Physics

Dense plasmas occur in stars, giant planets and in inertial fusion experiments. Accurate modeling of the electronic structure of these plasmas allows for prediction of material properties that can in turn be used to simulate these astrophysical objects and terrestrial experiments. But modeling them remains a challenge. Here we explore the Korringa-Kohn-Rostoker Green's function (KKR-GF) method for this purpose. We find that it is able to predict equation of state in good agreement with other state of the art methods, where they are accurate and viable. In addition, it is shown that the computational cost does not significantly change with temperature, in contrast with other approaches. Moreover, the method does not use pseudopotentials - core states are calculated self consistently. We conclude that KKR-GF is a very promising method for dense plasma simulation.

Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of the deformation, its application in natural geoscientific applications is not straightforward. This is mainly due to the fact that subsurface formations are heterogeneous and span large length scales with many fractures at different scales. In this work, we propose a novel multiscale formulation for XFEM, based on locally computed basis functions. The local multiscale basis functions capture the heterogeneity and discontinuities introduced by fractures. Local boundary conditions are set to follow a reduced-dimensional system, in order to preserve the accuracy of the basis functions. Using these multiscale bases, a multiscale coarse-scale system is then governed algebraically and solved, in which no enrichment due to the fractures exist. Such formulation allows for significant computational cost reduction, at the same time, it preserves the accuracy of the discrete displacement vector space. The coarse-scale solution is finally interpolated back to the fine scale system, using the same multiscale basis functions. The proposed multiscale XFEM (MS-XFEM) is also integrated within a two-stage algebraic iterative solver, through which error reduction to any desired level can be achieved. Several proof-of-concept numerical tests are presented to assess the performance of the developed method. It is shown that the MS-XFEM is accurate, when compared with the fine-scale reference XFEM solutions. At the same time, it is significantly more efficient than the XFEM on fine-scale resolution. As such, it develops the first scalable XFEM method for large-scale heavily fractured porous media.

We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24000 CPU cores. In this paper, we describe the core functionalities of NECI and recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green's functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs and it is licensed under GPL-3.0.

Carbon nitride two-dimensional (2D) materials are among the most attractive class of nanomaterials, with wide range of application prospects. As a continuous progress, most recently, two novel carbon nitride 2D lattices of C3N5 and C3N4 have been successfully experimentally realized. Motivated by these latest accomplishments and also by taking into account the well-known C3N4 triazine-based graphitic carbon nitride structures, we predicted two novel C3N6 and C3N4 counterparts. We then conducted extensive density functional theory simulations to explore the thermal stability, mechanical, electronic and optical properties of these novel nanoporous carbon-nitride nanosheets. According to our results all studied nanosheets were found to exhibit desirable thermal stability and mechanical properties. Non-equilibrium molecular dynamics simulations on the basis of machine learning interatomic potentials predict ultralow thermal conductivities for these novel nanosheets. Electronic structure analyses confirm direct band gap semiconducting electronic character and optical calculations reveal the ability of these novel 2D systems to adsorb visible range of light. Extensive first-principles based results by this study provide a comprehensive vision on the stability, mechanical, electronic and optical responses of C3N4, C3N5 and C3N6 as novel 2D semiconductors and suggest them as promising candidates for the design of advanced nanoelectronics and energy storage/conversion systems.

Detailed numerical studies of the ablation of a single neon pellet in the plasma disruption mitigation parameter space have been performed. Simulations were carried out using FronTier, a hydrodynamic and low magnetic Reynolds number MHD code with explicit tracking of material interfaces. FronTier's physics models resolve the pellet surface ablation and the formation of a dense, cold cloud of ablated material, the deposition of energy from hot plasma electrons passing through the ablation cloud, expansion of the ablation cloud along magnetic field lines and the radiation losses. A local thermodynamic equilibrium model based on Saha equations has been used to resolve atomic processes in the cloud and Redlich-Kwong corrections to the ideal gas equation of state for cold and dense gases have been used near the pellet surface. The FronTier pellet code is the next generation of the code described in [R. Samulyak, T. Lu, P. Parks, Nuclear Fusion, (47) 2007, 103--118]. It has been validated against the semi-analytic improved Neutral Gas Shielding model in the 1D spherically symmetric approximation. Main results include quantification of the influence of atomic processes and Redlich-Kwong corrections on the pellet ablation in spherically symmetric approximation and verification of analytic scaling laws in a broad range of pellet and plasma parameters. Using axially symmetric MHD simulations, properties of ablation channels and the reduction of pellet ablation rates in magnetic fields of increasing strength have been studied. While the main emphasis has been given to neon pellets for the plasma disruption mitigation, selected results on deuterium fueling pellets have also been presented.

We propose a general framework to extract microscopic interactions from raw configurations with deep neural networks. The approach replaces the modeling Hamiltonian by the neural networks, in which the interaction is encoded. It can be trained with data collected from Ab initio computations or experiments. The well-trained neural networks give an accurate estimation of the possibility distribution of the configurations at fixed external parameters. It can be spontaneously extrapolated to detect the phase structures since classical statistical mechanics as prior knowledge here. We apply the approach to a 2D spin system, training at a fixed temperature, and reproducing the phase structure. Scaling the configuration on lattice exhibits the interaction changes with the degree of freedom, which can be naturally applied to the experimental measurements. Our approach bridges the gap between the real configurations and the microscopic dynamics with an autoregressive neural network.

We show a new family of neural networks based on the Schrödinger equation (SE-NET). In this analogy, the trainable weights of the neural networks correspond to the physical quantities of the Schrödinger equation. These physical quantities can be trained using the complex-valued adjoint method. Since the propagation of the SE-NET can be described by the evolution of physical systems, its outputs can be computed by using a physical solver. As a demonstration, we implemented the SE-NET using the finite difference method. The trained network is transferable to actual optical systems. Based on this concept, we show a numerical demonstration of end-to-end machine learning with an optical frontend. Our results extend the application field of machine learning to hybrid physical-digital optimizations.

In the field of fluid numerical analysis, there has been a long-standing problem: lacking of a rigorous mathematical tool to map from a continuous flow field to discrete vortex particles, hurdling the Lagrangian particles from inheriting the high resolution of a large-scale Eulerian solver. To tackle this challenge, we propose a novel learning-based framework, the Neural Vortex Method (NVM), which builds a neural-network description of the Lagrangian vortex structures and their interaction dynamics to reconstruct the high-resolution Eulerian flow field in a physically-precise manner. The key components of our infrastructure consist of two networks: a vortex representation network to identify the Lagrangian vortices from a grid-based velocity field and a vortex interaction network to learn the underlying governing dynamics of these finite structures. By embedding these two networks with a vorticity-to-velocity Poisson solver and training its parameters using the high-fidelity data obtained from high-resolution direct numerical simulation, we can predict the accurate fluid dynamics on a precision level that was infeasible for all the previous conventional vortex methods (CVMs). To the best of our knowledge, our method is the first approach that can utilize motions of finite particles to learn infinite dimensional dynamic systems. We demonstrate the efficacy of our method in generating highly accurate prediction results, with low computational cost, of the leapfrogging vortex rings system, the turbulence system, and the systems governed by Euler equations with different external forces.

In this paper, mathematical models for cuff-tissue-artery system are developed and simplified into an axisymmetric problem in space. It is nonlinear properties of cuff and artery wall that make it difficult to solve elastic equations directly with the finite element method, hence a new iteration algorithm derived from principle of virtual work is designed to deal with nonlinear boundary conditions. Numerical accuracy is highly significant in numerical simulation, so it is necessary to analyze the influence different finite elements and grid generation on numerical accuracy. By dimensional analysis, it is estimated that numerical errors must be O( 10 −5 )cm or less. To reach desired accuracy, the number of grids using higher order elements becomes one-fourth as large as that using low order elements by convergence rate analysis. Moreover, dealing with displacement problem under specific blood pressure needs much small grid size to make numerical errors sufficiently small, which is not taken seriously in previous papers. However, it only takes a quarter of grids or less for displacement change problem to guarantee numerical accuracy and reduce computing cost.

Most meso-scale simulation methods assume Gaussian distributions of velocity-like quantities. These quantities are not true velocities, however, but rather time-averaged velocities or displacements of particles. We show that there is a large range of coarse-graining scales where the assumption of a Gaussian distribution of these displacements fails, and a more complex distribution is required to adequately express these distribution functions of displacements.