Pub Date : 2012-09-14DOI: 10.1080/00411450.2012.671210
J. Rosato, H. Capes, Y. Marandet, A. Mekkaoui, R. Stamm
The Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) formalism is revisited in the framework of plasma spectroscopy. We address the issue of Stark line shape modeling by using kinetic transport equations. In the most simplified treatment of these equations, triple correlations between an emitter and the perturbing charged particles are neglected and a collisional description of Stark effect is obtained. Here we relax this assumption and retain triple correlations using a generalization of the Kirkwood truncature hypothesis to quantum operator. An application to hydrogen lines is done in the context of plasma diagnostic. It is shown that the neglect of triple correlations can lead to a significant overestimate of the line width.
{"title":"Kinetic Equations for Stark Line Shapes","authors":"J. Rosato, H. Capes, Y. Marandet, A. Mekkaoui, R. Stamm","doi":"10.1080/00411450.2012.671210","DOIUrl":"https://doi.org/10.1080/00411450.2012.671210","url":null,"abstract":"The Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) formalism is revisited in the framework of plasma spectroscopy. We address the issue of Stark line shape modeling by using kinetic transport equations. In the most simplified treatment of these equations, triple correlations between an emitter and the perturbing charged particles are neglected and a collisional description of Stark effect is obtained. Here we relax this assumption and retain triple correlations using a generalization of the Kirkwood truncature hypothesis to quantum operator. An application to hydrogen lines is done in the context of plasma diagnostic. It is shown that the neglect of triple correlations can lead to a significant overestimate of the line width.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"337 - 344"},"PeriodicalIF":0.0,"publicationDate":"2012-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671210","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909635","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}
Pub Date : 2012-05-01DOI: 10.1080/00411450.2012.671211
J. Rosato
The quantum phase space formalism proposed by Wigner is applied to radiation transport problems. It is shown that a generalization of the radiative transfer equation, which accounts for coherence effects, can be obtained within the second quantization formalism. A simplification in the case of stationary medium and slab geometry is considered and applied to low- and high-density plasmas. The obtained results indicate that spectra can be misinterpreted if the light's spatial coherence is neglected.
{"title":"Quantum Corrections on the Radiative Transfer Equation","authors":"J. Rosato","doi":"10.1080/00411450.2012.671211","DOIUrl":"https://doi.org/10.1080/00411450.2012.671211","url":null,"abstract":"The quantum phase space formalism proposed by Wigner is applied to radiation transport problems. It is shown that a generalization of the radiative transfer equation, which accounts for coherence effects, can be obtained within the second quantization formalism. A simplification in the case of stationary medium and slab geometry is considered and applied to low- and high-density plasmas. The obtained results indicate that spectra can be misinterpreted if the light's spatial coherence is neglected.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"214 - 222"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671211","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909645","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}
Pub Date : 2012-05-01DOI: 10.1080/00411450.2012.671205
Shay I. Heizler
We develop the asymptotic P 1 approximation for the time-dependent thermal radiative transfer equation for a multidimensional general geometry. Careful derivation of the asymptotic P 1 equations, directly from the time-dependent Boltzmann equation, yields a particle velocity that is closer (v≈0.91c) to the exact value of c but is based on an asymptotic analysis rather than diffusion theory (infinite velocity) or conventional P 1 theory (which gives rise to the Telegrapher’s equation, ). While this approach does not match the exact value of c as does the P 1/3 method, the latter method is an ad hoc approach that has not been justified on theoretical grounds. This article provides the theoretical justification for the almost-correct value of c that yields improved results for the well-known (one-dimensional) Su-Olson benchmark for radiative transfer, for which we obtain a semi-analytic solution in the case of local thermodynamic equilibrium. We found that the asymptotic P 1 approximation yields a better solution than the diffusion, the classic P 1, and the P 1/3 approximations, yielding the correct steady-state behavior for the energy density and the (almost) correct particle velocity.
{"title":"The Asymptotic Telegrapher’s Equation (P1) Approximation for Time-Dependent, Thermal Radiative Transfer","authors":"Shay I. Heizler","doi":"10.1080/00411450.2012.671205","DOIUrl":"https://doi.org/10.1080/00411450.2012.671205","url":null,"abstract":"We develop the asymptotic P 1 approximation for the time-dependent thermal radiative transfer equation for a multidimensional general geometry. Careful derivation of the asymptotic P 1 equations, directly from the time-dependent Boltzmann equation, yields a particle velocity that is closer (v≈0.91c) to the exact value of c but is based on an asymptotic analysis rather than diffusion theory (infinite velocity) or conventional P 1 theory (which gives rise to the Telegrapher’s equation, ). While this approach does not match the exact value of c as does the P 1/3 method, the latter method is an ad hoc approach that has not been justified on theoretical grounds. This article provides the theoretical justification for the almost-correct value of c that yields improved results for the well-known (one-dimensional) Su-Olson benchmark for radiative transfer, for which we obtain a semi-analytic solution in the case of local thermodynamic equilibrium. We found that the asymptotic P 1 approximation yields a better solution than the diffusion, the classic P 1, and the P 1/3 approximations, yielding the correct steady-state behavior for the energy density and the (almost) correct particle velocity.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"175 - 199"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671205","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909219","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}
Pub Date : 2012-05-01DOI: 10.1080/00411450.2012.671224
H. Park, D. Knoll, R. M. Rauenzahn, A. Wollaber, J. Densmore
We present an efficient numerical algorithm for solving the time-dependent grey thermal radiative transfer (TRT) equations. The algorithm utilizes the first two angular moments of the TRT equations (Quasi-diffusion (QD)) together with the material temperature equation to form a nonlinear low-order (LO) system. The LO system is solved via the Jacobian-free Newton-Krylov method. The combined high-order (HO) TRT and LO-QD system is used to bridge the diffusion and transport scales. In addition, a “consistency” term is introduced to make the truncation error in the LO system identical to the truncation error in the HO equation. The derivation of the consistency term is rather general; therefore, it can be extended to a variety of spatial and temporal discretizations.
{"title":"A Consistent, Moment-Based, Multiscale Solution Approach for Thermal Radiative Transfer Problems","authors":"H. Park, D. Knoll, R. M. Rauenzahn, A. Wollaber, J. Densmore","doi":"10.1080/00411450.2012.671224","DOIUrl":"https://doi.org/10.1080/00411450.2012.671224","url":null,"abstract":"We present an efficient numerical algorithm for solving the time-dependent grey thermal radiative transfer (TRT) equations. The algorithm utilizes the first two angular moments of the TRT equations (Quasi-diffusion (QD)) together with the material temperature equation to form a nonlinear low-order (LO) system. The LO system is solved via the Jacobian-free Newton-Krylov method. The combined high-order (HO) TRT and LO-QD system is used to bridge the diffusion and transport scales. In addition, a “consistency” term is introduced to make the truncation error in the LO system identical to the truncation error in the HO equation. The derivation of the consistency term is rather general; therefore, it can be extended to a variety of spatial and temporal discretizations.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"284 - 303"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671224","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909948","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}
Pub Date : 2012-05-01DOI: 10.1080/00411450.2012.672358
Shay I. Heizler, P. Ravetto
This article is devoted to analyzing the physical features of the time-dependent P 2 model in plane geometry and the simplified P 2 (SP 2) model for general geometry. The relationships that can be established with the P 1 model (which gives rise to the telegrapher’s equation) are discussed in detail. In particular, the propagation properties are considered, showing that the signal is characterized by propagation velocity that is times the correct particle velocity. This result is also obtained by direct observation of the equivalent three discrete ordinates equations (S 3) in a slab geometry. In addition, a consistent asymptotic approach is carried out on the SP 2 equations, as can be done in a P 1 formulation. We find that in the diffusion limit, the SP 2 approximation yields the same asymptotic behavior as the asymptotic P 1 approximation that is derived from the exact time-dependent Boltzmann equation. In the absorbing limit, the asymptotic behavior of the SP 2 equations tends to be the exact behavior of SP 2; i.e., with a propagation velocity that is times the particle velocity, which is lower than that for the asymptotic P 1 approximation that tends to the exact particle velocity. These observations are supported by numerical results for a simple problem in a one-dimensional transport problem. The asymptotic P 1 and P 2 approximations are much closer to the exact transport solution than the classic P 1 approximation.
{"title":"SP 2—Asymptotic P 1 Equivalence","authors":"Shay I. Heizler, P. Ravetto","doi":"10.1080/00411450.2012.672358","DOIUrl":"https://doi.org/10.1080/00411450.2012.672358","url":null,"abstract":"This article is devoted to analyzing the physical features of the time-dependent P 2 model in plane geometry and the simplified P 2 (SP 2) model for general geometry. The relationships that can be established with the P 1 model (which gives rise to the telegrapher’s equation) are discussed in detail. In particular, the propagation properties are considered, showing that the signal is characterized by propagation velocity that is times the correct particle velocity. This result is also obtained by direct observation of the equivalent three discrete ordinates equations (S 3) in a slab geometry. In addition, a consistent asymptotic approach is carried out on the SP 2 equations, as can be done in a P 1 formulation. We find that in the diffusion limit, the SP 2 approximation yields the same asymptotic behavior as the asymptotic P 1 approximation that is derived from the exact time-dependent Boltzmann equation. In the absorbing limit, the asymptotic behavior of the SP 2 equations tends to be the exact behavior of SP 2; i.e., with a propagation velocity that is times the particle velocity, which is lower than that for the asymptotic P 1 approximation that tends to the exact particle velocity. These observations are supported by numerical results for a simple problem in a one-dimensional transport problem. The asymptotic P 1 and P 2 approximations are much closer to the exact transport solution than the classic P 1 approximation.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"304 - 324"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.672358","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58910015","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}
Pub Date : 2012-05-01DOI: 10.1080/00411450.2012.671208
N. Corngold
We describe situations where coherent and incoherent effects take place in a disordered medium illuminated by a coherent source. We illustrate the transition from coherence to incoherence by considering the propagation of a scalar wave in a medium of point, isotropic scatterers. We note how a traditional transport equation evolves and that it is enriched by a boundary layer in which coherence decays and the intensity is of damped oscillatory nature.
{"title":"Radiative Transport Reconsidered","authors":"N. Corngold","doi":"10.1080/00411450.2012.671208","DOIUrl":"https://doi.org/10.1080/00411450.2012.671208","url":null,"abstract":"We describe situations where coherent and incoherent effects take place in a disordered medium illuminated by a coherent source. We illustrate the transition from coherence to incoherence by considering the propagation of a scalar wave in a medium of point, isotropic scatterers. We note how a traditional transport equation evolves and that it is enriched by a boundary layer in which coherence decays and the intensity is of damped oscillatory nature.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"30 1","pages":"200 - 213"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671208","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909571","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}
Pub Date : 2012-05-01DOI: 10.1080/00411450.2012.671218
P. Picca, R. Furfaro, B. Ganapol
This article presents a review of the special features exhibited by the transport of photons in dense vegetation canopies. The conservation of photons for particles moving in canopy media yields a linear Boltzmann Equation similar to conventional participating media. However, because of the turbid medium approximation where the atomic leaves are modeled as a gas cloud of infinitesimal plates with specified orientation, the overall system is not rotationally invariant. The latter affects the mathematical nature of the canopy equation and requires special numerical treatment to generate accurate numerical solutions. Here, the most common solution techniques are reviewed with special emphasis on two highly accurate methodologies, namely the Singular Eigenfunction Expansion, which is the basis of the F N method for canopy transport and the Analytical Discrete Ordinate (ADO) method. It is shown that the conventional ADO method can be easily extended to canopy transport problems by taking advantage of special symmetries exhibited by the intercept function and the area scattering function employed to describe the canopy optical properties.
{"title":"On Radiative Transfer in Dense Vegetation Canopies","authors":"P. Picca, R. Furfaro, B. Ganapol","doi":"10.1080/00411450.2012.671218","DOIUrl":"https://doi.org/10.1080/00411450.2012.671218","url":null,"abstract":"This article presents a review of the special features exhibited by the transport of photons in dense vegetation canopies. The conservation of photons for particles moving in canopy media yields a linear Boltzmann Equation similar to conventional participating media. However, because of the turbid medium approximation where the atomic leaves are modeled as a gas cloud of infinitesimal plates with specified orientation, the overall system is not rotationally invariant. The latter affects the mathematical nature of the canopy equation and requires special numerical treatment to generate accurate numerical solutions. Here, the most common solution techniques are reviewed with special emphasis on two highly accurate methodologies, namely the Singular Eigenfunction Expansion, which is the basis of the F N method for canopy transport and the Analytical Discrete Ordinate (ADO) method. It is shown that the conventional ADO method can be easily extended to canopy transport problems by taking advantage of special symmetries exhibited by the intercept function and the area scattering function employed to describe the canopy optical properties.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"223 - 244"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671218","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909829","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}
Pub Date : 2012-05-01DOI: 10.1080/00411450.2012.671220
M. Makai
We discuss heat conductance and diffusion, two remarkable transport processes characterized by instantaneous actions. We show that the assumption of local thermal equilibrium sets a limit to the speed of change in the distribution function of a statistical system . Using Onsager’s approximation, we show that the balance equations of the extensive parameters also have solutions with finite velocities involved. At the same time the infinite speed is obtainable when second order terms are neglected. We show how the presented technique is applied in heat transfer, diffusion, and plasma physics to determine the speeds of the physical processes.
{"title":"Remarks on the Speed of Heat Waves","authors":"M. Makai","doi":"10.1080/00411450.2012.671220","DOIUrl":"https://doi.org/10.1080/00411450.2012.671220","url":null,"abstract":"We discuss heat conductance and diffusion, two remarkable transport processes characterized by instantaneous actions. We show that the assumption of local thermal equilibrium sets a limit to the speed of change in the distribution function of a statistical system . Using Onsager’s approximation, we show that the balance equations of the extensive parameters also have solutions with finite velocities involved. At the same time the infinite speed is obtainable when second order terms are neglected. We show how the presented technique is applied in heat transfer, diffusion, and plasma physics to determine the speeds of the physical processes.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"245 - 264"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671220","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909893","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}
Pub Date : 2012-05-01DOI: 10.1080/00411450.2012.671221
T. Trahan, N. Gentile
Statistical uncertainty is inherent to any Monte Carlo simulation of radiation transport problems. In space-angle-frequency independent radiative transfer calculations, the uncertainty in the solution is entirely due to random sampling of source photon emission times. We have developed a modification to the Implicit Monte Carlo algorithm that eliminates noise due to sampling of the emission time of source photons. In problems that are independent of space, angle, and energy, the new algorithm generates a smooth solution, while a standard implicit Monte Carlo solution is noisy. For space- and angle-dependent problems, the new algorithm exhibits reduced noise relative to standard implicit Monte Carlo in some cases, and comparable noise in all other cases. The improvements are limited to short time scales; over long time scales, noise due to random sampling of spatial and angular variables tends to dominate the noise reduction from the new algorithm.
{"title":"Analytic Treatment of Source Photon Emission Times to Reduce Noise in Implicit Monte Carlo Calculations","authors":"T. Trahan, N. Gentile","doi":"10.1080/00411450.2012.671221","DOIUrl":"https://doi.org/10.1080/00411450.2012.671221","url":null,"abstract":"Statistical uncertainty is inherent to any Monte Carlo simulation of radiation transport problems. In space-angle-frequency independent radiative transfer calculations, the uncertainty in the solution is entirely due to random sampling of source photon emission times. We have developed a modification to the Implicit Monte Carlo algorithm that eliminates noise due to sampling of the emission time of source photons. In problems that are independent of space, angle, and energy, the new algorithm generates a smooth solution, while a standard implicit Monte Carlo solution is noisy. For space- and angle-dependent problems, the new algorithm exhibits reduced noise relative to standard implicit Monte Carlo in some cases, and comparable noise in all other cases. The improvements are limited to short time scales; over long time scales, noise due to random sampling of spatial and angular variables tends to dominate the noise reduction from the new algorithm.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"265 - 283"},"PeriodicalIF":0.0,"publicationDate":"2012-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671221","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58909908","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}
Pub Date : 2012-01-18DOI: 10.1080/00411459708221778
Liu Guangjun
Abstract The expansion method in the kinetic theory of gases is often used for the calculation of entropy production in rarefied gas flows, usually in terms of Her-mite polynomials. In this paper, the method of Sonine polynomials expansion is used and the calculation of entropy production is carried out. First, the formal evaluation of the entropy production in rarefied gas flows is introduced. Then the calculation of the entropy production for arbitrary molecules with spherically symmetric intermolecular forces by Sonine polynomials expansion is presented and the formula for entropy production in the thirteen-moment approximation is obtained. It is shown that the entropy production can be expressed as a linear combination of square terms in the thirteen-moment approximation. This formula can be applied to slightly rarefied gas flows.
{"title":"Calculation of entropy production in slightly rarefied gas flows by Sonine polynomial expansion","authors":"Liu Guangjun","doi":"10.1080/00411459708221778","DOIUrl":"https://doi.org/10.1080/00411459708221778","url":null,"abstract":"Abstract The expansion method in the kinetic theory of gases is often used for the calculation of entropy production in rarefied gas flows, usually in terms of Her-mite polynomials. In this paper, the method of Sonine polynomials expansion is used and the calculation of entropy production is carried out. First, the formal evaluation of the entropy production in rarefied gas flows is introduced. Then the calculation of the entropy production for arbitrary molecules with spherically symmetric intermolecular forces by Sonine polynomials expansion is presented and the formula for entropy production in the thirteen-moment approximation is obtained. It is shown that the entropy production can be expressed as a linear combination of square terms in the thirteen-moment approximation. This formula can be applied to slightly rarefied gas flows.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"26 1","pages":"121-137"},"PeriodicalIF":0.0,"publicationDate":"2012-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411459708221778","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58924840","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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