Using Random Walks to Establish Wavelike Behavior in an FPUT System with Random Coefficients

2021/04/01 by Joshua A. McGinnis, James Wright, McGinnis, Joshua A. +1
Computer Science · Mathematics · Physics and Astronomy · #37L55 #37L60 #74J35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2104.00463

openalex publication_date 2021/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Construction of higher order symplectic integrators

Related

• Approximation of (some) FPUT lattices by KdV Equations
• Macroscopic Wave Propagation for 2D Lattice with Random Masses
• Radiating Solitary Waves in an FPUT Lattice with Random Coefficients
• Tail estimates for homogenization theorems in random media
• Coherent structures in long range FPUT lattices, Part I: Solitary Waves