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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2022

A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation

We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient Space–Time Reduced Order Model for Linear Dynamical Systems in Python Using Less than 120 Lines of Code

A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space–time ROM for linear dynamical problems has been developed [Choi et al., Space–tume reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems, Journal of Computational Physics, 2020], which further reduces the problem size by introducing a temporal reduction in addition to a spatial reduction without much loss in accuracy. The authors show an order of a thousand speed-up with a relative error of less than 10−5 for a large-scale Boltzmann transport problem. In this work, we present for the first time the derivation of the space–time least-squares Petrov–Galerkin (LSPG) projection for linear dynamical systems and its corresponding block structures. Utilizing these block structures, we demonstrate the ease of construction of the space–time ROM method with two model problems: 2D diffusion and 2D convection diffusion, with and without a linear source term. For each problem, we demonstrate the entire process of generating the full order model (FOM) data, constructing the space–time ROM, and predicting the reduced-order solutions, all in less than 120 lines of Python code. We compare our LSPG method with the traditional Galerkin method and show that the space–time ROMs can achieve O(10−3) to O(10−4) relative errors for these problems. Depending on parameter–separability, online speed-ups may or may not be achieved. For the FOMs with parameter–separability, the space–time ROMs can achieve O(10) online speed-ups. Finally, we present an error analysis for the space–time LSPG projection and derive an error bound, which shows an improvement compared to traditional spatial Galerkin ROM methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Parallel physics-informed neural networks via domain decomposition

Here we develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation capacity, efficient hyperparameter tuning, and is particularly effective for multi-scale and multi-physics problems. Here, we present a parallel algorithm for cPINNs and XPINNs constructed with a hybrid programming model described by MPI + X, where X ∈ {CPUs, GPUs}. The main advantage of cPINN and XPINN over the more classical data and model parallel approaches is the flexibility of optimizing all hyperparameters of each neural network separately in each subdomain. We compare the performance of distributed cPINNs and XPINNs for various forward problems, using both weak and strong scalings. Our results indicate that for space domain decomposition, cPINNs are more efficient in terms of communication cost but XPINNs provide greater flexibility as they can also handle time-domain decomposition for any differential equations, and can deal with any arbitrarily shaped complex subdomains. To this end, we also present an application of the parallel XPINN method for solving an inverse diffusion problem with variable conductivity on the United States map, using ten regions as subdomains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Root-N Krylov-space correction vectors for spectral functions with the density matrix renormalization group

In this work, we propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov-space decomposition to compute the correction vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov-space decomposition and repeating this procedure N times to obtain the actual correction vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, whereas achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry and provide evidence that the root-N approach reaches a much improved spectral resolution compared to the conventional correction vector.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Time-dependent-bases with local CUR decomposition method for accelerating turbulent combustion simulations

Here, this study presents a novel reduced-order modeling framework, Time-Dependent Bases with Local CUR decomposition (TDB-L-CUR), designed to efficiently and accurately approximate the species transport equations in reacting flow simulations. The method extends the existing TDB-CUR approach for chemically reacting flows (Jung et al. Comput. Methods Appl. Mech. Engrg. 437 (2025) 117758), which leverages matrix decomposition techniques to form a global-in-space, time-dependent low-dimensional manifold. While TDB-CUR performs well in homogeneous systems, it may be less well-suited to spatially heterogeneous systems such as turbulent flames, where higher-rank approximations are typically required. The proposed TDB-L-CUR framework introduces two methodological extensions to the baseline approach. First, it applies unsupervised clustering to partition the physical domain into distinct regions, enabling spatially localized manifold construction, thereby reducing the rank required for the reduced-order representation. Second, it incorporates a computational singular perturbation (CSP)-based scheme for identifying and penalizing fast species, allowing for spatio-temporally adaptive mitigation of chemical stiffness. The proposed framework is validated on a hierarchy of test cases, including a one-dimensional premixed flame, a two-dimensional nonpremixed ignition case with vortex interaction, and a three-dimensional turbulent premixed flame. TDB-L-CUR significantly improves accuracy over TDB-CUR while further reducing computational cost. The fully on-the-fly formulation of TDB-L-CUR (i.e., requiring no offline training or prior knowledge) makes it a robust and scalable tool for reduced-order modeling of reactive flows.

Local manifold↗
DOE OSTI2024

Galaxy bispectrum in the spherical Fourier-Bessel basis

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z 2 into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

On the interaction of a wind turbine wake with a conventionally neutral atmospheric boundary layer

In this work, we investigate the dynamics of wind turbine tip-vortex breakdown in a conventionally neutral atmospheric boundary layer (ABL). To this end, high-resolution data are collected from large-eddy simulations of a wind turbine operating within a neutral ABL and studied by means of proper orthogonal decomposition (POD) and Fourier analysis. The high resolution of the generated data in both space and time allows us to gain insight into the tip-vortex breakdown mechanisms by (i) capturing the energy modes of the coherent structures, (ii) studying their contribution to the tip-vortex breakdown through their power spectra functions and mean kinetic energy (MKE) flux, and (iii) analysing the growth rate of each contributing perturbation frequency along tip vortices. Our analysis shows that under a fully turbulent scenario, the growth rate of perturbations along the tip vortices is largest for low wave numbers, i.e. long-wave perturbations. Additionally, the MKE flux reaches its highest value at two diameters downstream of the rotor plane, a behaviour that can be attributed to the coexistence of multiple interacting POD modes, with the streamwise vortex roller mode being the primary contributor to the total MKE flux budget, contributing approximately . Finally, comparisons with a laminar, uniform flow scenario subject to a single-frequency perturbation highlight the differences between the two ambient flow conditions. In the non-turbulent, uniform flow scenario, the growth rate attains its maximum value at a wave number corresponding to the out-of-phase mutual-inductance mechanism, whereas the MKE flux exhibits local minima and maxima along the wake and at different downstream locations depending on the perturbation frequency. Our analyses suggest that the breakdown of the wind turbine tip vortices under a fully turbulent neutral ABL inflow is due to complex interactions across a range of excitation frequencies, in which the mutual-inductance instability may not be the dominant one.

17 WIND ENERGY↗
DOE OSTI2022

Pele: An Exascale-Ready Suite of Combustion Codes

High fidelity simulations of realistic combustion devices are extremely demanding computationally because of the requirements to capture complex fuel chemical decomposition, its intricate interactions with turbulent, often multiphase, flows, and the wide separation of space and time scales between the thin flame and the device boundaries. Software required to carry out such computations tends to be extremely complex, particularly when designed to exploit hardware accelerators, and can be difficult to port and maintain. We present Pele, a performance portable suite of tools for the simulation of combustion systems, including codes to evolve reactive multiphase configurations in the low Mach number and compressible flow regimes, along with a set of inter-compatible post processing and in situ analysis tools. The Pele suite of tools is built on top of the AMReX framework for block-structured adaptive mesh refinement, which provides efficient data structures and algorithms that enable the development of a wide variety of efficient mesh and particle based PDE integration schemes. A hierarchical MPI+X parallelism scheme supports CPU-only and accelerated architectures, where X can be OpenMP, CUDA, and HIP based approaches for intra-node computational work distribution. The algorithms and data structures underlying the Pele simulation and analysis tools are highly scalable and performant across a wide variety of high-performance computing platforms, including DOEs newest exascale-class machines, Frontier and Aurora. The simulation and analysis tools are fully documented and freely distributed as open source via GitHub. We present key algorithmic and software challenges, solution strategies, performance and resulting set of capabilities.

AMReX↗
DOE OSTI2024

A collision-based hybrid method for the BGK equation

In this article, we apply the collision-based hybrid method introduced by Hauck and McClarren to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Transforming polymorphs, melting, and boiling during cookoff of PETN

Transforming polymorphs, melting, and boiling are physical processes that can accelerate decomposition rates during cookoff of PETN and make measurements difficult. For example, splashing liquids from large bubbles filled with decomposition products clog pressure tubing in sealed experiments. Boil over can also extinguish thermal excursions in vented experiments making ignition difficult. For better measurements, we have modified the Sandia Instrumented Thermal Ignition (SITI) experiment to obtain better sealed and vented cookoff data for PETN by reducing the sample size and including additional gas space to prevent clogged tubing and boil over. Ignition times were not affected by 1) increasing the gas space by a factor of 3 in sealed SITI experiments or by 2) venting the decomposition gasses. That is, thermal ignition of PETN is not pressure dependent and the rate-limiting step during PETN decomposition likely occurs in the condensed phase. A simple decomposition model was calibrated using these observations and includes rate acceleration caused by melting and boiling. The model is used to predict internal temperatures, pressurization, and thermal ignition in a wide variety of experiments. Furthermore, the model is also used with SITI data to estimate the previously unreported latent enthalpy (5 J/g) associated with the α (PETN-I) to β (PETN-II) polymorphic phase transformation of PETN.

42 ENGINEERING↗
DOE OSTI2022

Time dependent supervisory control update with FARM using rolling window

This report describes improvements to the Feasible Actuator Range Modifier (FARM) component of the RAVEN-based HYBRID framework for analysis of Integrated Energy Systems (IES). FARM supports the HERON plug-in that solves the power dispatch problem. The solution to the dispatch problem involves economically optimal dispatches that satisfy limits on production variables and their rates of variation (explicit constraints) as well as process variables tied to the service life of equipment (implicit constraints). FARM serves to validate or confirm that a HERON solution for explicit constraints also satisfies the implicit constraints. FARM-alpha was released by Argonne National Laboratory in January 2021 followed by FARM-Beta in January 2022 with the latter providing increased flexibility for the user. In this report, FARM-Gamma, the latest version of the code, is described. The major improvement is the implementation of a system identification algorithm based on the Dynamic Mode Decomposition with Control (DMDc) coupled with a “Rolling Window” scheme that allows obtaining linear time-varying state-space models. This feature equips FARM with the most accurate approximation of system dynamics, and it relieves the user from the burden of performing an exhaustive off-line characterization of the dynamics. FARM-Gamma capabilities are assessed by solving the power dispatch problem for a representative IES unit. The simulation times corresponding to the different releases are estimated and compared. These values capture the increasing computational burden of the successively higher fidelity state-space models adopted by FARM-Alpha, FARM-Beta and FARM-Gamma. The code implementation provides significant flexibility, i.e., the user can always select the most suitable version of FARM according to the problem to be solved and the available computational resources. It is anticipated that FARM will play a role in addressing several future IES applications. We outline how it can support the coordinated management and safe operation of a nuclear plant coupled to industrial processes to produce hydrogen and synfuels.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
DOE OSTI2024

Accelerating particle-in-cell kinetic plasma simulations via reduced-order modeling of space-charge dynamics using dynamic mode decomposition

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. Here, we demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Stabilizing Nickel‐Rich Cathodes in Aqueous Process through Nanocellulose as Water Barrier

Nickel-rich LiNi 0.8 Co 0.1 Mn 0.1 O 2 (NMC 811) cathode offers high voltage and high specific capacity, making it promising for high energy density batteries. However, large-scale manufacturing of aqueous-processed NMC 811 electrodes remains challenging due to proton exchange causing material decomposition and capacity loss. This work addresses this issue by constructing an in situ nanocellulose protective layer for NMC 811 particles via electrostatic interactions during the slurry preparation. For the first time, the interatomic spacing between inter-chains of nanocellulose is measured through wide-angle X-ray scattering and demonstrate the ability to effectively confine interlayer water using atomistic simulations. Moreover, this nanocellulose coverage simultaneously minimizes Li + surface segregation and mitigates water infiltration. Owing to less material decomposition during the aqueous processing, nanocellulose-protected NMC electrodes exhibit higher initial coulombic efficiency (83% vs 62% at 0.1C) and capacity (133 vs 59 mAh g −1 at 6C) than unprotected electrodes. Additionally, optimized aqueous-processed NMC electrodes offer comparable or even superior electrochemical properties compared to the electrodes fabricated using the conventional toxic organic solvent, N-methyl-2-pyrrolidone. Consequently, the developed approach enables affordable, sustainable aqueous processing for Nickel-rich NMC 811 cathodes with excellent electrochemical performances.

25 ENERGY STORAGE↗
DOE OSTI2025

Spatiotemporal Energy Cascade in Three-Dimensional Magnetohydrodynamic Turbulence

We present a new scale decomposition method to investigate turbulence in wavenumber-frequency space. Using 3D magnetohydrodynamic turbulence simulations, we show that magnetic fluctuations with time scales longer than the nonlinear time exhibit an inverse cascade toward even smaller frequencies. Low frequency magnetic fluctuations support turbulence, acting as an energy reservoir that is converted into plasma kinetic energy, the latter cascading toward large wavenumbers and frequencies, where it is dissipated. Our results shed new light on the spatiotemporal properties of turbulence, potentially explaining the origin and role of low frequency turbulent fluctuations in the solar wind.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Development of Multiresolution Capabilities for the Holistic Energy Resource Optimization Network (HERON) tool A progress update

INL researchers work on technoeconomic analyses for integrated energy systems (IES) using the Framework for Optimization of ResourCes and Economics (FORCE). Within FORCE, researchers use the Holistic Energy Resource Optimization Network (HERON) tool to conduct optimization of grid portfolios under uncertain market conditions. These optimizations determine optimal capacities for all IES components and strategies for resource dispatch which maximize some economic metric (e.g., net present value). Resource dispatch occurs on finer timescales (typically hours) and thus are asked to respond to a given time series (e.g. hourly load demand profiles for a grid, or pre-determined electricity prices). Volatile and complex bidding dynamics as well as poorly forecasted weather events within deregulated markets add uncertainty to the time series; FORCE can address this uncertainty by training a reduced order model on historical time series and generate unique synthetic time series which represent individual scenarios or realizations of the market. The IES configuration can be simulated under these different sampled realizations and a stochastic optimization is conducted which optimizes the expected value of the desired economic metric. The training of a synthetic time series generator is limited by the chosen time resolution; dynamics can occur on different time scales. Seasonal demand trends can dominate faster dynamical events (such as power outages from certain sectors or severe weather events) which might not get captured correctly by the trained model. In this report, we investigate different ways of addressing the training and generation of time series on multiple time scales using three main algorithms: wavelet decomposition, dynamic mode decomposition, and generative adversarial networks for time series. We demonstrate a time series analysis that yields information on not just the frequency space but also temporal space: where a fast Fourier transform can provide what frequencies dominate, the new algorithms can provide when the frequencies dominate as well. These analyses can help improve IES optimization by allowing researchers to couple simulations at different timescales when it is most needed - seasonal, day-ahead, and real time optimization - with greater computational efficiency. Future work will include implementation of a subset of the proposed algorithms into the FORCE toolset and application of these analyses into multiple timescale optimization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗