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spatio-temporal dynamics


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1: 31.14 General Fuchsian Equation
The algorithm returns a list of solutions if they exist. For applications of Kovacic’s algorithm in spatio-temporal dynamics see Rod and Sleeman (1995).
2: Bibliography R
  • W. Reinhardt (1982) Complex Coordinates in the Theory of Atomic and Molecular Structure and Dynamics. Annual Review of Physical Chemistry 33, pp. 223–255.
  • D. L. Rod and B. D. Sleeman (1995) Complexity in spatio-temporal dynamics. Proc. Roy. Soc. Edinburgh Sect. A 125 (5), pp. 959–974.
  • 3: 32.16 Physical Applications
    §32.16 Physical Applications
    Integrable Continuous Dynamical Systems
    4: 11.12 Physical Applications
    §11.12 Physical Applications
    More recently Struve functions have appeared in many particle quantum dynamical studies of spin decoherence (Shao and Hänggi (1998)) and nanotubes (Pedersen (2003)). …
    5: 15.18 Physical Applications
    The hypergeometric function has allowed the development of “solvable” models for one-dimensional quantum scattering through and over barriers (Eckart (1930), Bhattacharjie and Sudarshan (1962)), and generalized to include position-dependent effective masses (Dekar et al. (1999)). More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).
    6: 19.35 Other Applications
    §19.35(ii) Physical
    Elliptic integrals appear in lattice models of critical phenomena (Guttmann and Prellberg (1993)); theories of layered materials (Parkinson (1969)); fluid dynamics (Kida (1981)); string theory (Arutyunov and Staudacher (2004)); astrophysics (Dexter and Agol (2009)). …
    7: William P. Reinhardt
    He has recently carried out research on non-linear dynamics of Bose–Einstein condensates that served to motivate his interest in elliptic functions. … This is closely connected with his interests in classical dynamical “chaos,” an area where he coauthored a book, Chaos in atomic physics with Reinhold Blümel. …
    8: Bruce R. Miller
    There, he carried out research in non-linear dynamics and celestial mechanics, developing a specialized computer algebra system for high-order Lie transformations. …
    9: Bonita V. Saunders
    As the principal developer of graphics for the DLMF, she has collaborated with other NIST mathematicians, computer scientists, and student interns to produce informative graphs and dynamic interactive visualizations of elementary and higher mathematical functions over both simply and multiply connected domains. …
    10: 23.21 Physical Applications
    §23.21 Physical Applications
    §23.21(i) Classical Dynamics
    In §22.19(ii) it is noted that Jacobian elliptic functions provide a natural basis of solutions for problems in Newtonian classical dynamics with quartic potentials in canonical form ( 1 x 2 ) ( 1 k 2 x 2 ) . …