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  • 1
    Monograph available for loan
    Monograph available for loan
    Continuum mechanics in the earth sciences : William I. Newman (2012)
    Cambridge : Cambridge University Press
    Details Availability
    Call number: M 12.0249
    Description / Table of Contents: Continuum mechanics underlies many geological and geophysical phenomena, from earthquakes and faults to the fluid dynamics of the Earth. This interdisciplinary book provides geoscientists, physicists and applied mathematicians with a class-tested, accessible overview of continuum mechanics. Starting from thermodynamic principles and geometrical insights, the book surveys solid, fluid and gas dynamics. In later review chapters, it explores new aspects of the field emerging from nonlinearity and dynamical complexity and provides a brief introduction to computational modeling. Simple, yet rigorous, derivations are used to review the essential mathematics. The author emphasizes the full three-dimensional geometries of real-world examples, enabling students to apply this in deconstructing solid earth and planet-related problems. Problem sets and worked examples are provided, making this a practical resource for graduate students in geophysics, planetary physics and geology and a beneficial tool for professional scientists seeking a better understanding of the mathematics and physics within Earth sciences.
    Type of Medium: Monograph available for loan
    Pages: XI, 182 S. : Ill.
    ISBN: 9780521562898
    Classification:
    Geodynamics
    Location: Upper compact magazine
    Branch Library: GFZ Library
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  • 2
    Monograph available for loan
    Monograph available for loan
    Nonlinear dynamics and predictability of geophysical phenomena (1994)
    Washington, DC : American Geophysical Union [u.a.]
    Associated volumes
    Details Availability
    Call number: 5/M 95.0088
    In: Geophysical monograph
    Type of Medium: Monograph available for loan
    Pages: xi, 107 S.
    ISBN: 0875904696
    Series Statement: Geophysical monograph 83
    Classification:
    B.4.1.
    Language: English
    Location: Reading room
    Branch Library: GFZ Library
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  • 3
    Electronic Resource
    Electronic Resource
    Identifying coherent structures in nonlinear wave propagation (1991)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 1 (1991), S. 77-94 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Nonlinear wave phenomena are often characterized by the appearance of "solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that time intervals exist in which these structures are essentially noninteracting, a method for identifying the number of independent features and their respective speeds is proposed and developed. The method is illustrated with a variety of increasingly realistic specific applications, beginning with a simple nonlinear but analytically tractable Gaussian model, continuing with (numerically generated) data describing multisoliton solutions to the Korteweg–de Vries equation, and concluding with (numerical) data from a realistic simulation of nonlinear wave interactions in plasma turbulence. These studies reveal both strengths and limitations of the method in its present incarnation and suggest topics for future investigations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.165813
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  • 4
    Electronic Resource
    Electronic Resource
    Inverse cascade via Burgers equation (2000)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 10 (2000), S. 393-397 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Burgers equation is employed as a pedagogical device for analytically demonstrating the emergence of a form of inverse cascade to the lowest wavenumber in a flow. The transition from highly nonlinear mode–mode coupling to an ordered preference for large scale structure is shown, both analytically (revealing the presence of a global attractor) and via a numerical example. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166506
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  • 5
    Electronic Resource
    Electronic Resource
    Stochastic forcing of magnetized particles: A kinematic mechanism for particle energization (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 915-920 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Charged particles in a uniform magnetized field respond both to Larmor and electric forces. The kinematic behavior for a smoothly varying electric force is simply determined and may generally be described as having gyrational motion superimposed upon a continuously evolving "guiding center'' or drift motion. When the electric force is stochastic (i.e., the time scale over which the electric field changes is much shorter than the gyroperiod) but has stationary statistical properties, the kinematics are a variant of an Ornstein–Uhlenbeck process and the asymptotic behavior of the particle motion and the resulting Fokker–Planck solution can be exactly obtained. The random walk character of the particle trajectories results in drift velocities whose rms value is preserved while the rms gyration speed increases linearly with time, providing a relatively efficient mechanism for introducing thermal energy into an ensemble of particles. The stochastic behavior, therefore, is demonstrably nonadiabatic, and there are no "adiabatic invariants'' describing the kinematics. An illustrative example where the electric force varies according to discontinuous instantaneous jumps with random orientation at random times is considered. This example represents a potential energization mechanism for space and laboratory plasmas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859997
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  • 6
    Electronic Resource
    Electronic Resource
    Lagrangian coordinate transformations in self-similar supernova blast-wave models (1977)
    Springer
    Astrophysics and space science 47 (1977), S. 99-108 
    Details
    ISSN: 1572-946X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Sedov self-similar solution of the fluid equations provides a description of a spherical supernova blast-wave during its adiabatic phase in a stationary (Eulerian) reference frame. We provide an exact transformation to a Lagrangian coordinate system, a non-inertial frame of reference which follows each individual gas particle. The physical properties of the gas in this comoving reference system are evaluated as a function of time. Numerical methods to facilitate Eulerian-Lagrangian and Lagrangian-Eulerian coordinate transformations are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00651361
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  • 7
    Electronic Resource
    Electronic Resource
    Scale invariance in brittle fracture and the dynamics of crack fusion (1990)
    Springer
    International journal of fracture 43 (1990), S. 19-24 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Résumé On pose l'hypothèse que la rupture fragile des solides soumis à des contraintes différentielles est une conséquence de la fusion en série de petites fissures en de grandes. Des méthodes de renormalisation décrivant de manière quantitative la dynamique qui préside à la cascade de fusion conduisant à l'extrême à la rupture, y compris la durée à rupture par rapport à la loi de croissance de la contrainte.
    Notes: Abstract The brittle fracture of solids subject to extreme differential stress is assumed to be a consequence of the sequential fusion of smaller cracks into larger ones. Renormalization methods quantitatively describe the dynamics of the cascade of fusion events that culminates in failure, including the observed time-to-failure versus stress scaling law.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00018124
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  • 8
    Electronic Resource
    Electronic Resource
    Failure of hierarchical distributions of fibre bundles. I (1991)
    Springer
    International journal of fracture 50 (1991), S. 1-14 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We consider by computational and analytic means the failure properties of hierarchically organized bundles of fibres with equal load sharing, a problem that may be treated exactly by renormalization methods. We show, independent of the specific failure properties of an individual fibre, that the threshold for failure of a fibre bundle obeys a universal scaling law with respect to the size of the bundle. Moreover, this scaling law is preserved for any hierarchical organization of fibre bundles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00035165
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  • 9
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    New Method for Rapid Numerical Solution of the One-Dimensional Schrödinger Equation (1972)
    American Physical Society
    Details
    Publication Date: 1972-11-06
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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  • 10
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    An exact renormalization model for earthquakes and material failure statics and dynamics (1994)
    Elsevier
    Details
    Publication Date: 1994-10-01
    Print ISSN: 0167-2789
    Electronic ISSN: 1872-8022
    Topics: Physics
    Published by Elsevier
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