The constructal law and the evolution of design in nature

The constructal law accounts for the universal phenomenon of generation and evolution of design (configuration, shape, structure, pattern, rhythm). This phenomenon is observed across the board, in animate, inanimate and human systems. The constructal law states the time direction of the evolutionary design phenomenon. It defines the concept of design evolution in physics. Along with the first and second law, the constructal law elevates thermodynamics to a science of systems with configuration. In this article we review the more recent work of our group, with emphasis on the advances made with the constructal law in the natural sciences. Highlighted are the oneness of animate and inanimate designs, the origin of finite-size organs on animals and vehicles, the flow of stresses as the generator of design in solid structures (skeletons, vegetation), the universality and rigidity of hierarchy in all flow systems, and the global design of human flows. Noteworthy is the tapestry of distributed energy systems, which balances nodes of production with networks of distribution on the landscape, and serves as key to energy sustainability and empowerment. At the global level, the constructal law accounts for the geography and design of human movement, wealth and communications.     

The principle that generates dissimilar patterns inside aggregates of organisms

Pattern formation and self-organization are phenomena that occur across the board, in animate and inanimate systems. In this paper, we rely on the constructal law to explain the generation of patterns (shapes, structures) in aggregates of organisms-pedestrian crowds and stony corals. In pedestrian crowds a variety of patterns are often observed, from ‘chaotic’ appearances to spontaneous organization in lanes of uniform walking direction. Stony corals and other organisms also present intraspecific variability in shape. We show that flow systems develop in time patterns which provide easier access to the nutrients and space, within a set of constraints imposed by each situation. Flow systems have the freedom to morph their shape in search for architectures that allows them to have greater access to the space that they inhabit. We identify the mechanisms allowing pedestrians to evolve in space and time. We also show that stony corals may develop branched or spherical shapes, depending on which shape performs best in response to the environmental conditions. The constructal law allows systems with complex internal flows to be described and understood for a unified view.     

The emergence of design in pedestrian dynamics: Locomotion,self-organization,walking paths and constructal law

Gait is inherent to human life and hence its importance is often overlooked. But walking remains the most basic form of transportation and almost all journeys begin and end with a walk, regardless of the modes used in-between. Gaining a good understanding of pedestrian?s dynamics is thus a crucial step in meeting the mobility and accessibility needs of people by providing safe and quick walking flows.This paper presents a critical and integrative review of research on pedestrian?s dynamics and associated topics. The review focuses on comprehensive theories and models, with an emphasis on the advances made possible by the application of the constructal law. Constructal law points out that the emergence and evolution of design in pedestrian dynamics is analogous to that of animate flow systems. Most importantly, it also highlights that the basic features of pedestrian dynamics and supportive walking infrastructures can be optimally envisaged with the help of a few fundamental physics laws.     

Equipartition,optimal allocation,and the constructal approach to predicting organization in nature

This is a review of recent engineering developments in thermodynamic optimization, which shed light on a universal design principle that accounts for macroscopic organization in nature. It is shown that the optimal performance of a finite-size system with purpose is always characterized by the equipartition of driving forces or the optimal allocation of material subject to overall constraints. Examples are drawn from natural inanimate systems (river basins, turbulent flow) and animate systems (living trees). It is shown that this principle also governs the architecture of tree networks. Tree networks can be obtained in purely deterministic fashion by minimizing the flow resistance (or the time of travel) between one point and a finite area or a finite volume (an infinite number of points). The shape of each volume element can be optimized for minimal flow resistance. The network is ‘constructed’ by assembling the shape-optimized building blocks, and proceeding in time from the smallest volume element toward larger constructs. In constructal theory small size and shapeless flow (diffusion) come first, and larger sizes and geometrical form (channels, streams) come later.     

On the static and kinetic methods of conservative system stability,and Rayleigh's principle: A reexamination

The relation between the static and kinetic variational methods of the stability of equilibrium analysis of conservative systems and the corresponding static and kinetic Rayleigh's principles is reexamined. Specifically made explicit are the connections between (i) the virtual work principle (for the adjacent equilibrium configuration) and Rayleigh's principle of extremum critical loads and buckled modes, and (ii) Hamilton's principle (for the adjacent non-equilibrium configuration) and Rayleigh's principle of extremum frequencies and mode shapes, through simple familiar examples. These connections are found by considering, in addition to the familiar mode amplitude variations, variations of the load which in turn produce variations in the space (i) and time (ii) domain lengths, respectively; one is thus led to a variable endpoints variational problem (instead of the customary fixed endpoints one) which, by invoking the energetics of these adjacent configurations, is simplified and finally brought to the standard Rayleigh's principle form.     

Equilibrium state and non-equilibrium steady state in an isolated human system

The principle of increasing entropy （PIE） is commonly considered as a universal physical law tbr natural systems. It also means that a non-equilibrium steady state （NESS） must not appear in any isolated natural systems. Here we experimentally investigate an isolated human social system with a clustering effect. We report that the PIE cannot always hold, and that NESSs can come to appear. Our study highlights the role of human adaptability in the PIE, and makes it possible to study human social systems by using some laws originating from traditional physics.     

The Emergence of Temporal Structures in Dynamical Systems

Dynamical systems in classical, relativistic and quantum physics are ruled by laws with time reversibility. Complex dynamical systems with time-irreversibility are known from thermodynamics, biological evolution, growth of organisms, brain research, aging of people, and historical processes in social sciences. Complex systems are systems that compromise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous emergence of distinctive temporal, spatial or functional structures. But, emergence is no mystery. In a general meaning, the emergence of macroscopic features results from the nonlinear interactions of the elements in a complex system. Mathematically, the emergence of irreversible structures is modelled by phase transitions in non-equilibrium dynamics of complex systems. These methods have been modified even for chemical, biological, economic and societal applications (e.g., econophysics). Emergence of irreversible structures can also be simulated by computational systems. The question arises how the emergence of irreversible structures is compatible with the reversibility of fundamental physical laws. It is argued that, according to quantum cosmology, cosmic evolution leads from symmetry to complexity of irreversible structures by symmetry breaking and phase transitions. Thus, arrows of time and aging processes are not only subjective experiences or even contradictions to natural laws, but they can be explained by quantum cosmology and the nonlinear dynamics of complex systems. Human experiences and religious concepts of arrows of time are considered in a modern scientific framework. Platonic ideas of eternity are at least understandable with respect to mathematical invariance and symmetry of physical laws. Heraclit’s world of change and dynamics can be mapped onto our daily real-life experiences of arrows of time.     

The Contingency of Laws of Nature in Science and Theology

The belief that laws of nature are contingent played an important role in the emergence of the empirical method of modern physics. During the scientific revolution, this belief was based on the idea of voluntary creation. Taking up Peter Mittelstaedt’s work on laws of nature, this article explores several alternative answers which do not overtly make use of metaphysics: some laws are laws of mathematics; macroscopic laws can emerge from the interplay of numerous subsystems without any specific microscopic nomic structures (John Wheeler’s “law without law”); laws are the preconditions of scientific experience (Kant); laws are theoretical abstractions which only apply in very limited circumstances (Nancy Cartwright). Whereas Cartwright’s approach is in tension with modern scientific methodology, the first three strategies count as illuminating, though partial answers. It is important for the empirical method of modern physics that these three strategies, even when taken together, do not provide a complete explanation of the order of nature. Thus the question of why laws are valid is still relevant. In the concluding section, I argue that the traditional answer, based on voluntary creation, provides the right balance of contingency and coherence which is in harmony with modern scientific method.     

Quantization as Selection Problem

Quantum systems exhibit a smaller number of energetic states than classical systems (A. Einstein, 1907, Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme, Ann. Phys. 22, 180ff). We take up the selection criterion for this in two parts. (1) The selection problem between classical and nonclassical mechanical systems is formulated in terms of possible and impossible configurations (among others, this overcomes the difficulties occurring when discussing the behavior of quantum particles in terms of paths). (2) The (nonclassical) selection of the quantum states is formulated, using recurrence relations and the energy law. The reformulation of “quantization as eigenvalue problem” in terms of “quantization as selection problem” allows one to derive Schrödinger’s stationary equation from classical mechanics through a straightforward and unique procedure; the nonstationary and multibody equations are subsequently acquired within the same frame. In contrast to the (classical) eigenvalue problem, the (nonclassical) selection problem can be formulated and solved without any reference to additional a priori assumptions on the nature of the quantum system, such as the wave-corpuscle dualism or an underlying wave equation or the existence of Planck’s finite action parameter. The existence of such an additional parameter—as the only additional one—is inherent in the procedure. Within our axiomatic-deductive approach, we modify classical mechanics only where it itself indicates an inherent limitation.     

Universal long-time behavior of nuclear spin decays in a solid

Magnetic resonance studies of nuclear spins in solids are exceptionally well suited to probe the limits of statistical physics. We report experimental results indicating that isolated macroscopic systems of interacting nuclear spins possess the following fundamental property: spin decays that start from different initial configurations quickly evolve towards the same long-time behavior. This long-time behavior is characterized by the shortest ballistic microscopic time scale of the system and therefore falls outside of the validity range for conventional approximations of statistical physics. We find that the nuclear free-induction decay and different solid echoes in hyperpolarized solid xenon all exhibit sinusoidally modulated exponential long-time behavior characterized by identical time constants. This universality was previously predicted on the basis of analogy with resonances in classical chaotic systems.     

Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle

Causality describes the process and consequences from an action: a cause has an effect. Causality is preserved in classical physics as well as in special and general theories of relativity. Surprisingly, causality as a relationship between the cause and its effect is in neither of these theories considered a law or a principle. Its existence in physics has even been challenged by prominent opponents in part due to the time symmetric nature of the physical laws. With the use of the reduced action and the least action principle of Maupertuis along with a discrete dynamical time physics yielding an arrow of time, causality is defined as the partial spatial derivative of the reduced action and as such is position- and momentum-dependent and requests the presence of space. With this definition the system evolves from one step to the next without the need of time, while (discrete) time can be reconstructed.     

The Inertial Transformations and the Relativity Principle

Our recently proposed inertial transformations of the space and time variables based on absolute simultaneity imply the existence of a single isotropic inertial reference system (“privileged system”). We show, however, that aresynchronization of clocks in all inertial systems is possible leading to a different, arbitrarily chosen,isotropic “privileged” system. Such a resynchronization does not modify any one of the empirical consequences of the theory,which is thus compatible with a formulation of the relativity principle weaker than adopted in Einstein’s theory of special relativity.     

Gamma-ray bursts and related phenomena

Gamma-ray bursts (GRBs) have puzzled astronomers since their accidental discovery in the sixties. The BATSE detector on the COMPTON-GRO satellite has been detecting one burst per day for the last six years. Its findings have revolutionized our ideas about the nature of these objects. They have shown that GRBs are at cosmological distances. This idea was accepted with difficulties at first. However, the recent discovery of an X-ray afterglow by the Italian/Dutch satellite BeppoSAX led to a detection of high red-shift absorption lines in the optical afterglow of GRB970508 and to a confirmation of its cosmological origin. The simplest and practically inevitable interpretation of these observations is that GRBs result from the conversion of the kinetic energy of ultra-relativistic particles flux to radiation in an optically thin region. The “inner engine” that accelerates the particles is hidden from direct observations. Recent studies suggest the “internal-external” model: internal shocks that take place within the relativistic flow produce the GRB while the subsequent interaction of the flow with the external medium produce the afterglow. The “inner engine” that produces the flow is, however, hidden from direct observations. We review this model with a specific emphasis on its implications to underground physics.     

Area laws in quantum systems: mutual information and correlations

The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. In this Letter we show that this phenomenon not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of degrees of freedom, it may diverge as the inverse temperature in quantum systems. It is shown that an area law is generally implied by a finite correlation length when measured in terms of the mutual information.     

Monte Carlo simulation of polymers at interfaces

Polymers at interfaces pose challenging problems to statistical physics because their configurations often differ greatly from the bulk. Computer simulation of coarse-grained models then gives valuable insight and allows stringent tests of various theoretical predictions. Three examples are briefly treated: chain configurations of B-chains in the surface-enriched B-rich layer of an (AB) binary polymer mixture; “frustrated” lamellar ordering in ultra-thin block-copolymer films; and the collapse of polymer brushes in bad solvents.     

Simulations of Two-Dimensional Photon Scanning Tunneling Microscope by Boundary Integral Equation Method: p-polarization

Accurate simulations of a two-dimensional photon scanning tunneling microscope (2D-PSTM) for incident p-polarized waves (TM-mode) have been performed by the boundary integral equations called guided-mode extracted integral equations. The method used in this paper is a global method and the case of uncoated dielectric probe is treated. Complete and rigorous integral equations for a given configuration of 2D-PSTM have been solved numerically by the conventional boundary-element method with high accuracy. Using three universal laws, i.e., the optical theorem, the energy conservation law and the reciprocity relation for incident p-polarized waves, numerical results have been confirmed. The basic physical characteristics of interaction between probe-tip and near-field for incident p-polarized waves are compared in detail with those of incident s-polarized waves (TE-mode) which are previously reported.This paper was originally presented at the 5th International Conference on NEAR FIELD OPTICS and RELATED TECHNOLOGIES(NFO-5), which was held on December 6–10, 1998 at Coganoi Bay Hotel, Shirahama, Japan, in cooperation with the Japan Society of Applied Physics and Mombusho Grant-in Aid for Scientific Research on Priority Areas “Nearfield Nano-optics” Project, sponsored by Japan Society for the Promotion of Science.     

Transport mechanisms controlling soot production inside a non-buoyant laminar diffusion flame

This study integrates new and existing numerical modeling and experimental observations to provide a consistent explanation to observations pertaining flame length and soot volume fractions for laminar diffusion flames. Integration has been attempted by means of scaling analysis. Emphasis has been given to boundary layer flames. For the experiments, ethylene is injected through a flat porous burner into an oxidizer flowing parallel to the burner surface. The oxidizer is a mixture of oxygen and nitrogen, flowing at various velocities. All experiments were conducted in microgravity to minimize the role of buoyancy in distorting the aerodynamics of the flames. A previous numerical study emphasizing fuel transport was extended to include the oxidizer flow. Fictitious tracer particles were used to establish the conditions in which fuel and oxidizer interact. This allowed establishing regions of soot formation and oxidation as well as relevant characteristic length and time scales. Adequate scaling parameters then allow to establish explanations that are consistent for different burner configurations as well as “open-tip” and “closed-tip” flames.     

Computer simulation of hexapole aberration correctors

The use of hexapole electron-optical elements to correct the spherical aberrations of the objective lenses of a low-voltage scanning electron microscope is investigated. Compared with the conventional quadrupole-octupole correctors, hexapole systems are simpler in design, easier to tune, and less sensitive to manufacturing imperfections and power supply instabilities. Two configurations of hexapole correctors, RHRHR and HRRH (where R and H stand for round lens and hexapole component, respectively), are considered. Both configurations considerably suppress the spherical aberration of the electron microscope objective lens but cannot correct chromatic aberrations. The second configuration possesses important advantages over the first one: it is mechanically and electrically simpler and also is easier to tune. In addition, as follows from our investigation, the hexapole electrode voltages in the second configuration are lower, the correction accuracy is higher, and the sensitivity to mechanical defects is lower. However, the chromatic aberration in the second configuration is somewhat larger.     

Independent variables in foam clusters

We find, by counting the degrees of freedom of two-dimensional bubble clusters (finite or periodic) of given topology and bubble areas, that the Plateau laws determine a unique configuration of a finite free cluster, but allow an infinite number of configurations of a periodic cluster. Each of these configurations is associated with a particular strain (stress) state of the cluster; there is in general one unstrained configuration, which corresponds to the minimum of the (surface) energy. Configurations of given topology that satisfy Plateau's laws may only exist in certain ranges of bubble area ratios and/or strains. Received 31 May 2001 and Received in final form 12 September 2001     

Constructal tree network for fluid flow between a finite-size volume and one source or sink

The ‘constructal theory’ of formation of structure in nature is extended to fluid-flow systems. The fluid flow path between one point and a finite-size volume (an infinite number of points) is optimized by minimizing the overall flow resistance when the flow rate and the duct volume are fixed. The solution is constructed as a sequence of optimization and organization steps. The sequence has a definite time direction: it begins with the smallest building block (elemental system, with flow by volumetric diffusion), and proceeds toward larger building blocks (assemblies, with flow collected in ducts). Optimized at each level are the shape of the assembly, the number of constituents (ie, smaller assemblies), and the distribution of the duct volume. It is shown that the ducts of the optimized assemblies form a tree-like structure, in which every architectural detail is deterministic. It is also shown that the structure cannot be determined when the time direction is reversed, from large elements toward smaller elements. The general importance of the constructal law (access-optimization principle) in physics, biology and economics is discussed.