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Award ID contains: 2006172

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  1. (, SIAM Journal on Mathematical Analysis)
    Free, publicly-accessible full text available August 31, 2025
  2. ; (, Physica D: Nonlinear Phenomena)
    We consider a Fermi–Pasta–Ulam–Tsingou lattice with randomly varying coefficients. We discover a relatively simple condition which when placed on the nature of the randomness allows us to prove that small amplitude/long wavelength solutions are almost surely rigorously approximated by solutions of Korteweg–de Vries equations for very long times. The key ideas combine energy estimates with homogenization theory and the technical proof requires a novel application of autoregressive processes. 
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    Free, publicly-accessible full text available July 1, 2025
  3. (, Wave Motion)
    Full Text Available 
  4. ; (, Discrete and Continuous Dynamical Systems - S)
    We consider a linear Fermi-Pasta-Ulam-Tsingou lattice with random spatially varying material coefficients. Using the methods of stochastic homogenization we show that solutions with long wave initial data converge in an appropriate sense to solutions of a wave equation. The convergence is strong and both almost sure and in expectation, but the rate is quite slow. The technique combines energy estimates with powerful classical results about random walks, specifically the law of the iterated logarithm. 
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    Full Text Available 
  5. ; ; (, SIAM Journal on Applied Dynamical Systems)
    Full Text Available 
  6. ; (, Studies in Applied Mathematics)
    null (Ed.)
    Full Text Available 
  7. ; ; (, Zeitschrift für angewandte Mathematik und Physik)
    null (Ed.)
    Full Text Available