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Recent questions in Spread
College StatisticsAnswered question
Palmosigx Palmosigx 2022-07-07

Do cracks in solids spread at a characteristic speed?
I have a feeling this is actually a pretty complicated problem in detail as I know a tremendous amount of research is done on the behavior of materials under stress, and I think the way materials fracture/crack is a useful diagnostic tool.
As a starting point, waves travel at the speed of sound in a material, which is to say they are mechanical waves. Do cracks also propagate at the speed of sound?
Another related question is, do the cracks in a solid move at a constant speed? Obviously it is possible for a crack to form and stop propagating, so this might imply a dissipation of some vibrational amplitude until the energy is below the point of being able to break bonds/fragment atoms (sheets for some solids). It also might imply that the crack does not behave like a wave and spreads at a non-constant speed. Which is right?
Lastly, do all solids follow the same rules for the speed at which they fracture? I'm thinking of glass, which probably is not a good place to start on this question because it is an amorphous solid (some people say incredibly viscous liquid but this feels like semantics). Obviously some glass will crack into large pieces and some will fracture like a spiderweb. Are these processes fundamentally the same but with different microscopic details? And how does fracturing in glass relate to something simpler like the breaking of a single atom solid? I haven't seen this happen, but surely it is possible.
Obviously there were quite a few question there, but they were only meant to give a general idea of the types of questions would be nice to have answered. Maybe the question is actually quite simple and one answer will suffice, or maybe it's complicated and there are multiple good answers.

College StatisticsAnswered question
Manteo2h Manteo2h 2022-06-22

Does accelerating cosmological expansion increase beam spread?
In the standard textbook case, a transmitter of diameter D can produce an electromagnetic beam of wavelength λ that has spread angle θ = 1.22 λ / D. But what happens in an expanding cosmology, especially one that accelerates so that there is an event horizon? Does θ increase with distance?
Obviously each photon will travel along a null geodesic and after conformal time τ have travelled χ = c τ units of co-moving distance. The distance between the beam edges would in flat space be growing as δ = 2 c sin ( θ / 2 ) τ. Now, co-moving coordinates are nice and behave well with conformal time, so I would be mildly confident that this distance is true as measured in co-moving coordinates.
But that means that in proper distance the beam diameter is multiplied by the scale factor, a ( t ) δ (where t is the time corresponding to τ), and hence θ increases. However, the distance to the origin in these coordinates has also increased to a ( t ) ( c t ), so that seems to cancel the expansion - if we measure θ ( t ) globally by dividing the lengths.
But it seems that locally we should see the edges getting separated at an accelerating pace; after all, the local observers will see the emitter accelerating away from them, producing a wider and wider beam near their location since it was emitted further away. From this perspective as time goes by the beam ends up closer and closer to θ = π (and ever more red-shifted, which presumably keeps the total power across it constant).
Does this analysis work, or did I slip on one or more coordinate systems?

College StatisticsAnswered question
Adriana Ayers Adriana Ayers 2022-06-21

The shape characteristics of gravitational wells given different masses and spread of objects
I am curious as to research that calculates the shape of gravitational wells, and their limits, and affect on time, for different masses and spread of mass. The actual question is st the end.
For example: When the sun becomes a red giant the Earth's orbit is supposed to move out with the redistribution of mass, but what is the science behind this? Re-edit: Which I think was explained as the spreading density of the suns mass (it was a "TV" program. Another example, is it is said that the termination of the Sun's gravity field is 1.5 light years out. I am unaware of any distance studies to measure shape to specifically prove the theory.
The Question: Explanation of how the shape, time over distance, and extent of a gravitational well changes with the density of the mass, and the science behind this please? Re-edit: The curvature, research to verify theory, and actual simple graphical description of how the physical shape responds and changes based on contributing mass distribution. Say, does a more dense matter object cause the gravity well to more tightly curve to the surface of the matter, than to the surface of a cloud of gas of equal weight but magnitudes bigger. How does that look in physical shape over distance, how does the field terminate in shape. I'm interested in observational research on the profile. For instance does it continue the same decay equation or does it change/flatten out etc to a different equation at distance. This is more looking at verification/explanation of the conventional versus deviations. If we can only say so much at X distance from verified studies, that would be appreciated?
As we know there has been speculation based on deviations in observation of gravity on grander scales, such as across the galaxy. But I do not wish to go into those hypothesises, only the limits of what we have verified we know, which is a good starting point onto looking into this further.

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