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DOE OSTI2026

A meshing framework for digital twins for extrusion based additive manufacturing

Additive manufacturing (AM) allows for manufacturing of complex three-dimensional geometries not typically realizable with standard manufacturing practices. The internal microstructure of AM components has a significant impact on mechanical, vibrational, and shock properties and permits richer design space when this is controllable. Due to complex interactions of internal geometry of an extrusion-based AM component, it is common practice to assume homogeneous behavior or to perform characterization testing on specific toolpath configurations. To avoid testing or material waste, it is necessary to develop a consistently accurate numerical simulation framework with relevant boundary value problems that can handle the complicated geometry of internal material microstructure present in AM components. Herein, a framework is proposed to directly create computational meshes suitable for finite element analysis (FEA) of the fine-scale features generated from extrusion-based AM tool paths to maintain a strong process–structure–property-performance linkage. This mesh can be manually or automatically analyzed using standard FEA simulations such as quasi-static preloading or modal analysis. The framework allows an in-silico assessment of a target AM geometry where fine-scale features greatly impact quantities of design interest such as in soft elastomeric lattices where toolpath infill can greatly influence the self-contact of a structure in compression, which we use as a motivating exemplar. This approach greatly reduces both time and resource waste present in traditional build and test design cycles for non-intuitive design spaces, and acts as a tool for use in the production of a key component of a digital twin, a mesh suitable for finite element analysis. In conclusion, it also further allows for the exploration of toolpath infill to optimize component properties beyond simple linear properties such as density and stiffness.

Additive manufacturing↗

DOE OSTI2025

RE-INTEGRATE EMT Simulation Software: Graph Convolutional Network for Sparse Matrix Pattern Detection

The increasing complexity of power networks, driven by proliferation of inverters, presents analytical challenges that simplified models often fail to capture, necessitating Electromagnetic Transient (EMT) simulations. EMT models are represented as discretized differential-algebraic equations (DAEs), forming a linear system Ax = b that is computationally intensive to solve. Due to inherent sparsity of adjacency matrix A, distinct patterns emerge that, when accurately identified, enable efficient solver selection to minimize computation time. However, identifying ideal pattern is complicated by numerous reordering algorithms and limited structural insights. To address this, we introduce a Graph Convolutional Network (GCN) model for classifying sparse matrix patterns common in power system analysis. The model, achieving 96% test accuracy, is validated using PV plant models of 125 MW capacities connected to New England 39-bus transmission system (TS), and further scaled to a 4,992-bus network with 384 PV plants, yielding 191, 616 × 191, 616 sized A matrix. For all cases, the GCN model accurately identifies the matrix’s intrinsic sparse pattern, demonstrating its potential to enhance solver performance in EMT analysis.

Hossain, Md Rifat [Florida International Universit↗

DOE OSTI2025

Development of an Advanced Multiphysics Simulation Capability for Radiant's Microreactor Design

Argonne National Laboratory and Idaho National Laboratory, through a Department of Energy Gateway for Accelerated Innovation in Nuclear Voucher, supported key analysis needs of Radiant related to (i) air jacket thermal fluid performance, (ii) evaluation of decay heat source terms defining air jacket technical requirements, and (iii) assessment of modeling methodologies employed for core analysis. All of these activities center on numerical simulation of various aspects of Kaleidos using the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, the Cardinal multiphysics application, the OpenMC Monte Carlo code, and the Nek5000 computational fluid dynamics (CFD) code. This project builds upon an earlier Nuclear Energy Advanced Modeling and Simulation (NEAMS) Thermal-Hydraulic (T/H) Center of Excellence (CoE) project focused on initial demonstration of Cardinal multiphysics simulation of High Temperature Gas Reactors (HTGRs) and now focuses on Radiant’s Kaleidos concept.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Validation of Numerical Tools for Calculating Reactivity Feedback in Sodium Fast Reactors Using SEFOR Experimental Data

The Southwest Experimental Fast Oxide Reactor (SEFOR) was an experimental sodium-cooled fast breeder reactor operated from 1969 to 1972 with experiments designed to measure Doppler reactivity feedback in a wide temperature range from around 350 °F to temperatures approaching the melting point of mixed oxide fuel of around 5000 °F, providing valuable data for code validations. Co-supported by the Department of Energy (DOE) Fast Reactor Program (FRP) and the DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the SEFOR benchmark project focused on using the experimental data to validate numerical tools that are used in industry and academia to design and license sodium-cooled fast reactors (SFRs). By the end of FY-25, substantial progress was achieved in the SEFOR benchmark study. A variety of numerical tools commonly used for modeling SFRs were applied to develop models for SEFOR core configurations I-D, I-E, I-I, and I-J. These included Monte Carlo codes such as MCNP, Serpent, and Shift; deterministic codes such as the legacy Argonne Reactor Computation (ARC) suite and the high-fidelity NEAMS code Griffin; and the system analysis code SAS4A/SASSYS-1 (SAS). Using these models, both SEFOR zero-power experiments and power-ascending tests were successfully simulated. Comparisons were performed against experimental measurements of core criticalities, reflector worth, kinetics parameters (Λ/βeff), isothermal reactivity feedback (from 350 °F to 760 °F at zero power), and power-ascending reactivity feedback (as power increased from 0.4 MW to 17 MW). In general, these comparisons demonstrated very good agreement between numerical results and experimental data. In Fiscal Year 26 (FY-26), the SEFOR benchmark project will continue to address the modeling issues identified in FY-25. Effort will focus on the simulation of reactivity insertion transients in SEFOR core II using the ARC/SAS model. Future work will also focus on incorporating BISON into the SEFOR core modeling process to enable the first Multiphysics simulations of the isothermal tests based on the MOOSE framework.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Design and Analysis of Liquid Lithium Plasma Facing Components

In this study, liquid metal (LM) on plasma-facing components (PFCs) creates a renewable protective cover enhancing power exhaust and protecting the solid substrate. Additionally, energy confinement improvement through particle pumping can be achieved in the case of liquid lithium (LL). A new variant of PFCs was recently introduced at Princeton Plasma Physics Laboratory (PPPL) where a porous wall is used to stabilize the LM surface, while using magnetohydrodynamic (MHD) drive to push the LM flow inside the component. This arrangement allows efficient heat exhaust, and enhanced control of the LM surface temperature, leading to spatial control of evaporation and condensation of LL on the plasma interface. This feature is particularly attractive when vapor shielding is introduced to allow heat flux redistribution. This system has the advantage that as the heat flux increases, the evaporation rate will increase, while decreasing heat flux will decrease the evaporation rate of lithium, ideally creating a feedback effect which could self-regulate the amount of lithium evaporated. Analytical and numerical models for LL PFCs were developed in PPPL. To calculate the target temperature distribution for the case of evaporation from the divertor, we apply an iterative process allowing two-way coupling between the fluid-kinetic analysis of plasma using SOLPS-ITER code and the flow and heat transfer analysis of the PFC using an analytical model. In the last stage, the results are validated using computational fluid dynamics (CFD) analysis with customized version of the CFX code from ANSYS. CFX was modified at PPPL to allow MHD analysis at the high magnetic field typical for fusion applications. Results of the analysis for NSTX-U tokamak conditions will be presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Feasibility Study on Implementing a Staggered-Grid Finite Volume Method for System Analysis Code Development Under the MOOSE Framework

Here, this work summarizes a feasibility study on testing numerical algorithms that are suitable and efficient for advanced system analysis code development under the mutli-physics framework, MOOSE. The key to the test bed is the implementation of high-order one-dimensional staggered-grid finite volume method (SG-FVM), and its direct interaction with the linear/nonlinear solver, PETSc. The test bed utilized a more flexible code structure to enable the finite volume method implementation and direct interacting with the solver package, instead of using the natively supported finite element method by the framework. Using a suite of selected test problems with different problem sizes and levels of complexity, the implemented SG-FVM demonstrated superior performance improvement against a direct finite element method implementation through MOOSE. On two computer systems, the speedup was observed to be significant, with at least one order of magnitude of solving time reduction. For a complex reactor model, transient simulation was performed using the newly developed finite volume method code, the results of which agree very well with the reference results from the finite element method code. Overall, this study demonstrates a successful feasibility study on the proposed numerical algorithms and software structure to support advanced system analysis tool development.

MOOSE↗

DOE OSTI2024

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

Dynamic mode decomposition (DMD)↗

DOE OSTI2024

Thermodynamics of the near-extremal Kerr spacetime

We examine the thermodynamics of a near-extremal Kerr black hole, and demonstrate that the geometry behaves as an ordinary quantum system with a vanishingly small degeneracy at low temperatures. This is in contrast with the classical analysis, which instead predicts a macroscopic entropy for the extremal Kerr black hole. Our results follow from a careful analysis of the gravitational path integral. Specifically, the low temperature canonical partition function behaves as Z ~ T$\frac{3}{2}$ e S 0 +c log S 0 , with S 0 the classical degeneracy and c a numerical coefficient we compute. This is in line with the general expectations for non-supersymmetric near-extremal black hole thermodynamics, as has been clarified in the recent past, although cases without spherical symmetry have not yet been fully analyzed until now. We also point out some curious features relating to the rotational zero modes of the near-extremal Kerr black hole background that affects the coefficient c. This raises a puzzle when considering similar black holes in string theory. Our results generalize to other rotating black holes, as we briefly exemplify.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Speeding up and reducing memory usage for scientific machine learning via mixed precision

Scientific machine learning (SciML) has emerged as a versatile approach to address complex computational science and engineering problems. Within this field, physics-informed neural networks (PINNs) and deep operator networks (DeepONets) stand out as the leading techniques for solving partial differential equations by incorporating both physical equations and experimental data. However, training PINNs and DeepONets require significant computational resources, including long computational times and large amounts of memory. In search of computational efficiency, training neural networks using half precision (float16) rather than the conventional single (float32) or double (float64) precision has gained substantial interest, given the inherent benefits of reduced computational time and memory consumed. However, we find that float16 cannot be applied to SciML methods, because of gradient divergence at the start of training, weight updates going to zero, and the inability to converge to a local minima. To overcome these limitations, we explore mixed precision, which is an approach that combines the float16 and float32 numerical formats to reduce memory usage and increase computational speed. Our experiments showcase that mixed precision training not only substantially decreases training times and memory demands but also maintains model accuracy. Here, we also reinforce our empirical observations with a theoretical analysis. The research has broad implications for SciML in various computational applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Ultra-narrow-linewidth hybrid-integrated self-injection locked laser at 780 nm

Narrow-linewidth lasers are essential across a wide range of applications, including classical and quantum sensing, trapped ion systems, position/navigation/timing systems, optical clocks, and microwave frequency synthesizers. In the visible and near-visible spectrum, low-noise lasers are particularly important for laser trapping and cooling techniques, which are vital for trapped ion quantum computing, sensing, and atomic clocks. In this context, our work showcases a hybrid-integrated narrow-linewidth laser that operates at 780 nm, achieving a self-heterodyne linewidth of 105 Hz. To validate the experimental results, we performed a numerical analysis that combines insights from a many-body theory applied to the gain region with a travelling-wave model to capture the laser dynamics. Our investigation further delves into how the linewidth of the self-injection locked lasers is influenced by the parameters of micro-ring resonators, aiming to assess the potential for achieving Hz-level integrated laser linewidths at 780 nm. This work not only demonstrates the technical feasibility of Hz-level narrow-linewidth lasers but also lays the groundwork for future explorations in the field.

Prokoshin, Artem (ORCID:0009000699760238)↗

DOE OSTI2024

CICE on a C-grid: new momentum, stress, and transport schemes for CICEv6.5

Abstract. This article presents the C-grid implementation of the CICE sea ice model, including the C-grid discretization of the momentum equation, the boundary conditions (BCs), and the modifications to the code required to use the incremental remapping transport scheme. To validate the new C-grid implementation, many numerical experiments were conducted and compared to the B-grid solutions. In idealized experiments, the standard advection method (incremental remapping with C-grid velocities interpolated to the cell corners) leads to a checkerboard pattern. A modal analysis demonstrates that this computational noise originates from the spatial averaging of C-grid velocities at corners. The checkerboard pattern can be eliminated by adjusting the departure regions to match the divergence obtained from the solution of the momentum equation. We refer to this novel approach as the edge flux adjustment (EFA) method. The C-grid discretization with edge flux adjustment allows for transport in channels that are one grid cell wide – a capability that is not possible with the B-grid discretization nor with the C-grid and standard remapping advection. Simulation results match the predicted values of a novel analytical solution for one-grid-cell-wide channels.

Lemieux, Jean-François (ORCID:0000000320845759)↗

DOE OSTI2026

Symmetry dilemmas in quantum computing for chemistry: A comprehensive analysis

Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically generate long and deep quantum circuits; gate-efficient universal operator pools generally break symmetries; and gate-efficient, fully symmetry-adapted operator pools may not be universal. In this work, we analyze such symmetry dilemmas both theoretically and numerically. On the theory side, we prove that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced. To demonstrate the strengths and weaknesses of the three types of pools, we perform numerical simulations using an adaptive algorithm paired with operator pools that are (i) fully symmetry-adapted and universal, (ii) fully symmetry-adapted and non-universal, and (iii) breaking a single symmetry and universal. Our numerical simulations encompass three physically relevant scenarios in which the target state is (i) the global ground state, (ii) the ground state crossed by a state differing in multiple symmetry properties, and (iii) the ground state crossed by a state differing in a single symmetry property. Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved to avoid variational collapse. Together, the formal and numerical analyses provide a practical guide for designing and benchmarking symmetry-adapted operator pools that balance universality, resource requirements, and robust state targeting in quantum simulations for chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

TRUST Contact Thermal Conductance (TRUST-CTC) Report: FY24

The objective of the Delivery Environments (DE) Testbeds to Reduce Uncertainties in Simulations and Tests (TRUST) project is to quantify and help increase confidence in specific areas of computational and experimental capabilities that are applicable to current and future delivery environments. More complete quantification of confidence in experimental and computational capabilities and the sufficient increase of confidence in those capabilities is critical to improving weapons engineering design, qualification, and assessment efforts that are critical to the current and future stockpile. Staff development will include cross-discipline collaboration to provide engineers with experience in both numerical simulations and experimental methods. This work uses and provides feedback on analysis tools and experimental results databases for efficient and responsive engineering which are currently under development. TRUST currently includes five testbeds and their associated engineering analysis baseline models (EABMs): 1. contact thermal conductivity, (CTC) 2. nonlinear dynamics, (ND) 3. sensors in environments for accelerometers, (SEA) 4. sensors in environments for fiber optic displacement gages, and (SEFOD) 5. sensors in environments for thermocouples (SETC). The TRUST project uses single-feature testbeds to quantify uncertainties in specific models and experiments and to identify capability development needs that can help to reduce these uncertainties. Each testbed is designed, configured, and tested in collaboration with groups with design and experimental capability: E-14 and MPA-CINT. The complementary simulations are conducted using W-13 analysis tools and stored in model repositories with plans for incremental progress toward EABM requirements. W-13 extends and exercises the testbed simulations in collaboration with experimentalists for uncertainty quantification of current and future materials, geometries, and environments. Additionally, TRUST is intended to provide engineers in W-13 and E-14 with experience in both numerical simulations and experimental methods through cross-discipline collaborations. Following the introduction to the TRUST project, the remainder of this report focuses on experimental and analytical efforts conducted in Fiscal Year (FY) 2024 relevant to the TRUST Contact Thermal Conductance (CTC) testbed.

42 ENGINEERING↗

DOE OSTI2024

Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green’s functions

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green’s function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green’s function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green’s function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green’s function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green’s function approach and other Green’s function approaches in the numerical exact limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Architectures and random properties of symplectic quantum circuits

Parametrized and random unitary (or orthogonal) n-qubit circuits play a central role in quantum information. As such, one could naturally assume that circuits implementing symplectic transformations would attract similar attention. However, this is not the case, as $\mathbb{SP}(d/2)$—the group of d × d unitary symplectic matrices—has thus far been overlooked. In this work, we aim at starting to fill this gap. We begin by presenting a universal set of generators $\mathcal{G}$ for the symplectic algebra $\mathfrak{sp}(d/2)$, consisting of one- and two-qubit Pauli operators acting on neighboring sites in a one-dimensional lattice. Here, we uncover two critical differences between such set, and equivalent ones for unitary and orthogonal circuits. Namely, we find that the operators in $\mathcal{G}$ cannot generate arbitrary local symplectic unitaries and that they are not translationally invariant. We then review the Schur–Weyl duality between the symplectic group and the Brauer algebra, and use tools from Weingarten calculus to prove that Pauli measurements at the output of Haar random symplectic circuits can converge to Gaussian processes. As a by-product, such analysis provides us with concentration bounds for Pauli measurements in circuits that form t-designs over $\mathbb{SP}(d/2)$. To finish, we present tensor-network tools to analyze shallow random symplectic circuits, and we use these to numerically show that computational-basis measurements anti-concentrate at logarithmic depth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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

Mechanism of Ni-Catalyzed Photochemical Halogen Atom-Mediated C(sp 3 )–H Arylation

Within the context of Ni photoredox catalysis, halogen atom photoelimination from Ni has emerged as a fruitful strategy for enabling hydrogen atom transfer (HAT)-mediated C(sp 3 )–H functionalization. Despite the numerous synthetic transformations invoking this paradigm, a unified mechanistic hypothesis that is consistent with experimental findings on the catalytic systems and accounts for halogen radical formation and facile C(sp 2 )–C(sp 3 ) bond formation remains elusive. We employ kinetic analysis, organometallic synthesis, and computational investigations to decipher the mechanism of a prototypical Ni-catalyzed photochemical C(sp 3 )–H arylation reaction. Our findings revise the previous mechanistic proposals, first by examining the relevance of SET and EnT processes from Ni intermediates relevant to the HAT-based arylation reaction. Our investigation highlights the ability for blue light to promote efficient Ni–C(sp 2 ) bond homolysis from cationic Ni III and C(sp 2 )–C(sp 3 ) reductive elimination from bipyridine Ni II complexes. However interesting, the rates and selectivities of these processes do not account for the productive catalytic pathway. Instead, our studies support a mechanism that involves halogen atom evolution from in situ generated Ni II dihalide intermediates, radical capture by a Ni II (aryl)(halide) resting state, and key C–C bond formation from Ni III . Oxidative addition to Ni I , as opposed to Ni 0 , and rapid Ni III /Ni I comproportionation play key roles in this process. Furthermore, the findings presented herein offer fundamental insight into the reactivity of Ni in the broader context of catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗