The present paper examines the differential analysis of fows on normal congruence of spacelike surfaces with spacelike normal vector in terms of anholonomic coordinates in three dimensional Lorentzian space. Eight parameters which are related by three partial differential equations are discussed. Then, it is seen that the curl of tangent vector field does not include any component with principal normal direction. Thus there exists a surface which contains both s-lines and b-lines. Also, we examine a normal congruence of spacelike surfaces containing the s-lines and b-lines. By compatibility conditions, Gauss-Mainardi-Codazzi equations for this normal congruence of spacelike surface are obtained: Intrinsic geometric properties of this normal congruence of spacelike surfaces are given.
{"title":"On Differential Analysis of Flows on Normal Congruence of Spacelike Surfaces","authors":"M. Erdoğdu, Ayşe Yavuz","doi":"10.2139/ssrn.3935585","DOIUrl":"https://doi.org/10.2139/ssrn.3935585","url":null,"abstract":"The present paper examines the differential analysis of fows on normal congruence of spacelike surfaces with spacelike normal vector in terms of anholonomic coordinates in three dimensional Lorentzian space. Eight parameters which are related by three partial differential equations are discussed. Then, it is seen that the curl of tangent vector field does not include any component with principal normal direction. Thus there exists a surface which contains both s-lines and b-lines. Also, we examine a normal congruence of spacelike surfaces containing the s-lines and b-lines. By compatibility conditions, Gauss-Mainardi-Codazzi equations for this normal congruence of spacelike surface are obtained: Intrinsic geometric properties of this normal congruence of spacelike surfaces are given.","PeriodicalId":220342,"journal":{"name":"Materials Science Educator: Courses","volume":"23 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":"132407382","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}
We developed a theoretical model of an electron conductivity of a nanolayer in the view of quantum theory of transport phenomena. The layer thickness can be comparable to or less than the de Broglie wavelength of charge carriers. We suppose an isoenergy surface has a form of an ellipsoid of revolution. We derived analytical expressions for conductivity tensor components as functions of the non-dimensional layer thickness, chemical potential, ellipticity parameter and surface roughness parameters. The dependences of longitudinal and transverse conductivity tensor components on the above parameters were analyzed. We compared the results obtained for a metal and semiconductor. The comparison between theoretical calculations and experimental data for bismuth and silicon films was made.
{"title":"Influence of Quantum Electron Transport and Surface Scattering of Charge Carriers on the Conductivity of Nanolayer","authors":"I. A. Kuznetsova, O. Savenko, D. Romanov","doi":"10.2139/ssrn.3925507","DOIUrl":"https://doi.org/10.2139/ssrn.3925507","url":null,"abstract":"We developed a theoretical model of an electron conductivity of a nanolayer in the view of quantum theory of transport phenomena. The layer thickness can be comparable to or less than the de Broglie wavelength of charge carriers. We suppose an isoenergy surface has a form of an ellipsoid of revolution. We derived analytical expressions for conductivity tensor components as functions of the non-dimensional layer thickness, chemical potential, ellipticity parameter and surface roughness parameters. The dependences of longitudinal and transverse conductivity tensor components on the above parameters were analyzed. We compared the results obtained for a metal and semiconductor. The comparison between theoretical calculations and experimental data for bismuth and silicon films was made.","PeriodicalId":220342,"journal":{"name":"Materials Science Educator: Courses","volume":"3 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":"128860215","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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