Data Analysis Techniques

Part of the Springer Theses book series (Springer Theses)


In the following sections the concepts and techniques used in the data analysis are illustrated. Section 4.1 shortly explains the calculation of charge and screening parameter by wave spectra analysis. The structural properties of the two-dimensional system, and the methods to obtain them are described in Sect. 4.2 starting with the defect analysis in Sect. 4.2.1. The long range translational and orientational order of the system are described by means of the pair- and bond-correlation functions in Sect. 4.2.2 and 4.2.3. A measure for local order is introduced in Sect. 4.2.4 with the bond order parameter which can be defined at each respective particle position within the lattice. The last Sect. 4.3 concludes this section with the statistical description of the dynamics of a system of particles with regard to distribution functions of displacements and velocities.


Lattice Site Sound Velocity Particle Temperature Pair Correlation Function Interparticle Distance 
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  1. 1.
    F.M. Peeters, X. Wu, Wigner crystal of a screened-Coulomb-interaction colloidal system in two dimensions. Phys. Rev. A 35(7), 3109–3114 (1987)ADSCrossRefGoogle Scholar
  2. 2.
    X. Wang, A. Bhattacharjee, S. Hu, Longitudinal and transverse waves in Yukawa crystals. Phys. Rev. Lett. 86(12), 2569–2572 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    S. Nunomura, J. Goree, S. Hu, X. Wang, A. Bhattacharjee, Dispersion relations of longitudinal and transverse waves in two-dimensional screened Coulomb crystals. Phys. Rev. E 65, 066402–111 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    S. Nunomura, J. Goree, S. Hu, X. Wang, A. Bhattacharjee, K. Avinash, Phonon spectrum in a plasma crystal. Phys. Rev. Lett. 89(3), 035001 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    S.K. Zhdanov, S. Nunomura, D. Samsonov, G.E. Morfill, Polarization of wave modes in a two-dimensional hexagonal lattcie using a complex (dusty) plasma. Phys. Rev. E 68, 035401 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    S. Nunomura, S. Zhdanov, D. Samsonov, G.E. Morfill, Wave spectra in solid and liquid complex (dusty) plasmas. Phys. Rev. Lett. 94, 045001 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    J.R. Shewchuk. Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In: M.C. Lin, D. Manocha (eds.), Applied Computational Geometry: Towards Geometric Engineering, number 1148 in Lecture Notes in Computer Science, pp. 203–222, Berlin, may 1986. First ACM Workshop on Applied Computational Geometry, Springer.Google Scholar
  8. 8.
    J.M. Burgers, Geometrical considerations concerning the structural irregularities to be assumed in a crystal. Proc. Phys. Soc. 52, 23–33 (1940)ADSCrossRefGoogle Scholar
  9. 9.
    C. Kittel, Introduction to solid state physics. (Wiley, Toronto, 1976)Google Scholar
  10. 10.
    D. C. Wallace, Statistical Physics of Crystals and Liquids, Chap. 5. World Scientific Publishing Co. Pte. Ltd Singapore (2002)Google Scholar
  11. 11.
    D.G. Grier, C.A. Murray, The microscopic dynamics of freezing in supercooled colloidal fluids. J. Chem. Phys. 100(12), 9088–9095 (1994)ADSCrossRefGoogle Scholar
  12. 12.
    R.A. Quinn, C. Cui, J. Goree, J.B. Pieper, H. Thomas, G.E. Morfill, Structural analysis of a coulomb lattice in a dusty plasma. Phys. Rev. E 53(3), R2049–R2052 (1996)ADSCrossRefGoogle Scholar
  13. 13.
    B.I. Halperin, D.R. Nelson, Theory of two-dimensional melting. Phys. Rev. Lett. 41, 121 (1978)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. Classical systems. Sov. Phys. JETP 32(3), 493–500 (1971)MathSciNetADSGoogle Scholar
  15. 15.
    V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group II. Quantum systems. Sov. Phys. JETP 34(3), 1144–1156 (1971)Google Scholar
  16. 16.
    C.B. Markwardt, Non-linear Least-squares Fitting in IDL with MPFIT. In: D.A. Bohlender, D. Durand, P. Dowler (eds) Astronomical Society of the Pacific Conference Series, vol 411, pp 251–254 (2009)Google Scholar
  17. 17.
    T.V. William, H.P. William, A.T. Saul, P.F. Brian, Numerical Recipes in C. Cambridge University Press, Online Edition:, 2nd edn. (2002)Google Scholar
  18. 18.
    D.R. Nelson, B.I. Halperin, Dislocation-mediated melting in two dimensions. Phys. Rev. B 19, 2457 (1979)ADSCrossRefGoogle Scholar
  19. 19.
    K.J. Strandburg, J.A. Zollweg, G.V. Chester, Bond-angular order in two-dimensional Lennard-Jones and hard-disksystems. Phys. Rev. B 30(5), 2755–2759 (1984)ADSCrossRefGoogle Scholar
  20. 20.
    R.A. Quinn, J. Goree, Single-particle Langevin model of particle temperature in dusty plasmas. Phys. Rev. E 61(3), 3033–3041 (2000)ADSCrossRefGoogle Scholar
  21. 21.
    P.S. Epstein, On the resistance experienced by spheres in their motion through gases. Phys. Rev. 23(6), 710–733 (1924)ADSCrossRefGoogle Scholar
  22. 22.
    U. Konopka, Wechselwirkungen geladener Staubteilchen in Hochfrequenzplasmen.PhD thesis, Fakultät für Physik und Astronomie der Ruhr-Universität-Bochum (2000)Google Scholar
  23. 23.
    B. Liu, J. Goree, V. Nosenko, L. Boufendi, Radiation pressure and gas drag forces on a melamine-formaldehyde microsphere in a dusty plasma. Phys. Plasma. 10(1), 9–20 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    C.A. Knapek, Experimental investigation of dynamical properties and ergodicity in plasma crystals. Diploma thesis, Technische Universität München (2004)Google Scholar
  25. 25.
    R.A. Quinn, J. Goree, Experimental test of two-dimensional melting through disclination unbinding. Phys. Rev. E 64, 051404 (2001)ADSCrossRefGoogle Scholar
  26. 26.
    V. Nosenko, J. Goree, A. Piel, Laser method of heating monolayer dusty plasmas. Phys. Plasmas. 13, 032106 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    J.B. Pieper, J. Goree, Dispersion of plasma dust accoustic waves in the strong-coupling regime. Phys. Rev. Lett. 77(15), 3137–3140 (1996)ADSCrossRefGoogle Scholar
  28. 28.
    A.G. Zagorodny, P.P.J.M. Schram, S.A. Trigger, Stationary velocity and charge distributions of grains in dusty plasmas. Phys. Rev. Lett. 84(16), 3594–3597 (2000)ADSCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg  2011

Authors and Affiliations

  1. 1.Max Planck Institute for Extraterrestrial PhysicsGarchingGermany

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