LOGIN TO YOUR ACCOUNT

Username
Password
Remember Me
Or use your Academic/Social account:

CREATE AN ACCOUNT

Or use your Academic/Social account:

Congratulations!

You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.

Important!

Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message

CREATE AN ACCOUNT

Name:
Username:
Password:
Verify Password:
E-mail:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Publisher: Springer
Languages: English
Types: Article
Subjects: QA
We present sharp convergence results for the Cauchy-Born approximation of general classical atomistic interactions, for static problems with small data and for dynamic problems on a macroscopic time interval.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] N. C. Admal and E. B. Tadmor. A uni ed interpretation of stress in molecular systems. J. Elasticity, 100(1-2):63{143, 2010.
    • [2] A. P. Bartok, M. C. Payne, R. Kondor, and G. Csanyi. Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett., 104:136403, 2010.
    • [3] X. Blanc, C. Le Bris, and P.-L. Lions. From molecular models to continuum mechanics. Arch. Ration. Mech. Anal., 164(4):341{381, 2002.
    • [4] X. Blanc, C. Le Bris, and P.L. Lions. From the newton equation to the wave equation in some simple cases. Netw. Heterog. Media, 7(1):1{41, 2012.
    • [5] P. G. Ciarlet. The nite element method for elliptic problems, volume 40 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002. Reprint of the 1978 original.
    • [6] S. Conti, G. Dolzmann, B. Kirchheim, and S. Muller. Su cient conditions for the validity of the Cauchy{ Born rule close to so(n). j. Eur. Math. Soc, 8:515{530, 2006.
    • [7] M. S. Daw and M. I. Baskes. Embedded-Atom Method: Derivation and Application to Impurities, Surfaces, and other Defects in Metals. Physical Review B, 20, 1984.
    • [8] J. Deny and J.-L. Lions. Les espaces du type de Beppo Levi. Annales de l'institut Fourier, 5:305{370, 1954.
    • [9] W. E and P. Ming. Cauchy-Born rule and the stability of crystalline solids: dynamic problems. Acta Math. Appl. Sin. Engl. Ser., 23(4):529{550, 2007.
    • [10] W. E and P. Ming. Cauchy-Born rule and the stability of crystalline solids: static problems. Arch. Ration. Mech. Anal., 183(2):241{297, 2007.
    • [11] G. Friesecke and F. Theil. Validity and failure of the the Cauchy{Born hypothesis in a two-dimensional mass-spring lattice. J. Nonlin. Sci., 12:445{478, 2002.
    • [12] R.J. Hardy. Formulas for determining local properties in molecular dynamics simulations: Shock waves. J. Chem. Phys., 76(622):622{628, 1982.
    • [13] L. Harris, J. Lukkarinen, S. Teufel, and F. Theil. Energy transport by acoustic modes of harmonic lattices. SIAM J. Anal., 40:1392{1418, 2008.
    • [14] K. Hollig. Finite Element Methdos with B-Splines. SIAM, 2003.
    • [15] T. Hudson and C. Ortner. On the stability of Bravais lattices and their Cauchy{Born approximations. ESAIM:M2AN, 46:81{110, 2012.
    • [16] T. J. R. Hughes, T. Kato, and J. E. Marsden. Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity. Arch. Rational Mech. Anal., 63(3):273{294 (1977), 1976.
    • [17] J. E. Jones. On the Determination of Molecular Fields. III. From Crystal Measurements and Kinetic Theory Data. Proc. Roy. Soc. London A., 106:709{718, 1924.
    • [18] J. Lukkarinen and H. Spohn. Kinetic limit for wave propagation in a random medium. Arch. Rat. Mech. Anal., 2007:93{162, 2008.
    • [19] J. Lukkarinen and H. Spohn. Weakly nonlinear Schrodinger zxcZc equation with random initial data. Invent. Math., 183:79{188, 2011.
    • [20] M. Luskin and C. Ortner. Atomistic-to-continuum coupling. to appear in Acta Numerica.
    • [21] C. Makridakis and E. Suli. Finite element analysis of Cauchy{Born approximations to atomistic models. preprint.
    • [22] C. G. Makridakis. Finite element approximations of nonlinear elastic waves. Math. Comp., 61(204):569{594, 1993.
    • [23] P. M. Morse. Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels. Phys.Rev., 34:57{64, 1929.
    • [24] C. Ortner. A posteriori existence in numerical computations. SIAM Journal on Numerical Analysis, 47(4):2550{2577, 2009.
    • [25] C. Ortner and A. Shapeev. Interpolation of lattice functions and applications to atomistic/continuum multiscale methods. manuscript.
    • [26] C. Ortner and A. V. Shapeev. Analysis of an energy-based atomistic/continuum coupling approximation of a vacancy in the 2d triangular lattice. to appear in Math. Comp.
    • [27] C. Ortner and E. Suli. A note on linear elliptic systems on Rd. arXiv:1202.3970.
    • [28] C. Ortner and B. Van Koten. Consistency of blended atomistic/continuum models for simple and multilattices. manuscript.
    • [29] C. Ortner and L. Zhang. A general consistency result for atomistic-to-continuum coupling methods. manuscript.
    • [30] M. Reed and B. Simon. Methods of Modern Mathematical Physics. I: Functional Analysis. Academic Press, 1980. Revised and Enlarged Edition.
    • [31] A. Shapeev. Personal communication.
    • [32] D. Wallace. Thermodynamics of Crystals. Dover Publications, New York, 1998.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article