We present a novel technique to obtain relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy function. We derive a general expression for a generalized potential energy function for all powers of the velocity, which when made a part of the regular classical Lagrangian can reproduce the correct (relativistic) force equation. We then go on to derive the Hamiltonian and estimate the corrections to the total energy of the system up to the fourth power in $|vec{v}|/c$. We found that our work is able to provide a more comprehensive understanding of relativistic corrections to the central force results and provides corrections to both the kinetic and potential energy of the system. We employ our methodology to calculate relativistic corrections to the circular orbit under the gravitational force and also the first-order corrections to the ground state energy of the hydrogen atom using a semi-classical approach. Our predictions in both problems give reasonable agreement with the known results. Thus we feel that this work has pedagogical value and can be used by undergraduate students to better understand the central force and the relativistic corrections to it.
{"title":"Relativistic corrections to the central force problem in a generalized potential approach","authors":"Ashmeet Singh, B. Patra","doi":"10.1139/cjp-2014-0261","DOIUrl":"https://doi.org/10.1139/cjp-2014-0261","url":null,"abstract":"We present a novel technique to obtain relativistic corrections to the central force problem in the Lagrangian formulation, using a generalized potential energy function. We derive a general expression for a generalized potential energy function for all powers of the velocity, which when made a part of the regular classical Lagrangian can reproduce the correct (relativistic) force equation. We then go on to derive the Hamiltonian and estimate the corrections to the total energy of the system up to the fourth power in $|vec{v}|/c$. We found that our work is able to provide a more comprehensive understanding of relativistic corrections to the central force results and provides corrections to both the kinetic and potential energy of the system. We employ our methodology to calculate relativistic corrections to the circular orbit under the gravitational force and also the first-order corrections to the ground state energy of the hydrogen atom using a semi-classical approach. Our predictions in both problems give reasonable agreement with the known results. Thus we feel that this work has pedagogical value and can be used by undergraduate students to better understand the central force and the relativistic corrections to it.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127881355","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}
Since they correspond to a jump from a given note to another one, the mouth pressure thresholds leading to regime changes are particularly important quantities in flute-like instruments. In this paper, a comparison of such thresholds between an artificial mouth, an experienced flutist and a non player is provided. It highlights the ability of the experienced player to considerabily shift regime change thresholds, and thus to enlarge its control in terms of nuances and spectrum. Based on recent works on other wind instruments and on the theory of dynamic bifurcations, the hypothe- sis is tested experimentally and numerically that the dynamics of the blowing pressure influences regime change thresholds. The results highlight the strong influence of this parameter on thresholds, suggesting its wide use by experienced musicians. Starting from these observations and from an analysis of a physical model of flute-like instruments, involving numerical continuation methods and Floquet stability analysis, a phenomenological modelling of regime change is proposed and validated. It allows to predict the regime change thresholds in the dynamic case, in which time variations of the blowing pressure are taken into account.
{"title":"Regime change thresholds in flute-like instruments: influence of the mouth pressure dynamics","authors":"S. Terrien, R. Blandin, C. Vergez, B. Fabre","doi":"10.3813/AAA.918828","DOIUrl":"https://doi.org/10.3813/AAA.918828","url":null,"abstract":"Since they correspond to a jump from a given note to another one, the mouth pressure thresholds leading to regime changes are particularly important quantities in flute-like instruments. In this paper, a comparison of such thresholds between an artificial mouth, an experienced flutist and a non player is provided. It highlights the ability of the experienced player to considerabily shift regime change thresholds, and thus to enlarge its control in terms of nuances and spectrum. Based on recent works on other wind instruments and on the theory of dynamic bifurcations, the hypothe- sis is tested experimentally and numerically that the dynamics of the blowing pressure influences regime change thresholds. The results highlight the strong influence of this parameter on thresholds, suggesting its wide use by experienced musicians. Starting from these observations and from an analysis of a physical model of flute-like instruments, involving numerical continuation methods and Floquet stability analysis, a phenomenological modelling of regime change is proposed and validated. It allows to predict the regime change thresholds in the dynamic case, in which time variations of the blowing pressure are taken into account.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129118418","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}
Distribution of the electric potential in a very long plate (for example a long metal ruler) is determined. This is achieved by conformally mapping the plate into a plane, simplifying the geometry of boundary conditions. Singularities of the potential are discussed as well as their regularization by the final size of electrical contacts. An analogy with renormalization is pointed out. Results are compared with previous studies.
{"title":"Current distribution in an infinite plate","authors":"A. Czarnecki","doi":"10.1139/cjp-2014-0136","DOIUrl":"https://doi.org/10.1139/cjp-2014-0136","url":null,"abstract":"Distribution of the electric potential in a very long plate (for example a long metal ruler) is determined. This is achieved by conformally mapping the plate into a plane, simplifying the geometry of boundary conditions. Singularities of the potential are discussed as well as their regularization by the final size of electrical contacts. An analogy with renormalization is pointed out. Results are compared with previous studies.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134401223","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 show that the explanation of Thomas-Wigner rotation (TWR) and Thomas precession (TP) in the framework of special theory of relativity (STR) contains a number of points of inconsistency, in particular, with respect to physical interpretation of the Einstein velocity composition law in successive space-time transformations. In addition, we show that the common interpretation of TP falls into conflict with the causality principle. In order to eliminate such a conflict, we suggest considering the velocity parameter, entering into expression for the frequency of TP, as being always related to a rotation-free Lorentz transformation. Such an assumption (which actually resolves any causal paradoxes with respect to TP), comes however to be in contradiction with the spirit of STR. The results obtained are discussed.
{"title":"Thomas-Wigner rotation and Thomas precession: actualized approach","authors":"A. Kholmetskii, T. Yarman","doi":"10.1139/cjp-2014-0015","DOIUrl":"https://doi.org/10.1139/cjp-2014-0015","url":null,"abstract":"We show that the explanation of Thomas-Wigner rotation (TWR) and Thomas precession (TP) in the framework of special theory of relativity (STR) contains a number of points of inconsistency, in particular, with respect to physical interpretation of the Einstein velocity composition law in successive space-time transformations. In addition, we show that the common interpretation of TP falls into conflict with the causality principle. In order to eliminate such a conflict, we suggest considering the velocity parameter, entering into expression for the frequency of TP, as being always related to a rotation-free Lorentz transformation. Such an assumption (which actually resolves any causal paradoxes with respect to TP), comes however to be in contradiction with the spirit of STR. The results obtained are discussed.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124496953","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 : 2014-03-03DOI: 10.4172/2157-7544.1000129
G. Sonnino, A. Sonnino
The concept of {it equivalent systems} from the thermodynamic point of view, originally introduced by Th. De Donder and I. Prigogine, is deeply investigated and revised. From our point of view, two systems are thermodynamically equivalent if, under transformation of the thermodynamic forces, both the entropy production and the Glansdorff-Prigogine dissipative quantity remain unaltered. This kind of transformations may be referred to as the {it Thermodynamic Coordinate Transformations} (TCT). The general class of transformations satisfying the TCT is determined. We shall see that, also in the nonlinear region ({it i.e.}, out of the Onsager region), the TCT preserve the reciprocity relations of the transformed transport matrix. The equivalent character of two transformations under TCT, leads to the concept of {it Thermodynamic Covariance Principle} (TCP) stating that all thermodynamic equations involving the thermodynamic forces and flows ({it e.g.}, the closure flux-force relations) should be covariant under TCT.
{"title":"The Thermodynamic Covariance Principle","authors":"G. Sonnino, A. Sonnino","doi":"10.4172/2157-7544.1000129","DOIUrl":"https://doi.org/10.4172/2157-7544.1000129","url":null,"abstract":"The concept of {it equivalent systems} from the thermodynamic point of view, originally introduced by Th. De Donder and I. Prigogine, is deeply investigated and revised. From our point of view, two systems are thermodynamically equivalent if, under transformation of the thermodynamic forces, both the entropy production and the Glansdorff-Prigogine dissipative quantity remain unaltered. This kind of transformations may be referred to as the {it Thermodynamic Coordinate Transformations} (TCT). The general class of transformations satisfying the TCT is determined. We shall see that, also in the nonlinear region ({it i.e.}, out of the Onsager region), the TCT preserve the reciprocity relations of the transformed transport matrix. The equivalent character of two transformations under TCT, leads to the concept of {it Thermodynamic Covariance Principle} (TCP) stating that all thermodynamic equations involving the thermodynamic forces and flows ({it e.g.}, the closure flux-force relations) should be covariant under TCT.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126220880","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 : 2013-10-30DOI: 10.1142/S0217732313501629
L. Visinelli
We extend the duality symmetry between the electric and the magnetic fields to the case in which an additional axion-like term is present, and we derive the set of Maxwell's equations that preserves this symmetry. This new set of equations allows for a gauge symmetry extending the ordinary symmetry in the classical electrodynamics. We obtain explicit solutions for the new set of equations in the absence of external sources, and we discuss the implications of a new internal symmetry between the axion field and the electromagnetic gauge potential.
{"title":"Axion-Electromagnetic Waves","authors":"L. Visinelli","doi":"10.1142/S0217732313501629","DOIUrl":"https://doi.org/10.1142/S0217732313501629","url":null,"abstract":"We extend the duality symmetry between the electric and the magnetic fields to the case in which an additional axion-like term is present, and we derive the set of Maxwell's equations that preserves this symmetry. This new set of equations allows for a gauge symmetry extending the ordinary symmetry in the classical electrodynamics. We obtain explicit solutions for the new set of equations in the absence of external sources, and we discuss the implications of a new internal symmetry between the axion field and the electromagnetic gauge potential.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121487806","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 : 2013-09-17DOI: 10.12693/APhysPolA.124.1063
R. A. Méndez-Sánchez, L. Gutiérrez, A. Morales, J. Flores, A. Díaz-de-Anda, G. Monsivais
The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional waves. The first set is analyzed numerically whereas the second one is studied both experimentally and theoretically. In particular, we discuss the localization properties of the waves as a function of the frequency. In doing that we have used the inverse participation ratio, which is related to the localization length. We find that the normal modes localize exponentially according to Anderson theory. In the elastic systems, the localization length decreases with frequency. This behavior is in contrast with what happens in analogous quantum mechanical systems, for which the localization length grows with energy. This difference is explained by means of the properties of the re ection coefficient of a single scatterer in each case.
{"title":"Anderson Localization Phenomenon in One-dimensional Elastic Systems","authors":"R. A. Méndez-Sánchez, L. Gutiérrez, A. Morales, J. Flores, A. Díaz-de-Anda, G. Monsivais","doi":"10.12693/APhysPolA.124.1063","DOIUrl":"https://doi.org/10.12693/APhysPolA.124.1063","url":null,"abstract":"The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional waves. The first set is analyzed numerically whereas the second one is studied both experimentally and theoretically. In particular, we discuss the localization properties of the waves as a function of the frequency. In doing that we have used the inverse participation ratio, which is related to the localization length. We find that the normal modes localize exponentially according to Anderson theory. In the elastic systems, the localization length decreases with frequency. This behavior is in contrast with what happens in analogous quantum mechanical systems, for which the localization length grows with energy. This difference is explained by means of the properties of the re ection coefficient of a single scatterer in each case.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"3 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120833627","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 : 2013-08-30DOI: 10.1007/978-3-642-37537-8_14
H. Ouerdane, C. Goupil, Y. Apertet, A. Michot, A. Abbout
{"title":"A Linear Nonequilibrium Thermodynamics Approach to Optimization of Thermoelectric Devices","authors":"H. Ouerdane, C. Goupil, Y. Apertet, A. Michot, A. Abbout","doi":"10.1007/978-3-642-37537-8_14","DOIUrl":"https://doi.org/10.1007/978-3-642-37537-8_14","url":null,"abstract":"","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129570445","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}
In this paper a novel compressor for static magnetic fields is proposed based on finite embedded transformation optics. When the DC magnetic field passes through the designed device, the magnetic field can be compressed inside the device. After it passes through the device, one can obtain an enhanced static magnetic field behind the output surface of the device (in a free space region). We can also combine our compressor with some other structures to get a higher static magnetic field enhancement in a free space region. In contrast with other devices based on transformation optics for enhancing static magnetic fields, our device is not a closed structure and thus has some special applications (e.g., for controlling magnetic nano-particles for gene and drag delivery). The designed compressor can be constructed by using currently available materials or DC meta-materials with positive permeability. Numerical simulation verifies good performance of our device.
{"title":"Static magnetic field concentration and enhancement using magnetic materials with positive permeability","authors":"F. Sun, S. He","doi":"10.2528/PIER13082102","DOIUrl":"https://doi.org/10.2528/PIER13082102","url":null,"abstract":"In this paper a novel compressor for static magnetic fields is proposed based on finite embedded transformation optics. When the DC magnetic field passes through the designed device, the magnetic field can be compressed inside the device. After it passes through the device, one can obtain an enhanced static magnetic field behind the output surface of the device (in a free space region). We can also combine our compressor with some other structures to get a higher static magnetic field enhancement in a free space region. In contrast with other devices based on transformation optics for enhancing static magnetic fields, our device is not a closed structure and thus has some special applications (e.g., for controlling magnetic nano-particles for gene and drag delivery). The designed compressor can be constructed by using currently available materials or DC meta-materials with positive permeability. Numerical simulation verifies good performance of our device.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130680151","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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