Daniel Messenger

Daniel Messenger, Daniel Serino, Balu Nadiga et al.

Efficient modeling of the Richtmyer-Meshkov instability (RMI) is essential to many engineering tasks, including high-speed combustion and drive and capsule geometry optimization in Inertial Confinement Fusion (ICF). In the latter, RMI causes the ablator and fuel to mix, introducing cold spots into the fuel and lowering performance; controlling RMI is thus a core ICF design concern. In this work, we introduce a reduced-order model for two-dimensional RMI based on the Latent Space Dynamics Identification (LaSDI) algorithm. We demonstrate the efficacy of the proposed methodology in efficiently parametrizing the solution space over a high-dimensional parameter vector consisting of material EOS parameters and initial conditions known to affect RMI growth rates. Using only late-time partial observations of the dynamics, we use our framework to not only provide a highly efficient dynamic surrogate model, but to reveal that the RMI exhibits the structure of a surprisingly low-dimensional and linear dynamical system, into the nonlinear growth regime, after a suitable nonlinear transformation is applied to the material interface, which we approximate as a trained autoencoder. Our use of practical observables and fundamental parameters suggests that such ROMs may be useful for downstream engineering tasks which confront the RMI, while the low-dimensional representation suggests a new direction for theoretical work.

Reuben R. W. Wang, Daniel Messenger

We study the relaxation of a highly collisional, ultracold but nondegenerate gas of polar molecules. Confined within a harmonic trap, the gas is subject to fluid-gaseous coupled dynamics that lead to a breakdown of first-order hydrodynamics. An attempt to treat these higher-order hydrodynamic effects was previously made with a Gaussian ansatz and coarse-graining model parameter [R. R. W. Wang & J. L. Bohn, Phys. Rev. A 108, 013322 (2023)], leading to an approximate set of equations for a few collective observables accessible to experiments. Here we present substantially improved reduced-order models for these same observables, admissible beyond previous parameter regimes, discovered directly from particle simulations using the WSINDy algorithm (Weak-form Sparse Identification of Nonlinear Dynamics). The interpretable nature of the learning algorithm enables estimation of previously unknown physical quantities and discovery of model terms with candidate physical mechanisms, revealing new physics in mixed collisional regimes. Our approach constitutes a general framework for data-driven model identification leveraging known physics.

Razvan C. Fetecau, Hui Huang, Daniel Messenger et al.

We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in [44], our approach is different and relies on a coupling method connecting PDEs with their underlying SDEs. Moreover, our result relaxes the regularity assumptions on the interaction and external potentials and improves the convergence rate (in terms of the diffusion coefficient). The particular rate we derive is shown to be consistent with numerical computations.