## Fractal River Basins: Chance and Self-OrganizationCambridge University Press, 27. kol 2001. - Broj stranica: 547 This volume brings to a triumphant conclusion this monumental project to catalogue, describe and illustrate every Romano-British mosaic. The area covered by the fourth and final volume in the corpus is one of the richest regions of Britain in economic as well as architectural and artistic terms and this is reflected in the quantity and quality of the region's mosaics, which include the largest figured mosaic ever found in Britain - the Woodchester Orpheus pavement - which was perhaps the inspiration for the other famous Orpheus mosaics of the Roman Cotswolds. At the heart of this affluent region is Cirencester, Roman Britain's second largest town, represented here by more than sixty mosaics, the second-century examples being the most exquisite in the country. There are also many fine mosaics from the region's highly ornate villas, as well as from the towns of Gloucester, Caerwent and Wroxeter. The catalogue follows the format of earlier volumes in providing an account of each mosaic's discovery and locating the mosaic within its building plan. Following the description are notable parallels and major references. Many of the illustrations are by the authors, with additional ones by Luigi Thompson, as well as photographs and historical engravings, a high proportion of the latter by Samuel Lysons whose home was in Gloucestershire where he did much of his pioneering work in archaeological excavation and illustration. Brief biographies of Lysons and all the other artists whose work grace all four volumes appear at the end of this volume. As with previous volume the work is preceded with a substantial introduction. This deals with the history and topography of the region, buildings and rooms, an assessment of regional workshops, and schemes, ending with a consideration of mosaics in relation to the end of Roman Britain. |

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### Sadržaj

A View of River Basins | 1 |

A Brief Review | 4 |

122 Drainage Density and the Hillslope Scale | 7 |

123 Relation of Area to Length | 9 |

124 Relation of Area to Discharge | 11 |

125 Relation between Magnitude and Area | 12 |

127 The Width Function | 15 |

128 The ThreeDimensional Structure of River Basins | 18 |

372 Conservative Random Cascades and Width Functions | 247 |

Optimal Channel Networks Minimum Energy and Fractal Structures | 251 |

42 The Connectivity Issue | 252 |

43 Principles of Energy Expenditure in Drainage Networks | 253 |

44 Energy Expenditure and Optimal Network Configurations | 254 |

45 Stationary Dendritic Patterns in a Potential Force Field | 259 |

46 Scaling Implications of Optimal Energy Expenditure | 263 |

47 Optimal Channel Networks | 267 |

129 River Basins from Digital Elevation Models | 19 |

1210 SlopeArea Scaling | 26 |

1211 Empirical Evidence | 31 |

1212 Where Do Channels Begin? | 34 |

1213 Experimental Fluvial Geomorphology | 44 |

13 Statistical Models of Network Evolution | 47 |

132 RandomWalk Drainage Basin Models | 49 |

133 The RandomTopology Model | 55 |

134 Limitations of Statistical Models | 63 |

142 Models Based on Junction Angle Adjustments | 64 |

143 Models of Erosion and the Evolution of River Networks | 67 |

144 A ProcessResponse Model of Catchment and Network Development | 77 |

145 DetachmentLimited Basin Evolution | 83 |

146 Limitations of Deterministic Models | 93 |

15 Lattice Models | 95 |

Fractal Characteristics of River Basins | 99 |

212 The BoxCounting Dimension | 105 |

213 The Cluster Dimension or Mass Dimension | 106 |

214 The Correlation Dimension | 108 |

215 SelfSimilarity and Power Laws | 109 |

22 SelfSimilarity in River Basins | 110 |

23 Hortons Laws and the Fractal Structure of Drainage Networks | 120 |

24 Peanos River Basin | 123 |

25 Power Law Scaling in River Basins | 128 |

251 Scaling of Slopes | 129 |

252 Scaling of Contributing Areas Discharge and Energy | 133 |

Topographic Contours | 145 |

271 Brownian Motion and Fractional Brownian Motion | 146 |

272 Power Spectrum and Correlation Structure of Fractional Brownian Motion | 149 |

273 Characterization of SelfAffine Records | 152 |

274 SelfAffine Characteristics of Topographic Transects | 157 |

275 SelfAffine Characteristics of Width Functions | 160 |

276 Other SelfAffine Characterizations | 161 |

277 SelfAffine Scaling of Watercourses | 165 |

278 SelfAffine Scaling of Basin Boundaries | 168 |

28 Transects Contours Watercourses and Mountain Ridges as Parts of the Basin Landscape | 171 |

29 Hacks Law the SelfAffinity of Basin Boundaries and the Power Law of Contributing Areas | 174 |

292 Power Law of Contributing Areas Hacks Relationship and the SelfAffinity of Basin Boundaries | 179 |

293 Hacks Law and the Probability Distribution of Stream Lengths to the Divide | 182 |

210 Generalized Scaling Laws for River Networks | 185 |

2101 Scaling of Areas | 186 |

2102 Scaling of Lengths | 190 |

Multifractal Characteristics of River Basins | 196 |

32 Peanos Basin and the Binomial Multiplicative Process | 198 |

33 Multifractal Spectra | 208 |

34 Multifractal Spectra of Width Functions | 220 |

35 Multiscaling and Multifractality | 223 |

351 Other Multifractal Descriptors | 228 |

36 Multifractal Topographies | 232 |

362 Generalized Variogram Analysis | 238 |

37 Random Cascades | 241 |

371 Canonical Random Cascades | 242 |

48 Geomorphologic Properties of OCNs | 278 |

49 Fractal Characteristics of OCNs | 279 |

410 Multifractal Characteristics of OCNs | 285 |

411 Multiscaling in OCNs | 287 |

Least Energy Dissipation Structures? | 289 |

413 On Feasible Optimality | 292 |

414 OCNs Hillslope and Channel Processes | 298 |

415 On the Interaction of Shape and Size | 303 |

416 Are River Basins OCNs? | 308 |

417 Hacks Relation and OCNs | 313 |

418 Renormalization Groups for OCNs | 316 |

419 OCNs with Open Boundary Conditions | 323 |

420 DisorderDominated OCNs | 327 |

421 Thermodynamics of OCNs | 331 |

422 SpaceTime Dynamics of Optimal Networks | 339 |

423 Exact Solutions for Global Minima and Feasible Optimality | 347 |

SelfOrganized Fractal River Networks | 356 |

52 SelfOrganized Criticality | 358 |

53 SOC Systems in Geophysics | 362 |

54 On Forest Fires Turbulence and Life at the Edge | 366 |

55 Sandpile Models and Abelian Groups | 370 |

56 Fractals and SelfOrganized Criticality | 377 |

57 SelfOrganized Fractal Channel Networks | 379 |

58 Optimality of SelfOrganized River Networks | 389 |

59 River Models and Temporal Fluctuations | 393 |

510 Fractal SOC Landscapes | 397 |

511 Renormalization Groups for SOC Landscapes | 404 |

512 Thermodynamics of Fractal Networks | 405 |

513 SelfOrganized Networks and Feasible Optimality | 410 |

On Landscape SelfOrganization | 417 |

62 Slope Evolution Processes and Hillslope Models | 419 |

621 The Effects of Nonlinearity | 423 |

622 The Effects of a Driving Noise | 425 |

63 Landscape SelfOrganization | 429 |

64 On Heterogeneity | 436 |

65 Fractal and Multifractal Descriptors of Landscapes | 444 |

66 Geomorphologic Signatures of Varying Climate | 457 |

Geomorphologic Hydrologic Response | 468 |

72 Travel Time Formulation of Transport | 469 |

73 Geomorphologic Unit Hydrograph | 477 |

74 Travel Time Distributions in Channel Links | 487 |

75 Geomorphologic Dispersion | 493 |

76 Hortonian Networks | 498 |

77 Width Function Formulation of the GIUH | 504 |

78 Can One Gauge the Shape of a Basin? | 508 |

781 Estimation of Basin Shape from the Width Function | 509 |

782 Geomorphologic Hydrologic Response | 511 |

791 Introduction | 514 |

792 The Effect of Aggregation on the Statistics of the Soil Moisture Field | 518 |

525 | |

540 | |

### Ostala izdanja - Prikaži sve

Fractal River Basins: Chance and Self-Organization Ignacio Rodríguez-Iturbe,Andrea Rinaldo Pregled nije dostupan - 1997 |

### Uobičajeni izrazi i fraze

aggregation allowed analysis assumed average boundary channel channel network Chapter characteristics characterized characters computed configuration constant contributing area corresponding critical defined density depends described direction discharge discussed distance distribution drainage dynamics effects elevation energy energy expenditure equal equation erosion estimation et al evolution example exponent fact field Figure flow fluvial fractal dimension function given growth hillslope important initial conditions interest landscape lattice length mass mean measure multifractal nature Notice observed obtained OCNs optimal outlet patterns pixels plot power law probability procedure processes properties random range relationship response river basins scaling seen self-organized shown in Figure shows similar slope soil spatial statistical stream structure suggests threshold tion transport unit variable variance versus width function yields

### Popularni odlomci

Stranica 528 - Stream gradient as a function of order, magnitude and discharge, Water Resour.

Stranica 539 - Massachusetts Institute of Technology, Department of Earth, Atmospheric and Planetary Sciences, Cambridge, MA, USA University of Copenhagen, Geological Institute, Copenhagen, Denmark S.