photo Dionisios Margetis

Associate Professor

Department of Mathematics &

Institute for Physical Science and Technology &
Center for Scientific Computation and Mathematical Modeling &
Materials Research Science and Eng. Center &
Maryland NanoCenter

University of Maryland
College Park, Maryland 20742, USA

Office: 4416 Mathematics Bldg. (Bldg. No: 084)
Phone : (++1-)301-405-5455
FAX : (++1-)301-314-0827
E- address : dio (followed by @math.umd.edu)

Education

BS: Electrical Eng. (5-year program), National Technical University of Athens, 1992
SM: Applied Physics, Harvard University, 1994
PhD: Applied Physics, Harvard University, 1999

Research

Materials Modeling; Mathematical Physics
Applied Analysis: Asymptotics; PDEs; Integral Equations; Stochastic Differential Equations
Applications: Materials Science; Statistical Mechanics; Many-Body Quantum Mechanics; Quantum Information; Electromagnetics

Professor Margetis's research lies broadly in materials modeling and analysis, at the interface of applied mathematics and physics.
His research is motivated by physical experiments and primarily explores the connection of
continuum laws (e.g. PDEs) to discrete or microscopic models in classical and quantum mechanics.
Of particular interest are microscale effects that leave their signatures even at large scales.

Topics of current, active interest (with links to publications):

  • Aspects of epitaxial growth and relaxation:
    Morphological evolution of crystal surfaces below the roughening temperature;
    free-boundary problems with microscale effects

  • Bose-Einstein condensation of atomic gases:
    Nonlocal macroscopic laws beyond the nonlinear Schrödinger (``Gross-Pitaevskii'') equation;
    effects of atomic pair excitations

  • Decoherence in quantum computing via scattering theory

  • Aspects of mathematical biology (in progress):
    Interplay of geometry and chemical signaling in dynamics of biomembranes;
    homogenization of microscopic models for lipid bilayers

  • Electromagnetic wave theory and applications

  • Growth phenomena via a prototypical advection-diffusion problem;
    analysis of a class of first-kind Fredholm integral equations.

  • Atomistic study of behavior of materials under extreme pressure

    Group

    Graduate students:
  • University of Maryland, College Park:

    -- Ms. Rongrong Wang, Appl. Math. & Sci. Computation (AMSC) program:
    Rigorous notions of noise for non-Hamiltonian particle schemes.

    -- Mr. Paul Patrone, Physics Dept:
    Aspects of epitaxial fluctuations: Mean field theory and beyond.
    Co-advised by Prof. T. L. Einstein (Physics, UMD).

    --Mr. John Quah, Appl. Math. & Sci. Computation (AMSC) program:
    PhD earned in 08/2009; thesis in PDF:
    Modeling, applied analysis and numerics for 2D crystal surface morphological evolution.

    -- Ms. Amy Finkbiner, AMSC program:
    PhD earned in 12/2007; thesis in PDF:
    Analysis of discrete models for step instabilities (bunching).
    Co-advised (for work on networks) by Prof. J. Yorke (Mathematics, Physics, IPST).

  • M.I.T., Department of Mathematics:

    --Mr. Pak-Wing Fok, Applied Mathematics:
    PhD earned in 06/2006; thesis in PDF:
    Simulations of axisymmetric stepped surfaces with a facet.
    Co-advised by Prof. R. R. Rosales (Appl. Math., MIT).
    Positions: von Karman instructor in Comp. & Appl. Math., CalTech;
    as of Sept. 2009: Assistant Prof., Mathematics, Univ. Delaware.

    Other students, co-advised informally at M.I.T.:
    -- Mr. Nikos Savva (PhD earned in 09/2007 - now postdoc in Imperial College, London)
    --Mr. Jaehyuk Choi (PhD earned in 06/2005 - currently with Goldman Sachs, New York City)

    Undergraduate students:
  • University of Maryland, College Park:

    Mathematics and Materials Research Science & Engineering Center (MRSEC) :
    -- Mr. Li Peng Liang, Montgomery College.
    Project: Modeling and analysis of crystal-step interactions.
    Summer 2009, Research Experience for Undergraduates (REU) program.
    -- Mr. Jerrod Young, Norfolk State University (major: Optical Engineering).
    Project: Modeling and numerics for crystal surfaces under stress.
    Summer 2008, Research Experience for Undergraduates (REU) program.

    Synergistic activities in the University of Maryland, College Park