Pub Date : 2023-10-17DOI: 10.1088/1361-6404/acfbc4
Sam Silliman, Mishkatul Bhattacharya
Abstract (Avoided) crossings are ubiquitous in physics and are connected to many physical phenomena such as hidden symmetries, the Berry phase, entanglement, Landau–Zener processes, the onset of chaos, etc. A pedagogical approach to cataloging (avoided) crossings has been proposed in the past, using matrices whose eigenvalues avoid or cross as a function of some parameter. The approach relies on the mathematical tool of the discriminant, which can be calculated from the characteristic polynomial of the matrix, and whose roots as a function of the parameter being varied yield the locations as well as degeneracies of the (avoided) crossings. In this article we consider matrices whose symmetries force two or more eigenvalues to be degenerate across the entire range of variation of the parameter of interest, thus leading to an identically vanishing discriminant. To show how this case can be handled systematically, we introduce a perturbation to the matrix and calculate the roots of the discriminant in the limit as the perturbation vanishes. We show that this approach correctly generates a nonzero ‘reduced’ discriminant that yields the locations and degeneracies of the (avoided) crossings. We illustrate our technique using the matrix Hamiltonian for benzene in Hückel theory, which has recently been discussed in the context of (avoided) crossings in its spectrum.
{"title":"(Avoided) crossings in the spectra of matrices with globally degenerate eigenvalues","authors":"Sam Silliman, Mishkatul Bhattacharya","doi":"10.1088/1361-6404/acfbc4","DOIUrl":"https://doi.org/10.1088/1361-6404/acfbc4","url":null,"abstract":"Abstract (Avoided) crossings are ubiquitous in physics and are connected to many physical phenomena such as hidden symmetries, the Berry phase, entanglement, Landau–Zener processes, the onset of chaos, etc. A pedagogical approach to cataloging (avoided) crossings has been proposed in the past, using matrices whose eigenvalues avoid or cross as a function of some parameter. The approach relies on the mathematical tool of the discriminant, which can be calculated from the characteristic polynomial of the matrix, and whose roots as a function of the parameter being varied yield the locations as well as degeneracies of the (avoided) crossings. In this article we consider matrices whose symmetries force two or more eigenvalues to be degenerate across the entire range of variation of the parameter of interest, thus leading to an identically vanishing discriminant. To show how this case can be handled systematically, we introduce a perturbation to the matrix and calculate the roots of the discriminant in the limit as the perturbation vanishes. We show that this approach correctly generates a nonzero ‘reduced’ discriminant that yields the locations and degeneracies of the (avoided) crossings. We illustrate our technique using the matrix Hamiltonian for benzene in Hückel theory, which has recently been discussed in the context of (avoided) crossings in its spectrum.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-13DOI: 10.1088/1361-6404/ad0346
Luis Peralta
Abstract In Radiation Physics classes, point sources are typically used, for which it is relatively easy to describe the signal obtained by a radiation detector, such as the NaI(Tl) scintillation detector. The use of large extended radiation sources is generally avoided due to the mathematical complexity that their description may involve. However, the use of Monte Carlo simulation methods allows this limitation to be overcome. Potassium chloride, containing the 40K isotope, is an ideal candidate for carrying out this type of experiment. The source activity is obtained through the detection of the 1460.8 keV gamma- photon emitted in the 40K decay. In the first experiment, a cylindrical container is used, placing the NaI(Tl) detector in its center and filling the remaining space with potassium chloride. In a second, more complex case, a large radioactive source consisting of a container filled with a mixture of sand and potassium chloride, with the NaI(Tl) detector placed in the center of the mixture, is used. In this case, the mass of potassium chloride is approximately 1/5 of the sand mass. In both experiments, the detection efficiency is obtained by Monte Carlo simulation. A careful analysis of the experimental data allows to obtain a good agreement between the measured and calculated value of the activity.
{"title":"Radioactivity in a bucket","authors":"Luis Peralta","doi":"10.1088/1361-6404/ad0346","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0346","url":null,"abstract":"Abstract In Radiation Physics classes, point sources are typically used, for which it is relatively easy to describe the signal obtained by a radiation detector, such as the NaI(Tl) scintillation detector. The use of large extended radiation sources is generally avoided due to the mathematical complexity that their description may involve. However, the use of Monte Carlo simulation methods allows this limitation to be overcome. Potassium chloride, containing the 40K isotope, is an ideal candidate for carrying out this type of experiment. The source activity is obtained through the detection of the 1460.8 keV gamma- photon emitted in the 40K decay. In the first experiment, a cylindrical container is used, placing the NaI(Tl) detector in its center and filling the remaining space with potassium chloride. In a second, more complex case, a large radioactive source consisting of a container filled with a mixture of sand and potassium chloride, with the NaI(Tl) detector placed in the center of the mixture, is used. In this case, the mass of potassium chloride is approximately 1/5 of the sand mass. In both experiments, the detection efficiency is obtained by Monte Carlo simulation. A careful analysis of the experimental data allows to obtain a good agreement between the measured and calculated value of the activity.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-11DOI: 10.1088/1361-6404/ad026a
Friedrich Herrmann, Michael Pohlig
Abstract We consider the Earth moving through empty space at 30 km/s (in the sun’s frame of reference). Associated with this motion is a convective flow of kinetic and internal energy. Since there is high pressure inside the earth, and since the earth is moving, there is yet another “hydraulic” energy flow. This latter is what this article is about. Although this energy flow is huge, it is not addressed in the textbooks. The reason is that for the explanation one needs a concept which is not introduced in traditional presentations of classical gravitation: the gravitomagnetic field. The corresponding theory, gravitoelectromagnetism, was formulated in 1893 by Heaviside in analogy to Maxwell's theory of electromagnetism.

We discuss the question of what are the sources and sinks of this hydraulic, non-convective energy flow. To answer the question, we need to study the energy flow density distribution within the gravitational field. In doing so, we will make some interesting observations. The energy flow within the field is twice as large as it should be to transfer the field energy from one side of the Earth to the other. The excess flow goes back through the matter of the Earth.

Since our readers may not be familiar with Heaviside’s theory, we first treat the electromagnetic analogue of our problem and then translate the results to the gravitational situation.
{"title":"A hydraulic energy flow within the moving Earth","authors":"Friedrich Herrmann, Michael Pohlig","doi":"10.1088/1361-6404/ad026a","DOIUrl":"https://doi.org/10.1088/1361-6404/ad026a","url":null,"abstract":"Abstract We consider the Earth moving through empty space at 30 km/s (in the sun’s frame of reference). Associated with this motion is a convective flow of kinetic and internal energy. Since there is high pressure inside the earth, and since the earth is moving, there is yet another “hydraulic” energy flow. This latter is what this article is about. Although this energy flow is huge, it is not addressed in the textbooks. The reason is that for the explanation one needs a concept which is not introduced in traditional presentations of classical gravitation: the gravitomagnetic field. The corresponding theory, gravitoelectromagnetism, was formulated in 1893 by Heaviside in analogy to Maxwell's theory of electromagnetism.

We discuss the question of what are the sources and sinks of this hydraulic, non-convective energy flow. To answer the question, we need to study the energy flow density distribution within the gravitational field. In doing so, we will make some interesting observations. The energy flow within the field is twice as large as it should be to transfer the field energy from one side of the Earth to the other. The excess flow goes back through the matter of the Earth.

Since our readers may not be familiar with Heaviside’s theory, we first treat the electromagnetic analogue of our problem and then translate the results to the gravitational situation.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136063101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-11DOI: 10.1088/1361-6404/ad026b
J Güémez, Jose Angel Mier
Abstract Two thermodynamic processes, an adiabatic gas compression and an isothermal gas compression, taking place in a moving lab are analysed using a four-vector fundamental equation, ${rm d} E^mu = delta W^mu + delta Q^mu$, a relativistic generalization of the first law of thermodynamics ${rm d}E=delta W+ delta Q$. These processes are first described in frame S, with the lab at rest, and then in frame ${bar {rm S}}$, moving with constant velocity relative to S. This formalism shows that Lorentz transformation preserves the principle of relativity in thermodynamics. The physical meaning of the norm of a four-vector is analysed, and Clausius definition of entropy variation is generalised to relativity. The classical description of the process is obtained in a moving lab by taking the low-speed limit in the four-vector fundamental equation. The formalism naturally incorporates the role of the laws of mechanics when analysing processes that are typically considered as purely thermodynamic.
{"title":"Relativistic Mechanics and Thermodynamics. IV. Thermodynamic processes","authors":"J Güémez, Jose Angel Mier","doi":"10.1088/1361-6404/ad026b","DOIUrl":"https://doi.org/10.1088/1361-6404/ad026b","url":null,"abstract":"Abstract Two thermodynamic processes, an adiabatic gas compression and an isothermal gas compression, taking place in a moving lab are analysed using a four-vector fundamental equation, ${rm d} E^mu = delta W^mu + delta Q^mu$, a relativistic generalization of the first law of thermodynamics ${rm d}E=delta W+ delta Q$. These processes are first described in frame S, with the lab at rest, and then in frame ${bar {rm S}}$, moving with constant velocity relative to S. This formalism shows that Lorentz transformation preserves the principle of relativity in thermodynamics. The physical meaning of the norm of a four-vector is analysed, and Clausius definition of entropy variation is generalised to relativity. The classical description of the process is obtained in a moving lab by taking the low-speed limit in the four-vector fundamental equation. The formalism naturally incorporates the role of the laws of mechanics when analysing processes that are typically considered as purely thermodynamic.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136063376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1088/1361-6404/ad0187
Petar Zugec, Horvatic Davor, Ivica Smolić
Abstract In light of a recent direct experimental confirmation of a Lorentz contraction of Coulomb field (an electric field of a point charge in a uniform motion), we revisit some common confusions related to it, to be mindful of in teaching the subject. These include the questions about a radial nature of the field, a role of the retardation effect due to a finite speed of information transfer and some issues related to a depiction of Coulomb field by means of the Lorentz contracted field lines.
{"title":"Students' confusions about the electric field of a uniformly moving charge","authors":"Petar Zugec, Horvatic Davor, Ivica Smolić","doi":"10.1088/1361-6404/ad0187","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0187","url":null,"abstract":"Abstract In light of a recent direct experimental confirmation of a Lorentz contraction of Coulomb field (an electric field of a point charge in a uniform motion), we revisit some common confusions related to it, to be mindful of in teaching the subject. These include the questions about a radial nature of the field, a role of the retardation effect due to a finite speed of information transfer and some issues related to a depiction of Coulomb field by means of the Lorentz contracted field lines.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-05DOI: 10.1088/1361-6404/ad009d
Ahmed Houari
Abstract Analytical solutions in physics are always preferred for the sake of mathematical completeness. For this, using the Lambert W function, I derive closed-form analytical expressions for the equilibrium interionic distance in an ionic crystal, the formation energy of a vacancy in a crystal, the zero-temperature energy gap of a clean-limit superconductor and the critical Kosterlitz-Thouless temperature for the phase transition in 2D-XY model. Besides their theoretical interest, some of the present results suggest alternative experimental determinations of the relevant physical quantities. In addition, I similarly derive an explicit analytical formula based on the Lambert W function for a determination of the Boltzmann constant. This formula is proposed here as a theoretical basis for an experimental method to measure this constant. This method is suitable for undergraduate physics students.
{"title":"New analytical results in solid state physics using the Lambert W function","authors":"Ahmed Houari","doi":"10.1088/1361-6404/ad009d","DOIUrl":"https://doi.org/10.1088/1361-6404/ad009d","url":null,"abstract":"Abstract Analytical solutions in physics are always preferred for the sake of mathematical completeness. For this, using the Lambert W function, I derive closed-form analytical expressions for the equilibrium interionic distance in an ionic crystal, the formation energy of a vacancy in a crystal, the zero-temperature energy gap of a clean-limit superconductor and the critical Kosterlitz-Thouless temperature for the phase transition in 2D-XY model. Besides their theoretical interest, some of the present results suggest alternative experimental determinations of the relevant physical quantities. In addition, I similarly derive an explicit analytical formula based on the Lambert W function for a determination of the Boltzmann constant. This formula is proposed here as a theoretical basis for an experimental method to measure this constant. This method is suitable for undergraduate physics students.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135482159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-05DOI: 10.1088/1361-6404/ad009c
Thales Brito de Souza Fonseca Rodrigues, Bruno Ferreira Rizzuti
Abstract In this work, we demonstrate explicitly the unified nature of electric and magnetic fields, from the principles of special relativity and Lorentz transformations of the electromagnetic field tensor. Using an operational approach we construct the tensor and its corresponding transformation law, based on the principle of relativity. Our work helps to elucidate concepts of advanced courses on electromagnetism for primary-level learners and shows an alternative path to derive the Lenz’s law based on the connection between relativity arguments and a standard electromagnetism experiment.
{"title":"On the connection between Lenz's law and relativity","authors":"Thales Brito de Souza Fonseca Rodrigues, Bruno Ferreira Rizzuti","doi":"10.1088/1361-6404/ad009c","DOIUrl":"https://doi.org/10.1088/1361-6404/ad009c","url":null,"abstract":"Abstract In this work, we demonstrate explicitly the unified nature of electric and magnetic fields, from the principles of special relativity and Lorentz transformations of the electromagnetic field tensor. Using an operational approach we construct the tensor and its corresponding transformation law, based on the principle of relativity. Our work helps to elucidate concepts of advanced courses on electromagnetism for primary-level learners and shows an alternative path to derive the Lenz’s law based on the connection between relativity arguments and a standard electromagnetism experiment.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135482878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-04DOI: 10.1088/1361-6404/ad0010
Ali Irannezhad, Aisling Baragry, Denis Weaire, Adil Mughal, Stefan Hutzler
Abstract We describe a number of different experimental set-ups that use hydrogel spheres to demonstrate dense packings of deformable spheres in various geometries. The arrangements are similar to those of bubbles in foams, drops in emulsions, biological cells, etc. The experiments are easy to perform in the class-room or an undergraduate science laboratory. They are describe in the context of the history of packing problems to which this convenient system, not yet fully explored, can add significant new findings.
{"title":"Packing Soft Spheres: Experimental Demonstrations with Hydrogels","authors":"Ali Irannezhad, Aisling Baragry, Denis Weaire, Adil Mughal, Stefan Hutzler","doi":"10.1088/1361-6404/ad0010","DOIUrl":"https://doi.org/10.1088/1361-6404/ad0010","url":null,"abstract":"Abstract We describe a number of different experimental set-ups that use hydrogel spheres to demonstrate dense packings of deformable spheres in various geometries. The arrangements are similar to those of bubbles in foams, drops in emulsions, biological cells, etc. The experiments are easy to perform in the class-room or an undergraduate science laboratory. They are describe in the context of the history of packing problems to which this convenient system, not yet fully explored, can add significant new findings.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135645203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-03DOI: 10.1088/1361-6404/acff9a
Wittaya Kanchanapusakit, Pattarapon Tanalikhit
Abstract An ideal classical gas under uniform gravity is a commonly discussed problem in statistical thermodynamics. At an introductory level, the condition of hydrostatic equilibrium gives rise to the barometric formula, which describes the variation of gas pressure with height. At an advanced level, the partition function can be used to find the density and the internal energy of the gas. These methods rely heavily on mathematical concepts, which may pose a difficulty to some students. This article presents teaching the problem via the virial theorem, emphasising the physical picture of the particle distribution. The virial theorem allows the internal energy to be expressed as an integral over the surface of the container. For the pedagogical purpose, visualisation of how the particles distribute themselves at extreme temperatures helps determine the internal energy of the gas. Student feedback is used as a basis for evaluating different approaches to the problem.
{"title":"Teaching ideal gas in a uniform field: Exploring student preferences","authors":"Wittaya Kanchanapusakit, Pattarapon Tanalikhit","doi":"10.1088/1361-6404/acff9a","DOIUrl":"https://doi.org/10.1088/1361-6404/acff9a","url":null,"abstract":"Abstract An ideal classical gas under uniform gravity is a commonly discussed problem in statistical thermodynamics. At an introductory level, the condition of hydrostatic equilibrium gives rise to the barometric formula, which describes the variation of gas pressure with height. At an advanced level, the partition function can be used to find the density and the internal energy of the gas. These methods rely heavily on mathematical concepts, which may pose a difficulty to some students. This article presents teaching the problem via the virial theorem, emphasising the physical picture of the particle distribution. The virial theorem allows the internal energy to be expressed as an integral over the surface of the container. For the pedagogical purpose, visualisation of how the particles distribute themselves at extreme temperatures helps determine the internal energy of the gas. Student feedback is used as a basis for evaluating different approaches to the problem.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135689231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1088/1361-6404/acf906
Rubén Hurtado-Gutiérrez, Álvaro Tejero
Abstract In this article, we present a simple, inexpensive, and effective method for measuring the capacitor charge and discharge processes using a light-emitting diode (LED) and the light meter of a smartphone. We propose a simple circuit in which the LED’s brightness is linear on the capacitor’s voltage, allowing us to use the smartphone to monitor the capacitor state accurately. The method is tested experimentally, giving highly satisfactory results. Its exceptional combination of accuracy, minimal requirements, and ease of setup makes it an excellent way to introduce undergraduate students to the concepts of electricity and electronics in any educational setting.
{"title":"Measuring capacitor charge and discharge using a LED and a smartphone","authors":"Rubén Hurtado-Gutiérrez, Álvaro Tejero","doi":"10.1088/1361-6404/acf906","DOIUrl":"https://doi.org/10.1088/1361-6404/acf906","url":null,"abstract":"Abstract In this article, we present a simple, inexpensive, and effective method for measuring the capacitor charge and discharge processes using a light-emitting diode (LED) and the light meter of a smartphone. We propose a simple circuit in which the LED’s brightness is linear on the capacitor’s voltage, allowing us to use the smartphone to monitor the capacitor state accurately. The method is tested experimentally, giving highly satisfactory results. Its exceptional combination of accuracy, minimal requirements, and ease of setup makes it an excellent way to introduce undergraduate students to the concepts of electricity and electronics in any educational setting.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135131291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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