Nicolas G. Hadjiconstantinou

Many physical and biological systems evolve through metastable dynamics characterized by long intervals during which the trajectory remains confined to a small region of the configuration space punctuated by rare but rapid transitions between such regions. Accurately quantifying both the local relaxation and the first-escape behavior from each metastable set is central to many applications including enabling the simulation of long-time dynamics. In this work, we extend well-established data-driven methods for estimating Koopman operators to the setting of quasi-stationary distributions (QSDs) by enforcing absorbing boundary conditions on metastable states. We show that this absorbing Koopman formulation reliably recovers the spectral properties governing relaxation and escape using only short-trajectory data. Finally, we show how these spectral estimates naturally couple with a general parallel-in-time simulation scheme, enabling rigorous and substantial extensions of the time scales accessible to direct simulation of complex metastable systems.

Advances in machine-learned interatomic potentials have enabled the prediction of complex material properties with accuracy approaching that of ab initio methods. However, it is unclear how the finite capacity of such models affects their ability to achieve consistent accuracy across diverse thermodynamic conditions without introducing trade-offs. In this paper, we present two computationally efficient interatomic potentials capable of accurately simulating the behavior of hafnium and hafnium dioxide across a very wide variety of thermodynamic conditions. Our approach combines Latin Hypercube and Monte Carlo Sampling for generating diverse data sets, with an extended formulation of the recently-developed environment-adaptive proper orthogonal descriptors. Molecular dynamics simulations show that the resulting potentials accurately reproduce density functional theory results and experimental data for pressure- and temperature-induced phase transitions as well as other properties associated with the materials’ polymorphs and liquid phases. We further showcase the versatility of the environment-adaptive formulation by using our potential to compute the shock Hugoniot of hafnium up to temperatures and pressures of 1 MK and 1 TPa, respectively; good agreement with available experimental data is observed.

Transition state theory is used to model slip of a simple liquid at a liquid-solid interface. In the linear regime of low shear rate, the model leads to a simple expression for the slip that is in excellent agreement with molecular dynamics simulations for a wide range of system parameters and thermodynamic conditions.

We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted to particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the Wasserstein-Entropy distribution (WE), couples a physically-motivated Wasserstein penalty term to the traditional maximum-entropy distribution (MED) functions, which serves to regularize the latter. The penalty term becomes negligible near the local equilibrium, reducing the proposed model to the MED, known to reproduce the hydrodynamic limit. However, in contrast to the standard MED, the proposed WE closure can cover the entire physically realizable moment space, including the so-called Junk line. We also propose an efficient Monte Carlo algorithm for generating samples of the unknown distribution which is expected to outperform traditional non-linear optimization approaches used to solve the MED problem. Numerical tests demonstrate that, given moments up to the heat flux -- that is equivalent to the information contained in the Chapman-Enskog distribution -- the proposed methodology provides a reliable closure in the collision-dominated and early transition regime. Applications to larger rarefaction demand information from higher-order moments, which can be incorporated within the proposed closure.

We develop a model that describes the permeance of simple fluids as well as small hydrocarbon molecules through nanoporous, atomically thin membranes. The model is in agreement with molecular dynamics simulations for a wide range of pore sizes, including pores approaching the steric exclusion limit, as needed for understanding separation processes using such membranes.

By taking into account the inhomogeneity introduced by the presence of a solid boundary, slip-flow theory extends the range of applicability of the venerable Navier–Stokes description to smaller scales and into the regime where confinement starts to be important. Due to the inherently atomistic nature of solid–fluid interactions at their interface, slip flow can be described, at least in principle, predictively at this level. This review aims to summarize our current understanding of slip flow at the atomistic level in dilute gases and dense liquids. The discussion extends over the similarities and differences between slip in gases and liquids, characterization and measurement of slip by molecular simulation methods, models for predicting slip, and open questions requiring further investigation.

We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted to particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the Wasserstein-Entropy distribution (WE), couples a physically-motivated Wasserstein penalty term to the traditional maximum-entropy distribution (MED) functions, which serves to regularize the latter. The penalty term becomes negligible near the local equilibrium, reducing the proposed model to the MED, known to reproduce the hydrodynamic limit. However, in contrast to the standard MED, the proposed WE closure can cover the entire physically realizable moment space, including the so-called Junk line. We also propose an efficient Monte Carlo algorithm for generating samples of the unknown distribution which is expected to outperform traditional non-linear optimization approaches used to solve the MED problem. Numerical tests demonstrate that, given moments up to the heat flux -- that is equivalent to the information contained in the Chapman-Enskog distribution -- the proposed methodology provides a reliable closure in the collision-dominated and early transition regime. Applications to larger rarefaction demand information from higher-order moments, which can be incorporated within the proposed closure.

We introduce MESSY estimation, a Maximum-Entropy based Stochastic and Symbolic densitY estimation method. The proposed approach recovers probability density functions symbolically from samples using moments of a Gradient flow in which the ansatz serves as the driving force. In particular, we construct a gradient-based drift-diffusion process that connects samples of the unknown distribution function to a guess symbolic expression. We then show that when the guess distribution has the maximum entropy form, the parameters of this distribution can be found efficiently by solving a linear system of equations constructed using the moments of the provided samples. Furthermore, we use Symbolic regression to explore the space of smooth functions and find optimal basis functions for the exponent of the maximum entropy functional leading to good conditioning. The cost of the proposed method for each set of selected basis functions is linear with the number of samples and quadratic with the number of basis functions. However, the underlying acceptance/rejection procedure for finding optimal and well-conditioned bases adds to the computational cost. We validate the proposed MESSY estimation method against other benchmark methods for the case of a bi-modal and a discontinuous density, as well as a density at the limit of physical realizability. We find that the addition of a symbolic search for basis functions improves the accuracy of the estimation at a reasonable additional computational cost. Our results suggest that the proposed method outperforms existing density recovery methods in the limit of a small to moderate number of samples by providing a low-bias and tractable symbolic description of the unknown density at a reasonable computational cost.