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Nature's Numbers
Registrace 29. 10. 2022
This channel is about the numbers of nature and the nature of numbers, the dimensions behind the dimensionless.
MECHANICS (Intermission)
We're about mid-way through this series on mechanics so we thought it would be a good idea to take a little break, summarize what we've done so far, and outline what remains in store.
www.numbersnature.org/mechanics/intermission
Review covering episodes 1 to 8:
doi.org/10.1039/D4SM00263F
arxiv.org/abs/2401.15101
Chapters:
0:00 Intro
2:07 The Dynamical Paradigm
3:21 Duos
19:39 Trios
35:21 Quartets
41:00 Paradigm Shift
Authors:
Marc-Antoine Fardin (Institut Jacques Monod, CNRS, Université Paris Cité)
Mathieu Hautefeuille (Institut de Biologie Paris-Seine, Sorbonne Université)
Vivek Sharma (Department of Chemical Engineering, University of Illinois at Chicago)
MAF thanks Tom for the design of the thumbnail, based on the gif by Oliveirasjeh, displayed at the beginning of the first video of this series:
tenor.com/view/subida-gif-18379274
Copyright Disclaimer under section 107 of the Copyright Act 1976, allowance is made for “fair use” for purposes such as criticism, comment, news reporting, teaching, scholarship, education and research.
www.numbersnature.org/mechanics/intermission
Review covering episodes 1 to 8:
doi.org/10.1039/D4SM00263F
arxiv.org/abs/2401.15101
Chapters:
0:00 Intro
2:07 The Dynamical Paradigm
3:21 Duos
19:39 Trios
35:21 Quartets
41:00 Paradigm Shift
Authors:
Marc-Antoine Fardin (Institut Jacques Monod, CNRS, Université Paris Cité)
Mathieu Hautefeuille (Institut de Biologie Paris-Seine, Sorbonne Université)
Vivek Sharma (Department of Chemical Engineering, University of Illinois at Chicago)
MAF thanks Tom for the design of the thumbnail, based on the gif by Oliveirasjeh, displayed at the beginning of the first video of this series:
tenor.com/view/subida-gif-18379274
Copyright Disclaimer under section 107 of the Copyright Act 1976, allowance is made for “fair use” for purposes such as criticism, comment, news reporting, teaching, scholarship, education and research.
zhlédnutí: 229
Video
MECHANICS (11) Unfinished Business
zhlédnutí 196Před 5 měsíci
Since episode 9, we know we can understand turning points in dynamics by going from two mechanical quantities to three. The three pairs of the trio are associated with three lines intersecting at what we called a “proper” event. But as we saw in the last episode, there are a lot of cases out there, where only two mechanical quantities have been identified, resulting in an incomplete or “pseudo-...
MECHANICS (10) Undecided
zhlédnutí 166Před 6 měsíci
In the last episode of this series on mechanics, we talked for the first time about trios of mechanical quantities. We saw that trios of non-aligned mechanical quantities lead to special space-time points, or "events", which provide turning points of the dynamics, and truly objective units. At these "proper events", three regimes intersect. But what of places where only two regimes cross? This ...
MECHANICS (9) Events
zhlédnutí 134Před 8 měsíci
In the first episode of this series on mechanics, we introduced "mechanical quantities" or "mass-carrying quantities", mixing the dimensions of mass M, length L, and time T. In the following episodes we saw that these quantities can be understood by the effects they have when considered in pairs. Pairs of mechanical quantities lead to kinematic power laws. These power laws provide relationships...
MECHANICS (8) The Right Angle
zhlédnutí 217Před 10 měsíci
Since the beginning of this series we've established that the foundation of the relationship between mechanics and kinematics is the connection between pairs of mechanical quantities and kinematic power laws. This relationship can be conveniently expressed as a link between a variable length and a variable time. Nevertheless, we've seen in episode 7 that other kinematic perspectives are equally...
MECHANICS (7) Perspectives
zhlédnutí 308Před 10 měsíci
Since the beginning of this series we've presented mechanics from one particular kinematic perspective. We observed some kind of motion, like an explosion, or the pinching of a water droplet, or the fall of an object, or the orbit of a planet, and we represented motion by plotting a length versus a time. We saw that the relationships between space and time could be understood by invoking the in...
MECHANICS (6) Holy Motors
zhlédnutí 326Před rokem
Motions of all sorts can be understood as struggles between competing mechanical factors. One mechanical quantity impels motion while the other impedes it. For each pair of mechanical quantities the roles are assigned by their relative dimensions. However, a quantity can be impelling motion in one context and impeding it in another. This episode is dedicated to this relativity in the roles play...
MECHANICS (5) Struggle in Motion
zhlédnutí 294Před rokem
In the previous episodes we've seen how time, space and uniform motion can emerge from ratios of mechanical quantities with specific relative dimensions. In this fifth video we will generalize and consider the interplay of any pair of mechanical quantities, producing more complex spatio-temporal relationships. For instance we will discuss explosions, where the energy of a bomb is faced by the d...
MECHANICS (4) Simple Speeds
zhlédnutí 176Před rokem
In the previous episodes we've seen how time and space can emerge from ratios of mechanical quantities. In this fourth video we show that the interplay of mechanical quantities can also produce motion. We focus on uniform motion, at a constant speed. We give a few examples of speeds that can be understood from ratios of pairs of mechanical quantities. These simple speeds are found everywhere, t...
MECHANICS (3) Simple Times
zhlédnutí 294Před rokem
What is time? Another question that children may ask. Here again, mechanics offer an answer. A given time or duration can be understood as the result of a balance or ratio between opposing mechanical factors, one tending to increase it and the other tending to shorten it. In this third video of this series on mechanics we give a few examples of times that can be understood from ratios of pairs ...
MECHANICS (2) Simple Lengths
zhlédnutí 477Před rokem
Why do things have the size that they do? Where does the size of something come from? We can tell it's a deep question because it sounds as one a child would ask. Mechanics offer an answer. A given size or length can be understood as the result of a balance or ratio between opposing mechanical factors, one tending to grow and the other to shrink. In this second video of this series on mechanics...
EXPLOSIONS (8) Kinematic & Mechanical Variables
zhlédnutí 530Před rokem
For the first seven episodes of this series, we've built an understanding of explosions based almost exclusively on records of their radius over time. In this final episode we describe explosions from different perspectives. We first discuss alternative kinematic perspectives, like the ones offered by tracking the front speed over time, or the speed at various distances from ground zero. We the...
EXPLOSIONS (7) Physics Beyond Base 10
zhlédnutí 380Před rokem
The meter, the second and the traditional base 10 are useful standards to communicate quantitative measurements, for instance of the radius of an explosion over time. However, these subjective units for space, time and numbers themselves obscure the scale-invariant similarity of physical phenomena, like the deep kinship between explosions of all sorts, from tiny laser-induced blasts to supernov...
EXPLOSIONS (6) The Explosion Domain
zhlédnutí 513Před rokem
During the first five episodes of this series we've discussed explosions of all sizes, where the energy output is successively matched by the ejected mass, the density of the swept-up ambient medium, and finally by the characteristic pressure or stress of this medium, which can be a gas like air, a liquid like water, a solid like soil, or even the near vacuum of interstellar space. The dynamics...
EXPLOSIONS (5) Early Dynamics
zhlédnutí 1,1KPřed rokem
At the beginning of an explosion the radius cannot follow Taylor's 2/5 scaling, which would lead to a divergence of the front speed. In this fifth episode on the physics of explosions we describe the very early dynamics of explosions, which are often associated with a constant speed built from the opposition between the output of energy and the ejected mass. Eventually, as the front moves forwa...
EXPLOSIONS (3) The Taylor-Sedov Number
zhlédnutí 2,1KPřed rokem
EXPLOSIONS (3) The Taylor-Sedov Number
Regarding your note at the end: The Housatonic blast was detonated at ~12k feet, where the density of air is ~75% of that at ground level. The decreased density here should be accounted for when determining which linear plot on log/log axis it belongs to.
5:04 . Your choice of the important case when x = -1 appears to be a random choice, and post hoc, it provides the very satisfying result: Q is Σ and the intersection is with the speed of sound, but I think it needs the promised : "We will come back to the multiplicity of solutions at the end of this video" which would be very revealing.
Indeed, there could be many length scales built from a ratio of mechanical quantities with energy in the numerator (see episode 2 of the Mechanics series). Considering pressure is useful for the shock wave, but as mentioned at the end, the fireball stops at a different radius. From what we've read this final radius for the fireball scales as (E/Q)^(1/5), in which case Q would have dimensions ML^-3T^-2. Such quantity does not seem to have a standard name, but it could be interpreted as a force gradient per unit volume (MLT^-2/L)/L^3. We would love to come back to this in the future.
Is the capillary action that lifts water from the soil into the leaves of a tree an example of surface tension as an impelling factor?
Maybe, but I seem to remember that experts were not all in agreement about this. I'll have to check.
#SHRINKING The gaseous volume reduction during the condensation or solidification of detonation products over time as the temperature decays to ambient?
We haven't figured that yet ;)
Made it! Phew!
We're glad! We do believe that this renormalization of the number base is one of the most impressive outcome of dimensional analysis, and we haven't seen it done anywhere. The theoretical ramifications of this are far reaching, and we will come back to it in a few episodes in the Mechanics series.
#MASS&STRESS. I wonder if it is related to the condensation inside the fireball? PE-4 produces water vapour which condenses at ambient temps, occurring when the fireball decays, and in a nuclear blast, when the vapourised metal enclosure condenses and solidifies.
This regime remains a bit of a mystery for us at the moment. The same scaling show up in the 11th episode of the Mechanics series, in a different context. Our guess is that it is connected to some kind of collapse, but we haven't really done our homework on this yet :/
24:00 I would love to be future me in another 4 centuries to see if your prediction, that Tycho's super nova is entering a Taylor's regime, is in fact true!
A few older supernovae do seem to be along that regime, but since the density of their surrounding interstellar medium is rarely known with precision, it is hard to be definitive.
13:41 I was bothered by your equation c "is identical to" (triple equal sign,≡) root(sigma/rho) until I realised you probably meant c "is approximately equal to" since for a gas the speed of sound is also dependent on gamma: c = root(gamma x pressure/density) where, for air (mainly diatomic N2 and O2) , gamma = 1.4. [EDIT] but I see at 22:30, you have indeed scaled Σ by γ and shown Σ as 1.4 10^5 Pa, (not the previous value of 1 10^5) for air blasts.
Thanks for being so attentive ;) For a rough approximation, considering the pressure is enough, but for better prediction Sigma indeed needs to be the bulk modulus.
Brilliant series, many thanks. Can you confirm that after the Hopkinson-Cranz space-time point, the shock front propagates at the speed of sound? In particular, in reference to the Beirut Port explosion, that at a distance beyond around 600 metres where this video czcams.com/video/Hd6Z_pGx9_4/video.html, was shot, that the blast wave is travelling at the speed of sound?
Thanks! Assuming a yield of 1 kt, and the bulk modulus of the air to be 1.4 10^5, the "bare" formula for the distance of the H-C point would be around 300 meters, but numerical corrections may very well change that a bit. Looking at the video, the over-pressure seems to be pretty significant, which would suggest that the explosion front is still supersonic. You'll see that many data sets actually show a pretty smooth transition around the H-C point, such that the actual speed of the blast can be quite significantly higher than predicted by the scaling. However far away from the H-C point, the speed does go down to the speed of sound.
noclear bomb
Loving this series
Would Project Plowshare be helpful? #undergroundnuke
Thanks for the tip. We looked at Project Plowshare and a few others. Materials from several underground testing operations have been declassified, usually including the final size of the cavity (cf episode 4), but we could not find any data on the dynamics of the underground blast before the final radius is reached. No doubt that these data exist somewhere.
Very good video. I would say that as Von Neumann has a computing architecture and self replicating robot space probes named after him we can probably give Messers Taylor and Sedov that constant without feeling too bad for Herr Von Neumann.
In this episode we show how to construct the dimensionless number associated with the regime pairing energy and density. For a general discussion on this procedure, check out episode 8 of the Mechanics series czcams.com/video/aun0CHanq94/video.htmlsi=vIO16UsimTr9v_5J
fascinating.... thank you!
" ... and variables become constant.." <3
you are the fucking top g. Thanks bro
All explosions shown are conventional. Nuclear bombs are a psyop
I am blown away that I’m still here…, kinda almost able to keep / understand..🙏🙏🙏🙏🙏
And we're very glad you are here too :) You might actually be one of the first lol
🙏🙏🙏🙏🙏🙏🙏
Never thought of the mechanics in this way, thanks for the lectures!
Exceptional video
Great job!😮
I am curious how could be estimated the thickness of lateral boundary layers in vertical density gradients flows! Are you going to make a video in stratified flows?
Great explanation! What about x, y being fractions?
Absolutely love this table, never thought about it this way!
Bum!! Great video and explanation!!!