Faculty Robert Pego, Professor
Ph.D., University of California, Berkeley
E-mail: rpego AT cmu DOT edu
Office: Wean Hall 6130
Phone: 412-268-2553
Personal web site

Research:

In general terms I work on nonlinear dynamics for infinite-dimensional physical systems. One focus of current work is the emergence of `universal' behavior in models of complex systems, particularly systems that exhibit clustering and coarsening phenomena. In recent work on basic models of coagulation, for example, we make use of remarkable connections between probability and dynamical systems theory to carry out a rather complete dynamic analysis, revealing universal convergence to self-similar form in some regimes, signs of chaos in others.

Other areas of special interest concern nonlinear waves, emphasizing stability issues in dynamics and for computation. Nonlinear waves are important features in numerous physical models of fluids (both classical and quantum), plasmas, and elastic bodies. One aim 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:

• G. Menon and R. L. Pego, The scaling attractor and ultimate dynamics in Smoluchowski's coagulation equations, J. Nonl. Sci. 18 (2008) 143-190.
• J.-G. Liu, J. Liu and R. L. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Comm. Pure Appl. Math. 60 (2007) 1443-1487.
• 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 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.

Recent CNA Publications:

• 13-CNA-002, Limit Theorems for Smoluchowski Dynamics Associated with Critical Continuous-State Branching Processes , Gautam Iyer, Nicholas Leger, Robert L. Pego, (download paper)
• 12-CNA-003, Coercivity and Stability Results for an Extended Navier-Stokes System , Gautam Iyer, Robert L. Pego, Arghir Zarnescu, (download paper)
• 12-CNA-002, Asymptotic stability of solitary waves in the Benney-Luke model of water waves , Tetsu Mizumachi, Robert L. Pego, José Raúl Quintero, (download paper)
• 10-CNA-015, Asymptotic Linear Stability of Solitary Water Waves , Robert L. Pego, Shu-Ming Sun, (download paper)
• 09-CNA-020, On Optimal Estimates for the Laplace-Leray Commutator in Planar Domains with Corners , Elaine Cozzi, Robert L. Pego, (download paper)
• 09-CNA-017, Spectral Stability of Vortices in Two-Dimensional Bose-Einstein Condensates via the Evans Function and Krein Signature , Richard Kollár, Robert L. Pego, (download paper)
• 09-CNA-003, Crossover in coarsening rates for the monopole approximation of the Mullins-Sekerka model with kinetic drag , Shibin Dai, Barbara Niethammer, Robert L. Pego, (download paper)
• 08-CNA-018, Discretization of Magnetohydrodynamics in Bounded Domains , Jian-Guo Liu, Robert L. Pego, (download paper)
• 08-CNA-013, Dynamics and Self-Similarity in Min-Driven Clustering , Govind Menon, Barbara Niethammer, Robert L. Pego, (download paper)
• 07-CNA-008, Asymptotic stability of Toda lattice solitons , Tetsu Mizumachi, Robert L. Pego, (download paper)