Article  Why are rivers so mathematical? + 10,000 particles defy Newton’s 3rd law for an hour

#1
C C Offline
Physicists made 10,000 particles defy Newton’s 3rd law for an hour. Here’s how
https://gizmodo.com/physicists-made-1000...2000797161

EXCERPTS: Some laws of physics are so fundamental that they’ve served as the baseline for science for centuries. But with technological advancements, physicists can—albeit temporarily—create small worlds that evade these laws. And when they do, strange things occur.

In a recent study published in Physical Review Letters, Japanese physicists created a system of more than 10,000 particles that defied Newton’s third law of motion for an hour. According to this law, passive particles exert equal forces on each other, so none can just suddenly push itself along on its own. But in devising this system, the team subjected particles to an alternating electric field that caused passive particles to spontaneously form pairs and “chase” each other in a liquid environment.

“This research demonstrates that the breaking of action-reaction symmetry is a fundamental principle that generates new collective motions and self-organization of matter,” Yutaka Sumino, the study’s co-author and a physicist at the Tokyo University of Science in Japan, said in a statement.

[...] The team suspects that similar interactions take place in biological systems, such as cell colonies and animal groups. If true, the mechanism studied here could even inspire programmable materials and microrobotic systems, it noted. (MORE - missing details)


Why are rivers so mathematical?
https://www.quantamagazine.org/why-are-r...-20260810/

EXCERPT: There’s something appealing about this ubiquitous pattern, so appealing to me personally that I have it tattooed on my forearm: the silhouette of a tree, with leafless branches reaching upward and roots burrowing downward, almost in mirror image. “The shapes of rivers and leaf vasculature and so on — branching networks — you can just about grasp the pattern, but it’s still chaotic, so there’s something fascinating with that,” said Chris Paola, a river scientist at the University of Minnesota.

Systems that branch in this way are “transport networks”: They transport some fluid substance (water, blood, traffic) from every place to a single place (the sea, a heart, a city center). Of the various examples, rivers are especially revealing, I think, since they arise from neither biological evolution nor urban planning, but rather chaotic Earth processes. Yet they obey simple, universal laws.

A discovery about river networks in 2026 reignited my curiosity about their universal form and mathematical nature. These were hot topics in the 1980s and ’90s, when rivers were studied as natural examples of “fractals”: mathematical objects whose features repeat in roughly similar forms at many different scales. Geomorphologists, who specialize in the shape (and continual reshaping) of Earth’s surface, have studied the geometry of river networks far longer, since the late 1800s.

Though many details of river behavior are still being actively studied, the existing mountain of research has yielded explanations that add up to a somewhat satisfying basic understanding. The math is elegant, the geophysics is intuitive, and still my sense of wonder is undiminished.

Every square inch of land on Earth’s surface receives precipitation, and much of it drains out, eventually, to an ocean or lake. Rivers are the drainage system.

In 1957, a U.S. Geological Survey scientist named John Hack discovered the most important law of river networks. In rivers and streams in Virginia and Maryland, Hack measured the length of each stream and the area of the land that slopes toward that stream and therefore drains into it, called its basin or drainage area. What he discovered is now known as Hack’s law: Any stream, from the littlest brook to the mightiest river, has a length that’s proportional to its drainage area raised to the power of 0.6. (In symbolic form: L ~ A0.6.) There’s a bit of variance around that 0.6 value — Earth is, after all, a complicated place — but “the general regularity of the relation is nevertheless remarkable,” Hack wrote. “Stream lengths tend to increase proportionally to the 0.6 power of the drainage area, regardless of the geological or structural characteristics of the area.”

As more and better data has accrued, especially from satellite imagery, Hack’s law has held worldwide. Why this is the case is the essential mystery geomorphologists have grappled with ever since... (MORE - missing details)
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#2
Zinjanthropos Offline
(Aug 12, 2026 04:28 PM)C C Wrote: Why are rivers so mathematical?
https://www.quantamagazine.org/why-are-r...-20260810/

EXCERPT: There’s something appealing about this ubiquitous pattern, so appealing to me personally that I have it tattooed on my forearm: the silhouette of a tree, with leafless branches reaching upward and roots burrowing downward, almost in mirror image. “The shapes of rivers and leaf vasculature and so on — branching networks — you can just about grasp the pattern, but it’s still chaotic, so there’s something fascinating with that,” said Chris Paola, a river scientist at the University of Minnesota.

Systems that branch in this way are “transport networks”: They transport some fluid substance (water, blood, traffic) from every place to a single place (the sea, a heart, a city center). Of the various examples, rivers are especially revealing, I think, since they arise from neither biological evolution nor urban planning, but rather chaotic Earth processes. Yet they obey simple, universal laws.

A discovery about river networks in 2026 reignited my curiosity about their universal form and mathematical nature. These were hot topics in the 1980s and ’90s, when rivers were studied as natural examples of “fractals”: mathematical objects whose features repeat in roughly similar forms at many different scales. Geomorphologists, who specialize in the shape (and continual reshaping) of Earth’s surface, have studied the geometry of river networks far longer, since the late 1800s.

Though many details of river behavior are still being actively studied, the existing mountain of research has yielded explanations that add up to a somewhat satisfying basic understanding. The math is elegant, the geophysics is intuitive, and still my sense of wonder is undiminished.

Every square inch of land on Earth’s surface receives precipitation, and much of it drains out, eventually, to an ocean or lake. Rivers are the drainage system.

In 1957, a U.S. Geological Survey scientist named John Hack discovered the most important law of river networks. In rivers and streams in Virginia and Maryland, Hack measured the length of each stream and the area of the land that slopes toward that stream and therefore drains into it, called its basin or drainage area. What he discovered is now known as Hack’s law: Any stream, from the littlest brook to the mightiest river, has a length that’s proportional to its drainage area raised to the power of 0.6. (In symbolic form: L ~ A0.6.) There’s a bit of variance around that 0.6 value — Earth is, after all, a complicated place — but “the general regularity of the relation is nevertheless remarkable,” Hack wrote. “Stream lengths tend to increase proportionally to the 0.6 power of the drainage area, regardless of the geological or structural characteristics of the area.”

As more and better data has accrued, especially from satellite imagery, Hack’s law has held worldwide. Why this is the case is the essential mystery geomorphologists have grappled with ever since... (MORE - missing details)

Is Hack's Law universal?

Would the liquid hydrocarbon rivers of Saturn's moon Titan be subject to same law?
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#3
C C Offline
(Aug 12, 2026 11:18 PM)Zinjanthropos Wrote: Is Hack's Law universal?

Would the liquid hydrocarbon rivers of Saturn's moon Titan be subject to same law?

Somewhat, as long as those environments allow something to flow. But drainage metrics in super-cold temperatures with alien geology and water flow substitutes aren't going to be a perfect match to Earth's. And comparisons of Earth with other planets in this area is one that hasn't been well studied so far.

Saturn's moon Titan just broke one of chemistry’s oldest rules: The study, published in PNAS, reveals that methane, ethane, and hydrogen cyanide -- compounds abundant on Titan's surface and in its atmosphere -- can interact in ways once thought impossible. The fact that hydrogen cyanide, a strongly polar molecule, can form crystals together with nonpolar substances like methane and ethane is remarkable, since these types of molecules usually stay separate, much like oil and water.

"The discovery of the unexpected interaction between these substances could affect how we understand the Titan's geology and its strange landscapes of lakes, seas and sand dunes. In addition, hydrogen cyanide is likely to play an important role in the abiotic creation of several of life's building blocks, for example amino acids, which are used for the construction of proteins, and nucleobases, which are needed for the genetic code. So our work also contributes insights into chemistry before the emergence of life, and how it might proceed in extreme, inhospitable environments," says Martin Rahm, who led the study.

[...] Titan's extremely cold surface is home to lakes and rivers of liquid methane and ethane. It is the only other known place in our solar system, apart from Earth, where liquids form lakes on the surface. Titan has weather and seasons. There is wind, clouds form and it rains, albeit in the form of methane instead of water. Measurements also show that there is likely a large sea of liquid water many kilometres below the cold surface which, in principle, might harbour life.
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#4
Zinjanthropos Offline
From what I've heard and with AI confirming, the dry river and stream beds on Mars are still very much measurable. You'd think Hack Law proponents would be looking at that data too.
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#5
C C Offline
(Yesterday 02:49 PM)Zinjanthropos Wrote: From what I've heard and with AI confirming, the dry river and stream beds on Mars are still very much measurable. You'd think Hack Law proponents would be looking at that data too.

In contrast to places like Titan, Mars actually was Earth-like in the distant past, at least in terms of having liquid water instead of substances we'd normally experience as gases. But more in the context of desert-like areas on Earth. And periods of warmth and rainfall even then may have been sporadic rather than a non-fluctuating state of that early Martian environment. Hordes of meteorite impacts during that era would have been both triggering and disrupting climate phases (along with potential volcanic activity).

Global Spatial Distribution of Hack’s Law Exponent on Mars and its Early Climate
https://essopenarchive.org/doi/pdf/10.10...10512518.1

ABSTRACT: Widespread valley networks (VNs) on Mars and other evidence point to an early warm and wet climate. However, ongoing debates still exist about VN’s formation processes and climate conditions. The power law relationship between basin length and area (Hack’s Law) can be diagnostic of different fluvial processes and thus climate conditions.

Past studies of Hack’s Law on Mars at local sites have produced inconclusive results. Here we used a parameter-free method to delineate watersheds globally on Mars based on mapped VNs and then extracted their Hack’s Law exponent (h).

Spatial statistical analyses show that the spatial distribution of h on Mars is not random but with clustered high and low values, suggesting regional variations in controlling factors/processes responsible for VN formation. The majority of h values on Mars are most similar to values related to arid climates on Earth, implying similar conditions for early Mars. But the
- - - - - - - - - - - - -- -

The application of Hack's law and Flint's law to Mars and its implications for the Noachian climate
https://www.academia.edu/79885074/The_ap...n_No_2132_

AABSTRACT: This paper examines Martian valley networks through the lens of Hack's law and Flint's law, providing insights into the climatic conditions of Mars during the Noachian period. Utilizing various methods to analyze valley dimensions and drainage areas, the study finds that Martian valleys exhibit a similar scaling relationship to terrestrial systems, particularly supporting Hack's Law. The results indicate that these valley networks likely formed under ephemeral conditions, suggesting a dynamic and potentially wetter Noachian climate.
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