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RESEARCH INTERACTION TEAM (RIT):

Particle systems

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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

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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)

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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.
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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).

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**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)