Ultra-real-time simulation is crucial for ensuring the safe operation and control of nuclear power plants, as it enables rapid prediction and response to thermal-hydraulic behavior under accident conditions. This study proposes an ultra-real-time thermal-hydraulic modeling approach for the reactor primary circuit based on an intrusive reduced-order model (ROM). The governing equations of all components are discretized using a finite difference scheme, and variables for establishing ROMs are selected from these discretized equations to eliminate nonlinear terms. The transient solutions obtained from the initial 5% of time steps, calculated by the full-order model, served as snapshots, from which characteristic modes are extracted using the proper orthogonal decomposition. By projecting the discretized governing equations of each component onto the characteristic mode space, ultra-real-time thermal-hydraulic ROMs are constructed for each component. The integration of these ROMs for all components resulted in a comprehensive ultra-real-time model (URTM) of the primary circuit, capable of predicting system evolution. Simulation results demonstrated that the URTM achieves ultra-real-time performance while maintaining a maximum relative error of less than 0.15% for key thermal-hydraulic parameters.

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) by integrating physical laws into the training process. However, their application to multi-material neutron diffusion problems in nuclear reactor physics presents significant challenges due to discontinuities in material properties at interfaces, where abrupt changes in diffusion coefficients lead to non-smooth solutions that are difficult for neural networks to approximate accurately. To address these limitations, we propose an enhanced Physics-Specialized Neural Network (PSNN) approach, integrated with a Source Iteration (SI) technique. This method introduces improved construction methods for specialized functions, utilizing both low-order and high-order polynomial approaches, with specific implementations for one-dimensional and two-dimensional multi-material problems. The specialized functions are engineered to inherently satisfy value and flux continuity conditions at material interfaces as hard constraints, rather than as soft constraints incorporated into the loss function. The SI-PSNN method combines the interface handling capabilities of PSNN with the efficiency of source iteration for eigenvalue problems. We demonstrate the effectiveness of this approach through comprehensive numerical experiments. For multi-group eigenvalue problems, SI-PSNN achieves validation on classical reactor physics benchmarks, producing L-2 errors of 8.22x10(-4) and 1.34x10(-3) for two energy groups on the TWIGL benchmark, with a k(eff) error of only 10.20 pcm, significantly outperforming the SI-PINN, which records errors of 2.48 x 10-2 and 3.01 x 10-2 with a k(eff) error of 922.28 pcm. Additionally, high accuracy is maintained on the IAEA benchmark with 69 subdomains, yielding L-2 errors of 3.30 x 10(-3) and 3.10 x 10(-2), along with a k(eff) error of 124.54 pcm. The proposed method alleviates the limitations of PINNs in multi-material neutron diffusion problems, explores the application of PSNN in neutron diffusion eigenvalue problems, and enhances the capability of physics-informed neural networks in nuclear reactor physics calculations.

In lead bismuth eutectic (LBE) cooled steam generators, flexible heat exchanger tubes operate under external crossflow and internal evaporation, but the effect of evaporation induced axial mass variation on the coupled vibration, wake, and wall heat transfer response remains unresolved. An evaporation-informed quasi-three-dimensional URANS fluid-structure-interaction model was developed in which axial mass-ratio distributions from a separate fixed-tube three-dimensional internal-evaporation pre-calculation were prescribed slice by slice in a strip-theory sequential-coupling framework. The simulations covered a cylinder with L/D=200, three evaporation derived axial mass ratio distributions M1∗, M2∗, and M3∗, external LBE inflow velocities U1 of 0.1–0.5 m/s. Increasing inflow velocity changed the cross-flow response from a nearly uniform low amplitude state with Ay/D=0.33 to 0.60 at 0.1 m/s to a double peaked spanwise distribution with dominant peaks of 2.64 to 2.86 at 0.3 to 0.5 m/s, while the dominant frequency remained largely single and narrowband along the span. Under the prescribed-wall external-convective definition, the surface-averaged Nusselt number increased from 7.41 × 102 to 1.83 × 103 over the tested inflow range. At low U1, the reconstructed sectional wake showed slice-wise variation between supported 2S and P + S patterns with residual wake interaction near lock-in, whereas higher inflow velocities restored a more stable 2S shedding pattern.

Physics-Informed Neural Networks with hard constraints (HC-PINNs) enforce boundary conditions exactly via a trial function ansatz u˜=A+B·N, yet the theoretical mechanisms governing their training dynamics have remained unexplored. This work establishes a Neural Tangent Kernel (NTK) framework for HC-PINNs, revealing that the boundary function B acts as a multiplicative spatial modulator that fundamentally reshapes the kernel eigenspectrum-a mechanism fundamentally distinct from additive penalty terms in soft-constrained formulations. Through spectral analysis of the residual NTK Kr, the effective rank reff is identified as a robust, deterministic predictor of training convergence that outperforms classical condition numbers. It is shown that poorly chosen boundary functions can induce spectral collapse-the concentration of the eigenvalue spectrum toward zero-leading to optimization stagnation despite exact boundary satisfaction. The framework is extended to nonlinear PDEs via local Fréchet linearization and validated on the 1D viscous Burgers equation. A systematic finite-width and optimizer consistency study quantifies the gap between idealized NTK theory and practical training with Adam/L-BFGS, demonstrating that the initial reff retains diagnostic value as a convergence feasibility indicator despite feature learning. Building on these theoretical insights, an automated boundary function design algorithm is proposed that selects optimal candidates based on initialization-time spectral screening, bridging the gap from analysis to methodology. Validated across 1D/2D/3D linear diffusion benchmarks, nonlinear Burgers, and against representative soft-constraint and adaptive baselines, this framework transforms boundary function design from a heuristic choice into a principled spectral optimization problem, providing a solid theoretical foundation for hard constraints in scientific machine learning.

This study presents a general interpolation-supplemented lattice Boltzmann model (GILBM) for simulating neutron transport in complex geometries using non-uniform and non-orthogonal meshes. The physical domain with irregular geometry is transformed into a regular computational domain using the body-fitted mesh method, where the lattice Boltzmann method is applied. An additional interpolation step between migration and collision processes is used, maximizing the preservation of locality and parallelism inherent in the standard lattice Boltzmann method. The accuracy and flexibility of the GILBM are demonstrated through simulations of three representative neutron transport benchmark problems, including the neutron shielding problem, the heterogeneous 3 x 3 fuel pins problem, and the plate fuel problem. Numerical results exhibit good agreement with reference solutions, validating the effectiveness of the proposed methodology. This work can provide valuable insights into simulating neutron transport in complex geometries, contributing to developing more accurate and efficient simulation tools.

Simulation of flow and heat transfer in rod channels is essential for nuclear reactor safety. Its complexity poses significant challenges for computational implementations. This paper presents a numerical study on the thermal-hydraulic behavior in rod channels using the Direct Numerical Simulation (DNS) method. The flow and temperature distributions in a 3 x 3 square rod bundle with a Reynolds number of 22876 are investigated. The flowing and heat transfer characteristics in different regions are analyzed. A comparison of various turbulence models, including the k-" models, k-! models, and the Reynolds Stress models, are conducted to evaluate their performance in predicting the velocity and temperature distributions. The results show that the Stress-BSL model and SST k-! model exhibit better overall performance. This work can provide some data reference for the subsequent detailed flow and heat transfer analysis of fuel rod bundles, and provide some insights for the improvement of turbulence models.

The Medium-Earth Orbit(MEO)-airborne bistatic synthetic aperture radar (SAR) system provides advantages such as high transmitter altitude, strong survivability, and high observation flexibility. However, the inherent characteristics of this system result in spatial variation in the slant range history of different scattering points within the observed area. This paper presents the qualitative assessment on the two-dimensional (2-D) spatial variation caused by the system geometric configuration firstly, and the accurate slant range history model is established followed by the proposal of a virtual scattering points fitting method to analyze the impact of 2-D spatial variation in SAR imaging procedure quantitatively. Then, the correction algorithm is proposed to compensate the spatial variation in the range dimension through the block processing and mitigate the azimuth dimension variation by the nonlinear chirp scaling(NCS) method. Finally, the experimental results with simulated and semi-real data validate the generalizability and practicality of the proposed approach.

The high-dimensional characteristics of the neutron transport equation coupled with the k-eigenvalue problem in steady-state scenarios present formidable computational complexity and memory consumption challenges for full-core detailed modeling. This work introduces a massively parallel GPU accelerated discontinuous-Galerkin method for SN equation solving based on upwind sweeping, utilizing an angle-space two-level parallelization scheme integrated with efficient JFNK iteration and double-buffered memory management. Validation via a series of large-scale benchmarks confirms that the integrated approach can significantly enhance computational efficiency while reducing GPU memory requirements. During inner-iteration transport sweeps, parallel computation on a single A100 GPU achieves a speedup ratio of 362 to 3367 times per sweep compared to single-core CPU execution. For outer iterations, the JFNK algorithm significantly reduces the number of transport sweep relative to power iteration, yielding a further acceleration of 11 to 241 times in overall solution time. Moreover, a CMFD-based physics preconditioner is incorporated into the JFNK framework (PJFNK), further reducing the number of transport sweeps by a factor of 1.45-7.64 and decreasing total runtime by 1.14-5.25 & times;. The double-buffered strategy effectively minimizes memory consumption during transport sweeps and JFNK operations. In summary, the integrated numerical method can realize 3-D full-core pin-by-pin calculations efficiently using a single GPU with 24.99 GB memory, representing an efficient single-GPU computing tool of SN-DGM high-resolution neutron transport for engineering-scale full-core analysis.

As high-fidelity reactor burnup calculations advance toward large-scale spatial and full-core simulations, the complex evolution of nuclide dynamics imposes significant computational and storage burdens. Traditional linear model reduction methods exhibit theoretical limitations when processing highly stiff burnup systems, including the loss of initial state information and poor parameter adaptability. To address these issues, this paper proposes an efficient calculation method for burnup systems based on Augmented Invariant Manifolds (AIMs), grounded in nonlinear dynamical system theory. By constructing an augmented invariance equation, this method embeds the initial nuclide density as a geometric constraint into the manifold mapping, achieving high-fidelity reconstruction of the system's transient and global evolution characteristics. Coupled with an advanced Modified Gram Schmidt-Arnoldi (MGS-Arnoldi) iteration algorithm, the AIM method fully exploits the sparse structure of the burnup matrix. This algorithm avoids costly global matrix factorization and offline pre-computation, enabling real-time construction of Reduced-Order Models (ROMs) without the need for offline data sets. Numerical verification employs JAEA-MOX pin-cell and assembly benchmarks under both constant and variable power conditions. Results indicate that a low-order manifold of dimension 7 strictly restricts most nuclide prediction deviations to within 1%, while a 10th-order manifold limits total nuclide deviation to under 0.3%. The method remains highly stable even under strongly nonlinear conditions involving sudden power changes. Regarding computational performance, the speedup ratio for single-step solution is approximately 46 to 79 times depending on the model order, and memory consumption is reduced to below 10%. The proposed method achieves high-fidelity nuclide prediction based on a low-dimensional manifold while maintaining excellent parameter adaptability and significantly improving computational efficiency. It provides a theoretically rigorous and engineering-feasible nonlinear reduced-order approach for full-core high-fidelity neutronics-burnup coupling calculations.

The intrusive reduced-order model (IROM) has been developed for detailed neutron transport solving to reduce its expansive computational costs. These techniques take neutron angular fluxes with consistent spatial angular discretization format as snapshots, which limits the generality of existing computing software, especially commercial software. In this work, a general IROM (GIROM) for neutron transport equation (NTE) is proposed. The neutron scalar fluxes from any deterministic method can be directly used as snapshots, which effectively improves the universality of neutron transport IROM. Based on the angular integrated NTE, the corresponding neutron convection term can be calculated by neutron scalar flux. Both the neutron scalar flux and convection term are taken as snapshots to eliminate the dependency on snapshot discretize formats. Numerical results show that the GIROM is compatible with the neutron scalar flux of various deterministic neutron transport solvers, and the computational efficiency can be effectively improved.

Multiscale multiphysics simulation is a key technology for nuclear reactor system design and analysis. However, its application and development are limited by the complexity of cross-scale simulation coupling and long calculation times. To satisfy the real-time simulation requirements of modern reactor digital twins, this study establishes a digital twin of the reactor circuit using multiphysics and multiscale reduced-order methods. This digital twin is based on the plug-and-play approach, and all simulations of the components are replaced by independent 1D and 3D multiphysical reduced-order surrogate models. The complete system circuit can be composed of a combination of these surrogate models, which allows for the easy integration of new components and modification of existing components. A digital twin circuit is established for the test case. The reactor core is described using the 3D neutronics/thermal-hydraulics model, whereas the steam generator is described using the 3D CFD model. The other components, including the heat and cold pipes, are described using a 1D reduced-order model. The numerical results show that the digital twin can accurately predict the multiphysics and multiscale behavior of the reactor circuit. The maximum relative error of the tested circuit is not larger than 0.05%, and the simulation time can be reduced to less than 2 ms. The proposed plug-and-play digital twin can be used to develop a new real-time digital twin system that can support reactor system design and analysis.

Yttrium hydride emerges as a promising high-temperature solid moderator for advanced nuclear reactors. Irradiation-induced vacancies and voids, which critically influence hydrogen (H) redistribution and moderation performance, remain not fully understood. This study systematically investigates the mechanistic role of Y vacancies on H migration through first-principles calculations and on-the-fly machine learning molecular dynamics simulations. First-principles analyses of binding energies and migration barriers reveal a pronounced repulsive interaction between Y vacancies and adjacent H atoms. This phenomenon arises from (i) weakened H binding at first nearest neighbor tetrahedral sites (T-sites) and enhanced binding at second nearest neighbor T-sites of the Y vacancy, and (ii) reduced migration barriers for H migration away from Y vacancies and elevated barriers for their reverse processes. Molecular dynamics simulations quantify H diffusion coefficients, radial distribution functions, H site occupancies, and spatial H distributions in systems containing Y vacancies/voids. Notably, H atoms are entirely excluded from the cores of Y vacancies/voids, even at elevated temperatures, precluding spontaneous formation of H bubbles or clusters in these irradiation-induced defects. Furthermore, Y vacancies/voids may exhibit resistance to macroscopic H transport under external driving forces, as evidenced by the Y vacancy/void-mediated H redistribution. These atomic-scale insights into interactions of Y vacancy and H aides to establish a theoretical framework for predicting H transport in irradiated yttrium hydrides moderators and elucidating the impact on neutron moderation efficiency.

Yttrium hydride is a promising high-temperature neutron moderator for next-generation nuclear systems, but oxygen and fluorine impurities are inevitably introduced during fabrication. This study systematically explores the effects of isolated, clustered, and co-existing O and F impurities via first-principles calculations and on-the-fly molecular dynamics simulations. O exhibits a strong site-pinning effect due to its high migration barrier and strong Y-O binding, which restricts H pathways and prevents the dispersion of aggregated O; however, it simultaneously lowers the local H binding strength, thereby promoting H desorption. In contrast, F can migrate via site-exchange with H benefiting from its low migration barrier, imposing negligible influence at low concentration, but a kinetic hindrance was observed at high local aggregation due to its larger mass. Furthermore, an attractive interaction between O and F was identified. These atomic-scale insights provide fundamental understanding for predicting H transport and underscore the critical importance of oxygen control.

Hard-Constrained Physics-Informed Neural Networks (HC-PINNs) embed boundary conditions directly into the network architecture through specially designed trial functions, yet their practical performance is often bot tlenecked by boundary function construction and hyperparameter tuning on complex geometries. This work introduces a theoretically-grounded automated design criterion based on Neural Tangent Kernel (NTK) spectral analysis, connecting boundary function choices to training dynamics. The effective rank (reff) of the residual NTK matrix is identified as a training-free performance predictor, and an NTK-guided Bayesian Optimization framework is developed to efficiently tune boundary-function hyperparameters. On star-shaped and gear-shaped benchmarks, the proposed method achieves 89.2%-90.8% time reduction compared to exhaustive grid search, with identified configurations consistently outperforming 97% of grid search attempts. Overall, a systematic path way is established from NTK theory to automated boundary function design, enabling quantitative, theory-driven HC-PINN configuration with order-of-magnitude computational savings.

Carbon-based anode materials are frontrunners in the realm of potassium-ion storage, yet their performance is frequently hampered by insufficient reversible capacity and sluggish rate capabilities. To surmount this challenge, single-atomic sulfur incorporated nano carbon spheres (SASNCSs) were synthesized through a one-step co-carbonizing the mixture of nanosphere precursor and sulfur powder. Near edge X-ray absorption fine structure spectroscopy revealed the presence of single-atomic sulfur in the form of C-S-C bonds within the nanocarbon spheres. The single-atomic sulfur not only serves as active sites for K+ storage, enhancing reversible capacity, but also expands the interlayer spacing of the carbon structure, facilitating rapid K+ diffusion. Consequently, SASNCS 1-3, with an optimized single-atomic sulfur content of 24.54 wt%, showcased superior cyclability and an impressive reversible capacity of 414.6 mAh g(-1) at 0.1 A g(-1), marking a 66 % increase over pristine nano carbon spheres (249.3 mAh g(-1)). Moreover, SASNCS 1-3 demonstrates exceptional high-rate performance, retaining 173.9 mAh g(-1) at an ultra-high rate of 20 A g(-1) (charging/discharging within similar to 31 s). The enhanced electrochemical performance of SASNCS 1-3 is attributed to its non-diffusion-dominated mechanism with superior electrochemical kinetics. Theoretical calculations substantiate the strong potassium adsorption affinity and significant charge transfer at the single-atomic sulfur sites, which are pivotal for achieving outstanding potassium storage performance. The assembled K-ions capacitors utilizing SASNCS 1-3 anodes exhibit stable cycling performance with a high-capacity retention of 76.4 % after 4000 cycles and excellent charge/discharge characteristics, demonstrating promising future of SASNCS anodes in practical application. This work offers a simple yet effective strategy to develop carbon-based materials enriched with single-atomic sulfur, thereby boosting potassium storage performance and highlights their promising potential in potassium-based electrochemical energy storage devices.

Yttrium hydride (YHx) is a promising candidate for high-temperature neutron moderator in advanced nuclear reactors, with hydrogen migration significantly influencing its neutronic and thermal properties. To better understand the migration mechanism of hydrogen in YHx, this study employed first-principles calculations and on-the-fly machine learning molecular dynamics to investigate hydrogen migration pathways, energy barriers, and diffusion coefficients. The results indicate that hydrogen primarily diffuses via octahedral interstitial sites and the increase in H/Y ratio can lead to higher octahedral site occupation and slower diffusion. Additionally, vacancies tend to aggregate after hydrogen migration, particularly at higher temperatures. This study provided a detailed microscopic understanding of hydrogen migration mechanisms in YHx, offering valuable insights for predicting and optimizing material performance.

Transition metal dichalcogenides (TMDs) emerge as advanced anode materials of potassium-ion batteries (PIBs), owing to the impressive capacities, strong redox reversibility, and advantageous conversion reactions with relatively weak metal-sulfur bonds. However, TMDs face inherent drawbacks that contribute to suboptimal rate performance and limited cycling stability such as low electrical conductivity, sluggish reaction kinetics, and unsatisfactory structural stability. To overcome these challenges, ultrafine heterojunction (between CoS2 and FeS2) wrapped in two-dimensional transition metal carbides (MXene) and nitrogen-sulfur co-doped carbon network (MXene@CoS2/FeS2@NSC) is synthesized as anodes for PIBs. The built-in electric field generated by heterojunction and high specific surface area network of MXene and carbon both contribute to excellent electrochemical performance. Consequently, the synthesized MXene@CoS2/FeS2@NSC anode exhibits impressive reversible capacity (605/175 mA h g- 1 at 0.05/10 A g- 1) and outstanding cycling stability (304 mA h g- 1 at 0.5 A g-1 after 2000 cycles). The assembled potassium ion capacitors (PICs) with MXene@CoS2/FeS2@NSC anode exhibit outstanding cycling performance, maintaining nearly 100 % coulombic efficiency and over 10,000 cycles with 96 % capacity retention at 10 A g- 1. This work introduces a versatile synthetic method for preparing bimetallic sulfide heterojunction, providing useful points for the further study of advanced electrode materials for PIBs.

Developing transition metal-based catalysts is a feasible approach to decrease the cost of fuel cells. In this paper, we synthesized a worm-like carbon nanotubes (CNTs) encapsulated Fe3P and Fe0.8Mn0.2 alloy based catalysts (FP/FM@CNTs) for oxygen reduction reaction (ORR) by calcination method. The precursor for the calcination was prepared by hydrothermal method. The CNTs encapsulation structure was confirmed by SEM, HRTEM, XRD, XPS and EDS tests. The electrocatalytic performances for ORR of the catalyst were examined in 0.1 M KOH electrolyte by using CV, LSV, Tafel, EIS, RDE and RRDE tests. The obtained results presented that the half-wave potential(E1/2) of FP/FM@CNTs catalyzed ORR was 0.892 V (vs. RHE), the maximum current intensity and the Tafel slope of FP/FM@CNTs catalyzed ORR were superior to that of the Pt/C catalyst. The density function theory calculation ascertained that the encapsulated Fe3P made the carbon atoms in surface layer CNT in negative electron state that could transfer electrons easily to oxygen molecular and promote the ORR happening. On the other hand, the CNTs encapsulation structure protected the Fe0.8Mn0.2 alloy and Fe3P from the directly contact with electrolyte and other reactants, which assured the long-term operational stability of the catalysts. The content of this paper presents a novel approach for designing high-performance catalysts.

The Nuclear Reactor Digital Twin (NRDT) has garnered significant attention in recent years. One of the crucial aspects in NRDT is the real-time inversion of nuclear reactor core material cross-sections during reactor operation. In general, an inverse problem is solved by combining multiple iterations of the forward problem with an optimization algorithm. Even though the development of a surrogate model has significantly enhanced the computational efficiency of forward problems, the iteration process still poses a challenge to real-time inversion. To address this problem, this paper presents a real-time inverse problem solver (RIPS). During the offline stage, RIPS establishes a mapping between the sparse neutron detector data and the cross-sections through the reduced-order model and radial basis function. During the online stage, the corresponding cross-section can be calculated directly using the mapping and neutron detector data. Since the RIPS eliminates the multiple iterations of traditional methods, the efficiency of RIPS can be improved by orders of magnitude, and enables real-time online calculation. Three typical numerical benchmarks are tested for verification in this paper, which proves that the maximum relative error of RIPS does not exceed 0.54 % and the average relative error does not exceed 0.1986 %. Furthermore, for each test case, the calculation time of RIPS is within 0.01 s. This work can provide useful suggestions and applications, and further development in cross-section inversion.