The simulation of steady incompressible flows is nowadays routinely performed using low-order meth-ods such as the finite volume (FV) method [1]. When transient incompressible flows are to be considered, the task of generating a suitable mesh becomes more cumbersome. This is due to the increased difficulty of designing a mesh capable of capturing all the transient flow features. In practice, to balance accuracy and efficiency, the use of mesh adaptivity is often considered. Additionally, when flow features such as vortices are to be propagated over long distances, the excessive dissipation and dispersion errors associated with low-order methods force the use of excessively refined meshes. High-order methods have shown the ability to reduce dissipation and dispersion errors compared to low-order methods. However, it is still difficult to obtain high-quality curvilinear meshes of complex geometric objects and without this technology, the advantages of high-order methods cannot be realised. This work proposes the combination of low and high-order methods to simulate transient incompress-ible flows using meshes designed for steady simulations. In the vicinity of complex geometric objects, where the mesh used for steady simulations is fine enough, the FV method is employed. However, where the mesh is not good enough to capture the transient features, the solution is computed using the high-order hybridisable discontinuous Galerkin (HDG) method [2]. Contrary to other coupled methods presented, where a monolithic coupling was proposed, this work develops a strategy to produce a staggered coupling. This ensures that legacy FV codes can be employed, and the solution is enriched only where needed.
{"title":"A Coupled HDG-FV Method for Incompressible Flows Simulations","authors":"A. Felipe, R. Sevilla, O. Hassan","doi":"10.23967/admos.2023.063","DOIUrl":"https://doi.org/10.23967/admos.2023.063","url":null,"abstract":"The simulation of steady incompressible flows is nowadays routinely performed using low-order meth-ods such as the finite volume (FV) method [1]. When transient incompressible flows are to be considered, the task of generating a suitable mesh becomes more cumbersome. This is due to the increased difficulty of designing a mesh capable of capturing all the transient flow features. In practice, to balance accuracy and efficiency, the use of mesh adaptivity is often considered. Additionally, when flow features such as vortices are to be propagated over long distances, the excessive dissipation and dispersion errors associated with low-order methods force the use of excessively refined meshes. High-order methods have shown the ability to reduce dissipation and dispersion errors compared to low-order methods. However, it is still difficult to obtain high-quality curvilinear meshes of complex geometric objects and without this technology, the advantages of high-order methods cannot be realised. This work proposes the combination of low and high-order methods to simulate transient incompress-ible flows using meshes designed for steady simulations. In the vicinity of complex geometric objects, where the mesh used for steady simulations is fine enough, the FV method is employed. However, where the mesh is not good enough to capture the transient features, the solution is computed using the high-order hybridisable discontinuous Galerkin (HDG) method [2]. Contrary to other coupled methods presented, where a monolithic coupling was proposed, this work develops a strategy to produce a staggered coupling. This ensures that legacy FV codes can be employed, and the solution is enriched only where needed.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127886105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Martin Holler, Alexander Schl¨uter, Benedikt Wirth, §. Speaker
Stars in the sky or cells in the blood stream: many imaging problems require the reconstruction of moving point sources imaged over multiple frames. The central questions are how to resolve point locations and velocities from images where fine scale information is lost, e.g. due to the diffraction of light at the aperture of an optical instrument, and how to efficiently combine information from multiple frames. In the setting of Positron Emission Tomography (PET), the TraCAR project [6] in cooperation with experts from medicine, biology and physics recently required new techniques in order to track smallest populations of so-called ”CAR T-cells”, which are modified immune cells used for cancer treatments, with the goal to better understand e.g. their interaction with the microenvironment of a tumour. We build on a model by Alberti et al. [2], who proposed to solve a convex optimization problem over the space of Radon measures, where collections of point sources are represented by linear combinations of Dirac measures. In order to incorporate dynamic information, these measures live in phase space, the space combining positions and velocities, which results in a high problem dimensionality and makes finding numerical solutions challenging. In [1], we introduce a novel dimension reduction technique based on projections of phase space onto lower-dimensional subspaces, which reduces the problem dimension from 2 d to d + 1, where d is the space dimension. Indeed, we prove that exact reconstruction results known for the full-dimensional model still hold true after dimension reduction, and we additionally prove new error estimates for reconstructions from noisy data in optimal transport metrics, which
{"title":"Dimension Reduction of Dynamic Superresolution and Application to Cell Tracking in PET","authors":"Martin Holler, Alexander Schl¨uter, Benedikt Wirth, §. Speaker","doi":"10.23967/admos.2023.011","DOIUrl":"https://doi.org/10.23967/admos.2023.011","url":null,"abstract":"Stars in the sky or cells in the blood stream: many imaging problems require the reconstruction of moving point sources imaged over multiple frames. The central questions are how to resolve point locations and velocities from images where fine scale information is lost, e.g. due to the diffraction of light at the aperture of an optical instrument, and how to efficiently combine information from multiple frames. In the setting of Positron Emission Tomography (PET), the TraCAR project [6] in cooperation with experts from medicine, biology and physics recently required new techniques in order to track smallest populations of so-called ”CAR T-cells”, which are modified immune cells used for cancer treatments, with the goal to better understand e.g. their interaction with the microenvironment of a tumour. We build on a model by Alberti et al. [2], who proposed to solve a convex optimization problem over the space of Radon measures, where collections of point sources are represented by linear combinations of Dirac measures. In order to incorporate dynamic information, these measures live in phase space, the space combining positions and velocities, which results in a high problem dimensionality and makes finding numerical solutions challenging. In [1], we introduce a novel dimension reduction technique based on projections of phase space onto lower-dimensional subspaces, which reduces the problem dimension from 2 d to d + 1, where d is the space dimension. Indeed, we prove that exact reconstruction results known for the full-dimensional model still hold true after dimension reduction, and we additionally prove new error estimates for reconstructions from noisy data in optimal transport metrics, which","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114137189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Waeytens, T. Hamada, R. Chakir, D. Lejri, F. Dugay
According to the World Health Organization, every year more than 4 million premature death world-wide are due to outdoor air pollution. Many sectors, e.g traffic, agriculture, industry, and housing, contribute to this. Herein, we focus on NO 2 pollution in urban areas caused by traffic. In fact, at Universit´e Gustave Eiffel, on the one hand, experimental works are in progress to develop operational depolluting panels based on ZnO photocatalysis [1]. On the other hand, to reduce air pollutant human exposure we propose a full numerical strategy from diagnosis — via the determination of critical highly polluted areas — to remediation via the smart placement of the depolluting panels in urban areas. Firstly, a city digital twin and computational fluid dynamics (CFD) are used to get detailed cartography of the NO 2 concentration at the district scale. From these numerical simulations, we retain high-concentration areas in the frequented zone as a quantity of interest. Then, a goal-oriented placement of depolluting panels is proposed to improve the selected quantities of interest using the adjoint framework. This work can be seen as an extension of previous works from the authors dealing with goal-oriented error estimation [2], goal-oriented model updating [3] and goal-oriented sensor placement [3, 4]. The proposed numerical strategy will be illustrated over a district in Paris. We consider two wind scenarios (directions and amplitudes), which are characteristic of the Paris region, and realistic NO 2 sources on each road provided by the regional air quality agency “Airparif”. First practical recommendations for depolluting panels deployment will be presented.
{"title":"Goal-oriented placement of depolluting panels in urban areas - application to a Paris district","authors":"J. Waeytens, T. Hamada, R. Chakir, D. Lejri, F. Dugay","doi":"10.23967/admos.2023.019","DOIUrl":"https://doi.org/10.23967/admos.2023.019","url":null,"abstract":"According to the World Health Organization, every year more than 4 million premature death world-wide are due to outdoor air pollution. Many sectors, e.g traffic, agriculture, industry, and housing, contribute to this. Herein, we focus on NO 2 pollution in urban areas caused by traffic. In fact, at Universit´e Gustave Eiffel, on the one hand, experimental works are in progress to develop operational depolluting panels based on ZnO photocatalysis [1]. On the other hand, to reduce air pollutant human exposure we propose a full numerical strategy from diagnosis — via the determination of critical highly polluted areas — to remediation via the smart placement of the depolluting panels in urban areas. Firstly, a city digital twin and computational fluid dynamics (CFD) are used to get detailed cartography of the NO 2 concentration at the district scale. From these numerical simulations, we retain high-concentration areas in the frequented zone as a quantity of interest. Then, a goal-oriented placement of depolluting panels is proposed to improve the selected quantities of interest using the adjoint framework. This work can be seen as an extension of previous works from the authors dealing with goal-oriented error estimation [2], goal-oriented model updating [3] and goal-oriented sensor placement [3, 4]. The proposed numerical strategy will be illustrated over a district in Paris. We consider two wind scenarios (directions and amplitudes), which are characteristic of the Paris region, and realistic NO 2 sources on each road provided by the regional air quality agency “Airparif”. First practical recommendations for depolluting panels deployment will be presented.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116427412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Martínez, L. Alvarez-Vázquez, C. Rodríguez, M. Vázquez-Méndez
numerical modelling of the problem
问题的数值模拟
{"title":"Algal Cultivation for Bioenergy Production: First Mathematical Modelling Results in Raceways","authors":"A. Martínez, L. Alvarez-Vázquez, C. Rodríguez, M. Vázquez-Méndez","doi":"10.23967/admos.2023.016","DOIUrl":"https://doi.org/10.23967/admos.2023.016","url":null,"abstract":"numerical modelling of the problem","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131148524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mesh- and model adaptivity for elasto-plastic mean-field and full-field homogenization based on downwind and upwind approximations","authors":"A. Tchomgue-Simeu, R. Mahnker","doi":"10.23967/admos.2023.054","DOIUrl":"https://doi.org/10.23967/admos.2023.054","url":null,"abstract":"","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133948575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modelling and Simulating Cities with Digital Twins","authors":"A. Logg","doi":"10.23967/admos.2023.080","DOIUrl":"https://doi.org/10.23967/admos.2023.080","url":null,"abstract":"","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114833284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Various thin film flow models have been proposed in literature to study the flow of fluids in thin layers. These models have been widely used when the thin fluid film is only object of interest. However, these models are not applicable when a bulk flowing fluid hits a curved surface, and forms a thin layer of fluid over it. Such scenarios commonly occur, for example, in cleaning processes in the food industry. Simulations of such flow typically rely on bulk (3D) fluid models, with excessively fine resolutions in the thin flow regions, which make them prohibitively expensive. In this talk, we present a novel adaptive fluid modelling framework to simulate coupled bulk-surface fluid flow. The proposed framework uses a traditional 3D Navier--Stokes model for bulk fluid flow, and switches to a pseudo 2D thin film flow model when appropriate. The method automatically identifies regions where the thin film model is applicable, and adaptively changes the fluid model used. In this talk, we will discuss how the model adaptivity is achieved, and how mass conservation is ensured when switching between the two models. Numerical results are verified against fine bulk simulations. Applications to cleaning simulations in the food industry, and rain-on-car simulations are also presented.
{"title":"Adaptive Flow Modelling for Coupled Thin Film and Bulk Fluid Flow","authors":"P. Suchde","doi":"10.23967/admos.2023.038","DOIUrl":"https://doi.org/10.23967/admos.2023.038","url":null,"abstract":"Various thin film flow models have been proposed in literature to study the flow of fluids in thin layers. These models have been widely used when the thin fluid film is only object of interest. However, these models are not applicable when a bulk flowing fluid hits a curved surface, and forms a thin layer of fluid over it. Such scenarios commonly occur, for example, in cleaning processes in the food industry. Simulations of such flow typically rely on bulk (3D) fluid models, with excessively fine resolutions in the thin flow regions, which make them prohibitively expensive. In this talk, we present a novel adaptive fluid modelling framework to simulate coupled bulk-surface fluid flow. The proposed framework uses a traditional 3D Navier--Stokes model for bulk fluid flow, and switches to a pseudo 2D thin film flow model when appropriate. The method automatically identifies regions where the thin film model is applicable, and adaptively changes the fluid model used. In this talk, we will discuss how the model adaptivity is achieved, and how mass conservation is ensured when switching between the two models. Numerical results are verified against fine bulk simulations. Applications to cleaning simulations in the food industry, and rain-on-car simulations are also presented.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132958645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Computational simulations of physical phenomena, such as fluid dynamics or structural analysis, involve the numerical solution of partial differential equations (PDEs) on computational meshes. It is crucial that the PDEs be solved both accurately and efficiently to obtain reliable simulation results. Computational fluid dynamics simulations which employ quadrilateral meshes typically result in more accurate solutions than those which use triangular meshes since quadrilateral elements can be better aligned with the fluid flow. In addition, quadrilateral meshes typically contain fewer elements than triangular meshes and thus result in more efficient simulations. Furthermore, quadrilateral meshes are often preferred in dynamic simulations, such as car crashes or fracture studies, since constant-strain triangular elements typically perform poorly on bending problems. For meshes used in finite element analysis, a mesh is said to be explicitly tangled if one or more elements has a negative Jacobian determinant. Whereas the mesh is said to be implicitly tangled if one or more elements is partially inverted. Meshes can become tangled through mesh deformation or smoothing or by other means. Hence, mesh untangling and mesh quality improvement are two important areas of investigation. Traditionally, two separate optimization problems were solved in a sequential manner to untangle the mesh and improve its quality. In this talk, we will present our multiobjective optimization methods for mesh untangling and quality improvement. The methods solve a single optimization problem. The objective functions are developed by combining separate objective functions for untangling and mesh quality improvement in a single objective function using ``no articulation of preferences” [
{"title":"Quadrilateral Mesh Untangling and Mesh Quality Improvement Via Multiobjective Mesh Optimization","authors":"M. Moradi, Suzanne Shontz","doi":"10.23967/admos.2023.066","DOIUrl":"https://doi.org/10.23967/admos.2023.066","url":null,"abstract":"Computational simulations of physical phenomena, such as fluid dynamics or structural analysis, involve the numerical solution of partial differential equations (PDEs) on computational meshes. It is crucial that the PDEs be solved both accurately and efficiently to obtain reliable simulation results. Computational fluid dynamics simulations which employ quadrilateral meshes typically result in more accurate solutions than those which use triangular meshes since quadrilateral elements can be better aligned with the fluid flow. In addition, quadrilateral meshes typically contain fewer elements than triangular meshes and thus result in more efficient simulations. Furthermore, quadrilateral meshes are often preferred in dynamic simulations, such as car crashes or fracture studies, since constant-strain triangular elements typically perform poorly on bending problems. For meshes used in finite element analysis, a mesh is said to be explicitly tangled if one or more elements has a negative Jacobian determinant. Whereas the mesh is said to be implicitly tangled if one or more elements is partially inverted. Meshes can become tangled through mesh deformation or smoothing or by other means. Hence, mesh untangling and mesh quality improvement are two important areas of investigation. Traditionally, two separate optimization problems were solved in a sequential manner to untangle the mesh and improve its quality. In this talk, we will present our multiobjective optimization methods for mesh untangling and quality improvement. The methods solve a single optimization problem. The objective functions are developed by combining separate objective functions for untangling and mesh quality improvement in a single objective function using ``no articulation of preferences” [","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122128846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Huerta, A. Borrás, R. Perelló-Ribas, M. Giacomini
Detailed simulations of complex flow systems to determine critical quantities of interest (QoI) are often unaffordable due to their computational cost. At the same time, simplified models are usually not sufficiently accurate to achieve the precision required by physicists and engineers to provide reliable estimates of QoI. This computational bottleneck is a major challenge for the effective conception, design and operation of industrial systems, especially when geometric parameters are involved. A brief overview of recent a priori and a posteriori ROM strategies for geometrically parametrized incompressible flows is recalled first [1,2]. Then, the optimal strokes for the push-me-pull-you (PMPY), simplified model of an euglenoid micro-swimmer, are determined thanks to the explicit separated expression of the forces and velocity calculated by virtue of the non-intrusive Encapsulated PGD [3]. An alternative strategy is also explored to construct response surfaces of QoI, explicitly depending on the design parameters. The resulting methodology to treat complex systems is demonstrated through parametric studies involving viscous incompressible flows of interest in science and the automotive industry for many-queries problems like shape or path optimization.
{"title":"Surrogate Models of Geometrically Parameterized Flow Systems","authors":"A. Huerta, A. Borrás, R. Perelló-Ribas, M. Giacomini","doi":"10.23967/admos.2023.074","DOIUrl":"https://doi.org/10.23967/admos.2023.074","url":null,"abstract":"Detailed simulations of complex flow systems to determine critical quantities of interest (QoI) are often unaffordable due to their computational cost. At the same time, simplified models are usually not sufficiently accurate to achieve the precision required by physicists and engineers to provide reliable estimates of QoI. This computational bottleneck is a major challenge for the effective conception, design and operation of industrial systems, especially when geometric parameters are involved. A brief overview of recent a priori and a posteriori ROM strategies for geometrically parametrized incompressible flows is recalled first [1,2]. Then, the optimal strokes for the push-me-pull-you (PMPY), simplified model of an euglenoid micro-swimmer, are determined thanks to the explicit separated expression of the forces and velocity calculated by virtue of the non-intrusive Encapsulated PGD [3]. An alternative strategy is also explored to construct response surfaces of QoI, explicitly depending on the design parameters. The resulting methodology to treat complex systems is demonstrated through parametric studies involving viscous incompressible flows of interest in science and the automotive industry for many-queries problems like shape or path optimization.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123793625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Error estimation (due to discretization and/or modeling)","authors":"E. Maunder","doi":"10.23967/admos.2023.048","DOIUrl":"https://doi.org/10.23967/admos.2023.048","url":null,"abstract":"","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124948479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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