7 papers
Solving Functional PDEs with Gaussian Processes and Applications to Functional Renormalization Group Equations
Xianjin Yang, Matthieu Darcy, Matthew Hudes +3
We present an operator learning framework for solving non-perturbative functional renormalization group equations, which are integro-differential equations defined on functionals.…
Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data
Lothar Heimbach, Sebastian Kaltenbach, Petr Karnakov +2
Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational…
Clusters and Fluctuations at Mean-Field Critical Points and Spinodals
W. Klein, Harvey Gould, J. Tobochnik +3
We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different than the structure close to non-mean-field critical poin…
Spinodal decomposition in fluids: diffusive, viscous and inertial regimes
Turab Lookman, Yanan Wu, Francis Alexander +1
Using a Langevin description of spinodal decomposition in fluids, we examine domain growth in the diffusive, viscous and inertial regimes. In the framework of this model, numerical…
Statistical Mechanics of Kinks in (1+1)-Dimensions: Numerical Simulations and Double Gaussian Approximation
Francis J. Alexander, Salman Habib, Alex Kovner
We investigate the thermal equilibrium properties of kinks in a classical $\F^4$ field theory in dimensions. From large scale Langevin simulations we identify the temperature…
Hydrodynamic Spinodal Decomposition: Growth Kinetics and Scaling Functions
F. J. Alexander, S. Chen, D. W. Grunau
We examine the effects of hydrodynamics on the late stage kinetics in spinodal decomposition. From computer simulations of a lattice Boltzmann scheme we observe, for critical quenc…