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Issue No.01 - Jan.-Feb. (2012 vol.14)
pp: 33-39
Woosong Choi , Cornell University
Yong S. Chen , Cornell University
Stefanos Papanikolaou , Cornell University
James P. Sethna , Cornell University
<p>Intriguing analogies were found between a model of plastic deformation in crystals and turbulence in fluids. A study of this model provides remarkable explanations of known experiments and predicts fractal dislocation pattern formation. Further, the challenges encountered resemble those in turbulence, which is exemplified in a comparison with the Rayleigh-Taylor instability.</p>
Dislocation dynamics, turbulence, numerical convergence, fractal, shocks
Woosong Choi, Yong S. Chen, Stefanos Papanikolaou, James P. Sethna, "Is Dislocation Flow Turbulent in Deformed Crystals?", Computing in Science & Engineering, vol.14, no. 1, pp. 33-39, Jan.-Feb. 2012, doi:10.1109/MCSE.2011.94
1. T. Mura, Micromechanics of Defects in Solids, 2nd ed., Springer, 1987.
2. P. Hähner, K. Bay, and M. Zaiser, "Fractal Dislocation Patterning during Plastic Deformation," Physical Rev. Letters, vol. 81, no. 12, 1998, pp. 2470–2473.
3. Y.S. Chen et al., "Bending Crystals: Emergence of Fractal Dislocation Structures," Physical Rev. Letters, vol. 105, no. 10, 2010; doi:10.1103/PhysRevLett.105.105501.
4. A. Acharya, "A Model of Crystal Plasticity Based on the Theory of Continuously Distributed Dislocations," J. Mechanics and Physics of Solids, vol. 4, no. 49, 2001, pp. 761–784.
5. S. Limkumnerd and J.P. Sethna, "Mesoscale Theory of Grains and Cells: Crystal Plasticity and Coarsening," Physical Rev. Letters, vol. 96, no. 9, 2006; doi:10.1103/PhysRevLett.96.095503.
6. A. Kurganov, S. Noelle, and G. Petrova, "Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton–Jacobi Equations," SIAM J. Scientific Computing, vol. 23, no. 3, 2002, pp. 707–740.
7. A. Mignone et al., "Pluto: A Numerical Code for Computational Astrophysics," Astrophysical J. Supplement Series, vol. 170, no. 1, 2007, doi:10.1086/513316.
8. D.C. Tan et al., "Delta-Shock Waves as Limits of Vanishing Viscosity for Hyperbolic Systems of Conservation Laws," J. Differential Equations, vol. 112, no. 1, 1994, pp. 1–32.
9. J. Shi, Y.-T. Zhang, and C.-W. Shu, "Resolution of High Order WENO Schemes for Complicated Flow Structures," J. Computational Physics, vol. 186, no. 2, 2003, pp. 690–696.
10. U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov, Cambridge Univ. Press, 1995.
11. S. Limkumnerd and J.P. Sethna, "Mesoscale Theory of Grains and Cells: Polycrystals & Plasticity," J. Mechanics and Physics of Solids, vol. 56, no. 4, 2008, pp. 1450–1459.
12. C. Bardos and D. Lannes, "Turning Waves and Breakdown for Incompressible Flows," Proc. Nat'l Academy Sciences, vol. 108, no. 12, 2011, pp. 4754–4759.
13. A. Pumir and E.D. Siggia, "Finite Time Singularities in the Axisymmetric Three-Dimensional Euler Equation," Physical Rev. Letters, vol. 68, no. 10, 1992, pp. 1511–1513.
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