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Multi-dimensional direct numerical simulation (DNS) of the Schrödinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices, etc. In large-scale nanostructures, extensive computational effort needed in DNS may become prohibitive due to the high degrees of freedom (DoF). This study employs a physics-based reduced-order learning algorithm, enabled by the first principles, for simulation of the Schrödinger equation to achieve high accuracy and efficiency. The proposed simulation methodology is applied to investigate two quantum-dot structures; one operates under external electric field, and the other is influenced by internal potential variation with periodic boundary conditions. The former is similar to typical operations of nanoelectronic devices, and the latter is of interest to simulation and design of nanostructures and materials, such as applications of density functional theory. In each structure, cases within and beyond training conditions are examined. Using the proposed methodology, a very accurate prediction can be realized with a reduction in the DoF by more than 3 orders of magnitude and in the computational time by 2 orders, compared to DNS. An accurate prediction beyond the training conditions, including higher external field and larger internal potential in untrained quantum states, is also achieved. Comparison is also carried out between the physics-based learning and Fourier-based plane-wave approaches for a periodic case.

 

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD equations that include the “Hall” term from the general Ohm’s law. The Hall term decouples ion and electron motion physically on the ion inertial length scales. Implementing the Hall MHD equations in a numerical solver allows more physical simulations for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. The present effort is an important step towards producing physically correct results to important problems, such as the Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. The solver that is being modified is currently capable of solving the resistive MHD equations on unstructured grids using the spectral difference scheme which is an arbitrarily high-order method that is relatively simple to parallelize. The GEM Magnetic Reconnection problem is used to evaluate whether the Hall MHD equations have been correctly implemented in the solver using the spectral difference method with divergence cleaning (SDDC) algorithm by comparing against the reconnection rates reported in the literature. 

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD equations that include the “Hall” term from the general Ohm’s law. The Hall term decouples ion and electron motion physically on the ion inertial length scales. Implementing the Hall MHD equations in a numerical solver allows more physical simulations for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. The present effort is an important step towards producing physically correct results to important problems, such as the Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. The solver that is being modified is currently capable of solving the resistive MHD equations on unstructured grids using the spectral differencing scheme which is an arbitrarily high-order method that is relatively simple to parallelize. The GEM Magnetic Reconnection problem is used to evaluate whether the Hall MHD equations have been correctly implemented in the solver using the spectral differencing method with divergence cleaning (SDDC) algorithm by comparing against the reconnection rates reported in the literature. 

The accuracy of SimericsMP+ Unsteady Reynolds-Averaged Navier-Stokes (URANS) model is validated by studying turbulent flow past counter-rotating propellers (CRPs). Subsequently, URANS is used to study the axial flow in an Office of Naval Research (ONR) waterjet and its performance. Specifically, experimental data from Miller (1976) is employed for comparison against the URANS results. Due to the large number of degrees of freedom for both simulations, parallel computing over 80 cores is involved. For the CRP study, torque and thrust coefficients are plotted against a range of advance ratios, ensuring a Reynolds number of less than 500,000. For the waterjet, torque and head coefficients are plotted for a range of flow rates at a Reynolds number of 1.25 × 106. For both studies, two different mesh resolutions are utilized. The finer meshes of both studies contained roughly four times the total number of cells found in their respective coarse meshes. These refinements lead to minor improvements, showing good convergence. The URANS torque and thrust coefficients are found to be within 10% of that from experimental data across all advance ratios for the CRP set, showing good agreement. The torque and head coefficients for the waterjet displayed even better agreement, with the greatest error across all flow conditions remaining under 3%. It is concluded that the stator is responsible for 20% of the waterjets power production. 

With the proliferation of distributed energy resources (DERs) in the distribution grid, it is a challenge to effectively control a large number of DERs resilient to the communication and security disruptions, as well as to provide the online grid services, such as voltage regulation and virtual power plant (VPP) dispatch. To this end, a hybrid feedback-based optimization algorithm along with deep learning forecasting technique is proposed to specifically address the cyber-related issues. The online decentralized feedback-based DER optimization control requires timely, accurate voltage measurement from the grid. However, in practice such information may not be received by the control center or even be corrupted. Therefore, the long short-term memory (LSTM) deep learning algorithm is employed to forecast delayed/missed/attacked messages with high accuracy. The IEEE 37-node feeder with high penetration of PV systems is used to validate the efficiency of the proposed hybrid algorithm. The results show that 1) the LSTM-forecasted lost voltage can effectively improve the performance of the DER control algorithm in the practical cyber-physical architecture; and 2) the LSTM forecasting strategy outperforms other strategies of using previous message and skipping dual parameter update. 

This paper summarizes the best practices and lessons learned from organizing an effective remote REU Site during COVID-19. Our REU Site is a three-year program that is designed to offer closely-mentored summer research experience to a cohort of ten students in each of the three years. COVID-19 has disrupted our site by forcing us to split our second cohort to two groups, two students in summer 2020 and seven students in summer 2021. However, the experience that we gained in summer 2020 by mentoring the two students virtually online has provided us with the confidence that a virtual REU Site with a larger group can be as effective as in person and on campus. To further improve the quality of our REU Site in the on-line mode, we have applied multiple novel practices. Specifically, before the start of the 2021 REU site we as the site co-directors proactively worked with mentors to better understand the needs of the defined research projects. Subsequently, we tailored the topics covered by the crash course of our site to the needs of the research projects as well as purposefully increasing active learning activities and student interactions. In lieu of the previous in-person bond building activity (a two-day high rope course in a nearby camp), we added virtual scavenger image hunt in orientation and game nights every Wednesday. During the ten weeks, we also organized a half-hour daily check-in and check-out in the morning and afternoon respectively, through which students got ample opportunities to speak in a group setting about their own accomplishments and challenges for the day as well as their plans for the next day. Moreover, a PhD pathways panel and several professional development seminars on Graduate School and the research process were successfully organized to motivate students to pursue a research career. To facilitate communication, our site adopted multiple software tools (slack, google calendar, zoom, and moodle). An independent evaluator evaluated our program through online pre- and post-program surveys for both students and mentors as well as a focus group discussion with students. The evaluation report indicates significant improvement from the summer 2021 site regarding student satisfaction compared to the previous summer 2019 on-site program. Detailed quantitative analysis and lessons learned from the report will be presented in this paper to offer valuable experience and best practices for organizing effective cohort-based undergraduate research programs. 

A methodology of multi-dimensional physics simulations is investigated based on a data-driven learning algorithm derived from proper orthogonal decomposition (POD). The approach utilizes numerical simulation tools to collect solution data for the problems of interest subjected to parametric variations that may include interior excitations and/or boundary conditions influenced by exterior environments. The POD is applied to process the data and to generate a finite set of basis functions. The problem is then projected from the physical domain onto a mathematical space constituted by its basis functions. The effectiveness of the POD methodology thus depends on the data quality, which relies on the numerical settings implemented in the data collection (or the training). The simulation methodology is developed and demonstrated in a dynamic heat transfer problem for an entire CPU and in a quantum eigenvalue problem for a quantum-dot structure. Encouraging findings are observed for the POD simulation methodology in this investigation, including its extreme efficiency, high accuracy and great adaptability. The models constructed by the POD basis functions are even capable of predicting the solution of the problem beyond the conditions implemented in the training with a good accuracy.