PL EN


Preferences help
enabled [disable] Abstract
Number of results
2014 | 126 | 2 | 474-478
Article title

Recent Progress in Mathematical Diffraction

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the literature for further details.
Keywords
EN
Contributors
author
  • Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK
author
  • Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
References
  • [1] J.M. Cowley, Diffraction Physics, 3rd ed., North-Holland, Amsterdam 1995
  • [A] Hof, Commun. Math. Phys. 169, 25 (1995), doi: 10.1007/BF02101595
  • [3] M. Baake, D. Lenz, A.C.D. van Enter, arXiv:1307.7518, Erg. Th. & Dyn. Syst., in press
  • [4] R.L. Withers, Z. Kristallogr. 220, 1027 (2005), doi: 10.1524/zkri.2005.220.12.1027
  • [5] M. Baake, U. Grimm, Z. Kristallogr. 226, 711 (2011), doi: 10.1524/zkri.2011.1389
  • [6] M. Baake, U. Grimm, Chem. Soc. Rev. 41, 6821 (2012), doi: 10.1039/C2CS35120
  • [7] M. Baake, U. Grimm, Aperiodic Order, Vol. 1, Cambridge University Press, Cambridge 2013
  • [8] S. Kakutani, in: Proc. 6th Berkeley Symp. on Math. Statistics, and Probability, Eds.: L.M. LeCam, J. Neyman, E.L. Scott, Univ. of California Press, Berkeley 1972, p. 319
  • [9] M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, LNM 1294, 2nd ed., Springer, Berlin 2010
  • [10] A.C.D. van Enter, J. Miękisz, J. Stat. Phys. 66, 1147 (1992), doi: 10.1007/BF01055722
  • [11] M. Baake, F. Gähler, U. Grimm, J. Math. Phys. 53, 032701 (2012), doi: 10.1063/1.3688337
  • [12] M. Baake, U. Grimm, J. Phys. A: Math. Theor. 41, 422001 (2008), doi: 10.1088/1751-8113/41/42/422001
  • [13] M. Baake, U. Grimm, J. Nilsson, Acta Phys. Pol. A 126, 431 (2014), doi: http://dx.doi.org/10.12693/APhysPolA.126.431
  • [14] O. Knill, Discrete Contin. Dyn. Syst. 4, 33 (1998), doi: 10.3934/dcds.1998.4.33
  • [15] N.P. Frank, Topol. Appl. 152, 44 (2005), doi: 10.1016/j.topol.2004.08.014
  • [16] M. Baake, U. Grimm, arXiv:1205.1384, Erg. Th. & Dynam. Syst., in press
  • [17] M. Baake, D. Lenz, C. Richard, Lett. Math. Phys. 82, 61 (2007), doi: 10.1007/s11005-007-0186-7
  • [18] M. Baake, U. Grimm, Phys. Rev. B 79, 020203(R) (2009), doi: 10.1103/PhysRevB.79.020203
  • [18a] M. Baake, U. Grimm, erratum Phys. Rev. B 80, 029903(E) (2009), doi: 10.1103/PhysRevB.80.029903
  • [19] C. Godrèche, J.M. Luck, J. Stat. Phys. 55, 1 (1989), doi: 10.1007/BF01042590
  • [20] M. Baake, M. Moll, in: Aperiodic Crystals, Eds. S. Schmidt, R.L. Withers, R. Lifshitz, Springer, Dordrecht 2013, p. 19, arXiv:1210.3462
  • [21] N. Strungaru, Discr. Comput. Geom. 33, 483 (2005), doi: 10.1007/s00454-004-1156-9
  • [22] M. Moll, Acta Phys. Pol. A 126, 535 (2014), doi: http://dx.doi.org/10.12693/APhysPolA.126.535
  • [23] M. Baake, M. Birkner, R.V. Moody, Commun. Math. Phys. 293, 611 (2010), doi: 10.1007/s00220-009-0942-x
  • [24] D. Lenz, R.V. Moody, preprint arXiv:1111.3617, 2011
  • [25] V. Terauds, J. Stat. Phys. 152, 954 (2013), doi: 10.1007/s10955-013-0790-0
  • [26] V. Terauds, M. Baake, in: Aperiodic Crystals, Eds. S. Schmidt, R.L. Withers, R. Lifshitz, Springer, Dordrecht 2013, p. 35, arXiv:1210.3460
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv126n212kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.