This article uses two examples of mixing to demonstrate why the constructal law and the second law are distinct, self-standing laws. It begins with the definitions of two distinct phenomena: irreversibility versus design in nature (form in motion, configuration, rhythm). These are summarized in two distinct statements, the second law and the constructal law. The first example of mixing concerns the movement of a body that sinks in a pool of liquid. The second example is about pouring ball bearings of two sizes into a box and shaking the box up and down. In both examples, the mixing process (the approach to no flow) is accompanied by the evolution of flow configuration. In the first example, evolving is the flow design around the sinking body. In the second example, evolving is the stratification of the balls. The juxtaposition of the constructal and second laws clarifies misunderstandings that tend to creep into thermodynamics regarding the physics of evolution, arrow of time, universe, and intangibles. The two examples came from the author's classroom; they teach the importance of free questioning and common sense (not jargon) on the way to discovering what flows, how it flows (with what design), and in what discernible direction (evolution).

This article makes an unexpected, counterintuitive theoretical step. Excessive inactive body mass (fat, carried load) has a negative impact on the efficiency of life movement to distances. Also negative is the impact of loss of body heat to the cold ambient. Surprisingly, the two negative impacts evolve naturally to a tradeoff such that the living body benefits from maximal efficiency in movement and access on the globe. The tradeoff reveals the amount of inactive mass (e.g., thickness of fat layer) most beneficial for movement. Tradeoffs between negative impacts govern the evolution (the morphing) of all moving design (animal, vehicle, river, etc.). For example, fat tends to be stored primarily at the interface between the warm inner body and the cold ambient. That's design in nature, configuration evolution. Furthermore, the perception of cold is physical and measurable in terms of physical outcomes: design for greater efficiency in movement on the globe, greater power, easier access, farther reach, economy and longer lifespan. Traditionally, perceptions are thought of as intangibles, opinions, beyond the predictive reach of physics. The physics underpinnings of perceptions, reaffirmed in this article, are essential to the future of robotics and AI, if such technologies are ever to compete with naked animal thought and action.

This article unveils the connection between design in nature and a classic mathematics problem from 1696 to 1697: the brachistochrone. Some flow designs seem to act as obstacles to flow (cataracts, waterfalls, and roll waves), in contradiction with the natural tendency to facilitate flow (round ducts, bifurcated channels, animal speeds, and frequencies). The brachistochrone problem is to determine the curve of shortest-time descent without friction. The connection communicated in this article is that cataracts, roll waves, and the curve of shortest-time descent are about one natural phenomenon, which is predictable. This is demonstrated by comparing two ways for water to flow downhill: (i) on a stepped path (free fall over a dam, followed by accumulation in a large and nearly stagnant pool) and (ii) on a straight incline. We find that (i) is faster than (ii). In conclusion, brachistochrone-like paths are naturally occurring flow configurations, in accord with common observations of natural flow configurations that facilitate access.

The roofs of houses look similar in profile, especially in villages and old settlements. Why? The question is about the common angle of inclination. The answer comes from heat transfer by natural convection. Inspired by the evolution of the sapiens toward more power from the adoption of artifacts, we show that the existence of common roof shapes can be reasoned from the needs of those who live under the roof. Is there a shape that, while reducing the heat loss to the ambient, reduces the human effort (gathering firewood, etc.)? We consider two classes of roof shapes, Lambda and cone, and two roof sizes, small and large (respectively, two flow regimes, laminar and turbulent). In laminar natural convection, the common profile of the Lambda and the cone looks shallow, with height/base ratios comparable with 1/4. In turbulent flow, the Lambda and the cone look like an equilateral triangle. These findings reinforce the evolutionary record of human civilization toward economy of effort and longer life. They also present an opportunity for the future 'energy design' of buildings: the external shape has a significant effect on the heat loss from the building.

This research conducts an in-depth exploration of multi-objective optimization for a mini heat sink with fins using a genetic algorithm (GA). The objective is to reduce both thermal resistance and pump power consumption. The optimization problem consists of the use of increased design freedom: mixed-variable freedom factors, including fin angles, hole dimensions, and their placements. Computational fluid dynamics (CFD) simulations are used to evaluate the performance of the heat sink. A repair function is implemented to refine solutions by restricting continuous variables to specific values, streamlining the optimization process. The results reveal significant trade-offs between thermal resistance and pump power, emphasizing the importance of balancing these factors. The optimization process, completed in 20 h, cuts down the required time by 56 % compared to using a basic mixed variable algorithm. The optimized heat sink designs demonstrate considerable improvements, contributing to advancements in thermal engineering techniques. This study highlights the effectiveness of the proposed genetic algorithm in optimizing thermal management systems and may serve as a reference for future studies.

To clarify the place of time direction of change in nature (time arrow), the present article shows why Evolution and Irreversibility are two distinct phenomena. Their distinct laws of nature are the Constructal Law and the Second Law, respectively. The demonstration is based on the simplest setting imaginable: a solid body moving in a pool of water. The view is holistic: the system selected for analysis is the body and the pool, not the body alone, and the phenomenon is the evolution of the image (configuration) of the whole. New is also the answer to the question of what flows in this evolving flow configuration. Along the way, important terms are defined: phenomenon, law, irreversibility, nature, design, freedom, theory versus empiricism, information, knowledge, selection, purpose, engine, refrigeration, and wheel. More complex natural settings for the demonstration are in the second part of the article: engines, refrigeration, heating and cooling, the wheel, and a pushed boat sliding on water.

Porous materials are usually thought of as amorphous mixtures of two or more things, solids, fluids, and voids. I was drawn to the nature absent from the amorphous: the structure, flow, configuration, design, purpose, and evolution. This article is a pictorial review of the work. It begins with defining the terms: design, freedom, evolution, and prediction (theory). Vascular (tree shaped) architectures offer greater flow access than channels with only one length scale (diameter, slit, wall to wall spacing). The tendency to evolve with freedom toward flow configurations that provide greater access is everywhere in nature, bio, and non-bio. This universal phenomenon is summarized as the Constructal Law of evolution everywhere, which empowers us to predict evolution, miniaturization, high density of fluid flow and heat transfer, and scaling up (or down) of existing designs. Vascular designs are icons of the multiscale design called hierarchy. Vasculatures occur naturally because they flow more easily—they offer greater access—than one-scale designs. All movement in society is hierarchical, from city traffic to global air traffic, fuel consumption, and wealth. The future of evolutionary design everywhere points toward vascular, hierarchical flow architectures that will continue to morph with freedom and directionality.

A uniform stress distribution can improve the aeroelastic flight envelope of flying wing aircraft through the structure. We investigate the effect of spar and rib design on a flying wing aircraft's stress distribution and aeroelastic behavior. We apply the principles of Constructal law, ensuring that by avoiding the obstruction of stress pathways, we achieve the most efficient and stable design for wings. To investigate the stress distribution and stability of the flying wing aircraft, we employ the software Gmsh and VABS (Variational Asymptotic Beam Sectional Analysis), and code NATASHA (Nonlinear Aeroelastic Trim And Stability of HALE Aircraft). The findings suggest that specific wing cross-section designs promote even stress distribution, thereby enhancing aeroelastic stability. Configurations exhibiting higher flutter speeds demonstrate a more seamless and smoother stress flow within the wing's structure.

Nature abounds in examples of evolutionary designs (bio and non-bio) that evolve freely into configurations that provide easier and greater access for movement. The present article considers three seemingly unrelated phenomena that appear to obstruct flow: stick-slip friction, animal jump, and earthquake. The analysis is based on simple models of rhythmic energy store & release motion. In each case, the rhythm is the sole degree of freedom. The analyses show that stick-slip friction facilitates movement because the coefficient of static friction is greater than the coefficient of sliding friction. Next, all forms of animal locomotion under gravity consist of cycles of energy storage (jump to a height) and energy release (forward fall). The rhythm of the cycle is natural such that the forward advance of the animal is economical. Finally, the onset of the earthquake is modeled the same way, as shear stresses at the rock-on-rock interface, which are matched by bending stresses in the bent 'blades' of rock contained between fissures perpendicular to the interface. In sum, naturally evolved store & release rhythm facilitates the movement, contrary to the commonly held impression.

When a fluid accelerates as it sweeps a solid surface there are two consequences: the friction and the heat transfer (thermal contact) between fluid and solid increase simultaneously. This is known as the universal analogy between fluid friction and heat transfer. In thermal engineering these two effects are problematic because improved thermal contact is beneficial, and increased friction (i.e., pumping power) is detrimental to overall performance. In the present article we question whether the 'analogy' between these conflicting effects hampers the performance of animal movement. The theory focuses on warm-blooded swimmers and the effects (friction, heat transfer) that result from one change in the configuration of the body. Selected for analysis is a breaststroke swimmer. During gliding while reaching forward the 'one change' is from (a) legs spread apart, to (b) legs held tight together. The theory shows that the change from (a) to (b) has two consequences: greater swimming speed, and reduced body heat loss. In animal design both effects are beneficial, unlike in engineered flow systems. The analogy between fluid friction and heat transfer accelerated the evolution of animal design, and accounts for the 'divergent evolution' of fish and mammals.

Freedom, safety, and ease of movement are innate human urges attributed to conscience along with many other preferences such as attractiveness (beauty), economy, and life. This article addresses the physics basis of the innate urge to have freedom. It unveils the connection between animal freedom and the universal (constructal) tendency toward easier movement and greater access in all evolutionary systems throughout nature (animate & inanimate). The demonstration is made with a model of lack of freedom in animal movement: a man who walks his dog on a leash. When two animals are coerced to move at the same speed, their combined effort (the spent power) is greater than when they move freely, and independently. When the speed of the couple is dictated by the big body (man), the big one walks freely, and the small one must run. Participants in organized movement (life, society) are not equal. All participants move with less effort when they are not coerced to move the same way. The implications of this part of physics (nature) are numerous and help unify the animal realm with the design and evolution of human society. If you want diversity, give the population freedom, not prescriptions.

The new direction traced in this article is to vary freely and simultaneously the fin and flow channel aspect ratios in the search for the complete high-density heat transfer flow architecture. We show that when the combined solid and fluid volume is specified, and the fluid flow rate is known, it is possible to anticipate from theory the complete design (all the aspect ratios) of the flow configuration. The power to predict covers the overall heat transfer rate and the required pumping power. The configuration and performance owe their existence to the multiple degrees of freedom identified in the design, and exploited in the theory.

The universal phenomenon of evolution consists of change after change in flow configuration in a time direction that is perceptible to the observer. This reality clashes with the doctrine of precise optima, minima, and maxima, now rigidly in place because of calculus and computational simulations of all kinds of flowing and changing configurations. With two dissimilar examples, access on an area (a human settlement) and along a line (animal locomotion), it is shown that even a 1-percent imperfection in performance is accompanied by a sizable bandwidth of freedom to hit the 'target', that is, an easily accessible design with close to perfect performance. The evolutionary designs reveal the physics behind the phenomenon of diminishing returns in the vicinity of the mathematical optimum. In evolution what works is kept.

The universal phenomenon of evolution consists of change after change in flow configuration in a time direction that is perceptible to the observer. This reality clashes with the doctrine of precise optima, minima, and maxima, now rigidly in place because of calculus and computational simulations of all kinds of flowing and changing configurations. With two dissimilar examples, access on an area (a human settlement) and along a line (animal locomotion), it is shown that even a 1-percent imperfection in performance is accompanied by a sizable bandwidth of freedom to hit the ‘target’, that is, an easily accessible design with close to perfect performance. The evolutionary designs reveal the physics behind the phenomenon of diminishing returns in the vicinity of the mathematical optimum. In evolution what works is kept.

This article addresses two questions, why certain animals (frogs, breaststroke swimmers, hovering fliers, jellyfish) push rapidly against the surrounding fluid and then reach forward slowly, and whether this rhythm of propulsion is a manifestation of the universal phenomenon of design evolution in nature. Emphasis is on the distribution of time periods of locomotion in which, during the driving phase of cyclic movement (the motive stroke, phases 1 and 2, in alternating sequence with the dissipative stroke, phase 3), the work is generated (phase 1) and dissipated (phase 2). The relative lengths of the characteristic times t 1 and t 2 of the phases 1 and 2, are predicted. The relative duration of the proposed three phases of a cycle is the ‘rhythm’. The analysis is based on a model of how the effective cross-sections of the stroking body parts impact the surrounding medium, water, or air, and the total power required to account for the kinetic energy losses during phases 2 and 3, which are due to drag forces posed by the surrounding medium. The body configuration (limbs' cross-sections) determines the limbs' velocities that maximize mean power, and the times t 1 and t 2 within the motive stroke. Emphasis is placed on the freedom to change the evolving design. Freedom is represented in two ways: the number of degrees of freedom in changing the dimensions of the model and its deformation in time, and the effect that evolutionary changes have on the access that the body has to its available space. Freedom to change the locomotion design leads to greater power and speed.

This article addresses the main research areas identified in the call for contributions to this special issue. With examples from published articles and books, the present article shows that all the identified areas are already covered by the universal principle underlying all evolution: the constructal law (1996), i.e. the physics law of design evolution in nature (free morphing, flowing, moving systems). The universal principle of evolution belongs in thermodynamics because thermodynamics is a universal science and evolution is a universal phenomenon. The principle unites the natural sciences with the social sciences, and the living with the non-living. It unifies the world of science and its languages (energy, economy, evolution, sustainability, etc.), and brings together the natural and artificial flow architectures, the human made and the not human made. The principle establishes firmly in physics the reality that humans are part of nature. With the principle, physics extends its coverage over phenomena that were previously considered out of reach: social organization, economics and human perceptions. Such phenomena are physical, i.e. facts. The entire world depends on the science of useful things, and benefits greatly from a physics discipline with freedom, life, wealth, time, beauty and future. This article is part of the theme issue 'Thermodynamics 2.0: bridging the natural and social sciences (Part 1)'.

PURPOSE:Computational abnormalities (e.g., lesion models) for use in medical imaging simulation studies are frequently generated using data collected from clinical images. Although this approach allows for highly-customizable lesion detectability studies on clinical computed tomography (CT) data, the ground-truth lesion models produced with this method do not provide a sufficiently realistic lesion morphology for use with current anthropomorphic simulation studies. This work is intended to demonstrate that the new anatomically-informed lesion model presented here is not inferior to the previous lesion model under CT imaging, and can therefore provide a more biologically-informed model for use with simulated CT imaging studies. METHODS:The lesion model was simulated initially from a seed cell with 10 μm diameter placed in an anatomical location within segmented lung CT and was allowed to reproduce locally within the available solid angle in discrete time-intervals (corresponding to synchronous cell cycles) up to a size of ∼200 μm in diameter. Daughter cells of generation G were allowed also to reproduce on the next available time-step given sufficient space. At lesion sizes beyond 200 μm in diameter, the health of subregions of cells were tracked with a Markov chain technique, indicating which regions were likely to continue growing, which were likely stable, and which were likely to develop necrosis given their proximity to anatomical features and other lesion cells. For lesion sizes beyond 500 μm, the lesion was represented with three nested, triangulated surfaces (corresponding to proliferating, dormant, and necrotic regions), indicating how discrete volumes of the lesion were behaving at a particular time. Lesions were then assigned smoothly-varying material properties based on their cellular level health in each region, resulting in a multi-material lesion model. The lesions produced with this model were then voxelized and placed into lung CT images for comparison with both prior work and clinical data. This model was subject to an observer study in which cardiothoracic imaging radiologists assessed the realism of both clinical and synthetic lesions in CT images. RESULTS:The useable outputs of this work were voxel- or surface-based, validated, computational lesions, at a scale clearly visible on clinical CT (3-4 cm). Analysis of the observer study results indicated that the computationally-generated lesions were indistinguishable from clinical lesions (AUC = 0.49, 95% CI = [0.36, 0.61]) and non-inferior to an earlier image-based lesion model-indicating the advantage of the model for use in both hybrid CT images and in simulated CT imaging of the lungs. CONCLUSIONS:Results indicated the non-inferiority of this model as compared to previous methods, indicating the utility of the model for use in both hybrid CT images and in simulated CT imaging.

The aeroelastic flight envelops of flying wing aircraft can be extended with a better flow of stresses in the structure. In the present study, we investigate the effect of cross-section configuration on the stress distribution and aeroelastic behavior of a flying wing aircraft. We invoke the constructal law and the principle; the prevention of stress strangulation leads to a wing design associated with the most stable and lightest structure. We used three computer programs Gmsh, VABS (Variational Asymptotic Beam Sectional Analysis), and NATASHA (Nonlinear Aeroelastic Trim And Stability of HALE Aircraft) to study stress distribution and stability of the flying wing aircraft. The results indicate that different wing cross-section designs affect stress distribution as well as the aeroelastic stability of the aircraft. Furthermore, the design with less stress strangulation is associated with a higher flutter speed structure.