Adrian Bejan's Blog

The video explains how the evolution of solid structures follows the same logic as flow systems, aiming for efficiency, adaptability, and survival. The example of a beam under load introduces the connection between stiffness, strength, and material economy. From simple cantilever beams to tree branches and bones, the goal is always to minimize material while maintaining equal strength and stability throughout. The process of removing underused material leads to forms where stress is distributed uniformly, revealing nature’s preference for equality in failure and optimal use of resources.

The analysis begins with a beam loaded at its tip. Its stiffness is measured by how much it bends, and its strength by how much stress it can withstand before failure. These concepts, grounded in the work of early scientists like Navier and Cauchy, illustrate that every structure resists load through an internal balance of stress, where geometry and material properties determine performance.

The calculation shows that the highest stresses occur at the beam’s fixed end, where both the bending moment and the distance from the neutral axis reach their maximum. Cracks in balconies or branches appear there first, proving that local geometry controls vulnerability. The challenge in design is to reduce unused material without lowering stiffness or allowing stresses to exceed the allowable limit.

By gradually reshaping the structure to equalize stress, material is removed from areas that bear less load and added to those that bear more. This transformation leads to organic forms similar to bones or branches, which look irregular but are actually optimized for even stress distribution. These shapes are examples of “perfectly morphed” designs, where every part works equally hard.

Observations after a hurricane revealed that fallen branches were not just small or weak but of all sizes. This discovery demonstrated that the tree’s architecture had achieved equality in failure. Each branch, large or small, was loaded to the same maximum allowable stress, showing that nature builds for uniform readiness to fail rather than concentrating weakness in specific parts.

The conclusion links this principle of equal stress and proportional material use to broader patterns in nature. From single beams to branching trees and forests, the same rule of uniformity governs form and function. The result is a natural hierarchy of shapes that achieve maximum performance with minimum material, guided by the pursuit of structural harmony and balance.

---
Umit Gunes, Ph.D.
Assoc. Prof. | Yildiz Technical University
Editor | International Communications in Heat and Mass Transfer
Guest Editor | Philosophical Transactions of the Royal Society A
Guest Editor | BioSystems
Web | umitgunes.com

The video develops the idea of access as the foundation of design, contrasting it with terms like resistance or entropy that are abstract and less intuitive. Access is a word everyone understands because its absence is universally felt. From this starting point, the explanation shifts to the relationship between flows and the structures that contain them. Every flow system is accompanied by solids that must survive stress, weight, and time. Design is therefore always about the coupling of flow and structure, with purpose and performance as the guiding principles. The discussion links mechanics, elasticity, and stress to the broader theme that survival depends equally on the freedom of movement and the endurance of support.

Access is chosen as the most direct term because it conveys immediately the meaning of freedom of movement, unlike entropy or resistance, which seem abstract. This clarity allows design theory to be communicated in a way that resonates with both science and everyday life, making the principle universally accessible.

Every flow requires structure. A pipe not only conducts water but also holds its own weight and resists breaking. Structures such as beams, walls, and ducts are essential companions of flows. The flow may be colorless, but the solid line in the drawing gives it reality and permanence, uniting movement with support.

Stress analysis explains how structures survive under load. A bar in tension shows that internal stresses balance external forces, with tensile and compressive stress defined by the relation of force to area. These concepts from strength of materials demonstrate that survival is not only about movement but also about withstanding the pressures that movement imposes.

Elastic and plastic behavior reveal the limits of design. Up to a point, materials respond elastically and return to their shape, but beyond that, they yield and eventually break. The concept of maximum allowable stress defines the threshold that ensures survival, linking the endurance of the structure to the continuity of flow.

The discussion also extends to creativity and originality. Students are urged to submit their own ideas, however modest, since originality is what makes a contribution valuable. Just as structures support flows, individual insights support the survival of knowledge. Ideas, like flows, must have access, structure, and endurance to contribute to the larger system.

---
Umit Gunes, Ph.D.
Assoc. Prof. | Yildiz Technical University
Editor | International Communications in Heat and Mass Transfer
Guest Editor | Philosophical Transactions of the Royal Society A
Guest Editor | BioSystems
Web | umitgunes.com

The design in nature evolves as a flow of ideas — ideas of how to change to move and perform better — just as rivers, trees, and societies evolve to provide greater access to what flows and moves. Constructal GPT was created as a flow system of ideas —mental viewings— where every channel of ideas comes from Adrian Bejan’s complete works. It is not fragments, not summaries, but the bird's eye view of the full currents from the original sources. Constructal GPT was created using NotebookLM and is based on 300 of Adrian Bejan’s own works that carry the constructal imprint.

Try Constructal GPT

---
Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

The video explores the concept of store-and-release energy locomotion, demonstrating how certain animals achieve extraordinary jumps by compressing elastic structures that function like springs. Unlike continuous movers such as runners, swimmers, or flyers, these jumpers concentrate energy and then release it suddenly, creating motion far beyond what body size alone would predict. The explanation clarifies why insects like fleas and grasshoppers seem to defy scaling laws, while also extending the analysis to aquatic creatures and larger jumpers, demonstrating that the same mechanics apply across environments with different outcomes.

The cheetah appears as an outlier in speed–size scaling. Still, when considering its lifestyle, spending most of its time resting or watching, it falls back in line with theoretical expectations. This shows that what looks like deviation is often due to context, not contradiction, and highlights how purpose and behavior shape locomotion patterns.

Fleas, grasshoppers, and similar animals use an elastic organ that stores spring energy before release. When the latch is freed, the stored energy propels the body upward or forward, converting stored potential into kinetic energy. This explains why their jumps can cover distances many times their body length, a result of density ratios and spring mechanics rather than simple muscle force.

The theory considers drag and ambient density, showing that in air, the low density allows insects to leap far. In contrast, in water, the high density constrains aquatic jumpers like spiny lobsters to distances on the order of their body length. This contrast underlines how the same design principle yields different results depending on the medium.

When Reynolds numbers are high, drag coefficients remain constant, but at low Reynolds numbers, such as for very small creatures like fleas, drag depends on velocity and viscosity. Even so, the analysis still leads to predictable relationships between body size, density, and jump distance, demonstrating the robustness of the framework.

The same logic extends to larger jumpers such as frogs, kangaroos, and even basketball players. In these cases, gravitational potential energy sets the limit: the stored spring energy translates into vertical height rather than just horizontal displacement. Whether in insects, crustaceans, or humans, the principle remains: locomotion by jumping is governed by the storage and sudden release of elastic energy.

---
Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

The video contrasts education with indoctrination, making clear that the essence of learning lies in exchange rather than one-way transmission. True education is described as a dynamic enclosure where ideas travel in both directions, teacher to student and student to teacher, creating sparks that deepen understanding for all. In contrast, indoctrination is a rigid, one-way channel that silences dialogue, reflecting control rather than growth.

Education is presented as a two-way process in which both the giver and the receiver are engaged. Writing by hand is encouraged, as it enables learners to internalize and reinterpret the material, transforming it into a personal understanding rather than a passive reception.

Indoctrination, by contrast, is a top-down and one-directional process. It relies on a single voice filling the space, surrounded by silence, leaving no room for questioning or reinterpretation. The ideologue insists on a single idea, agreeing on the only possible outcome of such an encounter.

The danger of indoctrination lies in its refusal of reciprocity. Unlike education, which grows from the interplay of different perspectives, indoctrination eliminates the possibility of disagreement or discovery. It enforces silence, and in silence, the spark of learning disappears.

To avoid indoctrination, learners are encouraged to break out of passivity, engage actively in discussions, and contribute their ideas. Participation ensures that education retains its character as a shared process, one that produces insight both for the teacher and for the students.

---
Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

Abstract: The energy potential of sea waves has gained relevance, leading to extensive research on converters. The present work analyzes the contribution of Constructal Design to the development of wave energy converters. Constructal Design utilizes performance indicators to enhance system efficiency by varying the degrees of freedom where flow occurs. Thus, the systematic literature review methodology was applied to gather a collection of documents focused on the research topic. This study identified articles published between 2014 and 2024 by 40 authors affiliated with institutions in Brazil, Italy, and Portugal. The oscillating water column (OWC) converter received the most research attention, followed by the overtopping converter. Analyzing the documents collected for this study, the performance indicators revealed improvements ranging from 1.19 to 839 times, indicating the lowest and highest enhancements observed, respectively. The Constructal Design method has proven highly effective in identifying specific architectures or geometric arrangements that enhance flow configuration and improve the performance of wave energy converters. However, relatively few studies have applied the Constructal Design method to wave energy converters in comparison to other methodologies, presenting a significant opportunity for future research.

Read Full Paper

This video explains snake locomotion as part of the broader rhythm of animal movement, showing that even without legs, snakes follow the same principle of balancing difficulty and ease to move forward. Their motion comes from fish-like origins, adapted for land, where the whole body acts as a series of muscle-driven pushes. By examining how the body bends and presses at specific points, the explanation links snake movement to patterns in rivers, crawling infants, and skiing, highlighting that the theory of locomotion applies universally across different forms of life.

The movement of a snake is compared to a very long train winding through mountains, except that instead of locomotives pulling, the snake spreads muscular effort along its body. This creates a wave-like shape that leaves a sinusoidal trail, just like fish do when they move across wet sand. The similarities between these trails and meandering rivers suggest that snake movement is guided by pushing sideways against invisible boundaries, much like water pressing against a stream’s banks.

Seen from above, the snake’s body forms repeating S-shapes, but at ground level, you can notice that not all parts of the body touch the surface evenly. The snake lifts slightly and presses at selected “elbows,” generating forward motion by alternating contact points. This detail shows that movement relies on intermittent pushes rather than smooth sliding, making each part of the body both support and propel.

The crawling of infants follows the same rule. Before walking, babies move using their elbows and knees, applying pressure at specific spots while lifting their feet. This similarity emphasizes that locomotion is a universal rhythm of pushing and releasing, whether with legs, arms, or an elongated body.

In profile, the snake appears to create small air gaps between its body sections and the ground, proving that its movement isn’t a continuous drag but a pattern of lifting and pressing. These micro-adjustments reduce friction while providing thrust, much like other rhythmic movements, which balance effort with ease to keep moving forward.

The discussion relates this movement to skiing, where descending involves alternating pushes and directional changes that mirror the snake’s winding path. The term “slalom,” coming from Norwegian for descent, reinforces the comparison between human-designed movement and natural snake locomotion. This shows that whether in rivers, infants, snakes, or skiers, the pattern of alternating bends and pushes follows a consistent law of movement.

---
Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

Abstract: Tree-like self-similar branching networks with power-law fluid flow in elliptical cross-sectional tubes are ubiquitous in nature and engineered systems. This study optimizes flow conductance within these networks under tube volume and tube surface-area constraints for fully developed laminar power-law fluid flow in elliptical cross-sectional tubes. We identify key network parameters influencing flow conductance and find that efficient flow occurs when a specific ratio of the semi-major or semi-minor axis lengths is achieved. This ratio depends on the number of daughter branches splitting at each junction (bifurcation number N) and the fluid’s power-law index n. This study extends Hess–Murray’s law to non-Newtonian fluids (thinning and thickening fluids) with arbitrary branch numbers for elliptical cross-sectional tubes. We find that the maximum flow conductance occurs when a non-dimensional semi-major or semi-minor axis length ratio β* satisfies

under constrained-volume and constrained tube’s surface-area, respectively. We also analyze the spatial variation of shear stress within elliptical tube cross sections across generations. The stress field is found to be independent of rheological parameters and solely governed by pressure gradient and geometry. Under the volume constraint, stress distributions at optimal conditions are identical across generations, while under the surface-area constraint, the stress magnitude at optimal conditions increases with generation level as

These results provide insights into near-wall transport, wall stress anisotropy, and flow resistance. When the semi-major and semi-minor axis is equal, our findings are validated through experiments and theory under the limiting case of circular tube fractal networks. These insights provide important design principles for developing efficient and optimal transport and flow systems inspired by nature’s and engineered intricate networks.

Access to full paper: Optimal flow and scaling laws for power-law fluids in elliptical cross-sectional self-similar tree-like networks

The video develops the idea that movement in animals and humans follows a natural design that can be understood as a kind of wheel, showing how steps, strides, and rhythms are tied to physical form, balance, and efficiency. By looking at how walking, running, and swimming are shaped by size, strength, and body mechanics, the discussion connects the natural wheel of life to the history of human technology, including the wheel and the bicycle. It highlights how lighter and more efficient designs appear both in nature and in human invention, showing that movement always tends toward reducing wasted effort and increasing adaptability. In this way, the video links the laws of design in nature with human practices, drawing attention to the deep connection between biology, physics, and technology.

When describing the movement of humans and animals, the explanation shows that what appears to be straight walking is a falling and catching cycle, where each step prevents collapse. The body’s center of mass constantly leans forward and is restored by the action of the legs, making walking essentially a rhythm of controlled falling. This rhythmic pattern highlights why balance is delicate and why walking can be compared to an inverted pendulum, prone to instability yet sustained by repetition.

The size of the body strongly influences performance, as seen in both running and swimming. Taller athletes gain advantages because their movements lift their mass higher and project them forward with greater efficiency, making body length a predictor of speed. The same principle explains why sprinters begin races leaning forward, using rapid steps to prevent falling, and then transition to a vertical position as they stabilize their rhythm. The video shows that these mechanical patterns apply across different forms of movement and environments.

By comparing walking with the rotation of a cylinder or sphere, the explanation visualizes human gait as a wheel-like cycle. When the motion is traced step by step, it becomes clear that bipedal walking is equivalent to a wheel with two spokes, one leg replacing the other. This comparison reveals that nature already created the wheel before human technology, using legs as rotating supports that achieve rolling motion without a man-made axle.

The discussion of wheels in human history shows that technology gradually followed nature’s path toward lighter structures. Ancient solid wheels evolved into spoked designs, which became thinner and more numerous during the medieval period, and finally into aerodynamic versions with very few spokes for racing bicycles. The movement toward lighter wheels mirrors the principle found in nature, where legs bend and adapt to uneven terrain more effectively than rigid wheels ever could.

Extending the idea further, quadrupedal animals are shown to operate like four-spoked wheels, each leg forming part of a rolling cycle. The advantage of natural wheels lies in their flexibility: knees and joints allow rolling over irregular surfaces with stability, something technological wheels struggle to achieve. Even advanced vehicles built for uneven terrains cannot match the adaptability of living bodies, reminding us that natural design often outpaces human invention in efficiency and elegance.

---
Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com

In this video, Adrian Bejan challenges a widespread assumption in scientific literature that gravity does not matter to the fish. He revisits his earlier work on locomotion, which united flyers, runners, and swimmers under one principle: effort is divided into overcoming resistance horizontally and lifting weight vertically. But the fish remained an anomaly. Drawing from both personal experience and physics, Bejan delivers a breakthrough: when a fish moves, it lifts water, and that lifted water makes gravity matter.

Bejan recounts the origin of his theory, from his 2000 book Shape and Structure, to a pivotal moment in 2004 at Monte Verità, when biologist Jim Martin encouraged him to extend his theory of flying to running and swimming.

He explains how the fish, once thought to escape the vertical effort of gravity, in fact must displace water when they move. This displacement lifts a volume of water equivalent to the fish’s own body, creating a bulge on the water surface, a visible manifestation of vertical effort.

The pushed boat becomes Bejan’s thought experiment and proof: a body moving in water, like a boat or a fish, expends energy not only on drag but on lifting water. Without accounting for this, the motion appears endless, but in reality, it stops.

Bejan uses dimensional reasoning to show that kinetic energy from motion becomes gravitational potential energy stored in the lifted prism of water, explaining why a pushed boat (or a gliding swimmer) comes to rest.

He extends this insight to the pendulum in water, showing that oscillations stop because of both drag and the lifting of fluid, reinforcing that gravity is active even in aquatic environments.

---
Umit Gunes, Ph.D.
Assoc. Prof.​ |​ Yildiz Technical University
Editor​ | International Communications in Heat and Mass Transfer
Guest Editor​ |​ Philosophical Transactions of the Royal Society A
Guest Editor​ |​ BioSystems
​Web | umitgunes.com