Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-01T04:12:34.574Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 June 2012

William I. Newman
Affiliation:
University of California, Los Angeles
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ablowitz, M. J., and Segur, H. (1981). Solitons and the Inverse Scattering Transform. Vol. 4. Philadelphia: SIAM.CrossRefGoogle Scholar
Aki, K., and Richards, P. G. (2002). Quantitative Seismology. 2nd edn. Sausalito, CA: University Science Books.Google Scholar
Allègre, C. J., Le Mouel, J. L., and Provost, A. (1982). Scaling rules in rock fracture and possible implications for earthquake prediction. Nature, 297 (May), 47–49.CrossRefGoogle Scholar
Arfken, G. B., and Weber, H. J. (2005). Mathematical Methods for Physicists. 6th edn. Burlington, MA: Elsevier Academic Press.Google Scholar
Aris, R. (1989). Vectors, Tensors, and the Basic Equations of Fluid Mechanics. New York: Dover Publications.Google Scholar
Bak, P. (1996). How Nature Works: the Science of Self-organized Criticality. New York: Copernicus.CrossRefGoogle Scholar
Batchelor, G. K. (1953). The Theory of Homogeneous Turbulence. Cambridge: Cambridge University Press.Google Scholar
Batchelor, G. K. (1967). An Introduction to Fluid Dynamics. Cambridge: Cambridge University Press.Google Scholar
Ben-Menahem, A., and Singh, S. J. (2000). Seismic Waves and Sources. 2nd edn. Mineola, NY: Dover Publications.Google Scholar
Boas, M. L. (2006). Mathematical Methods in the Physical Sciences. 3rd edn. Hoboken, NJ: Wiley.Google Scholar
Bullen, K. E, and Bolt, B. A. (1985). An Introduction to the Theory of Seismology. 4th edn. Cambridge: Cambridge University Press.Google Scholar
Burridge, R., and Knopoff, L. (1967). Model and theoretical seismicity. Bulletin of the Seismological Society of America, 57(3), 341–371.Google Scholar
Butt, R. (2007). Introduction to Numerical Analysis using MATLAB. Hingham, MA: Infinity Science Press.Google Scholar
Carmichael, R. S. (1989). Practical Handbook of Physical Properties of Rocks and Minerals. Boca Raton, FL: CRC Press.Google Scholar
Carmo, M. P. do (1976). Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Chadwick, P. (1999). Continuum Mechanics: Concise Theory and Problems. 2nd corrected and enlarged edn. Mineola, NY: Dover Publications, Inc.Google Scholar
Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. New York: Dover Publications.Google Scholar
Chandrasekhar, S. (1995). Newton's Principia for the Common Reader. Oxford: Clarendon Press.Google Scholar
Cole, J. D. (1951). On a quasilinear parabolic equation occurring in aerodynamics. Quarterly of Applied Mathematics, 9, 225–236.CrossRefGoogle Scholar
Drazin, P. G. (1992). Nonlinear Systems. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Drazin, P. G. (2002). Introduction to Hydrodynamic Stability. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Drazin, P. G., and Johnson, R. S. (1989). Solitons: an Introduction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Drazin, P. G., and Reid, W. H. (2004). Hydrodynamic Stability. 2nd edn. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Dummit, D. S., and Foote, R. M. (2004). Abstract Algebra. 3rd edn. Hoboken, NJ: Wiley.Google Scholar
Faber, T. E. (1995). Fluid Dynamics for Physicists. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Feder, J. (1988). Fractals. New York: Plenum Press.CrossRefGoogle Scholar
Fowler, A. (2011). Mathematical Geoscience. 1st edn. Interdisciplinary applied mathematics, vol. 36. New York: Springer.CrossRefGoogle Scholar
Fox, L. (1962). Numerical Solution of Ordinary and Partial Differential Equations: Based on a Summer School held in Oxford, August–September 1961. Proceedings of summer schools organised by the Oxford University Computing Laboratory and the Delegacy for Extra-mural Studies, vol. 1. Oxford: Pergamon Press.Google Scholar
Fröberg, C. E. (1985). Numerical Mathematics: Theory and Computer Applications. Menlo Park, CA: Benjamin/Cummings Pub. Co.Google Scholar
Fung, Y. S. (1965). Foundations of Solid Mechanics. Englewood Cliffs, NJ: Prentice-Hall, Inc.Google Scholar
Gabrielov, A., Newman, W. I., and Turcotte, D. L. (1999). Exactly soluble hierarchical clustering model: inverse cascades, self-similarity, and scaling. Physical Review E, 60 (Nov.), 5293–5300.CrossRefGoogle Scholar
Gabrielov, A., Zaliapin, I., Newman, W. I., and Keilis-Borok, V. I. (2000a). Colliding cascades model for earthquake prediction. Geophysical Journal International, 143 (Nov.), 427–437.
Gabrielov, A., Keilis-Borok, V., Zaliapin, I., and Newman, W. I. (2000b). Critical transitions in colliding cascades. Physical Review E, 62 (July), 237–249.CrossRefGoogle ScholarPubMed
Gantmakher, F. R. (1959). The Theory of Matrices. New York: Chelsea Pub. Co.Google Scholar
Gear, C. W. (1971). Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall series in automatic computation. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Ghil, M., and Childress, S. (1987). Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics. Applied mathematical sciences, vol. 60. New York: Springer-Verlag.CrossRefGoogle Scholar
Gill, A. E. (1982). Atmosphere–Ocean Dynamics. New York: Academic Press.Google Scholar
Goldstein, H., Poole, C. P, and Safko, J. L. (2002). Classical Mechanics. 3rd edn. San Francisco: Addison Wesley.Google Scholar
Gurtin, M. E. (1981). An Introduction to Continuum Mechanics. Vol. 158. New York: Academic Press.Google Scholar
Helmholtz, H. von (1868). On the facts underlying geometry. Abhandlunger der Königlicher Gesellschaft der Wìsserschafter zu Göttinger. Vol. 15.Google Scholar
Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms. 2nd edn. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Holton, J. R. (2004). An Introduction to Dynamic Meteorology. 4th edn. Vol. 88. Burlington, MA: Elsevier Academic Press.Google Scholar
Hopf, E. (1950). The partial differential equation ut + uux = µxx. Communicators or Pure and Applied Mathematics, 3, 201–230.CrossRefGoogle Scholar
Houghton, J.T. (2002). The Physics of Atmospheres. 3rd edn. Cambridge: Cambridge University Press.Google Scholar
Jackson, J. D. (1999). Classical Electrodynamics. 3rd edn. New York: Wiley.Google Scholar
Jensen, H. J. (1998). Self-organized Criticality: Emergent Complex Behavior in Physical and Biological Systems. Vol. 10. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Johnson, C. (2009). Numerical Solution of Partial Differential Equations by the Finite Element Method. Dover books on mathematics. Mineola, NY: Dover Publications.Google Scholar
Kagan, Y. Y., and Knopoff, L. (1980). Spatial distribution of earthquakes: the two-point distribution problem. Geophysical Journal, 62, 303–320.CrossRefGoogle Scholar
Kasahara, K. (1981). Earthquake Mechanics. Cambridge Earth Science Series. Cambridge: Cambridge University Press.Google Scholar
Kennett, B. L. N. (1983). Seismic Wave Propagation in Stratified Media. Cambridge: Cambridge University Press.Google Scholar
Kincaid, D., and Cheney, E. W. (2009). Numerical Analysis: Mathematics of Scientific Computing. 3rd edn. The Sally series, vol. 2. Providence, RI: American Mathematical Society.Google Scholar
Knopoff, L., and Newman, W. I. (1983). Crack fusion as a model for repetitive seismicity. Pure and Applied Geophysics, 121 (May), 495–510.CrossRefGoogle Scholar
Landau, L. D., and Lifshitz, E.M. (1987). Fluid Mechanics. 2nd edn. Course of Theoretical Physics, vol. 6. Oxford, England: Pergamon Press.Google Scholar
Landau, L. D., Lifshitz, E. M., Kosevich, A. M., and Pitaevskiĭ, L. P. (1986). Theory of Elasticity. 3rd edn. Course of Theoretical Physics, vol. 7. Oxford: Pergamon Press.Google Scholar
Lawn, B. R. (1993). Fracture of Brittle Solids. 2nd edn. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. Updated and augmented edn. New York: W. H. Freeman.Google Scholar
Marshall, J., and Plumb, R. A. (2008). Atmosphere, Ocean, and Climate Dynamics: an Introductory Text. Vol. 93. Amsterdam: Elsevier Academic Press.Google Scholar
Mase, G. E., and Mase, G. T. (1990). Continuum Mechanics for Engineers. Boca Raton, FL: CRC Press.Google Scholar
Mathews, J., and Walker, R. L. (1970). Mathematical Methods of Physics. 2nd edn. New York: W. A. Benjamin.Google Scholar
McKelvey, J. P. (1984). Simple transcendental expressions for the roots of cubic equations. American Journal of Physics, 52(3), 269–270.CrossRefGoogle Scholar
Millman, R. S., and Parker, G. D. (1977). Elements of Differential Geometry. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Morse, P. M., and Feshbach, H. (1953). Methods of Theoretical Physics. International series in pure and applied physics. New York: McGraw-Hill.Google Scholar
Müser, M. H., Wenning, L., and Robbins, M. O. (2001). Simple microscopic theory of Amontons's laws for static friction. Physical Review Letters, 86(7), 1295–1298.CrossRefGoogle ScholarPubMed
Narasimhan, M. N. L. (1993). Principles of Continuum Mechanics. New York: Wiley.Google Scholar
Newman, W. I. (2000). Inverse cascade via Burgers equation. Chaos, 10 (June), 393–397.CrossRefGoogle ScholarPubMed
Newman, W. I., and Knopoff, L. (1982). Crack fusion dynamics: A model for large earthquakes. Geophysical Research Letters, 9, 735–738.CrossRefGoogle Scholar
Newman, W. I., and Knopoff, L. (1983). A model for repetitive cycles of large earthquakes. Geophysical Research Letters, 10 (Apr.), 305–308.CrossRefGoogle Scholar
Newman, W. I., and Turcotte, D. L. (2002). A simple model for the earthquake cycle combining self-organized complexity with critical point behavior. Nonlinear Processes in Geophysics, 9, 453–461.CrossRefGoogle Scholar
Nickalls, R. W. D. (1993). A new approach to solving the cubic; Cardan's solution revealed. The Mathematical Gazette, 77(480), 354–359.CrossRefGoogle Scholar
Oertel, G. F. (1996). Stress and Deformation: a Handbook on Tensors in Geology. New York: Oxford University Press.Google Scholar
Pedlosky, J. (1979). Geophysical Fluid Dynamics. New York: Springer Verlag.CrossRefGoogle Scholar
Peitgen, H.-O., Saupe, D., and Barnsley, M. F. (1988). The Science of Fractal Images. New York: Springer-Verlag.Google Scholar
Peyret, R. (2000). Handbook of Computational Fluid Mechanics. San Diego, CA: Academic Press.Google Scholar
Peyret, R., and Taylor, T. D. (1990). Computational Methods for Fluid Flow. Corr. 3rd print edn. New York: Springer-Verlag.Google Scholar
Pope, S. B. (2000). Turbulent Flows. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Press, F., and Siever, R. (1986). Earth. 4th edn. New York: W. H. Freeman.Google Scholar
Reid, H. F. (1911). The elastic-rebound theory of earthquakes. Bulletin of the Department of Geology, University of California Publications, 6(19), 413–444.Google Scholar
Richtmyer, R. D., and Morton, K. W. (1967). Difference Methods for Initial-value Problems. 2nd edn. Interscience tracts in pure and applied mathematics, vol. 4. New York: Interscience Publishers.Google Scholar
Schiesser, W. E. (1991). The Numerical Method of Lines: Integration of Partial Differential Equations. San Diego: Academic Press.Google Scholar
Scholz, C. H. (2002). The Mechanics of Earthquakes and Faulting. 2nd edn. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Schubert, G., Turcotte, D. L., and Olson, P. (2001). Mantle Convection in the Earth and Planets. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Schutz, B. F. (1980). Geometrical Methods of Mathematical Physics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Segall, P. (2010). Earthquake and Volcano Deformation. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Segel, L. A., and Handelman, G. H. (1987). Mathematics Applied to Continuum Mechanics. New York: Dover Publications.Google Scholar
Shearer, P. M. (2009). Introduction to Seismology. 2nd edn. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Sleep, N. H., and Fujita, K. (1997). Principles of Geophysics. Malden, MA: Blackwell Science.Google Scholar
Spencer, A. J. M. (1980). Continuum Mechanics. Longman mathematical texts. London: Longman.Google Scholar
Stauffer, D., and Aharony, A. (1994). Introduction to Percolation Theory. Rev., 2nd edn. London: Taylor and Francis.Google Scholar
Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Reading, MA: Addison-Wesley Pub.Google Scholar
Tennekes, H., and Lumley, J. L. (1972). A First Course in Turbulence. Cambridge, MA: MIT Press.Google Scholar
Turcotte, D. L. (1997). Fractals and Chaos in Geology and Geophysics. 2nd edn. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Turcotte, D. L., and Schubert, G. (2002). Geodynamics. 2nd edn. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Vallis, G. K. (2006). Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Largescale Circulation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Van Dyke, M. (1982). An Album of Fluid Motion. Stanford, CA: The Parabolic Press.Google Scholar
Whitham, G. B. (1974). Linear and Nonlinear Waves. Pure and applied mathematics. New York: Wiley.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • William I. Newman, University of California, Los Angeles
  • Book: Continuum Mechanics in the Earth Sciences
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511980121.011
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • William I. Newman, University of California, Los Angeles
  • Book: Continuum Mechanics in the Earth Sciences
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511980121.011
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • William I. Newman, University of California, Los Angeles
  • Book: Continuum Mechanics in the Earth Sciences
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511980121.011
Available formats
×