Physics

We are interested in solving the Boltzmann equation of chemically reacting rarefied gas flows using the Grad's-14 moment method. We first propose a novel mathematical model that describes the collision dynamics of chemically reacting hard spheres. Using the collision model, we present an algorithm to compute the moments of the Boltzmann collision operator. Our algorithm is general in the sense that it can be used to compute arbitrary order moments of the collision operator and not just the moments included in the Grad's-14 moment system. For a first-order chemical kinetics, we derive reaction rates for a chemical reaction outside of equilibrium thereby, extending the Arrhenius law that is valid only in equilibrium. We show that the derived reaction rates (i) are consistent in the sense that at equilibrium, we recover the Arrhenius law and (ii) have an explicit dependence on the scalar fourteenth moment, highlighting the importance of considering a fourteen moment system rather than a thirteen one. Through numerical experiments we study the relaxation of the Grad's-14 moment system to the equilibrium state.

Group IV and V monolayers are the promising state-of-the-art 2D materials owing to their high carrier mobility, tunable bandgaps, and optical linear dichroism along with outstanding electronic and thermoelectric properties. Furthermore, recent studies reveal the stability of free-standing 2D monolayers by hydrogenation. Inspired by this, we systematically predict and investigate the structure and properties of various hydrogen saturated silicon phosphide (H-Si-P) monolayers, based on first-principles calculations. According to the results, H-Si-P monolayers belong to indirect bandgap semiconductors with a highly stable structure. Their bandgaps and band edge positions assessed using accurate hybrid functional are shown to be effectively adjusted by applying a biaxial strain. Furthermore, the absorption spectra of these monolayers, simulated in the context of time-dependent density functional theory, exhibit their excellent potential for solar energy conversion and visible-light-driven photocatalytic water splitting. In this respect, this work provides valuable guidance for finding more 2D semiconductors and nanostructures for nanoelectronic and optoelectronic applications, as well as for photocatalytic water splitting.

Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection method, and Markov chain Monte Carlo to sample a probability distribution function, and methods for variance reduction to evaluate numerical integrals using the Monte Carlo simulation. We will also briefly introduce the quasi-Monte Carlo sampling at the end of this lecture.

Here we present the derivation, description and results of a Monte Carlo-based algorithm for simulating inelastic scattering of photo-electrons when passing through some scattering medium, such as a gas atmosphere or a solid material. The code used to run these simulations was written in python and is freely available online (this https URL).

In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced for the surrogate modeling of high-fidelity turbulent flow fields given the solution of a computationally inexpensive but inaccurate low-fidelity solver. The resulting surrogate is able to generate physically accurate turbulent realizations at a computational cost magnitudes lower than that of a high-fidelity simulation. The deep generative model developed is a conditional invertible neural network, built with normalizing flows, with recurrent LSTM connections that allow for stable training of transient systems with high predictive accuracy. The model is trained with a variational loss that combines both data-driven and physics-constrained learning. This deep generative model is applied to non-trivial high Reynolds number flows governed by the Navier-Stokes equations including turbulent flow over a backwards facing step at different Reynolds numbers and turbulent wake behind an array of bluff bodies. For both of these examples, the model is able to generate unique yet physically accurate turbulent fluid flows conditioned on an inexpensive low-fidelity solution.

We present a multi-level delumping method suitable for thermal enhanced oil recovery processes, for which hydrocarbon components are vaporized under high temperatures, move downstream in the gas phase and condense back to the liquid phase. To reduce the computational cost, it is standard practice to reduce the number of (pseudo-)components used in thermal reservoir simulation. Depending on the number and type of hydrocarbon pseudo-components retained in the simulations, we may not be able to capture the correct displacement due to large errors in the lumped phase behavior (flash) computations. We address that problem through a multi-level method: we use data obtained from a short simulation using the most detailed fluid description available, and leverage that information to guide a delumping process. We use temperature as a proxy variable for composition, and select reference temperatures. We extract the corresponding reference compositions from the detailed run and use them to extend the lumped pseudo-components to an approximate detailed composition. We test our method using six heavy oil samples, and under two different recovery processes: hot nitrogen injection and in-situ combustion (air injection and exothermic oxidation reactions). The average error on the liquid mole fraction is reduced by 4-12 times (depending on the oil samples) compared to the flash using pseudo-components, and the maximum error by 6-48 times. We illustrate that the method is amenable to manually adding more information about the physics of some oil samples. We also discuss how to efficiently pick the reference temperatures. For uniformly sampled temperatures (between a minimum and maximum temperature), we conduct a sensitivity study which led us to use six temperatures. We ran both local (Pattern Search, PS) and global (Particle Swarm Optimization, PSO) gradient-free optimization methods.

This paper represents a model for microstructure formation in metallic foams based on the multi-phase-field (MPF) approach. By the use of a no-coalescence boundary condition within this MPF-framework, it is possible to completely prevent coalescence of bubbles and thus focus on the formation of a closed porous microstructure. A modification of this non-wetting criterion allows for the controlled initiation of coalescence and the evolution of open structures. The method is validated and used to simulate foam structure formation both in two and three dimensions.

In this paper, we propose multi-scale deep neural networks (MscaleDNNs) using the idea of radial scaling in frequency domain and activation functions with compact support. The radial scaling converts the problem of approximation of high frequency contents of PDEs' solutions to a problem of learning about lower frequency functions, and the compact support activation functions facilitate the separation of frequency contents of the target function to be approximated by corresponding DNNs. As a result, the MscaleDNNs achieve fast uniform convergence over multiple scales. The proposed MscaleDNNs are shown to be superior to traditional fully connected DNNs and be an effective mesh-less numerical method for Poisson-Boltzmann equations with ample frequency contents over complex and singular domains.

Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of machine-learning schemes that predict quantum mechanical observables -- such as the cohesive energy, the electron density, or a variety of response properties -- as a sum of atom-centred contributions, based on a short-range representation of atomic environments. One of the main shortcomings of these approaches is their inability to capture physical effects, ranging from electrostatic interactions to quantum delocalization, which have a long-range nature. Here we show how to build a multi-scale scheme that combines in the same framework local and non-local information, overcoming such limitations. We show that the simplest version of such features can be put in formal correspondence with a multipole expansion of permanent electrostatics. The data-driven nature of the model construction, however, makes this simple form suitable to tackle also different types of delocalized and collective effects. We present several examples that range from molecular physics, to surface science and biophysics, demonstrating the ability of this multi-scale approach to model interactions driven by electrostatics, polarization and dispersion, as well as the cooperative behavior of dielectric response functions.

Drops on a free-flow/porous-medium-flow interface have a strong influence on the exchange of mass, momentum and energy between the two macroscopic flow regimes. Modeling droplet-related pore-scale processes in a macro-scale context is challenging due to the scale gap, but might be rewarding due to relatively low computational costs. We develop a three-domain approach to model drop formation, growth, detachment and film flow in a lower-dimensional interface domain. A simple upscaling technique allows to compute the drop-covered interface area fraction which affects the coupling fluxes. In a first scenario, only drop formation, growth and detachment are taken into account. Then, spreading and merging due to lateral fluxes are considered as well. The simulation results show that the impact of these droplet-related processes can be captured. However, extensions are necessary to represent the influence on the free flow more precisely.