Physics

We present a robust analysis code developed in the Python language and incorporating libraries of the ROOT data analysis framework for the state-of-the-art mass spectrometry method called phase-imaging ion-cyclotron-resonance (PI-ICR). A step-by-step description of the dataset construction and analysis algorithm is given. The code features a new phase-determination approach that offers up to 10 times smaller statistical uncertainties. This improvement in statistical uncertainty is confirmed using extensive Monte-Carlo simulations and allows for very high-precision studies of exotic nuclear masses to test, among others, the standard model of particle physics.

This work deals with a number of questions relative to the discrete and continuous adjoint fields associated with the compressible Euler equations and classical aerodynamic functions. The consistency of the discrete adjoint equations with the corresponding continuous adjoint partial differential equation is one of them. It is has been established or at least discussed only for a handful of numerical schemes and a contribution of this article is to give the adjoint consistency conditions for the 2D Jameson-Schmidt-Turkel scheme in cell-centred finite-volume formulation. The consistency issue is also studied here from a new heuristic point of view by discretizing the continuous adjoint equation for the discrete flow and adjoint fields. Both points of view prove to provide useful information. Besides, it has been often noted that discrete or continuous inviscid lift and drag adjoint exhibit numerical divergence close to the wall and stagnation streamline for a wide range of subsonic and transonic flow conditions. This is analyzed here using the physical source term perturbation method introduced in reference [Giles and Pierce, AIAA Paper 97-1850, 1997]. With this point of view, the fourth physical source term of appears to be the only one responsible for this behavior. It is also demonstrated that the numerical divergence of the adjoint variables corresponds to the response of the flow to the convected increment of stagnation pressure and diminution of entropy created at the source and the resulting change in lift and drag.

The plane-cube intersection problem has been around in literature since 1984 and iterative solutions to it have been used as part of piecewise linear interface construction (PLIC) in computational fluid dynamics simulation codes ever since. In many cases, PLIC is the bottleneck of these simulations regarding compute time, so a faster, analytic solution to the plane-cube intersection would greatly reduce compute time for such simulations. We derive an analytic solution for all intersection cases and compare it to the one previous solution from Scardovelli and Zaleski (Ruben Scardovelli and Stephane Zaleski. "Analytical relations connecting linear interfaces and volume fractions in rectangular grids". In: Journal of Computational Physics 164.1 (2000), pp. 228-237.), which we further improve to include edge cases and micro-optimize to reduce arithmetic operations and branching. We then extend our comparison regarding compute time and accuracy to include two different iterative solutions as well. We find that the best choice depends on the employed hardware platform: on the CPU, Newton-Raphson is fastest with vectorization while analytic solutions perform better without. The reason for this is that vectorization instruction sets do not include trigonometric functions as used in the analytic solutions. On the GPU, the fastest method is our optimized version of the analytic SZ solution. We finally provide details on one of the applications of PLIC: curvature calculation for the Volume-of-Fluid model used for free surface fluid simulations in combination with the lattice Boltzmann method.

Detailed derivation of the analytical, reciprocal-space approach of Hessian calculation within the self-consistent-charge density functional based tight-binding framework (SCC-DFTB) is presented. This approach provides an accurate and efficient way for obtaining the SCC-DFTB Hessian of periodic systems. Its superiority with respect to the traditional numerical force differentiation method is demonstrated for doped graphene, graphene nanoribbons, boron-nitride nanotubes, bulk zinc-oxide and other systems.

The transport of platelets in blood is commonly assumed to obey an advection-diffusion equation. Here we propose a disruptive view, by showing that the random part of their velocity is governed by a fat-tailed probability distribution, usually referred to as a Lévy flight. Although for small spatio-temporal scales, it is hard to distinguish it from the generally accepted "red blood cell enhanced" Brownian motion, for larger systems this effect is dramatic as the standard approach may underestimate the flux of platelets by several orders of magnitude, compromising in particular the validity of current platelet function tests.

Accurate interatomic potentials are in high demand for large-scale atomistic simulations of materials that are prohibitively expensive by density functional theory (DFT) calculation. In this study, we apply machine learning potentials in a recently constructed repository to the prediction of the grain boundary energy in face-centered-cubic elemental metals, i.e., Ag, Al, Au, Cu, Pd, and Pt. The systematic application of machine learning potentials shows that they enable us to predict grain boundary structures and their energies accurately. The grain boundary energies predicted by the MLPs are in agreement with those calculated by DFT, although no grain boundary structures were included in training datasets of the present MLPs.

Atomic-scale materials synthesis via layer deposition techniques present a unique opportunity to control material structures and yield systems that display unique functional properties that cannot be stabilized using traditional bulk synthetic routes. However, the deposition process itself presents a large, multidimensional space that is traditionally optimized via intuition and trial and error, slowing down progress. Here, we present an application of deep reinforcement learning to a simulated materials synthesis problem, utilizing the Stein variational policy gradient (SVPG) approach to train multiple agents to optimize a stochastic policy to yield desired functional properties. Our contributions are (1) A fully open source simulation environment for layered materials synthesis problems, utilizing a kinetic Monte-Carlo engine and implemented in the OpenAI Gym framework, (2) Extension of the Stein variational policy gradient approach to deal with both image and tabular input, and (3) Developing a parallel (synchronous) implementation of SVPG using Horovod, distributing multiple agents across GPUs and individual simulation environments on CPUs. We demonstrate the utility of this approach in optimizing for a material surface characteristic, surface roughness, and explore the strategies used by the agents as compared with a traditional actor-critic (A2C) baseline. Further, we find that SVPG stabilizes the training process over traditional A2C. Such trained agents can be useful to a variety of atomic-scale deposition techniques, including pulsed laser deposition and molecular beam epitaxy, if the implementation challenges are addressed.

Torsional modes within a complex molecule containing various functional groups are often strongly coupled so that the harmonic approximation and one-dimensional torsional treatment are inaccurate to evaluate their partition functions. A family of multi-structural approximation methods have been proposed and applied in recent years to deal with the torsional anharmonicity.However, these methods approximate the exact "almost periodic" potential energy as a summation of local periodic functions with symmetric barrier positions and heights. In the present theoretical study, we illustrated that the approximation is inaccurate when torsional modes present non-uniformly distributed local minima. Thereby, we proposed an improved method to reconstruct approximate potential to replace the periodic potential by using information of the local minima and their Voronoi tessellation. First, we established asymmetric barrier heights by introducing two periodicity parameters and assuming that the exact barrier positions are at the boundaries of Voronoi cells. Second, we used multiplicatively weighted Voronoi tessellation to refine the barrier heights and positions by defining a structure-related distance metric. The proposed method has been tested for a few higher-dimensional cases, all of which show promising improved accuracy.

We present a comprehensive study for common second order PDE's in two dimensional disk-like systems and show how their solution can be approximated by finding the Green function of an effective one dimensional system. After elaborating on the formalism, we propose to secure an exact solution via a Fourier expansion of the Green function, which entails to solve an infinitely countable system of differential equations for the Green-Fourier modes that in the simplest case yields the source-free Green distribution. We present results on non separable systems − or such whose solution cannot be obtained by the usual variable separation technique − on both annulus and disc geometries, and show how the resulting one dimensional Fourier modes potentially generate a near-exact solution. Numerical solutions will be obtained via finite differentiation using FDM or FEM with the three-point stencil approximation to derivatives. Comparing to known exact solutions, our results achieve an estimated numerical relative error below 10 −6 .

Numerical simulations of nonhydrostatic atmospheric flow, based on linearly decoupled semi-implicit or fully-implicit techniques, usually solve linear systems by a pre-conditioned Krylov method without preserving the skew-symmetry of convective operators. We propose to perform atmospheric simulations in such a fully-implicit manner that the difference operators preserve both the skew-symmetry and the tightly nonlinear coupling of the differential operators. We demonstrate that a symmetry-preserving Jacobian-free Newton-Krylov~(JFNK) method mimics a balance between convective transport and turbulence dissipation. We present a wavelet method as an effective symmetry preserving discretization technique. The symmetry-preserving JFNK method for solving equations of nonhydrostatic atmospheric flows has been examined using two benchmark simulations of penetrative convection -- a) dry thermals rising in a neutrally stratified and stably stratified environment, and b) urban heat island circulations for effects of the surface heat flux H 0 varying in the range of 25≤ H 0 ≤930 Wm −2 .The results show that an eddy viscosity model provides the necessary dissipation of the subgrid-scale modes, while the symmetry-preserving JFNK method provides the conservation of mass and energy at a satisfactory level. Comparisons of the results from a laboratory experiment of heat island circulation and a field measurement of potential temperature also suggest the modelling accuracy of the present symmetry-preserving JFNK framework.