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Fractals in physics : proceedings of the Sixth Trieste International Symposium on Fractals in Physics, ICTP, Trieste, Italy, July 9-12, 1985 /

The concepts of self-similarity and scale invariance have arisen independently in several areas. One is the study of the critical properties of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. These two areas have now come together, and t...

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Bibliographic Details
Corporate Authors: International Symposium on Fractals in Physics Trieste, Italy); Elsevier Science & Technology.; International Centre for Theoretical Physics.
Group Author: Pietronero, L. (Luciano) (Editor); Tosatti, E. (Erio) (Editor)
Published: North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science,
Publisher Address: Amsterdam ; New York : New York, N.Y., U.S.A. :
Publication Dates: 1986.
Literature type: eBook
Language: English
Subjects:
Fractals > Congresses.
Mathematical physics > Congresses.
Irreversible processes > Congresses.
Fractales > Congre s.
Physique mathe matique > Congre s.
Processus irre versibles > Congre s.
SCIENCE > Energy.
SCIENCE > General. > General.
Fractals.
Irreversible processes.
Mathematical physics.
Niet-lineaire dynamica.
Onomkeerbaarheid.
Fisica matematica.
Physics > Mathematics > Fractal sets
Electronic books.
Conference papers and proceedings.
Online Access: http://www.sciencedirect.com/science/book/9780444869951
Summary: The concepts of self-similarity and scale invariance have arisen independently in several areas. One is the study of the critical properties of phase transitions; another is fractal geometry, which involves the concept of (non-integer) fractal dimension. These two areas have now come together, and their methods have extended to various fields of physics. The purpose of this Symposium was to provide an overview of the physical phenomena that manifest scale invariance and fractal properties with the aim of bringing out the common mathematical features. The emphasis was on theoretical and experimental work related to well defined physical phenomena.
Carrier Form: 1 online resource (xii, 476 pages) : illustrations
Bibliography: Includes bibliographical references and index.
ISBN: 9780444598417
0444598413
Index Number: QC20
CLC: O411.1-532
Contents: Front Cover; Fractals in Physics; Copyright Page; PREFACE; Table of Contents; Part I: GENERAL PROPERTIESOF FRACTALS; CHAPTER 1. SELF-AFFINE FRACTAL SETS, I: THE BASIC FRACTAL DIMENSIONS; 1. INTRODUCTION; 2. THE NOTIONS OF AFFINITY, DIAGONALAFFINITY, AND SELF-AFFINITY; 3. THE MULTIPLE FRACTAL DIMENSIONS OF A SELF AFFINE SET; 4. THE GAP DIMENSION; 5. SELF-AFFINE PLANAR FRACTAL CURVESDEFINED AS RECORDS OF FUNCTIONS; 6. SELF-AFFINE RECURSIVE PLANAR FRACTALSWHOSE PROJECTIONS FILL THE AXES; 7. SELF-AFFINE PLANAR RECURSIVE FRACTALS AT LEAST ONE OF WHOSE PROJECTIONS IS A SIMPLE CANTOR DUST.
8. self-affine surfaces9. comment on ""physical"" extrapolationversus ""mathematical"" interpolation; chapter 2. self-affine fractal sets, ii: length and surface dimensions; 1. introduction; 2. measuring the length of self-affine fractal curves obtained as records of functions; 3. measuring the length of other self-affine curves, including peano motiontrails; 4. the schwarz area paradox; 5. measuring the area of self-affine fractal surfaces obtained as recordsof functions; chapter 3. self-affine fractal sets, iii:hausdorff dimension anomalies and their implications; 1. introduction.
2. a theorem yielding dhb and corollary3. expression for the vertical anomaly a""=dbl-dhb; 4. horizontal cuts' dimension; 5. a global counterpart, d*, for dhb, and the horizontal anomaly a' =d*-dbg; 6. self-affine continuous records notcovered by theorem a; 7. other random self-affine sets not covered by theorem a; 8. discussion; chapter 4. random fractals, flow fractals and the renormalisation group; 1. introduction; 2. construction; 3. expectations; 4. subsets of known modes; conclusions and outlook; acknowledgement; references; chapter 5. on finitely ramified fractals and their extensions.
ACKNOWLEDGEMENTREFERENCES; Part II: ANALYSIS OFFRACTAL PROPERTIES OF MATERIALS; CHAPTER 6. STRUCTURE OF RANDOM SILICATES: POLYMERS, COLLOIDS, AND POROUS SOLIDS*; 1. INTRODUCTION; 2. SCATTERING TECHNIQUES; 3. SILICATE POLYMERS; 4. SUPERMOLECULAR STRUCTURES; 5. POROUS SOLIDS; 6. CONCLUSION; REFERENCES; CHAPTER 7. INTERACTION OF FRACTALS WITH FRACTALS: ADSORPTION OF POLYSTYRENE ON POROUS A1203 .; 1. INTRODUCTION, STATEMENT OF THE PROBLEM; 2. THE FUNCTION n(r) IN TERMS OF D, Dcsol, Dcads; 3. THE PORE-SIZE DISTRIBUTION OF A1203; 4. DISCUSSION, THE ENTROPY BARRIER; 5. CONCLUSIONS; ACKNOWLEDGMENTS.

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