 Robert Pego
Professor
Ph.D., University of California, Berkeley
Office: 6130 Wean Hall
Phone: (412) 268-2553
E-mail: rpego AT cmu.edu
Research
Generally speaking, my research aims to develop the mathematics
to solve puzzles in nonlinear dynamics for infinite-dimensional
physical systems. Emphasis is on kinetics of phase transitions, coarsening
and clustering behavior, and nonlinear waves and their stability.
For example, Smoluchowski's 1917 mean-field model of the evolution of
cluster
size distributions spawned a large and diverse scientific literature. In
seeking to understand the seemingly universal trend toward self-similar
form,
remarkable connections between probability theory and dynamical scaling
analysis have turned up.
Nonlinear waves are important dynamical features in numerous physical models
of (classical and quantum) fluids, plasmas, and elastic bodies.
One problem is to understand why solitary waves in many Hamiltonian systems
are stable. A classic example that is still poorly understood is the
solitary
water wave famously followed on horseback by J. Scott Russell in 1834.
Selected Publications
Shibin Dai and R. L. Pego, Universal bounds on coarsening rates for
mean-field models of phase transitions, SIAM J. Math. Anal., to appear.
G. Menon and R. L. Pego, Approach to self-similarity in Smoluchowski's
coagulation equations, Comm. Pure Appl. Math. 57 (9) (2004) 1197--1232.
G. Friesecke and R. L. Pego, Solitary waves on Fermi-Pasta-Ulam lattices
IV: Proof of stability at low energy, Nonlinearity 17 (2004) 229--251.
R. L. Pego and H. Warchall, Spectrally stable encapsulated vortices
for nonlinear Schroedinger equations, J. Nonl. Sci. 12 (2002) 347--394.
R. L. Pego and J. R. Quintero, A host of traveling-wave solutions for a
model of three-dimensional water-wave dynamics, J. Nonl. Sci. 12 (2002)
59--83.
B. Niethammer and R. L. Pego, Non-self-similar behavior in the
LSW theory of Ostwald ripening, J. Stat. Phys. 95 (1999) 867--902.
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