀

prelights.biologists.com/highl

#biology #heart #cells #curvature #membranes

Khurram Wadee ✅mkwadee@mastodon.org.uk
2024-06-01

This is why #Engineers use #TransitionCurves in the form of #CornuSpirals or #Clothoids to connect from the straight segment onto a circular arc. It has the property that it starts with zero #curvature at the beginning and then the curvature increases linearly with distance travelled along the curve. At the appropriate curvature, it is connected to a circular arc with the same curvature.

#MyWork #WxMaxima #CivilEngineering #HighwayEngineering #CCBYSA

Jacob Somethingjkanev@fediscience.org
2024-05-27

#Cosmology #SpaceTime #BigBang #Curvature

Talking with my children about the time before the Big Bang. The best analogy we could come up with: Space-time is like the earth's surface, moving from the past to the future is like moving from north to south.
Asking "what was before the Big Bang?" is like asking "what's north of the north pole?".

Put differently: It all started with the Big Bang. Then things went south.

Joana de Castro Arnaudjcastroarnaud@mathstodon.xyz
2024-02-11

Whenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.

This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.

Given a #differentiable surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the #path, one can find the path's local #curvature. Then:

- Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.

- Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.

Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an #analytic solution, or are they possible only with numerical approximations?

#Analysis #DifferentialGeometry #Calculus #DifferentialEquations #NumericalMethods

Zougla.grzougla
2024-01-12

Curvature: Η εφαρμογή που σου δείχνει τους δρόμους με τα περισσότερα στροφιλίκια zougla.gr/automoto/automoto-ne

2024-01-01

'Large data limit of the MBO scheme for data clustering: convergence of the dynamics', by Tim Laux, Jona Lelmi.

jmlr.org/papers/v24/22-1089.ht

#viscosity #clustering #curvature

2023-12-30

Is the Universe finite?

++ Video is visually appealing, compact (28'). Tries to present the question of finiteness || infiniteness of Universe within the context of relativistic #cosmology. Intros to 2D #topology + #curvature are fair. Publicity for my group's research is nice :).

- - The relation to *3D* topo+curv is absent; there are several bloopers in the narration.

Overall a fair job. :)

peertube.stream/w/o5v3JXJkUmaR (*subtitles* en+fr)

@cartographer @stephenserjeant @ClaireLamman @cosmology

Screenshot from the film at around 17'40". In the background is the 15 m radio telescope RT-3 pointing upwards. In the foreground is a man (Dawid Myśliwiec) facing the camera, wearing a purple t-shirt, blue jeans, white sneakers and sunglasses, gesturing with his right hand towards the telescope, and leaning with his left hand on a small fence in front of a small body of water; the fence and water in the right and bottom right of the image. The left foreground is a grass field. A treeline of diverse species of trees is visible directly behind the telescope, from the left to right of the image. The sky is mostly covered by white clouds. An English subtitle translates the speaker's words as "Going on to the question of the finiteness or infiniteness of the Universe".
Erwin Schrödinger InstituteESIVienna@mathstodon.xyz
2023-09-14

Next week, the school of our thematic programme on #Geometry beyond #Riemann: #Curvature and #Rigidity is coming. 🤓 Hope everyone is registered who is into #Riemannian and #Lorentzian #conemanifolds, #Hilbert and #Finsler #metrics!

Find out more about the schedule here. 📝
esi.ac.at/events/e477/

@univienna

Click for the video here: twitter.com/ESIVienna/status/1

Daniel Pomarèdepomarede
2023-06-29

An intriguing cover for this 2003 issue of Nature, featuring a dodecahedral space topology and this question:

Is this the shape of the Universe?

☑️ The research paper: nature.com/articles/nature01944
☑️ A News & Views article: nature.com/articles/425566a
☑️ The full issue: nature.com/nature/volumes/425/

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