In this video, Adrian Bejan discusses a celebration at Duke and uses 7 slides to give a brief overview of his work. He begins with acknowledgments to Mary and their children, and he explains how two photographs make one point about footprints, the leopard, the giraffe, and the stability of quadripeds on the ground. He describes a career spanning more than four decades and says he enjoyed the freedom of a university professor, surrounded by inquisitive, bright students who appreciated learning. He recalls his start at MIT in thermodynamics and cryogenics, the difficult time getting a position, rejections, and how a book was published, which led to entropy generation minimization and textbooks in thermodynamics and heat transfer. He says what really matters is configuration, and he connects this to convection, freedom of the flow architecture, and a line of design science books. He ends with a punchline about a school of thought associated with Duke, the primordial presence of the idea before observation, and conferences from Duke to Paris and London.

• Bejan shows footprints of a leopard and says the rear foot touches the spot left by the front paw on the same side of the body. He says the giraffe photograph shows the same thing, and he connects it to extreme stability per unit weight of design.

• He says the recipe for an individual's happy and creative life is freedom and humility, surrounded by inquisitive, bright students appreciative of learning. He points to the Duke student who comes voluntarily to be shaped in life.

• Bejan describes the book cover as an accident from Africa, with an Egyptian goose on a branch, which he recognized as Adrian. He calls this an individual investigator standing on dead wood with infinite freedom to the blue sky of ideas.

• He recalls training at MIT and work in cryogenics, then a postdoc in Berkeley, and being hired at the University of Colorado. He says a book led to entropy generation minimization, and he connects thermodynamics and heat transfer to configuration and convection.

• Bejan says this kind of thinking represents a school of thought associated with Duke and calls it thermodynamics of 2026, tied to design in nature or constructal law. He says the idea is the fastest and cheapest investigation method, and he mentions the 16th Constructal Law Conference in Paris and the next year at Imperial College in London.

In this video, Adrian Bejan describes the design of the ice maker in a domestic refrigerator, where water freezes on a refrigerated surface called an evaporator, forming a layer of ice whose thickness increases over time, eventually reaching a point where it stops growing rapidly. He explains that the ice maker must then remove the manufactured ice to clean the surface, so the process repeats as a cycle with two time scales: a freezing time and a surface renewal time. He treats the surface renewal time as a known constant given by engineers and focuses on selecting the freezing time as the degree of freedom. The purpose is to maximize the time-averaged rate of ice production, which depends on how much ice is produced before removal and on the full cycle time. He connects this trade-off to familiar designs from domestic life to animal design and industry, where surfaces must be cleaned rhythmically to maintain high performance.

• The heart of ice making is a cold, refrigerated surface where water at the freezing point accumulates a layer of ice. Over time, the process runs out of zip because the layer no longer grows quickly, so the surface must be cleaned.

• Ice removal is a second time interval that renews the surface, and designs like ice trays with little cubicle alvoli help remove a whole bunch at once. This surface renewal time is treated as a constant, assumed to be known.

• The object of the game is to determine the freezing time as the degree of freedom selected rationally. The purpose is to maximize the time-averaged rate of ice production over the cycle, including freezing and surface renewal.

• The trade-off has two extremes: short freezing time on one side and long freezing time on the other. High values occur when the freezing time is determined by the time required to remove or clean the surface, which is good news for mechanical methods of scraping ice off.

• The same idea appears in the windshield wiper that cleans the window and in the eyelids that lubricate and clean the eyeball rhythmically. He also points to heat exchangers whose ducts get clogged by debris or gunk called scale, like plaque on teeth, and to the cost of shutting down a power plant to clean the tubes internally.

• Bejan starts from the idea of predicting the evolution of design and shifts from design in space to design in time. He connects this to rhythmic functioning in the body and the daily cycle.

• He frames respiration as a problem of posing the right questions, especially why inhaling time t1 equals exhaling time t2. He also links the same type of solution to heartbeating.

• Bejan models inhaling as atmospheric air entering the trachea and increasing the thorax volume by capital V, driven by a partial vacuum and limited by a global resistance R. He uses a pressure difference proportional to R and a velocity to an exponent n, and writes conservation of mass for the inflow and the accumulated air.

• He models exhaling as the thorax volume shrinking, indicated by a capital V, with an excess pressure delta p2, flowing out through the same resistance and cross-section, with an average velocity u2. He then computes work as the integral of p dv over the two parts and expresses average power in terms of V, af, and the time intervals.

• Bejan introduces alveoli and diffusion, where oxygen transfer scales with the square root of time and becomes inefficient, leading to intermittency and surface renewal through finite inhaling followed by exhaling. With a fixed oxygen requirement per unit time K, he minimizes average power and obtains the result that t1 and t2 are nearly equal, and higher K corresponds to shorter times and frequent breathing during running.

In this video, Adrian Bejan explains how the Atlanta airport story and a question at the 2009 ASHRAE congress led him from the golden ratio, or divine proportion, as a popular observation to a brief explanation of why it happens. He connects what people like in paintings, facades, the laptop screen, and other rectangles to how the two eyes scan an image with saccades, taking snapshots at 5 per second across the flat field of vision. He describes scanning horizontally and up and down, and considers the best shape to be the one that lets the eyes scan the whole area as quickly as possible, because fast scanning helps you grasp the meaning of a message and move on. He then uses the binoculars drawing, with two discs and their intersection, to argue that vertical and horizontal scanning differ because the eyes move upward in parallel but horizontally in series. He ends by tying well-proportioned and complex rectangles stacked on rectangles, and by saying eyes and ears sit on the horizontal because the world is flat, and because fast scanning and fast understanding are useful.

• Adrian Bejan says the Atlanta airport story first appeared in his 2000 book and was presented at the 2009 ASHRAE Congress. A participant said the drawing looked like the golden ratio, and Adrian Bejan said he figured out how to predict it and why it happens.

• Bejan describes two eyes that jiggle with saccades, taking snapshots at 5 per second as they scan the field of vision. He says the shape matters because scanning fast helps you understand fast, and that is useful.

• He treats the image as H and L, with scanning times along the horizontal and vertical axes, and he seeks the minimum total time. He says the fastest shape depends on the scanning speeds.

• Bejan uses binoculars and the intersection of two discs to compare how the eyes sweep vertically and horizontally. He gets an order-of-magnitude ratio and links it back to the rectangles people like.

• He connects the Renaissance and Uklid to the 618 dot dot dot ratio and the label divine proportion, then says science explains the attractiveness. He extends this to paragraphs, faces, and complexity as smaller rectangles stacked on bigger rectangles.

In this video, Adrian Bejan describes how a city grows from a small village road into a city block and then into a grid, and how the center and the periphery change over time as the population and the diameter increase. He explains that travel across the city becomes slower as the city grows, and he describes a stepwise change in which going around becomes shorter than going through, leading to the appearance of a beltway. He notes that speed on the beltway can increase because there are no traffic lights and because decisions are made by the city government and politicians, leading to an upward trend. He connects this to a threshold moment when people begin “banging on the doors” of decision makers, and he says that later another beltway with a bigger diameter will occur in the same predictable manner. He then links this way of looking at design and movement to earlier developments, moving to boats with sails, the Near East, the Mediterranean, and a Greek ship with oars on three floors that he compares to a gearbox.

• Bejan starts from the city block in the smallest and oldest village, describing a dirt road between a few houses that became the city block. He says cities grew from city blocks arranged in a grid and points to places like Paris, Florence, and Rome.

• He describes two kinds of cities: an old center of very narrow streets and almost square city blocks, built for carriages, horses, or oxen, and built in stone. He says the old city is not destroyed, while the periphery migrates outward as population increases.

• He explains that as the diameter increases, the time it takes to cross the city increases, even at relatively low speeds through the grid. He then describes the beltway as a way to avoid traffic, noting that going around is shorter than going across.

• Bejan says the beltway speed can increase over time because there are no traffic lights and because speed is increased by decisions made by the city government and politicians. He connects faster allowable vehicle speed with the earlier arrival of the beltway and says the tendency is tied to facilitating movement and life.

• He shifts to boats with sails and a story about the Near East and the Mediterranean, naming Lebanon, Israel, Iberia, the Phoenicians, Tunisia, Carthage, and the Greeks. He describes the Triim, with convicts pulling oars on three decks, and says this is the design of the gearbox, adding notes on Greek and Latin words.

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Adrian Bejan talks about denser packages that become lighter things to carry, and he connects this to what you want with your desires. He says that wanting bigger leads necessarily leads to opting for smaller objects, and he calls this the evolution of this technology toward miniaturization. He notes that what you have in your iPhone isn't this because the iPhone doesn’t have a fan inside, and he mentions a next, third variation on this theme. He says we like things that are smaller because we want to carry more of this artificial intelligence with us, beginning with arithmetic. He then links this to metabolism and to obesity, using the donkey, the whale, and the goose from Alaska flying to New Zealand, obese, where extra weight and so-called fat can be good under extreme circumstances for power and insulation in cold air at altitude in darkness.

Adrian Bejan presents three parts that go together, starting with how movement gives us the idea of the physics of wealth, underpinned by the natural birth of hierarchy on the map. He then turns to the birth of the beltway around the city, meaning beltways happened. He ends with the basic physics of attractiveness, also known as beauty, and calls it a pleasant surprise because there’s only one idea. He connects the urge to move stuff in an area with less fuel to a road map with a few larger and many small pathways, and then shows data where gross domestic product GDP and annual consumption of fuel crowd on a diagonal with a slope of one.

• He says the road map is a hierarchical display of movement, with a few larger pathways and many smaller ones. The large ones are traveled by big movers, and the smaller ones by smaller movers.

• He says the money people pay to make movement possible represents wealth, and the annual measure of wealth is called the gross domestic product GDP. He says fuel consumption to move stuff is synonymous with what people report as wealth: money spent annually.

• He describes a companion drawing in which GDP per capita and fuel per capita show the same distribution along the diagonal. He says the wealthier burn more, and the purpose of that so-called fuel consumption is to move stuff.

• He says life is movement because the antonym of no movement is death, and he calls reducing fuel consumption an argument for reducing the movement of life. He says no living group is reducing fuel consumption and never will, because history is a progression toward greater movement.

Design in Nature: The Evolution of Designs

16th Constructal Law Conference (CLC2026)

🗓️ 12-15 October 2026, Paris-Malaquais School of Architecture-PSL (Paris Sciences et Lettres) University, Paris, France

Deadlines

• Extended Abstract Submission: May 15, 2026

• Extended Abstract Acceptance: May 31, 2026

• Registration Deadline: June 30, 2026

Accepted abstracts will be presented as oral presentations or posters.

Submit Your Extended Abstract

Registration Fee

• Full: €400

• Student: €150

The registration fee covers admission to all conference sessions and coffee breaks. However, lunches and dinners are not included in this fee.

Contact: info@constructallaw.com

More Information about CLC2026

In this video, Adrian Bejan describes a story from this course about a student, Lee Ferber, a sailor who proposed an idea inspired by a toy boat with sails. Adrian Bejan looks at drawings of boats with sails from antiquity and notes that they all look the same from a distance, as tall as they are long. Adrian Bejan asks why the height of the sail is of the same order as the length, and frames the goal as changing the design so the boat's velocity on water gets closer to the wind velocity in air. Adrian Bejan connects this modest questioning to the maturation of technology and to why famous drawings show a consistent pattern. Adrian Bejan then highlights results about the hull shape and the mast, focusing on lightness and movement that becomes easier and more economical.

• Adrian Bejan starts with an image of a toy boat, with a hull in the water and a sail with a mast rising above it. Adrian Bejan links that simple image to history and to pictures of sails from antiquity.

• He emphasizes that boats with sails appear as tall as they are long, and asks why this repeating design shows up. Adrian Bejan treats that question as part of the freedom to change the design so the boat advances fastest when blown by the wind.

• He describes wind velocity in the air and boat velocity on the water, and says the object of the game is to bring the water speed closer to the air speed. Adrian Bejan notes this matters especially in antiquity, before steamships, when there was no other source of power on water.

• He says the mast diameter should scale with the sail height because of the maximum allowable stress at the deck where the mast is implanted. Adrian Bejan concludes that stronger material yields a lighter mast and a lighter hull, and that lightness and sail design make movement easier and more economical.

The Thesis: Generative Constructal Design

The thesis advances thermal design by unifying evolutionary principles with generative methods. Rooted in the Constructal Law — that systems evolve to facilitate easier access to what flows — the work proposes a methodology for designing thermal systems that are free to morph under changing physics and constraints.

The framework combines:

• evolutionary search,

• generative methods,

• and finite element multi-physics solvers

to learn a low-dimensional, navigable representation of flow architectures.

Unlike biomimicry, which is descriptive, or parametric methods, which are prescriptive, this approach is predictive: it reveals not only efficient configurations, but how architectures evolve when demands change.

Across four classes of systems — conductive heat sinks, hierarchical thermal metamaterials, waste heat recovery channels, and battery cooling networks — the designs evolved in silico exhibited a persistent tendency toward improved access and reduced global resistance.

Some highlights:

• Up to 13% multi-objective performance improvement over state-of-the-art gradient-based optimisation, with 6× faster convergence [1].

• Multi-objective thermal cloaks generated in under five minutes on a standard workstation [2].

• 35% heat transfer enhancement in pulsating convection experiments [3].

• 37% hotspot reduction and 50% pumping power reduction in battery cooling compared to parametric straight-channel designs.

Notably, all designs were generated on consumer-level hardware: a small gaming PC that cost less than $1,000.

The viva itself lasted a few hours; the journey behind it began more than 20 years ago. In many ways, the defence was not just about thermal systems, generative models, or evolutionary design. It was an opportunity to connect the dots of a development path that started when I was 5, sitting across a chessboard, trying to see three moves ahead.

Chess: Flow in Multiple Dimensions

Training as a competitive chess player taught me something that later resurfaced in my professional career: progress depends on discipline, freedom and access.

In chess, you assess a position not only in the present, but in the space of future possibilities. You ask:

• Which pieces have mobility?

• Which paths are blocked?

• Where is resistance accumulating?

A good position is one that improves access — to squares, to tempo, to initiative.

Constructal theory expresses this principle physically

For a finite size flow system to persist in time (to live), it must evolve with freedom such that it provides easier and greater access to what flows.

I did not know the Law when I was five, but I recognised the pattern.

Chess also taught me something equally important for research: how to lose. To analyse defeat without resentment, and move on. Move on quickly, the next game is tomorrow. And wasting time dwelling on the past is only useful for my next opponent.

I did not have a long Chess career, I quit at 11, when I found something more interesting.

Mathematics: Elegance Is Not Optional

Participating in national Mathematics Olympiads reinforced another lesson: representation is everything. A problem rarely becomes easier by brute force. It becomes easier when expressed properly, in simple terms. Just like in chess, a solution (i.e., the path to victory) is made by putting together the building blocks that you acquired in training. It is solely up to you to see the pattern.

Elegance is not aesthetic luxury — it reduces cognitive load and clarifies structure. This insight later guided my approach to design optimisation. Instead of repeatedly solving large PDE-constrained problems, could we find a representation that makes the search itself simpler?

Could we compress the space of feasible flow architectures into something continuous and navigable?

That question ultimately led to the generative framework developed in my thesis, now called DendrON. One that is both informed by nature (carbon wisdom) and enabled by machine learning (silicon intelligence).

Living and non-living: No Artificial Barriers

While my relationship with mathematics is not as short-lived as my Chess career, I kept finding more interesting things to preoccupy myself with. Here, I have to pay tribute to my family, who insisted that I avoid falling into the trap of playing video games on ever smaller screens, ultimately encouraging me to take up reading instead.

Physics and Biology where among my favourite subjects, and I trained for a couple of years to become a medic. While keeping my options open by studying Engineering, I became fascinated by the continuity between the so-called living and non-living systems.

People and engines breathe; hearts pop up in mammals, but also in complex analysis; neural networks are useful in brains and computers — the patterns repeat. The physics is shared. The differences are contextual, not fundamental.

Years later, when already in London, Constructal theory provided a language for this unity. It dissolves the artificial barrier between animate and inanimate structures by focusing on flow, and allowed me to put 1 (physics) and 1 (biology) together.

Photography: Saying More with Less

Photography entered as a hobby but became unexpectedly formative. Like most teenagers, I didn’t like how I looked at the time, so I hid behind a camera.

To take a good photograph is to:

• decide what to include,

• what to exclude,

• and how to use limited resolution to emphasise the main carrier of information.

Post-processing sharpened this awareness. A photograph is not just captured — it is revealed.

Working with generative models later felt strangely familiar. High-resolution geometries were compressed into low-dimensional latent spaces. The question was not how to store everything, but how to preserve what matters. Learning to see an image “through the eyes of the mind” is not very different from learning to see a design before it fully materialises.

Freedom and Discipline

Throughout my PhD, one theme resurfaced repeatedly: Freedom. Freedom in design means degrees of freedom — allowing geometry to change, configuration to adapt, structure to emerge. Freedom in research means resilience and the liberty to take up new problems, out of the so-called comfort zone.

Yet Freedom without Discipline collapses into noise.

One of the greatest lessons I learned from my supervisor, Professor Ricardo Martinez-Botas, is that freedom and structure are not opposites. They are partners. Discipline gives direction to freedom; freedom gives purpose to discipline. Constructal theory itself reflects this duality: constraints are not obstacles; they are the reason form emerges.

Endurance and Setbacks

Research, like sport, is less about intensity and more about consistency. I was fortunate to spend the summer before my graduate studies in Croatia, working for Rimac Technology in Zagreb. While completely alone, in a new country, I started training judiciously. Every day.

The conditioning I managed to complete there allowed me to take up new sports, roughly every year: cycling, running and swimming. During my PhD, I swam more than 500 km, ran and cycled more than 1000 km (each). These numbers are insignificant in athletic terms, but they hide behind something important: learning to go through setbacks without drama.

Papers rejected. Experiments delayed. Rigs breaking before a deadline.

Sport teaches you to keep moving.

Connecting the Dots

Looking back, the defence was not simply a technical milestone. It was a moment of convergence:

• Chess taught multi-dimensional thinking.

• Mathematics taught elegant representation.

• Physics and Biology revealed unity across systems.

• Photography sharpened perception and compression.

• Engineering provided impact.

• Sport built resilience.

The Constructal Law offered a unifying principle. The thesis did not optimise for rigid objectives, nor did it search for the end-design. It explored how we search for new configurations, at the border of chaos and order — how architectures evolve when given freedom to morph under physical constraints.

If systems persist by improving access, then perhaps research careers do too.

I am deeply grateful to the mentors, colleagues, friends who made this journey possible. I thank Prof. Adrian Bejan and the Constructal community for providing the intellectual compass.

I am forever indebted to my parents, Daniela and Claudiu, for fostering my moral compass and a growth mindset (before it was fashionable). I thank my sister, Iasmina, for being the perfect sparring partner (albeit a sore loser).

This is not the end. It is the end of the beginning.

About the author

The author was born on 19 December 1999 in București, România. He graduated from Colegiul Național de Informatică “Tudor Vianu” in 2018, and moved to the U.K. to study Mechanical Engineering at Imperial College London.

Matei graduated with an MEng in June 2022 and received his PhD in February 2026. He was recently awarded the Dr Ashraf Ben El-Shanawany Memorial Prize for the best PhD student, with outstanding achievements in research, public outreach and innovation.

His peer-reviewed publications include:

[1] Matei C. Ignuta-Ciuncanu, Hannes Stärk, and Ricardo F. Martinez-Botas. Evolutionary design of conductive pathways using a generative autoencoder. International Communications in Heat and Mass Transfer, 166:109098, 8 2025.

[2] Matei C. Ignuta-Ciuncanu, Philip Tabor, and Ricardo F. Martinez-Botas. A generative design framework for passive thermal control with macroscopic metamaterials. Thermal Science and Engineering Progress, 51:102637, 2024.

[3] Matei C. Ignuta-Ciuncanu, Jordan Michael, Shuyang Qian, Chris Noon, and Ricardo F. Martinez-Botas. Experimental characterization of heat transfer and fluid dynamics in pulsating exhaust flows. Journal of Turbomachinery, 148(3):031012, 10 2025.

[4] Matei C. Ignuta-Ciuncanu and Ricardo F. Martinez-Botas. Discrete svelteness: Evaluating flow structures in generative constructal design. BioSystems, 105459, 4 2025.

[5] Matei C. Ignuta-Ciuncanu and Ricardo F. Martinez-Botas. Evolutionary design of radial fins for forced and natural convection using generative methods. International Communications in Heat and Mass Transfer, 171:110027, 2026.

[6] Matei C. Ignuta-Ciuncanu, Chris Noon, and Ricardo F. Martinez-Botas. Heat Transfer Enhancement in Pulsating Flows: A Bayesian Approach to Experimental Correlations. Journal of Turbomachinery, 147(5):051009, 11 2024.

[7] Matei C. Ignuta-Ciuncanu, Philip Tabor, and Ricardo F. Martinez-Botas. Constructal Law, Biomimicry, and Topology Optimization Through The Lens Of Generative AI. 14th CONSTRUCTAL LAW CONFERENCE — 10-11 October 2024, Bucharest, Romania, 2024:41–44, 12 2024.

[8] Matei C. Ignuta-Ciuncanu, Philip Tabor, and Ricardo F. Martinez-Botas. Generative constructal design of a multi-physics heat sink for managing transient thermal loads. ASME Journal of Heat and Mass Transfer, pages 1–21, 10 2025.

[9] Philip Tabor, Matei C. Ignuta-Ciuncanu, and Ricardo F. Martinez-Botas. Thermal diodes, transistors and logic: Review of unconventional computing methods. BioSystems, 105491, 6 2025.

In this video, Adrian Bejan goes backward in time from today and connects the evolution of airplanes with something much simpler, the design of boats with sails, to complete your exposure to this design of how things move. In this video, Adrian Bejan promises a PDF and an article on predicting the evolution of helicopters, whose main purpose is to hover like a jellyfish or a hummingbird. In this video, Adrian Bejan explains that helicopters do not use two wings, but rather a rotor made of several wings called blades, plus a small propeller at the end that rotates in a vertical plane to keep the helicopter oriented in one direction. In this video, Adrian Bejan says the paper repeats the sequence of steps seen in the evolution of airplanes, but now the question is about the rotor radius and the overall mass, derived analytically before being compared with data from the entire helicopter industry. In this video, Adrian Bejan ends by pointing to sharp correlations and a convergent evolution in which helicopters, small and large, end up looking the same.

• Adrian Bejan links the path to today with antiquity and says the people selling the boats were actually very smart. In this video, Adrian Bejan uses this connection to set up the evolution of airplanes and then helicopters.

• Bejan describes the helicopter rotor and its blades, and he adds a small propeller that prevents the helicopter from rotating in the opposite direction to the rotor. In this video, Adrian Bejan frames this as the basic design for hover.

• He says the paper derives results analytically and then compares them with data from the entire helicopter industry. In this video, Adrian Bejan describes relationships that link the actual work to the engine size, and the engine mass to the fuel load and the total helicopter mass.

• Bejan points to very sharp correlations in the data and says this indicates principles of physics at work. In this video, Adrian Bejan mentions the Cold War, institutions working independently in secret, and how they arrived at the same conclusions, like convergent technology and drones today.

• He compares the airplane wing to the rotor blade, where air creates lift, the blade bends, and the stresses are highest at the axle, where the blades are attached. In this video, Adrian Bejan says this leads to the rotor radius being proportional to body mass and to the vehicle's length scale, which matches the convergent evolution of helicopters.

As Bejan recently said, “Design takes a long time to do, and then you have to go to the prototype and then to manufacturing. That costs money and takes time. But the idea takes zero money and zero time.” Good ideas are good for business, and ideas informed by science and the laws of nature are better than those that are not.

Bejan not only predicted the optimal design for heat flow in the 1990s laptop computer; his prediction still holds in the evolution of AI datacenter cooling. The constructal law that Bejan discovered also applies not only to heat flow but to everything that flows in spacetime, both animate and inanimate, as well as to material and immaterial (e.g., ideas, knowledge, wealth, culture).

Because the constructal law applies universally and can be observed at all scales, it also applies to businesses, supply chains, and distribution networks. As such, my objective is to focus on the commercial applications and implications of the constructal law, and to consider their implications for business leaders.

This article is intended to introduce these insights to an audience that doesn’t have much time for or interest in new science but rather values practical insights into industry, market dynamics, and competitive advantage. Why? Because the constructal law explains many of these business and market dynamics in a manner grounded in physics. As such, our ability to understand, predict, measure, and optimize key performance indicators in commerce and industry is significantly advanced by the scientific knowledge of the constructal law and its associated theory.

Primer on the Constructal Law

In 2018, Bejan was awarded the prestigious Franklin Medal for his discovery of the constructal law and for introducing constructal theory. As a Franklin Medalist, Bejan has joined the ranks of science luminaries such as Albert Einstein, Max Planck, Niels Bohr, John Archibald Wheeler, and Stephen Hawking. Yet at the time of writing this in 2026, the constructal law and constructal theory remain obscure, and the chance is high that you’re reading about it here for the first time.

Latency refers to the time and course required for ideas to spread and be adopted. William Gibson famously said, “The future is already here – it’s just not very evenly distributed.” The same could be said for knowledge of the constructal law and the insights and implications it yields. Bejan’s discovery of the constructal law offers powerful, practical insights that needn’t wait for mainstream awareness. The knowledge exists and needs only to be applied and further studied.

The constructal law is not yet a familiar household term, but it should be. It should replace any use of more familiar terms, such as fractals, complexity, and chaos, none of which have any foundation in physics, and all of which can be better explained by the constructal law, whose foundation is in physics.

As explained by Prof. Adrian Bejan, who discovered the constructal law in 1996, “Everything that moves, whether animate or inanimate, is a flow system. All flow systems generate shape and structure over time to facilitate this movement across a landscape filled with resistance … The designs we see in nature are not the results of chance. They emerge naturally, spontaneously, because they enhance access to flow in time.” (Bejan, A.and Zane, J.P., Design in Nature, 2012) In other words, the constructal law, as a law of physics, explains how nature designs itself. In nature, one can observe evidence of the constructal law in patterns seen virtually everywhere.

2. As a primer on the meaning and implications of constructal law and theory, the following figure illustrates some of the core concepts of constructal dynamics. More than just ideas, each of the phenomena illustrated below is representative of empirical observations of reality and an abstraction of a deeper universal truth, i.e., the constructal law.

In Figure 1 above, two examples illustrate emergent structure and form in nature that evolve directionally and purposefully toward greater detail and refinement. This phenomenon demonstrates diversity and hierarchy in the spontaneous evolution of the system, aimed at increasing flow access. The first row shows a plan view of a branching, tree-like flow system that flows from a point on the left to the area on the right. The second row shows a polygonal cross-section view that transitions to a circular cross-section, as seen, e.g., in veins and vascular channels. The constructal law explains why systems in nature do so: to enhance access to flow.

Enhanced access to flow, or flow efficiency, is shown in the bottom row, where the relative system performance is determined by the flow system's efficiency rate (η̇). Performance increases monotonically in the direction of the system’s evolution. All points of this space are either above or below the curve. The curve illustrates the boundary between the impossible above the curve and the possible below. What is this space above the curve? Why is it impossible? The answer lies in the 2nd law of thermodynamics, which defines a system's perfection as having zero energy loss and establishes that such perfection cannot be achieved by design. Impossibility here is directly related to and required by the 2nd law of thermodynamics. It cannot be avoided or eliminated, but can be reduced and minimized.

Why the Constructal Law Matters

James Watt did not invent the steam engine, but he more than doubled its efficiency at the time, thereby changing the industry and the world forever, effectively displacing slavery as a source of power for work. He was able to do so by understanding thermodynamics. The laws of thermodynamics are now known to apply universally, not only to steam engines but to all aspects of industry, commerce, and social organization.

Business leaders are already familiar with the concepts of throughput, distribution, performance curves, and performance improvement through innovation. The constructal law not only explains but governs how all these, in fact, all systems, evolve over time. It suggests that flow system efficiency is the principal driver of performance and that this efficiency arises from the flow system's shape within its environment. In both nature and industry (which is part of nature), flow systems, given the freedom to do so, will evolve with emergent structure to flow more efficiently.

On one level, this continuous drive for improvement will happen regardless. In the industry, this improvement is forced by competition and customer demand. For businesses to survive, they must grow and continuously innovate; otherwise, they risk going out of business. All of that still applies and accelerates. So, how does knowing the physics behind the throughput of flow systems help? It helps because science allows one to make predictions with confidence. When designing new products or services, being able to predict outcomes, minimize trial and error, reduce risks, and accelerate growth helps.

Considerations for Business Leaders

Many of the concepts described above are familiar. The only new news is that science has advanced to the point where it can offer a greater understanding of the concepts essential to business. My main recommendation is to encourage curiosity to learn more about science and how it can be applied to specific business challenges. For now, I list below a few of the ways in which I apply my knowledge of the constructal law with regard to how I approach my own work in business:

Optimizing flow systems

Know your priority flow systems and benchmark their performance. Note that everything in nature, as well as in business and the universe, is a flow system.

Whether the supply chain, assembly line, distribution, or sales, each is a flow system whose efficiency can be measured and optimized. However, other important flows also exist, such as people, culture, knowledge, and information. I work in IT Services, where the flow of knowledge and information is arguably the lifeblood of a modern IT services business. Understanding the science of flow systems can help optimize those most important aspects.

Reducing and eliminating bottlenecks

The importance of managing and mitigating bottlenecks has long been recognized in widget manufacturing. This had been essential for the industrial economy but has become even more so in the information economy. Information flows are harder to see than the path of a widget on an assembly line. Working in IT services, I am sometimes painfully aware of information bottlenecks. We know where the bar is for information to travel from one place to another: the speed of light. When your firm has information in one place that has value somewhere else, you have an information bottleneck if it is not getting there at the speed of light.

Knowing and exploiting degrees of freedom

Evolution and improvement can only happen when freedom exists. Sometimes you want guardrails, so there are limits placed on freedom to change. At other times, limiting the freedom to change has the unintended effect of preventing improvement. Businesses are now wrestling with AI, including which tools employees can or cannot use and what they can or cannot do with them. Making these decisions should be done with awareness of the degrees of freedom employees have to innovate.

If you’ve read this far, you may already have an advantage over business leaders who are unaware of constructal science. If you’d like to be more informed and engaged with a growing community of scientists, scholars, and business leaders, let me suggest the following:

• Read and Follow the Work of Professor Adrian Bejan
  Bejan has written many books and scholarly articles. Of all of these, I recommend business leaders start with Bejan’s book: Freedom and Evolution: Hierarchy in Nature, Society and Science, published by Springer Nature in 2020

• Engage in an active international community of scientists, scholars, and business leaders
  who are advancing Bejan’s work in terms of both application and theory. The leading edge of this can be found in the program and proceedings of the annual Constructal Law Conference.
  See the latest here: Proceedings of the 15th Constructal Law Conference (CLC2025)
  The next conference will be in Paris, Oct. 2026: 16th Constructal Law Conference (CLC2026)

• Stay up to date and informed
  Follow/Subscribe to the Constructal Law Newsletter at constructallaw.com

About the Author: John Mullaly

John Mullaly is a creative technologist whose career spans more than three decades at IBM and now Kyndryl, the 2021 spinout of IBM’s global services business. His work is at the intersection of emerging technology, design, strategy, and new business ventures. An IBM Master Inventor (emeritus), he has been issued more than forty patents in human–computer interaction. His work in technology has progressed from computer graphics and software design to building first-of-a-kind cloud and data analytics services. As a senior advisor in IBM Corporate Development, he interfaced with startups and venture capital firms and advised IBM leadership on more than forty acquisitions. He co-authored a book on user-centered software design and received the IBM Chairman’s Corporate Patent Award for his pioneering work in three-dimensional interactive environments. His education spans art, mathematics, and computer science (BS in General Studies, New York Institute of Technology) and business (MS in Technology Commercialization, University of Texas at Austin). Alongside his technical career, Mullaly is an active artist in painting, sculpture, and creative writing. He resides in the Hudson Valley in upstate New York.

In this video, Adrian Bejan explains the evolution of airplanes as part of the movement of people on Earth today, and uses that topic to lead into a concluding section on the design of society and the words used to describe that design. He reviews a simple airplane model with a fuel tank and an engine, and emphasizes that movement is the product of the stuff being moved and the distance, which is what costs money. He then shifts to movers on an elemental area, drawn as a rectangle, with one big mover traveling a long distance and many smaller movers traveling transversely, and he focuses on keeping the movement going while burning less fuel. He introduces a two-part model for each mover as an empty structure plus a motor, connects fuel consumption to work, and shows how economies of scale appear as the size of what is moved increases. From minimizing fuel use across the territory, he argues that movement becomes hierarchical, with many small moving short and few big moving long, and he ends by linking hierarchy in movement and fuel consumption to hierarchy in wealth on the same territory.

• He revisits the idea that big airplane, big engine, and big fuel load scale together, so one drawing can be magnified or reduced to represent different sizes. This sets up the idea that the same kind of correlation can be tried again on trucks on the highway and other groups.

• He defines movement as stuff times distance and treats that product as the real cost, because moving bigger things and moving farther are both more expensive. This leads him to treat fuel consumption as the key objective in economics, a very old attitude.

• He builds a territory model with two dimensions and a total mass composed of one big mover and a number of small movers, then identifies degrees of freedom such as the rectangle's shape, the ratio of vehicle sizes, and the number of small movers. He uses a simple plan to determine these, so the same movement can continue with less fuel.

• He models each mover as structure plus motor and argues that the trade-off in fuel requirement occurs when those two parts are of the same order of magnitude. From there, he connects the result to economies of scale, in which fuel cost per unit of mass moved decreases as the mass moved increases.

• He shows that the smaller movers should travel shorter distances while the bigger mover travels longer distances, and he calls the resulting pattern hierarchy. He then compares different drawings of how small movers join into a big mover, like a trunk that collects flow, and links this hierarchy in movement and fuel consumption to a hierarchy in wealth.

In this video, Adrian Bejan explains that body mass has two parts: the fuel load and the engine. He points to an airplane, where the fuel load is in the wings, and the wings are the burden relative to the empty fuselage. He connects one idea from burning the fuel to heat, then to the engine, and then to the power that drives the airplane, and he defines the relationship between heating and work through the efficiency of the engine. He returns to economies of scale and says that in bigger engines, the passages are wider and heat exchangers have greater surface areas, so engines must be more efficient as they get bigger, but at a decreasing rate, which makes a concave curve. He uses these predictions to relate fuel load, engine size, and travel, and then says they are tested against data from many airplane designs and agree with the figures in the book. He ends by answering questions about the cheetah and the elephant, steady movement and one-shot movement, and lifespan, and he repeats that size matters in speed and in living longer.

• The fuel load and the engine are related because fuel generates heat, and the engine converts that heat into work and power. The work requirement is proportional to the body weight and the range or travel length.

• The efficiency of the engine forms a cloud of data with engine size, and it cannot punch through a ceiling tied to reversible operation. Engines become more efficient as they get bigger, but the rate decreases, so the curve is concave.

• The movement of a piece of material called capital M to a distance L traveled increases when the engine is bigger and when the fuel is more voluminous. These two things do not change independently because they add up to the indicated size of the whole airplane.

• From minimization with a capital M constant, he derives results for the mass fraction occupied by fuel and the fuel-to-engine ratio. He also says that every organ scales in proportion to the total size of the capital M, and that these predictions match the airplane measurements shown in the book's figures.

• For the cheetah and the elephant, he says that average speed over daily life falls where it should on a line of assumed constant speed V, and he separates steady movement from one-shot movement. Regarding lifespan, he says larger things live longer, and he links this to the range, which increases monotonically with size.

In this video, Adrian Bejan compares the fighter jet to the designs of a hawk and a cheetah, and says this is the realm of outliers because its life is highly intermittent and not steady. He contrasts fighter jets that were underground during the Cold War and fly briefly with the B-52s that have been flying since the 50s, non-stop, and says it is no longer a surprise that they all kind of look the same as a commonality of design.

He challenges scientists who think that everything we have comes from copying from nature, which they call biomimetics or biomimicry, and says airplanes came from the flexing of the brains of very smart people from all sorts of countries who arrived at very similar designs.

Adrian Bejan says thinkers think and form images in their minds, and that believing in so-called copying from nature deprives you of the freedom to predict where the observed object came from in nature. He adds that he does not describe nature; he predicts it, because it is much shorter to predict than to describe, and he urges you to respect what occurs in your mind and write it down as soon as it does.

The video builds a drawing of a fuselage and two wings by predicting proportions, not millimeters or centimeters, using relative sizes called proportions and aspect ratios for slenderness, the shape of the cross-section, wingspan relative to fuselage length, and wing profile features. It starts from the premise that everything that flies operates at a balance between the effort to lift itself and the effort to overcome drag as the body falls forward, so the focus is on overcoming drag. The drag is expressed as a frontal area and a friction coefficient, with contributions from the fuselage and the wings combined; the video also introduces aerodynamic loads as the wing deflects upward under lift. The best fuselage cross-section is described as roundish, like that of a dolphin or orca, and the video links this to heat loss being least for warm-blooded animals, whereas fish have a vertical oval cross-section because the whole body paddles in a horizontal plane. With these moves, the video combines the equations and concludes that the wingspan-to-fuselage-length ratio is essentially constant across airplanes, birds, and insects.

• The drawing uses five degrees of freedom, including slenderness and wingspan relative to fuselage length, so you need proportions before you make it. The point is that the drawing conveys relative sizes through proportions or aspect ratios.

• The analysis focuses on the drag experienced by the body as a wind approaches at a given speed, with contributions from the fuselage, the wing, and the wings together. The drag model uses a frontal-area concept and a friction coefficient defined in terms of the wetted perimeter and length.

• Mechanical strength is added by looking at the wing in equilibrium in the armpit as it curls upward during takeoff. The lifting force balances weight, and the bending moment is tied to span and thickness with tension and compression over the cross-sectional area of the wing.

• The fuselage cross-section is pushed toward a roundish shape, with a story about a square cross-section not being very good for flying through the air, and comparisons to transport aircraft and buildings. The video shows that a round cross-section leaks the least heat when volume is fixed for warm-blooded animals such as dolphins, orcas, manatees, and whales, whereas fish differ.

• The wing is expected to be slender in cross-section when the profile area is fixed, and friction coefficients are evaluated using a Moody chart. After combining the equations, the video states that variations in body mass are negligible relative to the values you draw, so the wingspan-to-fuselage-length ratio is essentially constant across observations.

In this video, Adrian Bejan explains that predicting evolution entails predicting both the future direction and the present's origin, because without the power to predict, there is no basis for asking why things are the way they are today. He points to bipedal motion, quadripedal motion, the cross sections of rivers, and the dendrites in the lung as things that have arrived at being present today out of a universal tendency. That tendency is to acquire greater access to what flows, and to achieve this through the freedom to change. He then turns to airplanes as loaded structures that travel through space, and argues that what flies has organs, and that the sum of the organs and their positions constitutes the structure. He frames the day as a problem-solving session focused on predicting the size of the fuel load, the range while consuming that load, and the size of the engine, while also insisting that without the engine, there is no power, no movement, and no evolving design.

• Predicting evolution is valuable both prospectively and retrospectively, as it supports the question of why things are the way they are today. It is tied to predicting direction and the origin of the present.

• Many examples are presented as answers on the blackboard, including bipedal motion, quadripedal motion, cross sections of rivers, and dendrites in the lung. These are described as arriving to be present today out of a universal tendency.

• The universal tendency is described as the acquisition of greater access to what flows, enabled by the freedom to change. This frames the way designs evolve.

• Airplanes are treated as loaded structures that travel through space at constant speed for simplicity, and they are said to have organs. The structure is the sum of the organs and their positions within the whole.

• The objectives are to predict fuel load, range, and engine size, with the engine emphasized as essential for power and propulsion, and for evolving design. The same ideas are said to apply 100% to other moving and loaded objects, such as animal bodies, food on board, and muscle mass.

In 2023, I played with Adrian Bejan’s Constructal Law, which states that flow systems far from equilibrium evolve to maximize access to flow. For the climate, this means the system naturally rearranges itself to move as much heat as possible from the hot tropics to the cold poles. Here, the Earth is downgraded to a featureless ball with a hot equatorial belt and cold polar caps, and the only “decision” the system gets to make is how wide that hot belt is when it maximizes poleward heat flow.

The two‑zone sphere

Picture a smooth Earth with lines at ± θ around the equator; between them is the hot belt, and poleward of them are the cold caps. Heat flows from hot to cold, driven by the temperature difference, and the Constructal game is to let θ slide until that heat flow is as large as possible. Figure 1 is the cartoon, and Figure 2 shows the real Earth’s hot and cold zones from the Clouds and the Earth’s Radiant Energy System (CERES) top‑of‑atmosphere radiation balance; despite the missing continents and currents in the model, the real planet organizes into a very similar warm belt and cool caps.

In the hot zone, absorbed solar power is the projected area times the solar constant times one minus the hot‑zone albedo, and emitted power is the area times the sum of one minus the greenhouse fraction times σ times the hot‑zone temperature to the fourth power, with analogous expressions for the cold caps. The difference between absorbed and emitted power in each region is the heat flow q connecting hot to cold. For buoyancy‑driven circulation, Bejan and Reis found that q scales like a conductance C times the temperature difference to the three‑halves power. That leaves five unknowns (hot and cold temperatures, q, the hot‑zone area fraction x, and C) and only three radiative balance equations. As such, the Constructal Law supplies the missing condition: choose x to maximize q, which is the mathematical statement where dq/dx = 0 at the optimum.

In practice, this is a nested optimization. For a given x, solve for temperatures and q. Next, vary x to maximize q, then tune C so that the model’s hot–cold temperature difference matches the observed one. The only external inputs are the hot and cold albedos, hot and cold greenhouse fractions, a single conductance parameter, and small ocean heat‑absorption terms in each zone, all drawn from CERES and related data.

Temperatures, boundary, and heat flow

Over 2001–2024, the model gets the mean hot‑ and cold‑zone temperatures within about 0.1°C, tracks the year‑to‑year ups and downs, and captures the slight warming trend, as shown in Figure 3. The modeled swings are a bit larger than observed, but the timing and qualitative behavior match well.

The Constructal solution puts the hot/cold boundary at about 36°N/S, while CERES puts the top‑of‑atmosphere radiation‑balance boundary at around 34°, so the model is off by roughly 2° of latitude, about 220 km. Figure 6 shows that offset, which comes almost entirely from deserts. The Sahara, Arabia, Australia, and the Gobi radiate more than they absorb and so fall on the “cold” side observationally, while the smooth sphere has no deserts and assigns those latitudes to the hot belt.

For poleward heat transport, the modeled peak transport comes out around 14.9 petawatts versus the observed 12.3 petawatts, a global mean excess of about 5 watts per square meter, mostly because of those deserts being misassigned to the hot zone. But the anomalies are where the model shines: Figure 4 shows that the year‑to‑year changes in heat flow match very closely, with a root‑mean‑square error of only 0.04 petawatts, small compared to the natural variability.

That means that, armed only with annually updated albedo and greenhouse fields and a Constructal optimization, the two‑zone sphere captures the dynamics of how the climate’s heat transport responds to changing radiative conditions.

Climate sensitivity from a smooth ball

To get an equilibrium climate sensitivity (ECS), the model is run with an extra 3.7 watts per square meter of downward flux, the standard forcing for a doubling of CO₂, and then allowed to reoptimize. The hot belt warms by about 1.09°C and the cold caps by about 1.12°C, giving a global mean warming of about 1.10°C. Therefore, the ECS in this framework is roughly 1.1°C per CO₂ doubling. The model omits a whole gallery of emergent negative feedback—thunderstorms, organized deep convection, El Niño/La Niña, tornadoes—that rapidly move heat from the surface into the atmosphere and thus limit surface warming, so the real system is almost certainly less sensitive than this spherical cow.

The IPCC’s likely range is 1.5°C to 4.5°C per doubling, so this Constructal result lies below their range but aligns with several observational estimates such as those of Lewis and Curry. Figure 5 shows that the spherical cow sits about the lower, observation‑based estimates rather than the higher model‑based ones.

What the spherical cow is telling us

So, with two zones, four variables, three tuned parameters, and one maximization principle, this ultra‑simple smooth‑sphere model:

• Reproduces hot‑ and cold‑zone temperatures and their interannual variability, including the observed warming trend.

• Gets the hot/cold boundary within a couple of degrees, missing mainly where real‑world deserts sabotage the smooth‑sphere assumption.

• Tracks the temporal structure of poleward heat‑transport anomalies with very low error compared to natural variability.

On top of that, it yields an ECS of about 1.1°C per CO₂ doubling while omitting known negative feedback, strongly suggesting that the real climate sensitivity is modest, not extreme. The broader point is that if you honor basic radiative constraints, feed in real albedos and greenhouse fractions, and let the system maximize its own heat flow, you can capture the central behavior of Earth’s climate with a geometry to which any full‑blown GCM would be embarrassed to admit.

As always, it is not the last word on anything, but it is a useful reminder that the climate behaves like a robust flow system—not a delicate piece of clockwork forever on the brink of collapse—and that even a spherical cow can tell you that much.

The video explains the mathematical body of relations that connect measurable properties to derivable properties, moving from measurements to much more useful results. It revisits the first question, in which calculations and cookbook problems relied on steam tables and properties such as specific internal energy, specific enthalpy, and specific entropy, which are not directly measured and are often expressed in jargon. The video insists that these numbers derive from relations linking experiments to one another and, ultimately, to useful weapons in the hands of machine designers. It strongly argues that thermodynamics did not originate in physics and chemistry but in engineering, machines, and the steam engine driven by cheap power. The steam engine is presented as a huge invention that liberated the world from hard lives dependent on animals and slaves. The discussion closes by stressing common sense, intuition, and listening to people who know the pain of not having.

• The video explains that steam table properties are not directly measurable and should not be treated as jargon, because they derive from relations established through experiments. These relations connect measurements to practical uses.

• It emphasizes that thermodynamics emerged from machines and the steam engine, not from abstract subjects. The attraction of cheap power is described as central.

• James Watt is discussed as a machinist who improved efficiency by separating heating and cooling into different chambers. This intuition about not mixing more than doubled efficiency.

• The formation of the company with Matthew Bolton is described as a step that lifted Europe out of poverty. Patents and practical engineering mattered.

• Adrian Bejan advises seeking ideas from common folks and everyday places. It highlights the importance of listening to those who understand the pain of not having.

In this video, he repeatedly asks you to respond with comments, questions, reactions, clarifications, or more profound reflections that might benefit your experience as students at Duke. He says this is the beginning of his fifth decade of teaching at Duke, and that students once participated in the discussion but became quiet, not only because of the pandemic. He says the purpose is to bring out of each of you a source of ideas, your own ideas, and that if you keep quiet, you’re not helping yourselves. He advises keeping questioning, remaining firm in your opinion, and that he is not afraid of being corrected; in fact, he welcomes it.

• He repeats his invitation for comments, questions, reactions, and points of clarification related to your experience as students at Duke. He says he would learn from something new or personal coming from you, because you’re not sheep and you’re individuals.

• He states that this is the beginning of his fifth decade of teaching at Duke and that students were participating in the discussion in this enclosure. He reports that students became quiet and that the problem began before the pandemic.

• He says that if you keep quiet, you’re not helping yourselves, and it doesn’t mean screaming, throwing rocks, or breaking windows. He says to say “I didn’t understand that, can you say it better,” or “would you please repeat it.”

• He says if you ask a person who is spewing nonsense to repeat, an honest person will correct himself while repeating, because people make mistakes. He says you’re amazing, that you should keep questioning, and that he is not afraid of being corrected; in fact, he likes it.