Fractals in physics : Proceedings of the 6. Trieste International Symposium on Fractals in Physics, sponsored by ICTP, and held in Trieste, 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 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. Content: Front Matter , Page iii Copyright , Page iv PREFACE , Page v , L. Pietronero SELF-AFFINE FRACTAL SETS, I: THE BASIC FRACTAL DIMENSIONS , Pages 3-15 , Benoit B. MANDELBROT SELF-AFFINE FRACTAL SETS, II: LENGTH AND SURFACE DIMENSIONS , Pages 17-20 , Benoit B. MANDELBROT SELF-AFFINE FRACTAL SETS, III: HAUSDORFF DIMENSION ANOMALIES AND THEIR IMPLICATIONS , Pages 21-28 , Benoit B. MANDELBROT RANDOM FRACTALS, FLOW FRACTALS AND THE RENORMALISATION GROUP , Pages 29-32 , John MELROSE ON FINITELY RAMIFIED FRACTALS AND THEIR EXTENSIONS , Pages 33-36 , R. HILFER, A. BLUMEN STRUCTURE OF RANDOM SILICATES: POLYMERS, COLLOIDS, AND POROUS SOLIDS , Pages 39-45 , D.W. SCHAEFER, K.D. KEEFER INTERACTION OF FRACTALS WITH FRACTALS: ADSORPTION OF POLYSTYRENE ON POROUS Al 2 O 3 , Pages 47-53 , Peter PFEIFER SCATTERING BY FRACTALS , Pages 55-60 , Eric JAKEMAN OPTICAL FOURIER TRANSFORMS OF FRACTALS , Pages 61-64 , Catherine ALLAIN, Michel CLOITRE ON THE MEASURE OF FRACTAL DIMENSIONALITIES THROUGH PHYSICAL PROPERTIES , Pages 65-69 , Constantino TSALLIS RANDOM WALKS WITH MEMORY , Pages 73-81 , L. PELITI SURVIVAL PROBABILITY AND ENHANCEMENT FACTOR IN POLYMER STATISTICS , Pages 83-86 , L. PIETRONERO, L. PELITI THE LAPLACIAN RANDOM WALK , Pages 87-92 , J.W. LYKLEMA, Carl EVERTSZ KINETICALLY GROWING SELF-AVOIDING WALKS , Pages 93-96 , J.W. LYKLEMA THE COIL-GLOBULE TRANSITION IN 2-DIMENSIONS , Pages 97-99 , Naeem JAN, Antonio CONIGLIO, Imtiaz MAJID, H. Eugene STANLEY SELF-SIMILARITY OF MUTUAL AND SELF-INTERSECTIONS OF RANDOM FRACTALS , Pages 101-106 , A.L. STELLA, R. DEKEYSER, A. MARITAN STATISTICAL MECHANICS OF SELF-AVOIDING RANDOM SURFACES , Pages 107-110 , Amos MARITAN, Attilio L. STELLA BETHE - LIKE APPROXIMATION FOR SELF-AVOIDING RANDOM WALKS AND SURFACES (AND FRUSTRATIONS) , Pages 111-114 , Andrea CAPPELLI, Roberto LIVI, Amos MARITAN, Stefano RUFFO ON THE SELF-AVOIDING WALKS ON DISORDERED LATTICES , Pages 115-118 , S. MILOŠEVIĆ, A. CHERNOUTSAN PROTEINS IN THE EXPERIMENT , Pages 119-122 , Y.S. YANG FRACTAL DIMENSION AND THE SYNTHESIS OF BRANCHED POLYMERS , Pages 125-128 , Z. ALEXANDROWICZ FRACTAL DIMENSIONALITIES OF BACKBONES AND CLUSTERS IN A KINETIC GELATION MODEL , Pages 129-131 , Ashvin CHHABRA, H.J. HERRMANN, D.P. LANDAU A LATTICE MAGNETIC MODEL FOR BRANCHED POLYMERS AND THE SOL-GEL TRANSITION , Pages 133-135 , Agustín E. GONZALEZ PERCOLATION IN A CONCENTRATION GRADIENT , Pages 137-140 , Jean-François GOUYET, Michel ROSSO, Bernard SAPOVAL SURFACE TENSION IN POTTS MODELS AND PERCOLATION , Pages 141-144 , C.K. HARRIS PERCOLATION ON THE DAP , Pages 145-148 , R. DEWAR, C.K. HARRIS PROPERTIES OF LAPLACIAN FRACTALS FOR DIELECTRIC BREAKDOWN IN 2 AND 3 DIMENSIONS , Pages 151-157 , H.J. WIESMANN, L. PIETRONERO SCALING PROPERTIES OF GROWING ZONE AND CAPACITY OF LAPLACIAN FRACTALS , Pages 159-163 , L. PIETRONERO, C. EVERTSZ, H.J. WIESMANN AN INFINITE HIERARCHY OF EXPONENTS TO DESCRIBE GROWTH PHENOMENA , Pages 165-168 , Antonio CONIGLIO 2-D DIELECTRIC BREAKDOWN BETWEEN PARALLEL LINES , Pages 169-171 , Michael MURAT DIELECTRIC BREAKDOWN IN THREE DIMENSIONS , Pages 173-176 , S. SATPATHY THE FRACTAL NATURE OF FRACTURE , Pages 177-180 , E. LOUIS, F. GUINEA, F. FLORES PATTERN FORMATION OF DENDRITIC FRACTALS IN FRACTURE AND ELECTRIC BREAKDOWN , Pages 181-184 , Hideki TAKAYASU COLLAPSE OF LOADED FRACTAL TREES , Pages 185-188 , Sara A. SOLLA FRACTALS AND THE FRACTURE OF CRACKED METALS , Pages 189-192 , C.W. LUNG WHEN ARE VISCOUS FINGERS FRACTAL? , Pages 193-202 , Johann NITTMANN, Gérard DACCORD, H. Eugene STANLEY SOME RECENT ADVANCES IN THE SIMULATION OF DIFFUSION LIMITED AGGREGATION AND RELATED PROCESSES , Pages 205-212 , Paul MEAKIN INTERNAL ANISOTROPY OF DIFFUSION-LIMITED AGGREGATES , Pages 213-216 , Paul MEAKIN, Tamás VICSEK GROWING INTERFACE IN DIFFUSION-LIMITED AGGREGATION AND IN THE EDEN PROCESS , Pages 217-222 , M. PLISCHKE, Z. RÁCZ STICKING PROBABILITY SCALING IN DIFFUSION-LIMITED AGGREGATION , Pages 223-229 , Leonid A. TURKEVICH, Harvey SCHER CONE ANGLE PICTURE AND ANISOTROPY IN DLA CLUSTER GROWTH , Pages 231-236 , Giuseppe ROSSI, Bernard R. THOMPSON, Robin C. BALL, Robert M. BRADY GROWTH OF ANISOTROPIC DLA CLUSTERS , Pages 237-240 , Bernard R. THOMPSON, Giuseppe ROSSI, Robin C. BALL, Robert M. BRADY CONTINUUM DLA: RANDOM FRACTAL GROWTH GENERATED BY A DETERMINISTIC MODEL , Pages 241-246 , Leonard M. SANDER FORMATION OF SOLIDIFICATION PATTERNS IN AGGREGATION MODELS , Pages 247-250 , Tamás VICSEK SCALING PROPERTIES OF THE SURFACE OF THE EDEN MODEL , Pages 251-253 , R. JULLIEN, R. BOTET CLUSTER AGGREGATION , Pages 255-258 , R. BOTET, R. JULLIEN, M. KOLB ANISOTROPY IN CLUSTER AND PARTICLE AGGREGATION , Pages 259-261 , M. KOLB REVERSIBILITY IN CLUSTER AGGREGATION , Pages 263-266 , M. KOLB FILM ON AGGREGATION PROCESSES , Pages 267-268 , M. KOLB FIELD THEORY APPROACH TO THE EDEN MODEL AND DIFFUSION LIMITED-AGGREGATION , Pages 269-272 , Luca PELITI, ZHANG Yi-Cheng SPREADING OF EPIDEMIC PROCESSES LEADING TO FRACTAL STRUCTURES , Pages 273-278 , Peter GRASSBERGER RANDOM RAIN SIMULATIONS OF DENDRITIC GROWTH , Pages 279-282 , B. CAPRILE, A.C. LEVI, L. LIGGIERI EXPERIMENTAL STUDY OF TWO DIMENSIONAL AGGREGATION , Pages 283-285 , Catherine ALLAIN, Michel CLOITRE KINETICS OF CLUSTERING IN IRREVERSIBLE AGGREGATION , Pages 289-302 , M.H. ERNST TAIL DISTRIBUTION FOR LARGE CLUSTERS IN IRREVERSIBLE AGGREGATION , Pages 303-307 , P.G.J. VAN DONGEN, M.H. ERNST SCALING GENERALIZATION OF THE SMOLUCHOWSKI EQUATION , Pages 309-312 , Zoltán RÁCZ CLUSTERING IN THE UNIVERSE , Pages 313-318 , Francesco LUCCHIN STOCHASTIC APPROACH TO LARGE SCALE CLUSTERING OF MATTER IN THE UNIVERSE , Pages 319-324 , L. PIETRONERO, R. KUPERS FRACTAL SURFACES AND THE DE GENNES TERMITE MODEL FOR A TWO-COMPONENT RANDOM MATERIAL , Pages 327-335 , H. Eugene STANLEY DYNAMICAL PROPERTIES OF RANDOM AND NON-RANDOM FRACTALS , Pages 337-342 , Robin STINCHCOMBE THE ELASTIC BEHAVIOR OF FRACTAL STRUCTURES , Pages 343-349 , Itzhak WEBMAN STATIC AND DYNAMIC PROPERTIES OF LOOPLESS AGGREGATES , Pages 351-356 , S. HAVLIN THE FRACTAL DIMENSION OF GROWTH PERIMETERS , Pages 357-360 , Alla E. MARGOLINA PERCOLATION AND FRACTAL BEHAVIOR IN DISORDERED LATTICES , Pages 361-364 , Panos ARGYRAKIS HIERARCHICAL FRACTAL GRAPHS AND WALKS THEREUPON , Pages 365-368 , John MELROSE FRACTAL-LIKE EXCITON DYNAMICS: GEOMETRICAL AND ENERGETICAL DISORDER , Pages 369-371 , Raoul KOPELMAN NYQUIST, DIFFUSION and FLICKER (1/f) NOISE IN FRACTALS AND PERCOLATING NETWORKS , Pages 373-378 , Rammal RAMMAL A REAL-SPACE RENORMALIZATION GROUP APPROACH TO ELECTRICAL AND NOISE PROPERTIES OF PERCOLATION CLUSTERS , Pages 379-382 , J.M. LUCK THEORY OF THE AC RESPONSE OF ROUGH INTERFACES , Pages 383-389 , S.H. LIU, T. KAPLAN, L.J. GRAY THE NATURE OF TEMPORAL HIERARCHIES UNDERLYING RELAXATION IN DISORDERED SYSTEMS , Pages 393-398 , Michael F. SHLESINGER, Joseph KLAFTER REACTIONS IN DISORDERED MEDIA MODELLED BY FRACTALS , Pages 399-408 , A. BLUMEN, J. KLAFTER, G. ZUMOFEN SELF-SIMILAR TEMPORAL BEHAVIOR OF RANDOM WALKS IN ONE-DIMENSIONAL RANDOM MEDIA , Pages 409-412 , J. BERNASCONI, W.R. SCHNEIDER AN OBSERVATION OF SCALING IN TRAPPING REACTIONS , Pages 413-416 , Zoran B. DJORDJEVIC HIERARCHICALLY CONSTRAINED THERMODYNAMICS IN METASTABLE SYSTEMS AND GLASSES , Pages 417-420 , L. PIETRONERO FRACTAL CLUSTERS AND SCALING IN THE ISING MODEL , Pages 421-426 , J.L. CAMBIER, M. NAUENBERG DEVIL'S STAIRCASE AND STRANGE ATTRACTOR IN THE ISING MODEL WITH COMPETING INTERACTIONS , Pages 427-430 , M.J. de OLIVEIRA, S.R. SALINAS, C.S.O. YOKOI PROBLEMS ABOUT THE SELF-SIMILAR STRUCTURE OF WAVEFUNCTIONS IN DISORDERED SYSTEMS , Pages 431-435 , A.P. SIEBESMA, L. PIETRONERO CIRCLE MAPS IN THE COMPLEX PLANE , Pages 439-445 , Predrag CVITANOVIĆ, Mogens H. JENSEN, Leo P. KADANOFF, Itamar PROCACCIA FRACTAL MODELS FOR TWO- AND THREE-DIMENSIONAL TURBULENCE , Pages 447-452 , G. PALADIN, A. VULPIANI NUMERICAL INVESTIGATION OF NONUNIFORM FRACTALS , Pages 453-456 , Remo BADII, Antonio POLITI GENERALISED SCALE INVARIANCE AND ANISOTROPIC INHOMOGENEOUS FRACTALS IN TURBULENCE , Pages 457-460 , Daniel SCHERTZER, Shaun LOVEJOY ANALYSIS OF THE FRACTAL SHAPE OF SEVERE CONVECTIVE CLOUDS , Pages 461-464 , Franz S. RYS, A. WALDVOGEL NESTED CELLULAR AUTOMATA: CONTINUOUS ASPECTS OF DISCRETE SYSTEMS , Pages 465-468 , Uwe QUASTHOFF THE HYPERBOLIC HELIX HYPOTHESIS: STAPLETON'S FRACTAL MEASURE ON THE HYDROPHOBIC FREE ENERGY MODE DISTRIBUTIONS OF ALLOSTERIC PROTEINS , Pages 469-474 , Arnold J. MANDELL AUTHOR INDEX , Pages 475-476 NAMARRKON—THE LIGHTNING SPIRIT , Page ibc1