Articles by Dionisios Margetis
(PDF files can also be found under my Research Interests link)
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Research leading to some of the publications listed on this page was
supported by the National Science Foundation through grants: DMS1412769 (201518),
DMS1517162 (201518), DMS0847587 (200914)
and DMR0520471 (200709).
A. Preprints/Submitted Articles and Articles in preparation

72. Margetis, D., and S. Sorokanich, ``On family of nonHermitian Hamiltonians for excitation spectrum of Boson gas
at finite temperatures: Periodic case'', nearing completion for
submission to J. Math. Phys.

71. Margetis, D., ``Surface plasmonpolaritons on cylindrical and spherical conducting sheets'', nearing completion
for submission to the Journal of Applied Physics.

70. Johnson, I., C. Ratsch, F. Gibou, and D. Margetis, ``Slope selection in unstable multilayer growth
in 1+1 dimensions: A study of step flow models with downward funneling'', nearing completion for submission to
Physical Review E.

69. Maier, M., M. Mattheakis, E. Kaxiras, M. Luskin, and D. Margetis,
``Homogenization of
plasmonic crystals: Seeking the epsilonnearzero effect'', submitted to the Proceedings of the Royal Soc. A; preprint arXiv:1809.08276v1 [condmat.meshall], [math.NA].

68. Andreeva, V., M. Luskin, and D. Margetis, ``Nonperturbative nonlinear effects in the dispersion relations
for TE and TM plasmons on twodimensional materials'', submitted to Physical Review B; preprint arXiv:1808.01534v1 [condmat.meshall].

67. Schneider, J. P., D. Margetis, F. Gibou, and C. Ratsch, ``An examination of scaling
behavior in unstable epitaxial mound growth via kinetic Monte Carlo simulations'', submitted to Physical Review E.

66. Maier, M., D. Margetis, and A. Mellet, ``Homogenization of timeharmonic Maxwell's equations in nonhomogeneous
plasmonic structures'', submitted to SIAM J. Appl. Math.; preprint arXiv:1805.07671v1 [math.AP].

65. Liu, J.G., J. Lu, D. Margetis, and J. L. Marzuola,
``Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model'', submitted to
Physica D; preprint arXiv:1704.01554v3 [condmat.statmech].
B. Publications & Articles
Accepted for Publication

64. Mistani, P., A. Guittet, D. Bochkov, J. Schneider, D. Margetis, C. Ratsch, and F. Gibou (2018),
``The island dynamics model on parallel quadtree grids'', Journal of Computational Physics, Vol. 361, pp. 150166 (17pp).

63. Maier, M., M. Mattheakis, E. Kaxiras, M. Luskin, and D. Margetis (2018),
``Universal behavior of a dispersive Dirac cone in gradientindex plasmonic metamaterials'',
Physical Review B, Vol. 97, 035307 (7pp).

62. Schneider, J. P., P. N. Patrone, and D. Margetis (2018),
``Steric hindrance of crystal growth: Nonlinear step flow in 1+1 dimensions'',
(SIAM) Multiscale Modeling and Simulation, Vol. 16, pp. 266299 (33pp).

61. Maier, M., D. Margetis, and M. Luskin (2018),
``Generation of surface plasmonpolaritons by edge effects'', Communications in Mathematical Sciences,
Vol. 16, pp. 7795 (19pp).

60. Schneider, J. P., and D. Margetis (2017),
``Signature of microscale kinetics in mesoscale description of epitaxial growth'',
Physical Review E (Rapid Commun.), Vol. 96, 020802(R) (5pp).

59. Margetis, D., M. Maier, and M. Luskin (2017),
``On the WienerHopf method for surface plasmons:
Diffraction from semiinfinite metamaterial sheet'',
Studies in Applied Mathematics, Vol. 139, pp. 599625 (27pp).

58. Maier, M., D. Margetis, and M. Luskin (2017),
``Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation'',
Journal of Computational Physics, Vol. 339, pp. 126145 (20pp).

57. Grillakis, M. G., M. Machedon, and D. Margetis (2017),
``Evolution of the Boson gas at zero temperature: Meanfield limit and secondorder correction'' ,
Quarterly of Applied Mathematics, Vol. 75, pp. 69104 (36pp).

56. Margetis, D., and M. Luskin (2016),
``On solutions of Maxwell's equations with dipole sources over a thin conducting film'',
J. Math. Phys., Vol. 57, 042903 (32pp).

55. Lu, J., J.G. Liu, and D. Margetis (2015),
``Emergence of step flow from an atomistic scheme of epitaxial growth
in 1+1 dimensions'', Phys. Rev. E, Vol. 91, 032403 (8pp).

54. Papac, J., D. Margetis, F. Gibou, and C. Ratsch (2014),
``Island dynamics model for mound formation: Effect of a stepedge barrier'',
Physical Review E, Vol. 90, 022404 (8pp).

53. Schneider, J. P., K. Nakamura, and D. Margetis (2014),
``Role of chemical potential in relaxation of faceted crystal structure'',
Physical Review E, Vol. 89, 062408 (12pp).

52. Erlebacher, J., and D. Margetis (2014),
``Mechanism of hollow nanoparticle formation due to shape fluctuations,''
Physical Review Letters, Vol. 112, 155505 (5pp).

51. Patrone, P. N., T. L. Einstein, and
D. Margetis (2014),
``From atoms to steps: the microscopic origins of crystal evolution'',
Surface Science, Vol. 625, pp. 3743.

50. Patrone, P. N., and D. Margetis (2014),
``Connection of kinetic Monte Carlo model for surfaces to onestep
flow
theory in 1+1 dimensions'',
(SIAM)
Multiscale Modeling Simulation, Vol. 12(1), pp. 364395.

49. Nakamura, K., and D. Margetis (2013),
``Phase field model for reconstructed
stepped surface'',
Physical Review E, Vol. 88(1), art. 014401 (4pp).

48. Nakamura, K., and D. Margetis (2013),
``Discrete and continuum relaxation dynamics of faceted crystal surface in evaporation models'',
(SIAM Journal on) Multiscale Modeling & Simulation, Vol. 11(1), pp. 244281.

47.
Margetis, D., and K. Nakamura (2012),
``Homogenization of composite vicinal surfaces: Evolution laws in
1+1 dimensions'', Physica D, Vol. 241, pp. 11791189.

46. Margetis, D. (2012),
``BoseEinstein condensation beyond mean field:
Manybody bound state of periodic microstructure'',
(SIAM) Multiscale Modeling & Simulation, Vol. 10, pp. 383417;
Erratum (2013), Vol. 11, p. 410.

45.
Patrone, P. N., R. E. Caflisch, and D. Margetis (2012),
``Characterizing equilibrium in epitaxial growth'',
Europhys. Lett., Vol. 97, art. 48012 (5pp).

44.
Patrone, P. N., R. Wang, and D. Margetis (2011),
``Small fluctuations in epitaxial growth via
conservative noise'',
Journal of Physics A: Mathematical & Theoretical, Vol. 44, art. 315002 (22pp).

43. Grillakis, M. G., M. Machedon, and D. Margetis (2011),
``Secondorder corrections to mean field evolution of weakly interacting Bosons. II.''
Advances in Mathematics, Vol. 228, pp. 17881815.

42. Margetis, D., and K. Nakamura (2011),
``From crystal steps to continuum laws: behavior near
large facets in one dimension'', Physica D,
Vol. 240, pp. 11001110.

41. Margetis, D., P. N. Patrone, and T. L. Einstein (2011),
``Stochastic models of epitaxial growth",
2010 Materials Research Society
Fall Meeting Proceedings, Vol. 1318, pp.~UU7.4.1UU7.4.6 (mrsf101318uu0704);
DOI:10.1557/opl.2011.269
(6pp).

40.
Patrone, P., T. L. Einstein, and D. Margetis (2010),
``Onedimensional model of interactingstep fluctuations on vicinal surfaces:
Analytical formulas and kinetic MonteCarlo simulations'',
Physical Review E, Vol. 82, art. 061601, 18pp.

39. Quah, J., L. P. Liang, and D. Margetis (2010),
``Formulas for force dipole
interaction
of surface line
defects in homoepitaxy'',
J. Phys. A: Mathematical and Theoretical, Vol. 43, art. 455001,
20pp.

38. Margetis, D. (2010),
``A stochastic step flow model with growth in 1+1 dimensions'',
Journal of Physics A:
Mathematical & Theoretical, Vol. 43, art. 065003, 22pp.

37. Quah, J., and D. Margetis (2010),
``Electromigration in macroscopic relaxation of stepped surfaces'',
(SIAM) Multiscale Modeling & Simulation, Vol. 8, pp. 667700.

36. Grillakis, M. G., M. Machedon, and D. Margetis (2010),
``Secondorder corrections to mean field evolution of weakly interacting Bosons. I.'',
29pp,
Communications in Mathematical Physics, Vol. 294, pp. 273301;
DOI 10.1007/s002200090933y.

35.
Bonito, A., R. H. Nochetto, J. Quah, and D. Margetis (2009),
``Selforganization of decaying surface corrugations:
A numerical study'',
Physical Review E, Vol. 79, 050601(R), 4pp.

34. Margetis, D. (2009),
``Homogenization of reconstructed crystal surfaces: Fick's law of diffusion'',
Physical Review E, Vol. 79, 052601, 4pp.

33. Margetis, D., and A. E. Tzavaras (2009),
``Kinetic hierarchies and
macroscopic limits
for crystalline
steps in 1+1 dimensions'',
(SIAM) Multiscale Modeling & Simulation, Vol. 7, pp. 14281454.

32. Fok, P.W., R. R. Rosales, and D. Margetis (2008),
``Facet evolution on supported nanostructures: the effect of
finite height'',
Physical Review B, Vol. 78, 235401, 17pp.

31. Quah, J., J. Young, and D. Margetis (2008),
``Macroscopic view of crystalstep
transparency'',
Physical Review E, Vol. 78, 042602, 4pp.

30. Margetis, D. (2008),
``Solvable model for
pair excitation in trapped Boson gas at zero
temperature'',
Journal of Physics A: Mathematical
and Theoretical, Vol. 41, art. 385002, 18pp.;
Corrigendum, J. Phys. A: Math. Theor., Vol. 41, 459801 (1p).

29. Grillakis, M. G., and D. Margetis (2008),
``A priori estimates for
manybody Hamiltonian evolution of
interacting Boson system'',
Journal of Hyperbolic Differential Equations, Vol. 5, pp. 857883.

28. Quah, J., and D. Margetis (2008),
``Anisotropic diffusion in continuum relaxation of stepped crystal surfaces'',
Journal of Physics A: Mathematical & Theoretical, Vol. 41, art. 235004,
18pp.

27. Margetis, D., and R. E. Caflisch (2008),
``Anisotropic step stiffness from a kinetic model of epitaxial growth'',
(SIAM Journal on) Multiscale Modeling & Simulation,
Vol. 7, pp. 242273.

26. Margetis, D., and M. G. Grillakis (2008),
``Impurity and quaternions in nonrelativistic scattering from
a quantum memory'',
Journal of Physics A: Mathematical and
Theoretical, Vol. 41, art. 065307, 15pp.

25. Margetis, D. (2007),
``Unified continuum approach to crystal surface morphological relaxation'',
Physical Review B, Vol. 76, art. 193403, 4pp.

24. Fok, P.W., R. R. Rosales, and D. Margetis (2007),
``Unification of step bunching
phenomena on vicinal surfaces'',
Physical Review B, Vol. 76, art. 033408, 4pp.
Also selected to appear in the Virtual Journal of Nanoscale
Science & Technology, July 23, 2007
(
http://www.vjnano.org/nano/
).

23. Margetis, D., P.W. Fok, M. J. Aziz, and H. A. Stone (2006),
``Continuum theory of nanostructure
decay via a microscale condition'', Physical Review Letters, Vol. 97, art. 096102, 4pp.
Also selected to appear in the Virtual Journal of Nanoscale
Science & Technology, September 11, 2006
(
http://www.vjnano.org/nano/ ).

22. Margetis, D., and J. M. Myers (2006),
``Operationinduced decoherence by nonrelativistic scattering from a quantum memory'',
Journal of Physics A: Mathematical and General,
Vol. 39, pp. 1156711581.

21. Margetis, D., and R. V. Kohn (2006),
``Continuum relaxation of interacting steps on crystal surfaces
in 2+1 dimensions'',
(SIAM Journal on ) Multiscale Modeling & Simulation, Vol. 5, pp. 729758.

20. Margetis, D., and N. Savva (2006),
``Lowfrequency currents induced in adjacent spherical cells'',
Journal of Mathematical Physics, Vol. 47 art. 042902, 18pp.
Also selected to appear in the Virtual Journal of Biological Physics Research, May 1, 2006
( http://www.vjbio.org/bio/ ).

19. Margetis, D., and J. Choi (2006),
``Generalized iteration method for firstkind integral
equations,'' Studies in Applied Mathematics, Vol. 117,
pp. 125.

18. Choi, J., D. Margetis, T. M. Squires, and M. Z. Bazant (2005),
``Steady advectiondiffusion around
finite absorbers in twodimensional potential flows'', Journal of Fluid Mechanics, Vol. 536, pp. 155184.

17. Stone, H. A., M. J. Aziz, and D. Margetis (2005),
``Grooving of a grain boundary by evaporationcondensation
below the roughening transition'', Journal of Applied Physics Vol. 97, art. 113535, 6pp.

16. Stone, H. A., and D. Margetis (2005),
``Continuum descriptions of crystal surface evolution'',
review article in the book series Handbook of Materials Modeling, Vol. I: Methods and Models, pp. 13891401, S. Yip (Editor),
Springer Verlag, Netherlands.

15. Margetis, D., M. J. Aziz, and H. A. Stone (2005),
``Continuum approach to selfsimilarity and
scaling in morphological relaxation of a crystal with a facet'',
Physical Review B, Vol. 71, art. 165432, 22pp.

14. Margetis, D., M. J. Aziz, and H. A. Stone (2004),
``Continuum description of profile scaling in nanostructure decay'', Physical Review B, Rapid Communications,
Vol. 69, art. 041404(R), 4pp.

13. Margetis, D., E. Kaxiras, M. Elstner, Th. Frauenheim, and M. R. Manaa (2002),
``Electronic structure
of solid nitromethane: Effects of high pressure and molecular vacancies'',
Journal of Chemical Physics, Vol. 117 (2), pp. 788799.

12. King, R. W. P., and D. Margetis (2002),
``The lowfrequency electric fields
induced in a spherical cell including its nucleus,'' regular article in the book series
Progress in Electromagnetic Research (PIER),
Vol. 36, pp. 6179, J. A. Kong (Editor), EMW Publishing, Cambridge, MA.

11. Margetis, D. (2002),
``Radiation of horizontal electric dipole on large dielectric sphere,''
J. Math. Phys. Vol. 43 (6), pp. 31623201.

10. Margetis, D., and T. T. Wu (2001),
``Exactly calculable field components of
electric dipoles in planar boundary,'' J. Math. Phys. Vol. 42 (2), pp. 713745.

9. Margetis, D., and G. Fikioris (2000),
``Twodimensional, highly directive
currents on large circular loops,'' J. Math. Phys. Vol. 41 (9), pp. 61306172.

8. Margetis, D. (2000),
``Asymptotic formula for the condensate wave
function of a trapped Bose gas'', Phys. Rev. A Vol. 61, art. 055601,
2pp.

7. Margetis, D. (2000),
``Pulse propagation in sea water: The modulated
pulse,'' regular article in the book series Progress in Electromagnetic Research (PIER), Vol. 26,
pp. 89110, J. A. Kong, Editor, EMW Publishing, Cambridge, MA.

6. Margetis, D. (1999),
``BoseEinstein condensation in an external
potential at zero temperature: Solitarywave theory'', J. Math. Phys. Vol. 40 (11), pp. 55225543.

5. Margetis, D. (1998),
``Electromagnetic fields in air of travelingwave
currents above the earth'', J. Math. Phys. Vol. 39 (11),
pp. 58705893.

4. Margetis, D., G. Fikioris, J. M. Myers, and T. T. Wu (1998),
``Highly
directive current distributions: General theory'', Phys. Rev. E
Vol. 58 (2), pp. 25312547.

3. Kanellopoulos, J. D., and D. Margetis (1997),
``A predictive analysis of
differential attenuation on adjacent satellite
paths including rain height effects'', European Trans. Telecommunications Vol. 8 (2), pp. 141148.

2. Margetis, D., and R. W. P. King (1995),
``Comments on `Propagation of
EM pulses excited by an electric dipole in a conducting medium' '',
IEEE Trans. Antennas Propagat. Vol. 43 (1), pp. 119120.

1. Margetis, D. (1995),
``Pulse propagation in sea water,'' J. Appl.
Phys. Vol. 77 (7), pp. 28842888.