Engineering topics

Liang, Jiaxing

Publications and source records attributed to Liang, Jiaxing.

3 records

DOE OSTI2024

Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Furthermore, adaptive griding results in more accurate computation of geometric quantities such as x-points associated with the model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. Furthermore, the use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over 30.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Wafer-scale quasi-layered tungstate-doped polypyrrole film with high volumetric capacitance

Layered materials are particularly attractive for supercapacitors because of their unique physical, electrical and chemical properties. In this work, we demonstrate a facile and scalable electrochemical deposition method for wafer-scale synthesis of quasi-layered tungstate-doped polypyrrole films (named TALPy) with controllable thickness and size. The as-prepared TALPy film exhibits a high gravimetric density and excellent volumetric capacitance, exceeding many high-performing carbon- and polymer-based film electrodes. Based on combined results of ex-situ X-ray diffraction (XRD), Raman and X-ray photoelectron spectroscopy (XPS), it is determined that TALPy stores charge through an ion intercalation process accompanied by change in oxidation states of polypyrrole backbone, which is referred as intercalation pseudocapacitance. All these results suggest the great promise of electrochemical deposition as a scalable and controllable bottom-up approach for synthesizing quasi-layered conductive organic-inorganic hybrid films for electrochemical energy storage applications with high volumetric performance.

36 MATERIALS SCIENCE↗