Mitchell Luskin's Papers Available for Downloading

The complete list of Mitchell Luskin's papers can be found here.

BibTeX entries can be found here.

Please note that the versions below are preprints and that final versions can be found in the journal publications.

A more complete source of recent papers can be found at arxiv.org.

  1. Mitchell Luskin, On the computation of crystalline microstructure, Acta Numerica, 5:191-258, 1996.
  2. Mitchell Luskin, Approximation of a laminated microstructure for a rotationally invariant, double well energy density, Numer. Math., 75:205-221, 1997.
  3. Bo Li and Mitchell Luskin, Nonconforming finite element approximation of crystalline microstructure, Math. Comp., 67:917-946, 1998.
  4. Bo Li and Mitchell Luskin, Finite element analysis of microstructure for the cubic to tetragonal transformation, SIAM J. Numer. Anal., 35:376-392, 1998.
  5. Mitchell Luskin, The stability and numerical analysis of martensitic microstructure, in ENUMATH 97, H. Bock, F. Brezzi, R. Glowinski, G. Kanschat, Y. Kuznetsov, J. Periaux and R. Rannacher, editors, 1998, 54-69.
  6. Bo Li and Mitchell Luskin, Approximation of a laminate with varying volume fractions, Mathematical Modelling and Numerical Analysis, 33:67-87, 1999.
  7. Bo Li and Mitchell Luskin, Theory and computation for the microstructure near the interface between twinned layers and a pure variant of martensite, Materials Science & Engineering A, 273:237-240, 1999.
  8. Kaushik Bhattacharya and Bo Li and Mitchell Luskin, The simply laminated microstructure in martensitic crystals that undergo a cubic to orthorhombic phase transformation, Archive for Rational Mechanics and Analysis, 149:123-154, 1999.
  9. Pavel Belik and Mitchell Luskin, Stability of microstructure for tetragonal to monoclinic martensitic transformations, Mathematical Modelling and Numerical Analysis, 34:663-685, 2000.
  10. Mitchell Luskin, On the stability of microstructure for general martensitic transformations, in Lectures on Applied Mathematics, H.-J. Bungartz and R. W. Hoppe and C. Zenger, editors, Springer-Verlag, 2000, 31-44.
  11. Pavel Belik, Tim Brule, and Mitchell Luskin, On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films, Mathematical Modelling and Numerical Analysis, 35:525-548, 2001.
  12. Yalchin Efendiev and Mitchell Luskin, Stability of microstructures for some martensitic transformations, Mathematical and Computer Modelling, 34:1289-1305, 2000.
  13. Pavel Belik and Mitchell Luskin, A total-variation surface energy model for thin films of martensitic crystals, Interfaces and Free Boundaries, 4:71-88, 2002.
  14. Pavel Belik and Mitchell Luskin, A computational model for the indentation and phase transformation of a martensitic thin film, Journal of the Mechanics and Physics of Solids, 50:1789-1815, 2002.
  15. Mitchell Luskin, Computational modeling of microstructure, Proceedings of the International Congress of Mathematicians, ICM 2002, Beijing, 2002, volume=III, 707-716.
  16. Martin Kruzik and Mitchell Luskin, The computation of martensitic microstructure with piecewise laminates, Journal of Scientific Computing, 19:293-308, 2003.
  17. Pavel Belik and Mitchell Luskin, Approximation by piecewise constant functions in a BV metric, Mathematical Models & Methods in Applied Sciences, 13:373-393, 2003.
  18. Pavel Belik and Mitchell Luskin, A computational model for martensitic thin films with compositional fluctuation, Mathematical Models & Methods in Applied Sciences, 14:1585-1598, 2004.
  19. Pavel Belik and Mitchell Luskin, Computational modeling of softening in a structural phase transformation, Multiscale Modeling & Simulation, 3:764-781, 2005.
  20. Piotr Rybka and Mitchell Luskin, Existence of energy minimizers for magnetostrictive materials, SIAM J. Math. Anal., 36:2004-2019, 2005.
  21. Pavel Belik and Mitchell Luskin, The Gamma-convergence of a sharp interface thin film model with non-convex elastic energy, SIAM J. Math. Anal., 38: 414-433, 2006.
  22. Julia Liakhova, Mitchell Luskin, and Tianyu Zhang, Computational Modeling of Ferromagnetic Shape Memory Thin Films, Ferroelectrics, 342:73-82, 2006.
  23. Pavel Belik and Mitchell Luskin, A Finite Element Model for Martensitic Thin Films, Calcolo, 43: 197-215, 2006.
  24. Mitchell Luskin and Tianyu Zhang, Numerical Analysis of a Model for Ferromagnetic Shape Memory Thin Films, Computer Methods in Applied Mechanics and Engineering, 196: 3759-3770, 2007.
  25. Frederic Legoll, Mitchell Luskin, and Richard Moeckel, Non-ergodicity of the Nose-Hoover thermostatted harmonic oscillator, Archive for Rational Mechanics and Analysis, 184: 449-463, 2007.
  26. Marcel Arndt and Mitchell Luskin, Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation, International Journal for Multiscale Computational Engineering, 5: 407-415, 2007.
  27. Matthew Dobson, Ryan Elliott, Mitchell Luskin, and Ellad Tadmor. A Multilattice Quasicontinuum for Phase Transforming Materials: Cascading Cauchy Born Kinematics, Journal of Computer-Aided Materials Design, 14:219-237, 2007.
  28. Matthew Dobson and Mitchell Luskin, Analysis of a Force-Based Quasicontinuum Approximation, Mathematical Modeling and Numerical Analysis, 42: 113-139, 2008.
  29. Marcel Arndt and Mitchell Luskin, Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel-Kontorova Model, Multiscale Modeling and Simulation, 7:147-170, 2008.
  30. Marcel Arndt and Mitchell Luskin, Goal-oriented Adaptive Mesh Refinement for the Quasicontinuum Approximation of a Frenkel-Kontorova model, Computer Methods in Applied Mechanics and Engineering, 197:4298-4306, 2008.
  31. Matthew Dobson and Mitchell Luskin, Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation, Journal of Scientific Computing, 37:19-41, 2008.
  32. Matthew Dobson and Mitchell Luskin, An Analysis of the Effect Of Ghost Force Oscillation on Quasicontinuum Error, Mathematical Modelling and Numerical Analysis, 43:591-604, 2009.
  33. Frederic Legoll, Mitchell Luskin, and Richard Moeckel, Non-ergodicity of Nose-Hoover Dynamics, Nonlinearity, 22:1673-1694, 2009.
  34. Matthew Dobson and Mitchell Luskin, An optimal order error analysis of the one-dimensional quasicontinuum approximation, SIAM. J. Numer. Anal., 47:2455-2475, 2009.
  35. Mitchell Luskin and Christoph Ortner, An Analysis of Node-based Cluster Summation Rules in the Quasicontinuum method, SIAM. J. Numer. Anal., 47:3070-3086, 2009.
  36. Matthew Dobson and Mitchell Luskin and Christoph Ortner, Stability, Instability, and Error of the Force-based Quasicontinuum Approximation, Archive for Rational Mechanics and Analysis, 197:179-202, 2010. arXiv:0903.0610
  37. Matthew Dobson and Mitchell Luskin and Christoph Ortner, Sharp Stability Estimates for Force-based Quasicontinuum Methods, SIAM J. Multiscale Modeling & Simulation, 8:782-802, 2010. arXiv:0907.3861
  38. Matthew Dobson and Mitchell Luskin and Christoph Ortner, Accuracy of Quasicontinuum Approximations Near Instabilities, J. Mech. Phys. Solids, 58:1741–1757, 2010. arXiv:0905.2914v3
  39. Matthew Dobson , Mitchell Luskin and Christoph Ortner, Iterative Methods for the Force-based Quasicontinuum Approximation, Computer Methods in Applied Mechanics and Engineering, 200:2697–2709, 2011.arXiv:0910.2013v3
  40. Xingjie Helen Li and Mitchell Luskin, An Analysis of the Quasi-Nonlocal Quasicontinuum Approximation of the Embedded Atom Model, International Journal for Multiscale Computational Engineering, to appear. arXiv:1008.3628v4
  41. Xingjie Helen Li and Mitchell Luskin, A Generalized Quasi-Nonlocal Atomistic-to-Continuum Coupling Method with Finite Range Interaction, IMA Journal of Numerical Analysis, to appear. arXiv:1008.2336v2
  42. Mitchell Luskin and Christoph Ortner, Linear stationary iterative methods for the force-based quasicontinuum approximation, In Bjorn Engquist, Olof Runborg, and Richard Tsai, editors, Numerical Analysis and Multiscale Computations, volume 82 of Lect. Notes Comput. Sci. Eng. Springer Verlag, to appear. arXiv:1104.1774
  43. Pavel Belik and Mitchell Luskin, Sharp Stability and Optimal Order Error Analysis of the Quasi-nonlocal Approximation of Unconstrained Linear and Circular Chains in 2-D. arXiv:1008.3716
  44. Brian Van Koten and Mitchell Luskin, Development and Analysis of Blended Quasicontinuum Approximations. arXiv:1008.2138
  45. Brian Van Koten, Xingjie Helen Li, Mitchell Luskin, and Christoph Ortner, A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods. In Ivan Graham, Tom Hou, Omar Lakkis, and Rob Scheichl, editors, Numerical Analysis of Multiscale Problems. Springer, to appear. arXiv:1012.6031

    A more complete source for recent papers can be found at arxiv.org.