Particle systems

FALL 2014

Department of Mathematics
Institute for Physical Science and Technology (IPST)
and Center for Scientific Computation and Mathematical Modeling (CSCAMM)
University of Maryland, College Park

LECTURES: Mondays 3-4pm (time of Applied PDE RIT) or Thursdays 3:30-4:30pm (time of PDE seminar);
please see schedule at this site on a week-by-week basis

Room: MATH 1311 (Mon) or 3206 (Thu)

Manoussos Grillakis (,
Pierre-Emmanuel Jabin (,
Matei Machedon (,
Dio Margetis (

Scope & Research Focus:

Particle systems have been the subject of studies in various areas of science, including physics, chemistry, social sciences, economics, and mathematics.
One of the main goals in these studies is to extract relatively simple macroscopic laws from the underlying microscopic dynamics of particles, e.g., their interactions.
Such macroscopic laws can give rise to interesting patterns that can be used to understand and predict and even design the system behavior at large scales.

An element that makes this direction of research especially interesting today is the advancement of experimental techniques
that can probe the particle motion at small scales. At the same time, efforts to link the microscopic and macroscopic scales
have led to challenging questions in mathematical analysis.

Despite this rapid experimental progress, our understanding of basic linkages between the two scales (micro- and macro-) remains incomplete.
A crucial question concerns the improvement of modeling, analysis and simulation in order to describe far-from-equilibrium
phenomena related to particle evolution. A key concept underlying many developments is that of the mean field.

This RIT focuses on recent progress and emerging problems in the modeling, analysis, and numerics
of particle systems across lengths and time scales. This includes classical Hamiltonian systems, quantum systems with
Bosons or Fermions, and stochastic systems such as Hamiltonian-based mean field games.

CREDIT: Students can take 1-3 units of credit by attending this RIT, and
studying and presenting a paper on an acceptable topic agreed on with one of the organizers,
or discussing original research.
For details, contact one of the Organizers (above).

Schedule for Fall 2014:
(upcoming talk titles will be posted on a week-by-week basis)

  • Mon. September 8,
    Rm. Math 1311; 3-4pm
    Organizational meeting -- Introduction of topics
    by the organizers

  • Mon. September 15,
    Rm. Math 1311; 3-4pm
    The Boson System: An introduction. I.
    by Dio Margetis (Math., UMD)

  • Mon. September 22,
    Rm. Math 1311; 3-4pm
    The Boson System: An introduction. II.
    by Dio Margetis (Math., UMD)

  • Mon. October 6,
    Rm. Math 1311; 3-4pm
    Hydrodynamic Limits for Hamiltonian Systems
    by Sam Punshon-Smith (Math., UMD)

  • Mon. November 3,
    Rm. Math 1311; 3-4pm
    On the BCS Theory of Superconductivity
    by Manoussos Grillakis (Math., UMD)

  • Mon. November 24,
    Rm. Math 1311; 3-4pm
    Mean Field Limit of Stochastic Particles
    Zhenfu Wang (Math., UMD)

  • Thursday Dec. 11,
    Rm. Math 3206; 3:30-4:30pm
    Local Molecular Field Theory (tentative)
    by John Weeks (Chemistry & Biochemistry, UMD)