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Fractal geometry allows the description of natural patterns and the establishment and testing of models of pattern formation. In particular, it is a tool for geoscientists. The aim of this volume is to give an overview of the applications of fractal geometry and the theory of dynamic systems in the geosciences. The state of the art is presented and the reader obtains an impression of the variety of fields for which fractal geometry is a useful tool and of the different methods of fractal geometry which can be applied. In addition to specific information about new applications of fractal…mehr
Fractal geometry allows the description of natural patterns and the establishment and testing of models of pattern formation. In particular, it is a tool for geoscientists. The aim of this volume is to give an overview of the applications of fractal geometry and the theory of dynamic systems in the geosciences. The state of the art is presented and the reader obtains an impression of the variety of fields for which fractal geometry is a useful tool and of the different methods of fractal geometry which can be applied. In addition to specific information about new applications of fractal geometry in structural geology, physics of the solid earth, and mineralogy, proposals and ideas about how fractal geometry can be applied in the reader's field of studies will be put forward.
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I Deformation and Tectonic Structures.- 1 Crustal Deformation and Fractals, a Review.- 2 Scaling Laws of Fragmentation.- 3 Fractal Structure and Deformation of Fractured Rock Masses.- 4 Multi-Scale Model of Damage Evolution in Stochastic Rocks: Fractal Approach.- 5 Fractal Characteristics of Joint Development in Stochastic Rocks.- 6 Correlation of Fractal Surface Description Parameters with Fracture Toughness.- 7 Fractal Dimension of Fracture Patterns a Computer Simulation.- 8 The Formation of Extensional Veins: An Application of the Cantor-Dust Model.- 9 Fractal Fault Displacements: A Case Study from the Moray Firth, Scotland.- 10 High-Temperature Viscoelastic Behaviour and Long Time Tail of Rocks.- 11 The Fractal Geometry of Patterned Structures in Numerical Models of Rock Deformation.- II Physical Features and Behaviour of the Earth.- 12 Non-Linear Processes in Earthquake Prediction Research, a Review.- 13 Fractal Analysis as a Tool to Detect Seismic Cycle Phases.- 14 Binary Descriptions of Stick-Slip Phenomena.- 15 Main Topics of Fractal Research into Earthquakes in China, a Review.- 16 Evidence for Self-Similarities in the Harmonic Development of Earth Tides.- 17 Global Relief: Evidence of Fractal Geometry.- III Formation, Structure and Distribution of Minerals and Matter.- 18 Fractal Geometry and the Mining Industry, a Review.- 19 The Fractal Distribution of Gold Deposits: Two Examples from the Zimbabwe Archaean Craton.- 20 Self-Organization of Mineral Fabrics.- 21 The Formation and Fragmentation of Periodic Bands Through Precipitation and Ostwald Ripening.- 22 Agates, Geodes, Concretions and Orbicules: Self-Organized Zoning and Morphology.- 23 The Formation of Manganese Dendrites as the Mineral Record of Flow Structures.- 24 Structure and FractalProperties in Geological Crystallization Processes Due to Nucleation and Growth.- 25 Fractal Structure of Quasicrystals.- 26 Protolytic Weathering of Montmorillonite, Described by Its Effective Surface Fractal Dimension.- 27 Characteristics and Evolution of Artificial Anisotropic Rocks.- 28 Characteristic Multifractal Element Distributions in Recent Bioactive Marine Sediments.- 29 Fractal Analyses of Pleistocene Marine Oxygen Isotope Records.- IV Methods.- 30 "Counter-Scaling" Method for Estimation of Fractal Properties of Self-Affine Objects.- 31 Application of the Grassberger-Procaccia Algorithm to the ?18O Record from ODP Site 659: Selected Methodical Aspects.- Appendix List of Reviewers.
I Deformation and Tectonic Structures.- 1 Crustal Deformation and Fractals, a Review.- 2 Scaling Laws of Fragmentation.- 3 Fractal Structure and Deformation of Fractured Rock Masses.- 4 Multi-Scale Model of Damage Evolution in Stochastic Rocks: Fractal Approach.- 5 Fractal Characteristics of Joint Development in Stochastic Rocks.- 6 Correlation of Fractal Surface Description Parameters with Fracture Toughness.- 7 Fractal Dimension of Fracture Patterns a Computer Simulation.- 8 The Formation of Extensional Veins: An Application of the Cantor-Dust Model.- 9 Fractal Fault Displacements: A Case Study from the Moray Firth, Scotland.- 10 High-Temperature Viscoelastic Behaviour and Long Time Tail of Rocks.- 11 The Fractal Geometry of Patterned Structures in Numerical Models of Rock Deformation.- II Physical Features and Behaviour of the Earth.- 12 Non-Linear Processes in Earthquake Prediction Research, a Review.- 13 Fractal Analysis as a Tool to Detect Seismic Cycle Phases.- 14 Binary Descriptions of Stick-Slip Phenomena.- 15 Main Topics of Fractal Research into Earthquakes in China, a Review.- 16 Evidence for Self-Similarities in the Harmonic Development of Earth Tides.- 17 Global Relief: Evidence of Fractal Geometry.- III Formation, Structure and Distribution of Minerals and Matter.- 18 Fractal Geometry and the Mining Industry, a Review.- 19 The Fractal Distribution of Gold Deposits: Two Examples from the Zimbabwe Archaean Craton.- 20 Self-Organization of Mineral Fabrics.- 21 The Formation and Fragmentation of Periodic Bands Through Precipitation and Ostwald Ripening.- 22 Agates, Geodes, Concretions and Orbicules: Self-Organized Zoning and Morphology.- 23 The Formation of Manganese Dendrites as the Mineral Record of Flow Structures.- 24 Structure and FractalProperties in Geological Crystallization Processes Due to Nucleation and Growth.- 25 Fractal Structure of Quasicrystals.- 26 Protolytic Weathering of Montmorillonite, Described by Its Effective Surface Fractal Dimension.- 27 Characteristics and Evolution of Artificial Anisotropic Rocks.- 28 Characteristic Multifractal Element Distributions in Recent Bioactive Marine Sediments.- 29 Fractal Analyses of Pleistocene Marine Oxygen Isotope Records.- IV Methods.- 30 "Counter-Scaling" Method for Estimation of Fractal Properties of Self-Affine Objects.- 31 Application of the Grassberger-Procaccia Algorithm to the ?18O Record from ODP Site 659: Selected Methodical Aspects.- Appendix List of Reviewers.
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