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3D nanolithography with metalens arrays and spatially adaptive illumination

The growing demand for advanced materials, miniaturized devices and integrated microsystems calls for the reliable fabrication of complex, multiscale, three-dimensional (3D) architectures, a need increasingly addressed through light-based and laser-based processes. However, owing to the field-of-view (FOV) limitations of conventional imaging optics, existing 3D laser nanofabrication techniques face fundamental challenges in throughput, proximity error and stitching defects on the path to scaling. Here, in this study, we present a scalable 3D nanofabrication platform that uses a metalens-generated focal spot array to parallelize two-photon lithography (TPL) beyond centimetre-scale write field areas. Metalenses are ideally suited for producing submicron-scale focal spots for high-throughput nanolithography, as they uniquely feature large numerical apertures (NAs), immersion media compatibility and large-scale manufacturability. We experimentally demonstrate a printing system that uses a 12-cm 2 metalens array to produce more than 120,000 cooperative focal spots, corresponding to a throughput exceeding 10 8 voxels s −1 . By programmatically patterning the focal spot array using a spatial light modulator (SLM), an adaptive parallel printing strategy is developed for precise greyscale linewidth modulation and choreographed printing of semiperiodic and fully aperiodic 3D geometries. We demonstrate parallel printing of replicated microstructures (>50 M microparticles per day), centimetre-scale 3D architectures with feature sizes down to 113 nm, and photonic and mechanical metamaterials. This work demonstrates the potential of 3D nanolithography towards wafer-scale production, showing how TPL could be used at scale for applications in microelectronics, biomedicine, quantum technology and high-energy laser targets.

Materials science↗

Learning fuzzy logic control system

The performance of the Learning Fuzzy Logic Control System (LFLCS), developed in this thesis, has been evaluated. The Learning Fuzzy Logic Controller (LFLC) learns to control the motor by learning the set of teaching values that are generated by a classical PI controller. It is assumed that the classical PI controller is tuned to minimize the error of a position control system of the D.C. motor. The Learning Fuzzy Logic Controller developed in this thesis is a multi-input single-output network. Training of the Learning Fuzzy Logic Controller is implemented off-line. Upon completion of the training process (using Supervised Learning, and Unsupervised Learning), the LFLC replaces the classical PI controller. In this thesis, a closed loop position control system of a D.C. motor using the LFLC is implemented. The primary focus is on the learning capabilities of the Learning Fuzzy Logic Controller. The learning includes symbolic representation of the Input Linguistic Nodes set and Output Linguistic Notes set. In addition, we investigate the knowledge-based representation for the network. As part of the design process, we implement a digital computer simulation of the LFLCS. The computer simulation program is written in 'C' computer language, and it is implemented in DOS platform. The LFLCS, designed in this thesis, has been developed on a IBM compatible 486-DX2 66 computer. First, the performance of the Learning Fuzzy Logic Controller is evaluated by comparing the angular shaft position of the D.C. motor controlled by a conventional PI controller and that controlled by the LFLC. Second, the symbolic representation of the LFLC and the knowledge-based representation for the network are investigated by observing the parameters of the Fuzzy Logic membership functions and the links at each layer of the LFLC. While there are some limitations of application with this approach, the result of the simulation shows that the LFLC is able to control the angular shaft position of the D.C. motor. Furthermore, the LFLC has better performance in rise time, settling time and steady state error than to the conventional PI controller. This abstract accurately represents the content of the candidate's thesis. I recommend its publication.

Lung, Leung Kam↗

An implicit solution for Asay foil trajectories generated by separable, sustained-production ejecta source models

We present a simple implicit solution for the time-dependent trajectory of a thin Asay foil ejecta diagnostic for the general case where the impinging ejecta cloud is generated by a source function characterized by an arbitrary (sustained) time dependence and a time-independent (stationary) particle velocity distribution. In the limit that the source function time dependence becomes a delta function, this solution—which is amenable to rapid numerical calculations of arbitrary accuracy—exactly recovers a previously published solution for the special case of instantaneous ejecta production. We also derive simple expressions for the free-surface arrival (catch-up) time as well as the true ejecta areal mass accumulation on the accelerating foil and place bounds on the level of error incurred when applying instant-production mass solutions to a sustained-production trajectory. We demonstrate these solutions with example calculations for hypothetical source functions spanning a wide range of ejecta production durations, velocity distributions, and temporal behaviors. These calculations demonstrate how the foil trajectory is often insensitive to the temporal dependence of the source function, instead being dominated by the velocity distribution. We quantify this insensitivity using a “compatibility score” metric. Under certain conditions, one may capitalize upon this insensitivity to obtain a good approximation of the second integral of the velocity distribution from the observed foil trajectory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Verification of a quasi-linear model for gyrokinetic turbulent transport

The verification and calibration of a new quasi-linear transport model with a large database of gyrokinetic turbulence simulations is presented in this paper. In a previous paper (Staebler et al 2020 Plasma Phys. Control. Fusion 63 015013), a model for the saturated spectrum of electric potential fluctuations was developed based on the properties of the non-linear 3D spectrum. In this paper, a modification to the overall multiplicative factor in this model is found to be necessary to improve the fit to scans of the temperature and density gradients. The error in the fit of the quasi-linear fluxes of electron and ion energy fluxes is significantly better than for previous saturation models. The spectral shift model for the impact of equilibrium E × B velocity shear (Staebler et al 2013 Phys. Rev. Lett. 110 055003) and the zonal flow mixing model for electron-scale turbulence (Staebler et al 2016 Phys. Plasmas 23 062518) are both revised to be compatible with this new model. Furthermore, the models for the loss of bounce averaging and electron collisions in the TGLF reduced linear equations (Staebler et al 2005 Phys. Plasmas 12 102508) are also changed to improve the linear eigenmodes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Planck intermediate results (Corrigendum) : V. Pressure profiles of galaxy clusters from the Sunyaev-Zeldovich effect

Figure 7 of our original publication (Planck Collaboration 2013) is flawed. The correct figure is presented here and we stress that our original conclusion on the radial distribution of the gas fraction remains unchanged. There was an error in the reconstruction of the temperature profiles used to derive the gas mass distribution from the joint Planck and XMM-Newton pressure profile, and thereby a prediction for the gas fraction profiles. The error in the temperature profile reconstruction applies to this paper only. The predicted gas fraction profiles for both hypothesis on the temperature profiles, i.e., from hypothesis H1 and H2, were affected similarly. Now corrected, they are in better agreement at R 500 with the measurement by Pratt et al. (2009) on the REXCESS sample and with the expectations from the CMB. The Perseus profile (Simionescu et al. 2011) is still marginally compatible with our prediction within our large dispersion (shaded blue and red area on the figure).

79 ASTRONOMY AND ASTROPHYSICS↗

Development of a dynamic flow imaging phantom for dynamic contrast-enhanced CT

Purpose: Dynamic contrast enhanced CT (DCE-CT) studies with modeling of blood flow and tissue perfusion are becoming more prevalent in the clinic, with advances in wide volume CT scanners allowing the imaging of an entire organ with sub-second image frequency and sub-millimeter accuracy. Wide-spread implementation of perfusion DCE-CT, however, is pending fundamental validation of the quantitative parameters that result from dynamic contrast imaging and perfusion modeling. Therefore, the goal of this work was to design and construct a novel dynamic flow imaging phantom capable of producing typical clinical time-attenuation curves (TACs) with the purpose of developing a framework for the quantification and validation of DCE-CT measurements and kinetic modeling under realistic flow conditions. Methods: The phantom is based on a simple two-compartment model and was printed using a 3D printer. Initial analysis of the phantom involved simple flow measurements and progressed to DCE-CT experiments in order to test the phantoms range and reproducibility. The phantom was then utilized to generate realistic input TACs. A phantom prediction model was developed to compute the input and output TACs based on a given set of five experimental (control) parameters: pump flow rate, injection pump flow rate, injection contrast concentration, and both control valve positions. The prediction model is then inversely applied to determine the control parameters necessary to generate a set of desired input and output TACs. A protocol was developed and performed using the phantom to investigate image noise, partial volume effects and CT number accuracy under realistic flow conditionsResults: This phantom and its surrounding flow system are capable of creating a wide range of physiologically relevant TACs, which are reproducible with minimal error between experiments ({sigma}/{mu} < 5% for all metrics investigated). The dynamic flow phantom was capable of producing input and output TACs using either step function based or typical clinical arterial input function (AIF) inputs. The measured TACs were in excellent agreement with predictions across all comparison metrics with goodness of fit (R{sup 2}) for the input function between 0.95 and 0.98, while the maximum enhancement differed by no more than 3.3%. The predicted output functions were similarly accurate producing R{sup 2} values between 0.92 and 0.99 and maximum enhancement to within 9.0%. The effect of ROI size on the arterial input function (AIF) was investigated in order to determine an operating range of ROI sizes which were minimally affected by noise for small dimensions and partial volume effects for large dimensions. It was possible to establish the measurement sensitivity of both the Toshiba (ROI radius range from 1.5 to 3.2 mm ''low dose'', 1.4 to 3.0 mm ''high dose'') and GE scanner (1.5 to 2.6 mm ''low dose'', 1.1 to 3.4 mm ''high dose''). This application of the phantom also provides the ability to evaluate the effect of the AIF error on kinetic model parameter predictions. Conclusions: The dynamic flow imaging phantom is capable of producing accurate and reproducible results which can be predicted and quantified. This results in a unique tool for perfusion DCE-CT validation under realistic flow conditions which can be applied not only to compare different CT scanners and imaging protocols but also to provide a ground truth across multimodality dynamic imaging given its MRI and PET compatibility.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Conducted Susceptibility Data Adaptation Tool

The purpose of this research project is to help NASA scientists increase effectivity in testing by reducing the amount of time required for data conversion from initial measurements to the analysis stage. This project resulted in a data conversion tool developed in python using the openpyxl library. When lab personnel perform the Conducted Susceptibility 101 (CS101) and Conducted Susceptibility 02 (CS02) tests in the Semi-anechoic Electromagnetic Compatibility Test Facility at NASA Langley Research Center, the driving code produces a text file under the .DAT extension.The data must be manually converted the .DAT file into an Excel file line by line for data analysis.The Conducted Susceptibility Data Adaptation Tool (CSDAT) uses python code to convert the .DAT files to spreadsheets automatically which saves lab personnel time which they could use for faster analysis as well as prevents possible human error such as leaving out a line of data in the manual conversion process.

Gabriel Johnson↗

Dealing with Ion LET Uncertainties: An Application of Generalized Linear Models

Although most SEE rate estimation methods presume a fit to SEE cross section vs. LET, fitting SEE data is challenging because the data are not compatible with the assumptions of many common fitting techniques (e.g. linear regression. The difficulty of fitting such data is compounded when the LET of the ion responsible for an SEE is uncertain. We modify a Generalized Linear Model SEE data fitting methodology to accommodate uncertain LET and apply the method to the problem of backside heavy-ion SEE testing to demonstrate the utility of the method, explore the dependence of systematic errors that arise from improper treatment of LET uncertainty and develop guidelines for minimizing such systematic errors when proper treatment is not possible. Additional applications are suggested and assessed for suitability of treatment by the model.

Single-event effects↗

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order S{sub N} Equations in Near-Void Regions

The common definition of the diffusion coefficient as the inverse of three times the transport cross section is not compatible with voids. Morel introduced a non-local tensor diffusion coefficient that remains finite in voids. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coefficient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction. It was demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors have been applied to modeling the TREAT reactor confirming the findings of Larsen and Trahan. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S{sub N} equations discretized with the discontinuous finite element method (DFEM). This NDA method uses a scalar diffusion coefficient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it suffers from very large and potentially unbounded diffusion coefficients in the low order problem. However, it was noted that the choice of the diffusion coefficient does not influence consistency of the method at convergence and hence the diffusion coefficient is essentially a free parameter. The choice of the diffusion coefficient does, however, affect the convergence behavior of the nonlinear diffusion iterations. Within this work we use Morel's non-local diffusion coefficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant enhancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA with non-local diffusion coefficients, the periodical horizontal interface problem is used. This problem consists of alternating stripes of optically thin and thick materials both of which feature scattering ratios close to unity. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A methodology for decay heat characterization in molten salt reactors

Accurate decay heat prediction in molten salt reactors (MSRs) faces dual challenges: complex operational uncertainties and the need for interpretable models compatible with engineering workflows. This work presents a hybrid machine learning and segmented polynomial methodology that addresses both requirements through three key innovations. First, a modular data architecture encodes MSR-specific operational parameters (power density: 1-100 W cm -3 , humidity: 0-0.1 wt %, air ingress: 0-0.1 mol %) with uncertainty-aware temporal discretization spanning 15 orders of magnitude. Second, region-optimized machine learning models achieve 92.3 % root mean square error (RMSE) reduction over conventional polynomials while maintaining physical interpretability through automated piecewise equation generation. Third, dual front-end interfaces accelerate safety analyses — a Jupyter environment enables researchers to explore 10,000+ parameter combinations via interactive widgets, while a Streamlit web application reduces design iteration cycles through production-grade visualization tools. Operational deployment demonstrates prediction times of only a couple hundred milliseconds for 10 4 years decay profiles, enabling real-time optimization of spent fuel container designs.

42 - ENGINEERING↗

Intelligent Experiments through Real-Time AI: Fast Data Processing and Autonomous Detector Control for High-Energy Nuclear Experiments

The aim of this project is to develop software and hardware for fast real-time data processing and autonomous detector control and calibration for the sPHENIX and the future EIC experiments. Below summarizes Georgia Tech team efforts in the past year: 1. We developed a real-time clustering algorithm and FPGA-based pipeline architecture for processing fired pixel data from ALPIDE sensors in sPHENIX experiments. Our Columnar Clustering Co-Design introduces a hardware-aware, stream-friendly approach that segments pixel data by column pairs using a Column Pair Clustering (CPC) strategy, followed by Cluster Stitching to merge adjacent subclusters. Implemented in Vitis HLS, the pipeline comprises five stages—read-in, subclustering, stitching, analysis, and write-out—connected by tagged HLS streams with custom end-of-event signaling for robust synchronization. We designed a pipelined dataflow model optimized for throughput, low latency, and minimal buffering, enabling scalable clustering across events of arbitrary size. Our system maintains spatial precision via center-of-mass and shape key extraction and efficiently handles edge cases such as fragmented or nested clusters. Compared against DBSCAN in both software and hardware, our approach demonstrates competitive performance under FPGA constraints. 2. We also conducted a comprehensive algorithm-to-hardware co-design of connected component analysis tailored for sPHENIX experiments, focusing on real-time, low-latency processing using FPGAs and High-Level Synthesis (HLS). Starting from a Python-based particle tracking pipeline, the team translated the core logic—graph traversal via DFS and Union-Find—into an HLS-compatible C++ model, replacing dynamic memory and recursion with static arrays and pipelined control flow. The final design includes a fully streamed and dataflow-compatible Union-Find kernel optimized across five iterations, incorporating loop pipelining, array partitioning, AXI/FIFO interface tuning, and function flattening. Experimental results show up to 14.8× speedup over the CPU baseline, reducing per-graph latency to 1.58 μs and demonstrating strong resource efficiency with only ~7k LUTs and zero BRAM usage. The design maintains functional correctness against the Python reference using a Python-based C-simulation framework and Mean Squared Error metrics. This work validates the potential of HLS-driven FPGA designs for edge-level HEP data acquisition, laying a scalable foundation for future integration with real-time detector pipelines and multi-graph processing systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

New Levels of High Angular Resolution EBSD Performance via Inverse Compositional Gauss-Newton Digital Image Correlation

Conventional high angular resolution electron backscatter diffraction (HREBSD) uses cross-correlation to track features between diffraction patterns, which are then related to the relative elastic strain and misorientation between the diffracting volumes of material. This paper adapts inverse compositional Gauss Newton (ICGN) digital image correlation (DIC) to be compatible with HREBSD. ICGN works by efficiently tracking not just the shift in features, but also the change in their shape. Modeling a shape change as well as a shift results in greater accuracy. This method, ICGN HREBSD, is applied to a simulated data set, and its performance is compared to conventional cross-correlation HREBSD, and cross-correlation HREBSD with remapping. ICGN HREBSD is shown to have about half the strain error of the best cross-correlation method with a comparable computation time.

T. J. Ruggles↗

High-Fidelity 3D-Nanoprinting via Focused Electron Beams: Computer-Aided Design (3BID)

Currently, there are few techniques that allow true 3D-printing on the nanoscale. The most promising candidate to fill this void is focused electron-beam-induced deposition (FEBID), a resist-free, nanofabrication compatible, direct-write method. The basic working principles of a computer-aided design (CAD) program (3BID) enabling 3D-FEBID is presented and simultaneously released for download. The 3BID capability significantly expands the currently limited toolbox for 3D-nanoprinting, providing access to geometries for optoelectronic, plasmonic, and nanomagnetic applications that were previously unattainable due to the lack of a suitable method for synthesis. In conclusion, the CAD approach supplants trial and error toward more precise/accurate FEBID required for real applications/device prototyping.

3D-nanoprinting↗

TU-F-17A-03: A 4D Lung Phantom for Coupled Registration/Segmentation Evaluation

Purpose: Coupling the processes of segmentation and registration (regmentation) is a recent development that allows improved efficiency and accuracy for both steps and may improve the clinical feasibility of online adaptive radiotherapy. Presented is a multimodality animal tissue model designed specifically to provide a ground truth to simultaneously evaluate segmentation and registration errors during respiratory motion. Methods: Tumor surrogates were constructed from vacuum sealed hydrated natural sea sponges with catheters used for the injection of PET radiotracer. These contained two compartments allowing for two concentrations of radiotracer mimicking both tumor and background signals. The lungs were inflated to different volumes using an air pump and flow valve and scanned using PET/CT and MRI. Anatomical landmarks were used to evaluate the registration accuracy using an automated bifurcation tracking pipeline for reproducibility. The bifurcation tracking accuracy was assessed using virtual deformations of 2.6 cm, 5.2 cm and 7.8 cm of a CT scan of a corresponding human thorax. Bifurcations were detected in the deformed dataset and compared to known deformation coordinates for 76 points. Results: The bifurcation tracking accuracy was found to have a mean error of −0.94, 0.79 and −0.57 voxels in the left-right, anterior-posterior and inferior-superior axes using a 1×1×5 mm3 resolution after the CT volume was deformed 7.8 cm. The tumor surrogates provided a segmentation ground truth after being registered to the phantom image. Conclusion: A swine lung model in conjunction with vacuum sealed sponges and a bifurcation tracking algorithm is presented that is MRI, PET and CT compatible and anatomically and kinetically realistic. Corresponding software for tracking anatomical landmarks within the phantom shows sub-voxel accuracy. Vacuum sealed sponges provide realistic tumor surrogate with a known boundary. A ground truth with minimal uncertainty is thus realized that can be used for comparing the performance of registration and segmentation algorithms.

60 APPLIED LIFE SCIENCES↗

Surface accuracy measurement system deployable reflector antennas

Conceptual optical sensor configurations for measuring the surface deformations of large, deployable space antennas are described. These antennas include precision deployable reflectors up to 30 meters diameter and 1000 GHz frequency and mesh deployable reflectors up to 100 meters diameter and 30 GHz frequency. For each representative antenna configuration, the surface deformation sensor provides continuous, real-time measurements at a sufficient number of sample points to be compatible with active surface control. Moreover, the sensor system does not interfere with the mechanical or microwave characteristics of either the antenna surface or the feed. For the applications considered, the sensor system consists of a central receiver ring containing six to ten long focal length, angle measuring instruments, each viewing a dedicated set of bright point targets at the antenna. The targets, either light emitting diodes or illuminated retroreflectors, are modulated to eliminate errors from spurious backgrounds. Very preliminary performance estimates indicate that the sensor system, using commerical grade components, can produce a 20th to a 30th wavelength accuracy (3 sigma).

Neiswander, R. S.↗

A new stepwise carbon cycle data assimilation system using multiple data streams to constrain the simulated land surface carbon cycle

Here, large uncertainties in land surface models (LSMs) simulations still arise from inaccurate forcing, poor description of land surface heterogeneity (soil and vegetation properties), incorrect model parameter values and incomplete representation of biogeochemical processes. The recent increase in the number and type of carbon cycle-related observations, including both in situ and remote sensing measurements, has opened a new road to optimize model parameters via robust statistical model–data integration techniques, in order to reduce the uncertainties of simulated carbon fluxes and stocks. In this study we present a carbon cycle data assimilation system that assimilates three major data streams, namely the Moderate Resolution Imaging Spectroradiometer (MODIS)-Normalized Difference Vegetation Index (NDVI) observations of vegetation activity, net ecosystem exchange (NEE) and latent heat (LE) flux measurements at more than 70 sites (FLUXNET), as well as atmospheric CO 2 concentrations at 53 surface stations, in order to optimize the main parameters (around 180 parameters in total) of the Organizing Carbon and Hydrology in Dynamics Ecosystems (ORCHIDEE) LSM (version 1.9.5 used for the Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations). The system relies on a stepwise approach that assimilates each data stream in turn, propagating the information gained on the parameters from one step to the next. Overall, the ORCHIDEE model is able to achieve a consistent fit to all three data streams, which suggests that current LSMs have reached the level of development to assimilate these observations. The assimilation of MODIS-NDVI (step 1) reduced the growing season length in ORCHIDEE for temperate and boreal ecosystems, thus decreasing the global mean annual gross primary production (GPP). Using FLUXNET data (step 2) led to large improvements in the seasonal cycle of the NEE and LE fluxes for all ecosystems (i.e., increased amplitude for temperate ecosystems). The assimilation of atmospheric CO 2 , using the general circulation model (GCM) of the Laboratoire de Météorologie Dynamique (LMDz; step 3), provides an overall constraint (i.e., constraint on large-scale net CO 2 fluxes), resulting in an improvement of the fit to the observed atmospheric CO 2 growth rate. Thus, the optimized model predicts a land C (carbon) sink of around 2.2 PgC yr -1 (for the 2000–2009 period), which is more compatible with current estimates from the Global Carbon Project (GCP) than the prior value. The consistency of the stepwise approach is evaluated with back-compatibility checks. The final optimized model (after step 3) does not significantly degrade the fit to MODIS-NDVI and FLUXNET data that were assimilated in the first two steps, suggesting that a stepwise approach can be used instead of the more “challenging” implementation of a simultaneous optimization in which all data streams are assimilated together. Most parameters, including the scalar of the initial soil carbon pool size, changed during the optimization with a large error reduction. This work opens new perspectives for better predictions of the land carbon budgets.

58 GEOSCIENCES↗

Space Shuttle Interim Teleprinter System

This paper describes the Space Shuttle Interim Teleprinter System. The major design developments involved in selecting modifying, and testing a communications terminal for compatibility with the Space Shuttle communications system and crew are presented. The objective was to provide an onorbit capability to receive and reproduce text hardcopy data from the ground for crew activity changes. The Interim Teleprinter System is remotely controlled from the ground, and message retrieval requires minimal crew activity. It has performed well in flight, and has printed over 10,000 lines of text information to date while in earth orbit with no character errors.

Schuette, M. D.↗

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order SN Equations in Near-Void Regions

The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA with non-local diffusion coeffcients, the periodical horizontal interface problem is used [7]. This problem consists of alternating stripes of optically thin and thick materials both of which feature scattering ratios close to unity.

97 MATHEMATICS AND COMPUTING↗