The hidden rhythm of nature
How evolution shapes efficient movement across systems
Extensive evidence shows that flow systems, when free to change, evolve into structures that enhance movement and flow. This phenomenon can be observed across various domains and scales, including animal locomotion (from insects to large aircraft), river basins and deltas, human movement, lung structure and rhythm, urban development, air traffic, economies, and technological advancements, and many more evolutionary designs. The progression of these designs over time aligns with the natural direction of evolution, a concept referred to as the constructal law.
In nature, things are not what they seem. The technique (the rhythm) is deceptive. Adrian Bejan
Apparent obstacles
The universality of the evolution of flow configurations towards greater access has not been questioned until recently. An initial test examined three common phenomena that obstruct flow: cataracts (Figure 1), hydraulic jumps (Figure 2), and roll waves of rainwater on the pavement (Figure 3). Despite their seemingly obstructive nature, these designs enhance flow access. This is because vertical free-fall, seen over dams, allows for faster movement than flow hindered by surface friction. Similar to cataracts, roll waves exhibit the same phenomenon, though the pavement beneath roll waves is not erodible.
This unexpected finding is consistent with earlier examples of flow designs that promote access rather than obstruct access. Instances include turbulence against a surface, respiration, and other rhythmic physiological processes, as well as technologies inspired by mechanisms such as periodic ice formation, surface cleaning, and scheduled power plant maintenance for repair and renewal.
A new study examined another common phenomenon that hinders movement: the alternating sticking and sliding at the interface between two bodies in relative motion. The investigation, based on theoretical prediction rather than experimental observation, aimed to determine whether the stick-slip phenomenon obstructs or actually enhances relative motion.
Sticking and sliding
The sticking and sliding phenomenon occurs across various scales, from a metal piece machined on a lathe to active seismic zones where earthquakes are triggered by the sudden shift from sticking to sliding. This phenomenon is often accompanied by distinct screeching sounds, such as those from car tires or train wheels during abrupt stops, basketball shoes on a court, squeaky-clean skin, or the bow on string instruments such as violins.
Upon closer examination, the rhythmic stick-slip phenomenon was relevant to various seemingly unrelated examples, including animal locomotion, mechanical devices like catapults and trebuchets, and athletic activities involving throwing motions, such as baseball, hockey, and boxing.
The demonstration utilised a basic model of energy storage and release: a weight pulled by a spring sliding on a horizontal surface (figure.4). In this scenario, the coefficient of friction between the weight and the surface is typically higher during sticking than sliding. It was shown that the power required to move the weight is lower when the motion is periodic, involving alternating sticking and sliding, compared to steady, uniform sliding.
Animal locomotion
Animals of all sizes, whether in water, land, or air, display periodic movement (Figure 5, upper right) patterns that follow predictable trends. For instance, the average horizontal speed is proportional to the animal’s body mass (M) raised to the power of 1/6. This relationship also indicates that horizontal speed is proportional to body length raised to the power of 1/2. Additionally, the height of a jump and the distance covered during one movement cycle involving lift and forward motion is directly proportional to the animal’s body length.
The agreement with theory is accompanied by the diversity compacted in the data clouds. The diversity is also predictable if one accounts for additional features (degrees of freedom) in the assumed model of the moving body. Additional features include the body’s slenderness and the animal’s lifestyle (predator vs. prey).
Instances that deviate significantly from predicted patterns are commonly called “outliers” in scientific literature, awaiting integration into the broader understanding of animal design evolution. Notable examples of such outliers include animals that utilise stored elastic energy released through latch-like mechanisms. Fleas and grasshoppers are prime examples, as they can jump to heights and distances far exceeding their body length by orders of magnitude.
The predictability of the energy store-release design is suggested by the observation that aquatic animals propel themselves over much shorter distances than airborne insects. The jump is expected to be roughly equivalent to the animal’s body length in water. However, in the air, the jump height can exceed the body length by a factor of 100 to 1000, consistent with the remarkable jumping abilities observed in certain insects.
The medium (water, air) in which the store-release design (Figure. 6) propels the body is an important participant. This feature contributes to the diversity in the cloud of deviations from the constructal theory of locomotion (Figure. 5).
Earthquakes
Another example of energy storage and release is the motion between two rock layers under pressure at their interface. This periodic motion has traditionally been studied using various models, often resulting in complex movements described as randomness and noise. A new perspective offers a predictive approach, drawing parallels to the stick-slip phenomenon and animal jumping behaviour.
In the earthquake model (Figure 7), the upper rock layer is pushed left while remaining stuck to the lower layer. Shear at the interface causes cracks in the lower layer, with the shear force proportional to the static friction coefficient. These cracks are modelled as perpendicular to the interface, and vertical rock layers emerge between them. These layers bend at their tips in the direction of the shear force exerted by the upper layer.
A simple comb demonstration can help illustrate the physics behind the model. By pressing a palm against the teeth of the comb and pulling it across, each tooth bends independently. Applying more force eventually causes the palm to slide over the tips of the teeth. For those who find the sensation unpleasant, a piece of rubber, like an eraser, can be used in place of the palm to replicate the effect without the tickling feeling
To conclude
The conclusion drawn from recent research is that energy storage and release movements warrant further examination. A tendency towards greater accessibility plays a crucial role in the evolution of rhythmic configurations, which may appear to hinder movement. The study demonstrated that these energy store-and-release rhythms are both natural and predictable, ultimately facilitating movement.
Nature is filled with designs that function effectively. Successful features are retained, and rhythm is one such characteristic. This principle can be observed in team sports like soccer: less skilled players exhibit more complicated movements, while more proficient players move simply. The most skilled players focus on getting rid of the ball, as running is more efficient and faster than dribbling. In this way, nature evolves like the adept ballplayer, favouring simplicity and effectiveness.
Journal reference
Bejan, A. (2024). Energy store & release facilitating movement in stick & slip friction, animal jump, and earthquake. Scientific Reports, 14(1), 18832. https://doi.org/10.1038/s41598-024-68525-1
✒️ Source: The hidden rhythm of nature: How evolution shapes efficient movement across systems