FRACTALS IN FLUID MECHANICS

Fractals ◽  
1994 ◽  
Vol 02 (02) ◽  
pp. 253-263 ◽  
Author(s):  
K. R. SREENIVASAN
Keyword(s):  
Fluid Dynamics ◽  
Fluid Mechanics ◽  
Natural Science ◽  
Fractal Geometry ◽  
Fractal Structure ◽  
Fluid Flows ◽  
Chaotic Mixing ◽  
Physical Problems ◽  
Basic Concepts

The basic concepts of fractal geometry are relatively simple. Although they are not entirely new, the recognition that these simple notions form a unified language for a variety of disciplines in natural science is due to Mandelbrot.1 Our objective is to assess briefly the role of fractals and multifractal measures in fluid flows broadly, including turbulence and combustion. As applications have yet to mature, the report captures a snap-shot of the changing scene. We focus on activities that are common to both fluid dynamics and fractals and ignore some isolated aspects; we also omit comments on possible fractal structure obtained in chaotic mixing. Finally, we emphasize the question of how fractals enter physical problems, not the classical results. Much of the material to be covered below can be found in refererences cited in the bibliography2–7. Other references cited are not meant to be exhaustive.

Fundamentals of fluid dynamics with an introduction to the importance of interfaces

2017 ◽  
Author(s):  
H. A. Stone
Keyword(s):  
Fluid Dynamics ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Scaling Laws ◽  
Fluid Flows ◽  
Governing Equations ◽  
Soft Interfaces ◽  
Physical Intuition ◽  
Basic Fluid ◽  
Wide Range

The topics discussed are all related to basic fluid mechanics. In these introductory notes I highlight some of the main features of fluid flows and their mathematical characterization. There is much physical intuition encapsulated in the differential equations, and one of our goals is to gain more experience (i) understanding the governing equations and various related principles of kinematics, (ii) developing intuition with approximating the equations, (iii) applying the principles to a wide range of problems, which includes (iv) being able to rationalize scaling laws and quantitative trends, often without having a detailed solution in hand. Where possible we provide examples of the ideas with ‘soft interfaces’ in mind.

scholarly journals Recent Numerical Advances in Fluid Mechanics

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 73
Author(s):  
Omer San
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Fluid Mechanics ◽  
Fluid Flows ◽  
Advanced Computing

In recent decades, the field of computational fluid dynamics has made significant advances in enabling advanced computing architectures to understand many phenomena in biological, geophysical, and engineering fluid flows [...]

NATURAL SCIENTISTS AND RUSSIAN SCIENTIFIC FILMMAKING IN THE PRE-REVOLUTIONARY PERIOD (SCIENCE DIVISION OF THE A.A. KHANZHONKOV COMPANY)

2020 ◽  
Vol 42 (3) ◽  
pp. 355-368
Author(s):  
YEVGENIY ALEKSANDROV
Keyword(s):  
Information Transfer ◽  
Delayed Reaction ◽  
Russian Scientific ◽  
Physical Problems ◽  
Education Community ◽  
Future System ◽  
The Future ◽  
The Spectator ◽  
Revolutionary Period

The aim of the article is to recall the fi steps of comprehension by the scientific community of possibilities of a newly born means of the reality reflection. The means was initially oriented for obtaining reliable information and supposing a delayed reaction of the spectator in the process of communication. Recollection and understanding become more important under the distance education condition. Pre-revolutionary Russia lived anticipating changes, and the filmmaking was considered by the society as one of those progressive phenomena evidencing the coming of a new age. The scientists’ activity during the development of scientific fi in pre-revolutionary Russia was long hushed up and wasn’t considered as forming a basis for the future system of educational audio-visual communication. In this process there participated striking, creative personalities, mostly belonged to the community of Imperial Moscow University, which activity was during the age of changes. The significant contribution of pleiad of eminent scientists’ activity to the new direction formation was a reason to unify in one paper both their whole professional life data and information about their time-limited period of scientific fi In the future a more profound study of their achievements are considered to be promising. In the introduction the anterior period of the Russian fi appearance, where the scientific and education community of Russia was exploring the possibilities of a new means of information transfer for education purposes, is considered. Two main units are dedicated to the role of scientists in the development of scientific filmmaking for research and popularization of biomedical and physical problems.

The Study of Consciousness by Natural Science Methods: On a Possible Role of Wave-Like Integration Processes

Vestnik RFFI ◽  
2016 ◽  
pp. 61-71
Author(s):  
Boris M. Velichkovskiy ◽  
◽  
Mikhail V. Kovalchuk ◽  
Vadim L. Ushakov ◽  
Maksim G. Sharaev ◽  
...  
Keyword(s):  
Natural Science ◽  
Science Methods

Role of Reynolds and Archimedes numbers in particle-fluid flows

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Haim Kalman
Keyword(s):  
Flow Regime ◽  
Power Function ◽  
Fluid Flows ◽  
Limited Range ◽  
Operating Conditions ◽  
Pneumatic Conveying ◽  
Particulate Materials ◽  
Simple Power ◽  
Simple Power Function

AbstractAny scientific behavior is best represented by nondimensional numbers. However, in many cases, for pneumatic conveying systems, dimensional equations are developed and used. In some cases, many of the nondimensional equations include Reynolds (Re) and Froude (Fr) numbers; they are usually defined for a limited range of materials and operating conditions. This study demonstrates that most of the relevant flow types, whether in horizontal or vertical pipes, can be better described by Re and Archimedes (Ar) numbers. Ar can also be used in hydraulic conveying systems. This paper presents many threshold velocities that are accurately defined by Re as a simple power function of Ar. Many particulate materials are considered by Ar, thereby linking them to a common behavior. Using various threshold velocities, a flow regime chart for horizontal conveying is presented in this paper.

scholarly journals GEORGE KEITH BATCHELOR 8 March 1920–30 March 2000 Founding Editor, Journal of Fluid Mechanics, 1956

2000 ◽  
Vol 421 ◽  
pp. 1-14 ◽  
Author(s):  
HERBERT E. HUPPERT
Keyword(s):  
Fluid Mechanics ◽  
International Organizations ◽  
Solid Mechanics ◽  
Applied Mathematics ◽  
Fluid Flows ◽  
Theoretical Physics ◽  
Founding Editor ◽  
Number Of Factors ◽  
Quantitative Understanding ◽  
The Subject

George Batchelor was one of the giants of fluid mechanics in the second half of the twentieth century. He had a passion for physical and quantitative understanding of fluid flows and a single-minded determination that fluid mechanics should be pursued as a subject in its own right. He once wrote that he ‘spent a lifetime happily within its boundaries’. Six feet tall, thin and youthful in appearance, George's unchanging attire and demeanour contrasted with his ever-evolving scientific insights and contributions. His strongly held and carefully articulated opinions, coupled with his forthright objectivity, shone through everything he undertook.George's pervasive influence sprang from a number of factors. First, he conducted imaginative, ground-breaking research, which was always based on clear physical thinking. Second, he founded a school of fluid mechanics, inspired by his mentor G. I. Taylor, that became part of the world renowned Department of Applied Mathematics and Theoretical Physics (DAMTP) of which he was the Head from its inception in 1959 until he retired from his Professorship in 1983. Third, he established this Journal in 1956 and actively oversaw all its activities for more than forty years, until he relinquished his editorship at the end of 1998. Fourth, he wrote the monumental textbook An Introduction to Fluid Dynamics, which first appeared in 1967, has been translated into four languages and has been relaunched this year, the year of his death. This book, which describes the fundamentals of the subject and discusses many applications, has been closely studied and frequently cited by generations of students and research workers. It has already sold over 45 000 copies. And fifth, but not finally, he helped initiate a number of international organizations (often European), such as the European Mechanics Committee (now Society) and the biennial Polish Fluid Mechanics Meetings, and contributed extensively to the running of IUTAM, the International Union of Theoretical and Applied Mechanics. The aim of all of these associations is to foster fluid (and to some extent solid) mechanics and to encourage the development of the subject.

Cell cycle controls and the role of nerves and the regenerate epithelium in urodele forelimb regeneration: possible modifications of basic concepts

1987 ◽  
Vol 65 (8) ◽  
pp. 739-749 ◽  
Author(s):  
Roy A. Tassava ◽  
David J. Goldhamer ◽  
Bruce L. Tomlinson
Keyword(s):  
Cell Cycle ◽  
Monoclonal Antibody ◽  
Limb Regeneration ◽  
Blastema Formation ◽  
Basic Concepts ◽  
Regenerate Epithelium ◽  
Early Wound ◽  
Skin Epidermis ◽  
Wound Epithelium

Data from pulse and continuous labeling with [3H]thymidine and from studies with monoclonal antibody WE3 have led to the modification of existing models and established concepts pertinent to understanding limb regeneration. Not all cells of the adult newt blastema are randomly distributed and actively progressing through the cell cycle. Instead, many cells are in a position that we have designated transient quiescence (TQ) and are not actively cycling. We postulate that cells regularly leave the TQ population and enter the actively cycling population and vice versa. The size of the TQ population may be at least partly determined by the quantity of limb innervation. Larval Ambystoma may have only a small or nonexisting TQ, thus accounting for their rapid rate of regeneration. Examination of reactivity of monoclonal antibody WE3 suggests that the early wound epithelium, which is derived from skin epidermis, is later replaced by cells from skin glands concomitant with blastema formation. WE3 provides a useful tool to further investigate the regenerate epithelium.

scholarly journals The Invariant Set Postulate: a new geometric framework for the foundations of quantum theory and the role played by gravity

2009 ◽  
Vol 465 (2110) ◽  
pp. 3165-3185 ◽  
Author(s):  
T. N. Palmer
Keyword(s):  
Quantum Theory ◽  
Science Fiction ◽  
State Space ◽  
Fractal Geometry ◽  
Quantum Physics ◽  
Nonlinear Dynamical Systems ◽  
Physical Reality ◽  
Invariant Set ◽  
Geometric Framework

A new law of physics is proposed, defined on the cosmological scale but with significant implications for the microscale. Motivated by nonlinear dynamical systems theory and black-hole thermodynamics, the Invariant Set Postulate proposes that cosmological states of physical reality belong to a non-computable fractal state-space geometry I , invariant under the action of some subordinate deterministic causal dynamics D I . An exploratory analysis is made of a possible causal realistic framework for quantum physics based on key properties of I . For example, sparseness is used to relate generic counterfactual states to points p ∉ I of unreality, thus providing a geometric basis for the essential contextuality of quantum physics and the role of the abstract Hilbert Space in quantum theory. Also, self-similarity, described in a symbolic setting, provides a possible realistic perspective on the essential role of complex numbers and quaternions in quantum theory. A new interpretation is given to the standard ‘mysteries’ of quantum theory: superposition, measurement, non-locality, emergence of classicality and so on. It is proposed that heterogeneities in the fractal geometry of I are manifestations of the phenomenon of gravity. Since quantum theory is inherently blind to the existence of such state-space geometries, the analysis here suggests that attempts to formulate unified theories of physics within a conventional quantum-theoretic framework are misguided, and that a successful quantum theory of gravity should unify the causal non-Euclidean geometry of space–time with the atemporal fractal geometry of state space. The task is not to make sense of the quantum axioms by heaping more structure, more definitions, more science fiction imagery on top of them, but to throw them away wholesale and start afresh. We should be relentless in asking ourselves: From what deep physical principles might we derive this exquisite structure? These principles should be crisp, they should be compelling. They should stir the soul. Chris Fuchs ( Gilder 2008 , p. 335)

Logikôs Argumentation in Aristotle’s Natural Science

Apeiron ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Adam Woodcox
Keyword(s):  
Natural Science ◽  
Textual Analysis ◽  
Natural Philosophy ◽  
Close Textual Analysis ◽  
Standard Domain

AbstractThis paper offers a novel interpretation of the nature and role of logical (logikôs) argumentation in Aristotle’s natural philosophy. In contrast to the standard domain interpretation, which makes logikôs argumentation the contrary of phusikôs, relying on principles drawn from outside the domain of natural science, I propose that the essential or defining feature of logikôs argumentation is the use of principles that are general relative to the question under investigation. My interpretation is developed and illustrated with a close textual analysis of Aristotle’s explanation of mule sterility in Generation of Animals II 8.

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