e-book Distribution Theory: With Applications in Engineering and Physics

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The power is destroyed in the process of moving mass horizontally on land, on water and in the air Fig.

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Everything that flows and moves does so because it is being pushed. The push comes from the power generated because of design. The dissipation resides in the environment that is displaced penetrated by the moving entity. People like to say that nature is complicated. Not according to thermodynamics! Nature is the simplest imaginable, because it consists of only two systems, your system the portion selected by you for contemplation and the rest the environment.

Distribution Theory: With Applications in Engineering and Physics - Semantic Scholar

Other thinkers may contemplate other systems that generate power and move waterfalls, animals, etc. For all the thinkers together, the same world as yours is an endless collection of intertwined engine and brake flow systems. The physical effect of evolving design is more movement and greater access for all movers.


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This is the complete design of all animate or inanimate flow systems, from water flowing in river basins, to animal locomotion and urban traffic, and atmospheric and oceanic circulation. Organization in nature is in the eye of the observer. Where many see randomness, chance and nondeterminism, a few see organization and principle. Nowhere is this more evident than in the discussion of turbulence. For example, measurements of flow friction inside pipes and on solid surfaces have been lining up on curves that science and technology have used with confidence for more than a century.

This empirical body serves as skeleton for the computational models and software packages used today to simulate turbulent flows at all scales, all the way to atmospheric circulation and the weather. The natural occurrence of organization is an integral part of the phenomenon of turbulence, and has been calling for a physics principle. Progress was made in this direction based on the physics law of design evolution in nature. The constructal law was used to predict and unify the turbulence phenomena, for example, the transition to turbulence, the size of the smallest eddy, the large scale structure of jets and plumes, and the correlations for friction and heat transfer for reviews see refs.

The smoke from a row of closely spaced factory smoke stacks or a brush fire rises as a curtain, i. It is only above a certain predictable height that the curtain of smoke organizes itself into a round plume that, from a distance, looks like all the other plumes. The reason is the natural tendency of flow systems to morph into configurations that facilitate the access to what flows.

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In jets and plumes, it is momentum that flows from the mover the turbulent column to the non-mover the still surroundings. Momentum flows perpendicularly to the flow of fluid. When the lateral flow of momentum has greater access to the stationary environment, the fluid of the column mixes faster with the surrounding fluid, and its longitudinal speed decreases faster.

The tendency of the flow is to morph its cross section such that the mixing becomes more effective, and the longitudinal speed decreases faster. The jet cross section evolves from flat to round, not from round to flat. At bottom, this phenomenon adds to the growing evidence that the tendency toward evolutionary organization in nature is governed by a physics principle. In particular, the tendency toward round cross sections in simple one stream configurations unites the animate with the inanimate flow systems. In river channels, this natural tendency is made visible by the proportionality between depth and width in rivers of all sizes.

Growth is not evolution. The histories of collecting flows also exhibit S curves: examples are mining and the extraction of minerals, such as the Hubbert peak of oil extraction. Growth, or S-curve phenomena. The growth of brewer's yeast, the spreading of radios and TVs, and the growth of the readership of scientific publications. Rapid solidification is another common phenomenon, where the S-curve history is about the growth of solid in a subcooled liquid or gas. This phenomenon is classical textbook material in materials science, and has generated a voluminous body of research dedicated to explaining the S-shaped history.

We showed how to predict the S-curve of solidification purely theoretically. In view of the constructal law, we asked two questions:. First, what flow is spreading during solidification? It is not the solid, because the solid and its subcooled surroundings are motionless. The spreading flow is the flow of heat, which emanates from the solid surface and flows in all directions into the surroundings.

Second, what is the configuration of the heat flow system? We did not postulate the configuration: in fact, in the physics of evolution the configuration is the unknown. This runs against current doctrine, where the student is given the governing equations and boundary conditions, and is asked to discover the flow field. In the physics of evolution, the boundaries the drawings are to be discovered.

We showed that although the solidification is triggered as small spheres around nucleation sites, at longer times the greater solidification rate is associated with needles and dendrites, in accord with common observations. Solidification begins at point-size nucleation sites around which the solid grows as tiny spheres.

The spherical growth slows down and is replaced by needle-shaped growth, which is faster. The transition from spherical to needle-shaped growth is in accord with the constructal law, and defines the early part of the S. Advances in geophysics continue. Recent examples made based on the constructal law include dendritic flow structures, 52 permeable barriers for ground water, 53 beachface slope, 54 climate, 55 climate change, 56 and subsurface flow networks.

Theoretical advances on animal design evolution based on the constructal law appear regularly in the literature. This information is empirical. The purely theoretical prediction 63,64 is based on the view that animals are not the only moving bodies for which the larger size translates into a longer life span.


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  • Inanimate systems such as rivers, atmospheric currents, rolling stones and turbulent eddies persist longer in time when they are larger. They also travel farther during their lifetimes, and this unveils a second aspect of animal design that is not nearly as well known as the body size effect on life span: the bigger travel farther during their lives than the smaller.

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    This definition of life makes the life span vs. The same size effect on life span and distance traveled holds for the other flows that move mass on earth: atmospheric and oceanic jets and plumes, river basins, animals and human operated vehicles. In Bejan , 63 three theoretical steps were made. First, a theoretical framework unified the movement of inanimate mass flow fluid jets, rivers with the movement of animate mass flows human transportation, animals. This unifying theory showed that inanimate and animate mass flows exhibit the same size effect on life span and territory covered by movement: larger bodies move to greater distances during longer life times.

    Stanford and J. Browse book content About the book Search in this book. Browse content Table of contents.

    Description Physics for Students of Science and Engineering is a calculus-based textbook of introductory physics. Details ISBN All rights reserved. Authors A. Stanford Georgia Institute of Technology. Antonela Toma is professor at university "Politehnica" Bucharest. She published a monograph on Mathematical Methods in Elasticity and Viscoelasticity in Romanian , Convert currency.

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