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Pythonic Geodynamics: Implementations for Fast Computing 1st ed. 2018 [Kõva köide]

  • Formaat: Hardback, 227 pages, kõrgus x laius: 235x155 mm, kaal: 4912 g, 40 Illustrations, color; 6 Illustrations, black and white; XVI, 227 p. 46 illus., 40 illus. in color., 1 Hardback
  • Sari: Lecture Notes in Earth System Sciences
  • Ilmumisaeg: 02-Aug-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319556800
  • ISBN-13: 9783319556802
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  • Formaat: Hardback, 227 pages, kõrgus x laius: 235x155 mm, kaal: 4912 g, 40 Illustrations, color; 6 Illustrations, black and white; XVI, 227 p. 46 illus., 40 illus. in color., 1 Hardback
  • Sari: Lecture Notes in Earth System Sciences
  • Ilmumisaeg: 02-Aug-2017
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319556800
  • ISBN-13: 9783319556802
This book addresses students and young researchers who want to learn to use numerical modeling to solve problems in geodynamics. Intended as an easy-to-use and self-learning guide, readers only need a basic background in calculus to approach most of the material. The book difficulty increases very gradually, through four distinct parts. The first is an introduction to the Python techniques necessary to visualize and run vectorial calculations. The second is an overview with several examples on classical Mechanics with examples taken from standard introductory physics books. The third part is a detailed description of how to write Lagrangian, Eulerian and Particles in Cell codes for solving linear and non-linear continuum mechanics problems. Finally the last one address advanced techniques like tree-codes, Boundary Elements, and illustrates several applications to Geodynamics. The entire book is organized around numerous examples in Python, aiming at encouraging the reader to learn

by experimenting and experiencing, not by theory.

Bird"s eye view.- Visualization.- Fast Python: NumPy and Cython.- Mechanics I: Kinematics.- Mechanics II: Newtonian Dynamics.- Insights on the physics of Stokes Flow.- Lagrangian Transport.- Operator Formulation.- Laplacian Operator and Diffusion.- Beyond Linearity.- Trees, Particles and Boundaries.- Applications to Geodynamics.- The future.
Part I Introduction to Scientific Python
1 Bird's Eye View
3(12)
1.1 Bird's Eye View
3(1)
1.2 History
4(1)
1.3 Programming or Scripting
5(1)
1.4 Python Interfaces
5(3)
1.4.1 IPython: Interactive Python
6(2)
1.5 Few Words on Syntax
8(2)
1.6 Extending Python
10(1)
1.6.1 Importing Libraries
11(1)
1.7 NumPy: Numerical Python
11(1)
1.8 Visualization
12(3)
Summary
13(1)
Problems
13(2)
2 Visualization
15(20)
2.1 The MatPlotLib Visualization Library
16(8)
2.1.1 Plotting a 2D Field
17(1)
2.1.2 Plotting a Map
18(2)
2.1.3 NetCDF and ETOPO
20(2)
2.1.4 Plotting a Seismic Waveform
22(2)
2.2 Plotting in 3D with MatPlotLib
24(3)
2.2.1 VTK File Format
26(1)
2.3 Example: Length of the Day
27(2)
2.4 IPython and Jupyter Notebooks
29(1)
2.5 Paraview and Visit
30(1)
2.6 Python as a wrapper: SEATREE and Underworld
31(4)
Summary
32(1)
Problems
32(3)
3 Fast Python: NumPy and Cython
35(28)
3.1 How Fast is Your Computing Machine?
36(1)
3.2 Numerical Python
37(5)
3.2.1 NumPy Types
38(1)
3.2.2 Ndarrays
39(3)
3.3 Indexing and Slicing
42(5)
3.3.1 N-Dimensional Indexing
44(1)
3.3.2 Boolean Indexing
44(2)
3.3.3 Transposing and Axis Rotation
46(1)
3.4 Strides
47(1)
3.5 Vector Products
48(2)
3.6 Linear Algebra
50(2)
3.7 Cython
52(2)
3.7.1 Cython in iPython
53(1)
3.8 Going Parallel: mpi4py and PETSc4py
54(4)
3.9 Other Computational Modules
58(5)
Summary
59(1)
Problems
60(3)
Part II Second Part: Mechanics
4 Mechanics I: Kinematics
63(14)
4.1 Computation of Velocity and Acceleration
64(4)
4.2 Integrate Acceleration
68(3)
4.3 Projectile Trajectory
71(2)
4.4 Circular Motion
73(4)
Summary
74(1)
Problems
74(3)
5 Mechanics II: Newtonian Dynamics
77(16)
5.1 Analytical Solutions for ID Dynamics
77(7)
5.1.1 1-D Dynamics
79(1)
5.1.2 2D Dynamics
80(2)
5.1.3 Potential, Dissipated, Kinetic, Mechanical Energies for the Droplet
82(2)
5.2 Monte Carlo Simulation of the Pyroclastic flow During the 1944 Mt Vesuvio Volcanic Eruption
84(3)
5.3 Precession of a Gyroscope
87(6)
Summary
90(1)
Problems
90(3)
6 Physics of Stokes Flow
93(14)
6.1 Momentum and Continuity Equations
93(5)
6.1.1 Navier Stokes Equation
96(2)
6.2 Stokes Flow: Simple but Not Obvious
98(4)
6.2.1 Stokes' Paradox
98(2)
6.2.2 Flow Reversibility
100(1)
6.2.3 Origin of the Paradoxes
101(1)
6.3 Fundamental Solutions of Stokes Flow
102(5)
6.3.1 Rotlet
103(1)
6.3.2 Stokeslet
103(1)
Summary
104(3)
Part III Lattice Methods
7 Lagrangian Transport
107(22)
7.1 Strain and Strain Rate
107(2)
7.2 Rigid Rotation
109(7)
7.2.1 Cell-Particles Projections
112(2)
7.2.2 Motion of the Particles
114(2)
7.3 Thinning Flow
116(3)
7.4 Lagrangian Advection of a Continuous Field
119(6)
7.5 Upwind Scheme Versus Lagrangian Transport
125(4)
Summary
127(1)
Problems
127(2)
8 Operator Formulation
129(14)
8.1 Strain Rates
131(3)
8.2 Cell-Centered Strain Rates from Linear Operators
134(5)
8.2.1 Sparse Derivative Operator
138(1)
8.3 Reversible and Irreversible
139(4)
Summary
140(1)
Problems
141(2)
9 Laplacian Operator and Diffusion
143(18)
9.1 Diffusion Processes in Geodynamics
144(2)
9.2 Explicit Diffusion Implementation
146(2)
9.3 Explicit Formulation Using Operators
148(2)
9.4 Implicit Formulation
150(3)
9.5 Two-Dimensional Diffusion Equation
153(4)
9.6 Biharmonic Equation
157(4)
Summary
160(1)
Problems
160(1)
10 Beyond Linearity
161(20)
10.1 Operator Form of the Stokes Equation
161(2)
10.2 Implementation of the Homogeneous Stokes Equation
163(2)
10.3 The Finite Volume Method
165(2)
10.4 Implementation of the Nonhomogenous Stokes Equation
167(3)
10.5 Long-Range Interaction
170(5)
10.6 Advection--Diffusion Equation
175(6)
Summary
176(1)
Problems
176(5)
Part IV Advanced Techniques
11 Trees, Particles, and Boundaries
181(20)
11.1 Tree Building
182(4)
11.1.1 The Barnes and Hut Tree
182(1)
11.1.2 The Warren and Salmon Solution
183(3)
11.2 SciPy k-d Tree
186(1)
11.3 Boundary-Based Simulations
186(4)
11.3.1 Drag over a Rigid Particle
189(1)
11.4 Quadratic Triangular Elements Mesh
190(11)
11.4.1 Calculation of the influence matrix
193(3)
11.4.2 Calculation of the Resistance Matrix
196(3)
Summary
199(1)
Problems
199(2)
12 Applications to Geodynamics
201(8)
12.1 Plate Tectonics
201(2)
12.2 Raise of Gas in a Volcanic Conduit
203(2)
12.3 Interaction Between Faults
205(1)
12.4 Convection in 2D
205(4)
13 The Future
209(8)
13.1 Jupyter
209(1)
13.2 Machine Learning
210(5)
13.2.1 Theano and Tensor Flow
212(3)
13.3 Big Data
215(1)
13.4 Final Outlook
216(1)
References 217(8)
Index 225