Nuclear Engineering and Design最新文献

{"title":"Surface decontamination of uranium using a starch-based magnetic strippable hydrogel","authors":"Jian Li ,&nbsp;Yi Wang ,&nbsp;Zhanguo Li ,&nbsp;Jianlong Wang","doi":"10.1016/j.nucengdes.2025.114199","DOIUrl":"10.1016/j.nucengdes.2025.114199","url":null,"abstract":"<div><div>Strippable hydrogels are recognized as promising candidates for radioactive decontamination applications owing to their non-generation of liquid waste, negligible substrate damage potential, and scalable deployment characteristics. Nevertheless, limitations persist in conventional hydrogel systems regarding the retrieval of desiccated film residues. In this study, a starch/Fe₃O₄ composite hydrogel was developed through a one-pot polymerization methodology that capitalizes on the inherent non-toxicity of starch constituents and the magnetophoretic properties of Fe₃O₄ nanoparticles. The synthesized hydrogel demonstrated pronounced embrittlement characteristics upon dehydration, attaining a saturation magnetization value of 2.98 emu/g (at 4 % Fe₃O₄ loading), which facilitated magnetic recovery operations with retrieval efficiencies exceeding 96.67 %. Uranium decontamination efficiencies were quantified across multiple substrates, yielding values of 89.62 % for ceramic, 81.33 % for glass, 83.93 % for steel, 68.95 % for rubber, 54.64 % for paint, and 11.82 % for concrete. Rheological characterization revealed shear-thinning behavior, with viscosity reduced to 93.21 mPa·s under shear stress conditions, thereby enabling effective spray deposition. The Application trial demonstrated that starch/F₃O₄ hydrogel can be successfully applied to the concrete surface by spraying, and brittle fracture can be recycled by magnets. This investigation establishes a sustainable decontamination paradigm through the synergistic integration of magnetically assisted recovery mechanisms with the adsorptive capacity of starch-based matrices, addressing both operational efficacy and post-treatment waste management challenges.</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"442 ","pages":"Article 114199"},"PeriodicalIF":1.9,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144223648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"3DVar data assimilation for inversion optimization of main steam system parameters in nuclear power plants using forecast-gradient and residual FCN","authors":"Xiaoyu Luo ,&nbsp;Sheng Zheng ,&nbsp;Dazhi Zhang ,&nbsp;Xian Zhang ,&nbsp;Shanglong Huang","doi":"10.1016/j.nucengdes.2025.114170","DOIUrl":"10.1016/j.nucengdes.2025.114170","url":null,"abstract":"<div><div>The main steam system is crucial for the safety of nuclear power plants, and predicting its operating parameters is essential for monitoring system performance and improving energy efficiency. Since the damping coefficients in steam pipes cannot be directly measured, numerical simulations are typically used. However, model simplifications and uncertainties in modeling parameters lead to discrepancies between the simulations and actual. To address this issue, we propose ResFCN-3DVar, a novel data assimilation method that optimizes modeling parameters using observable quantities. The primary innovation lies in leveraging a residual-based fully connected network (ResFCN) to construct the observation operator, effectively handling the nonlinear and complex system-level model. Additionally, we incorporate a second-order finite difference matrix within the 3DVar framework to improve computational efficiency. Experiments using a dataset simulated by the full-scope simulator showed that the root-mean-square error (RMSE) of the assimilation results remained below 1%, demonstrating the effectiveness of ResFCN-3DVar in optimizing modeling parameters.</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"441 ","pages":"Article 114170"},"PeriodicalIF":1.9,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144213106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Digital engineering workflow for effective management of ITAAC using text analytics and 4D BIM concept for construction of nuclear power plants","authors":"Liannian Wang ,&nbsp;Harleen Kaur Sandhu ,&nbsp;Kevin Han ,&nbsp;Abhinav Gupta","doi":"10.1016/j.nucengdes.2025.114147","DOIUrl":"10.1016/j.nucengdes.2025.114147","url":null,"abstract":"<div><div>Ensuring conformity to the Inspections, Tests, Analyses, and Acceptance Criteria (ITAAC), as outlined in the combined license, is a prerequisite for the startup and operation of nuclear facilities within the United States. However, current ITAAC management practices are inefficient due to being voluminous document-centric, susceptible to omission, and laborious to maintain. To address these challenges, this study presents a framework for ITAAC management practices based on 4D Building Information Modeling (BIM) at the building elements level. The proposed framework integrates the building elements and corresponding ITAAC information by extracting properties associated with building elements from Industry Foundation Classes (IFC) files, and the design commitments mentioned in ITAAC documents. This digital integration can then be visualized within the 4D BIM platform. The efficiency and feasibility of the proposed approach, for both the nuclear licensees and the regulatory bodies, are demonstrated in a specific prototype implementation. It allows for the effective identification and verification of the conformity of building components with ITAAC, facilitates real-time tracking of ITAAC completion processes, and improves communication dynamics by incorporating a collaborative environment between licensees and regulators. Additionally, by automating manual tasks such as data entry and documentation management, the framework reduces the time and effort required from personnel. The framework’s feasibility enhances its practicality and applicability in real-world scenarios, further contributing to its effectiveness in streamlining ITAAC management. This research contributes to the field by providing a practical and efficient method to streamline ITAAC management, thereby enhancing the overall reliability and efficiency of nuclear facility licensing processes.</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"441 ","pages":"Article 114147"},"PeriodicalIF":1.9,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Small modular reactors and the transition to renewable energy","authors":"Efstathios E. Michaelides ,&nbsp;Dimitrios N. Michaelides","doi":"10.1016/j.nucengdes.2025.114207","DOIUrl":"10.1016/j.nucengdes.2025.114207","url":null,"abstract":"<div><div>Since the operation of nuclear reactors does not emit any carbon dioxide in the atmosphere, nuclear energy may significantly contribute to the decarbonization of the electricity generation industry. Small modular reactors can be parts of the local mini- and micro-grids that are touted to power in the decarbonized future local communities in combination with the highly diffused solar and wind power. Such a micro-grid, serving the equivalent of 50,000 buildings, is studied for the region of North Texas. The power demand of this community is satisfied by the combination of SMR, wind turbines, and photovoltaics. A hydrogen-based energy storage system is used to ensure that sufficient power is always available. With the known electric power and heating demand of the entire community, calculations are performed to match the energy supply and demand for all the hours of the year. Two cases are studied: a) when only the electric demand is supplied by the non-carbon sources; and b) when both electricity and the heating requirements of the community are supplied. Addition of nuclear power in the renewable energy mix significantly reduces the required nominal solar and wind power capacities with substitution factors in the range 2.7 to 7.0 MW per MW of installed nuclear capacity. The required energy storage capacity in the hydrogen system also drops by about 39 % in case (b).</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"441 ","pages":"Article 114207"},"PeriodicalIF":1.9,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Neutronics and thermal hydraulics multiscale simulation of a lead-cooled fast reactor","authors":"Alejandría D. Pérez-Valseca ,&nbsp;Roberto Lopez-Solis ,&nbsp;Luis Carlos Juárez-Martínez","doi":"10.1016/j.nucengdes.2025.114189","DOIUrl":"10.1016/j.nucengdes.2025.114189","url":null,"abstract":"<div><div>In this work, the application of an upscaling methodology to the thermal hydraulic model of an LFR is presented. The upscaling process is applied to local equations, where a rigorous mathematical process yields reactor-scale equations containing information from the pin scale, in addition to information on the properties of each phase. Two phases are considered: the fuel rods are the solid phase, and the lead coolant is the liquid phase. The upscaled thermal model is coupled with a neutron model, a simplified expression of the diffusion equation that considers reactivity feedback. The scaled thermal hydraulic model allows the entire core to be analyzed using only two heat transfer equations, which contain scaled coefficients for both phases. These were calculated at different lead velocities to understand their behavior under potential velocity changes. The core neutron parameters were calculated using the Serpent code, and the models and coupling were implemented in COMSOL Multiphysics. The results show that the neutron flux profiles, fuel and coolant temperatures behave as the reactor design values.</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"441 ","pages":"Article 114189"},"PeriodicalIF":1.9,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Verification and validation of SEMRA code shock propagation module","authors":"Ibrahim Batayneh,&nbsp;Dmitry Grishchenko,&nbsp;Pavel Kudinov","doi":"10.1016/j.nucengdes.2025.114186","DOIUrl":"10.1016/j.nucengdes.2025.114186","url":null,"abstract":"<div><div>The ex-vessel severe accident (SA) mitigation strategy in Nordic Boiling Water Reactors (BWRs) relies on drywell flooding. In the event of the reactor lower head failure corium is released into the water pool in the drywell. The corium jet is expected to fragment, quench, and form a coolable debris bed, ultimately preventing containment failure and release of radioactive products into the environment.</div><div>During corium fragmentation in water, a vapor film is formed around the melt preventing direct melt-water contact and limiting the heat transfer between the two liquids. In case of vapor film collapse an explosive conversion of thermal energy of the melt into the mechanical energy of the evaporating volatile coolant may be triggered. These phenomena are often called steam explosion (SE). The resulting pressure wave may propagate through the water-corium mixture, escalate and form a shock wave with the potential to challenge containment integrity. There are significant phenomenological and scenario uncertainties associated with steam explosion. The problem of the uncertainty quantification in the risk analysis is exacerbated further by (i) the chaotic nature of the steam explosion phenomena and (ii) the lack of steam explosion modelling codes based on the modern numerical methods with increased stability and accuracy.</div><div>The goal of this work is to develop a numerical code SEMRA (Steam Explosion Modelling and Risk Analysis) for modelling of melt-coolant interactions and assessment of the risk of containment failure due to steam explosion. In this paper, we focus on the development of the deterministic part of the code that utilizes improved numerical methods to assess the propagation of steam explosions. The objective is to verify the implemented numerical schemes for pressure propagation and to establish a reference solution for the next stage of code development which incorporates more comprehensive thermodynamic modelling and transport phenomena relevant to steam explosion.</div><div>Specifically, we address the phenomena shock wave triggering and propagation. We implement a numerically stable code using AUSM+ -up, Godunov and HLLC schemes to model multiphase flow. We evaluate the performance of SEMRA code against several known verification and validation problems. Then we use SEMRA code to simulate triggering tests carried out in KROTOS facility and compare the results against the experiment and TEXAS-V code calculations. We analyze the effect of the flux reconstruction method, the vanishing phase treatment and the spatial discretization on the results. We discuss the results and their contribution to the enhancement of triggering and propagation modelling in a SE code.</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"441 ","pages":"Article 114186"},"PeriodicalIF":1.9,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uncertainty and sensitivity analysis of turbulence models for flow in a bare rod bundle based on the Non-Intrusive Polynomial Chaos method","authors":"Zhenyang Sun ,&nbsp;Hongyang Wei ,&nbsp;Sichao Tan ,&nbsp;Yitung Chen","doi":"10.1016/j.nucengdes.2025.114197","DOIUrl":"10.1016/j.nucengdes.2025.114197","url":null,"abstract":"<div><div>This research investigates the uncertainty of turbulence model parameters within bare rod bundles and its impact on numerical prediction outcomes. Turbulent phenomena in the fuel rod bundle affect heat transfer and flow. The Reynolds-Averaged Navier-Stokes (RANS) method is widely used, but uncertainty in turbulence model parameters challenges simulation reliability. This study employs the Non-Intrusive Polynomial Chaos (NIPC) method to quantitatively evaluate the parameter uncertainty of three turbulence models: RNG <span><math><mrow><mi>k</mi><mo>-</mo><mi>ε</mi></mrow></math></span>, <span><math><mrow><mi>k</mi><mo>-</mo><mi>w</mi></mrow></math></span> SST, and LPS-RSM. Sobol index analysis is used to identify the key parameters. The results show that all three parameters of the RNG k-ε model are key, while the key parameters for k-ω SST and LPS-RSM include various coefficients related to turbulent kinetic energy, dissipation, and viscosity. The study finds turbulence model parameter variations significantly affect eddy viscosity in the mainstream region but have a lesser effect on the near-wall region, and the influence on macroscopic flow characteristics is also limited. This research quantitatively reveals the impact of uncertainty in fluid turbulence model parameters within bare rod bundles on non-dimensional turbulent kinetic energy, identifies the key parameters for different turbulence models, and provides a theoretical basis and technical support for the improvement and optimization of turbulence models in future.</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"441 ","pages":"Article 114197"},"PeriodicalIF":1.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermal conductivity of bentonite-based materials: model overview and physics constrained ensemble learning predictive framework","authors":"Shengkui Tian ,&nbsp;Qiong Wang ,&nbsp;Wei Su ,&nbsp;Yichun Liu ,&nbsp;Weimin Ye ,&nbsp;Guanshi Liu","doi":"10.1016/j.nucengdes.2025.114139","DOIUrl":"10.1016/j.nucengdes.2025.114139","url":null,"abstract":"<div><div>Bentonite-based materials (BBMs) are widely utilized as promising buffer/backfill materials in deep geological repositories (DGRs). Their thermal conductivity (λ) is critical for regulating temperature transfer and distribution, making reliable thermal conductivity functions (TCFs) indispensable for ensuring the long-term safety of DGR operations. In this study, a systematic database of BBM <em>λ</em> was established, and the underlying heat transfer mechanisms behind the response patterns of key factors were briefly summarized. The adaptability and accuracy of 49 reviewed TCFs were evaluated from multi-dimensional perspectives. To overcome their limitations, four physics constrained ensemble learning (PCEL) models optimized by the sparrow intelligence algorithm were developed for predicting BBM <em>λ</em>. Shapley Additive exPlanations (SHAP) and partial dependence plots (PDPs) were employed to explain models, enabling the quantitative identification of sensitivities, response patterns, and coupling effects among factors. In light of this, an improved normalized model was proposed, systematically integrating the impact of internal, structural, and environmental factors on the heat transfer mechanism. The results show that BBM <em>λ</em> is affected by various interrelated factors with highly nonlinear relationships, with water having the most pronounced impact. Traditional models fail to fully account for the coupling effects of factors, heat transfer paths, and transport mechanisms, leading to the overall poor performance of the reviewed TCFs. Among these, YK2021-2, CJ2011, and MJ1954 provide slightly improved results for pure bentonite, quartz-bentonite, and granite/graphite-bentonite, respectively. Some TCFs such as TF2009 and LY2024, which consider the impacts of water potential and pore structure on soil heat transfer mechanisms provide some improvements, so the improved normalized model yielded superior performance. The decision outcomes of the PCEL model possess physical consistency, and their accuracy is improved from 4 to 27 times over the reviewed TCFs, with CatBoost showing the best performance. The decision-making process of the PCEL model, as visualized through SHAP and PDPs, is consistent with the heat transfer mechanisms of unsaturated soils. This work can potentially support physics-driven TCFs and hydrothermal simulations in DGRs.</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"441 ","pages":"Article 114139"},"PeriodicalIF":1.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fluid–structure interactions in nuclear power plants: Review of some main phenomena and analysis of the related safety aspects","authors":"Daniele Vivaldi ,&nbsp;Angel Papukchiev ,&nbsp;Clément Viron ,&nbsp;Stéphanie Graff ,&nbsp;Mikael Kountchou","doi":"10.1016/j.nucengdes.2025.114121","DOIUrl":"10.1016/j.nucengdes.2025.114121","url":null,"abstract":"<div><div>Fluid–structure interactions such as fluid-induced vibrations are a source of wear and damage in nuclear power plants. Several issues linked with fluid–structure interaction phenomena have been constantly reported for a wide range of plant components. In order to understand the importance of fluid–structure related problems, the analysis of the underlying mechanisms should be combined to a discussion of the associated safety issues. This is what this article is intended to present. Some main fluid–structure related phenomena are presented, ranging from issues concerning reactor pressure vessel internals such as fuel rods/assemblies and thermal sleeves, to steam generator tube degradation. For each phenomenon, a review of the documented events is first presented, followed by the analysis of the underlying physical mechanisms and, finally, by the analysis of the associated safety concerns, that represents the main originality of this article. Beside, new numerical studies aimed at predicting the wear of thermal sleeves are presented: they rely on the CFD simulation of the core upper plenum. A dedicated analysis of the steam generator tube wear at the San Onofre nuclear power plant is proposed.</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"441 ","pages":"Article 114121"},"PeriodicalIF":1.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental and numerical investigation on debris bed quenching and development of an artificial neural network for quick quenching estimation","authors":"Markus Petroff ,&nbsp;Melissa Schütz ,&nbsp;Jasmin Joshi-Thompson ,&nbsp;Rudi Kulenovic ,&nbsp;Michael Buck ,&nbsp;Jörg Starflinger","doi":"10.1016/j.nucengdes.2025.114134","DOIUrl":"10.1016/j.nucengdes.2025.114134","url":null,"abstract":"<div><div>A debris bed can form in the reactor cavity during a beyond-design-basis accident of light water reactors with core degradation and RPV failure. With insufficient cooling water, the debris bed can melt, interacting with the concrete underneath and generating non-condensible gases at the bottom, affecting coolability for re-flooding the superheated particle bed. Thermal-hydraulic system codes like ATHLET can, in principle, consider the impact of an additional gas flow on the quenching process. However, there is still a need for experimental validation of the respective models and the validation of the corresponding simulation results. A specific extension to the existing experimental database is needed for the model validation of COCOMO, which is implemented in ATHLET. Since detailed simulation codes like COCOMO can require long computation times, there is a need for fast-running models for probabilistic risk analysis. Artificial neural networks can be utilised for quick estimations of the quenching process. Experimental results are presented for the top-flooding quenching behaviour of a monodisperse particle bed with the influence of additional non-condensable gas injection conducted at the FLOAT test facility. Consecutive numerical simulations are carried out for model validation. Since multi-dimensional simulations are computationally expensive, an artificial neural network is developed for quick estimation of the quenching process. COCOMO simulations capture the basic phenomenology of top-flooding quenching but deviate due to modelled 3D effects and underestimate the influence of NCG injection on quenching time. The developed ANN similarly underestimates this effect but shows promise for quick quenching estimation.</div></div>","PeriodicalId":19170,"journal":{"name":"Nuclear Engineering and Design","volume":"441 ","pages":"Article 114134"},"PeriodicalIF":1.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144204405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}