Pub Date : 2018-09-21DOI: 10.1103/PhysRevResearch.3.023242
Cisco Gooding, S. Weinfurtner, W. Unruh
We consider the wave-structure coupling between an orbital angular momentum beam and a rapidly rotating disk, and present a new configuration exhibiting the wave amplification effect known as rotational superradiance. While initially envisioned in terms of the scattering of an incident wave directed perpendicular to an object's rotation axis, we demonstrate in the context of acousto-mechanics that superradiant amplification can also occur with a vortex beam directed parallel to the rotation axis. We propose two different experimental routes: one must either work with rotations high enough that the tangential velocity at the outer edge of the disk exceeds the speed of sound, or use evanescent sound waves. We argue that the latter possibility is more promising, and provides the opportunity to probe a previously unexamined parameter regime in the acoustics of rotating porous media.
{"title":"Superradiant scattering of orbital angular momentum beams","authors":"Cisco Gooding, S. Weinfurtner, W. Unruh","doi":"10.1103/PhysRevResearch.3.023242","DOIUrl":"https://doi.org/10.1103/PhysRevResearch.3.023242","url":null,"abstract":"We consider the wave-structure coupling between an orbital angular momentum beam and a rapidly rotating disk, and present a new configuration exhibiting the wave amplification effect known as rotational superradiance. While initially envisioned in terms of the scattering of an incident wave directed perpendicular to an object's rotation axis, we demonstrate in the context of acousto-mechanics that superradiant amplification can also occur with a vortex beam directed parallel to the rotation axis. We propose two different experimental routes: one must either work with rotations high enough that the tangential velocity at the outer edge of the disk exceeds the speed of sound, or use evanescent sound waves. We argue that the latter possibility is more promising, and provides the opportunity to probe a previously unexamined parameter regime in the acoustics of rotating porous media.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126931174","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 : 2018-09-20DOI: 10.1590/1806-9126-rbef-2019-0323
D. Boito, L. D. Andrade, G. D. Sousa, R. Gama, C. Y. London
We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the usual three-dimensional case arise. These stem from the general form of the solutions of the wave equation in two dimensions, which we discuss using the Green's function method. We believe the topics presented here could be stimulating additions to an advanced electrodynamics course at the undergraduate level.
{"title":"On Maxwell’s electrodynamics in two spatial dimensions","authors":"D. Boito, L. D. Andrade, G. D. Sousa, R. Gama, C. Y. London","doi":"10.1590/1806-9126-rbef-2019-0323","DOIUrl":"https://doi.org/10.1590/1806-9126-rbef-2019-0323","url":null,"abstract":"We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the usual three-dimensional case arise. These stem from the general form of the solutions of the wave equation in two dimensions, which we discuss using the Green's function method. We believe the topics presented here could be stimulating additions to an advanced electrodynamics course at the undergraduate level.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132914239","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}
The concept of hidden momentum is reviewed and the first rigorous derivation from Maxwell's equations is provided for the electromagnetic force on electrically small perfect electric conductors of arbitrary shape in bandlimited but otherwise arbitrarily time-varying fields. It is proven for the Amperian magnetic dipoles of these perfect conductors that a "hidden-momentum" electromagnetic force exists that makes the force on these time varying Amperian magnetic dipoles equal to the force on magnetic-charge magnetic dipoles with the same time varying magnetic dipole moment in the same time varying externally applied fields. The exact Mie solution to the perfectly conducting sphere under plane-wave illumination is used to prove that the expressions for the total and hidden-momentum forces on the arbitrarily shaped electrically small perfect conductors correctly predict the forces on perfectly conducting spheres. Remarkably, it is found that the quadrupolar fields at the surface of the sphere are required to obtain the correct total force on the sphere even though the quadrupolar moments are negligible compared to the dipole moments as the electrical size of the sphere approaches zero.
{"title":"Force and Hidden Momentum for Classical Microscopic Dipoles","authors":"A. Yaghjian","doi":"10.2528/PIERB18092007","DOIUrl":"https://doi.org/10.2528/PIERB18092007","url":null,"abstract":"The concept of hidden momentum is reviewed and the first rigorous derivation from Maxwell's equations is provided for the electromagnetic force on electrically small perfect electric conductors of arbitrary shape in bandlimited but otherwise arbitrarily time-varying fields. It is proven for the Amperian magnetic dipoles of these perfect conductors that a \"hidden-momentum\" electromagnetic force exists that makes the force on these time varying Amperian magnetic dipoles equal to the force on magnetic-charge magnetic dipoles with the same time varying magnetic dipole moment in the same time varying externally applied fields. The exact Mie solution to the perfectly conducting sphere under plane-wave illumination is used to prove that the expressions for the total and hidden-momentum forces on the arbitrarily shaped electrically small perfect conductors correctly predict the forces on perfectly conducting spheres. Remarkably, it is found that the quadrupolar fields at the surface of the sphere are required to obtain the correct total force on the sphere even though the quadrupolar moments are negligible compared to the dipole moments as the electrical size of the sphere approaches zero.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129196762","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 revisit the electromagnetic problem of wave incidence upon a uniform, dissipative dielectric slab of finite thickness. While this problem is easily solved via interface field continuity, we treat it under the viewpoint of radiative self-consistency, with interior current sources gauged by ohmic/polarization comparisons against those of the exterior medium. Radiative self-consistency yields an integral equation over the slab field giving a fully constructive buildup of the reflected/transmitted contributions, without any need for implicit determination via boundary conditions. Solution steps lead to an exact cancellation of the interior field, and bring in still other contributions of a reference medium variety, required to balance the incoming excitation. Such balancing provides the linear conditions for slab field determination. This two-step solution provides evidence of Ewald-Oseen extinction, even though the analytic framework here differs from the proofs available. We solve the balancing equations by vector manipulation without determinants, and then offer a boundary value confirmation in the special case of perpendicular incidence. In an appendix, we allow the the upper/lower half spaces to differ, the upper serving as reference and remote launch site of the incoming excitation. Effective currents now exist both within the slab and throughout an entire half space, necessitating a provision for cross-talk between slab and the radiating half space. The appendix provides an accelerated presentation of these generalized features, but stops short of an explicit field solution by reason of algebraic inflation. All logical details are however displayed in plain view. The self-consistency program is far more elegant and physically far more satisfying than the prevailing method of scattered fields guessed as to their structure and then fixed by boundary conditions.
{"title":"Dielectric slab reflection/transmission as a self-consistent radiation phenomenon.","authors":"J. Grzesik","doi":"10.2528/PIERB18062303","DOIUrl":"https://doi.org/10.2528/PIERB18062303","url":null,"abstract":"We revisit the electromagnetic problem of wave incidence upon a uniform, dissipative dielectric slab of finite thickness. While this problem is easily solved via interface field continuity, we treat it under the viewpoint of radiative self-consistency, with interior current sources gauged by ohmic/polarization comparisons against those of the exterior medium. Radiative self-consistency yields an integral equation over the slab field giving a fully constructive buildup of the reflected/transmitted contributions, without any need for implicit determination via boundary conditions. Solution steps lead to an exact cancellation of the interior field, and bring in still other contributions of a reference medium variety, required to balance the incoming excitation. Such balancing provides the linear conditions for slab field determination. This two-step solution provides evidence of Ewald-Oseen extinction, even though the analytic framework here differs from the proofs available. We solve the balancing equations by vector manipulation without determinants, and then offer a boundary value confirmation in the special case of perpendicular incidence. In an appendix, we allow the the upper/lower half spaces to differ, the upper serving as reference and remote launch site of the incoming excitation. Effective currents now exist both within the slab and throughout an entire half space, necessitating a provision for cross-talk between slab and the radiating half space. The appendix provides an accelerated presentation of these generalized features, but stops short of an explicit field solution by reason of algebraic inflation. All logical details are however displayed in plain view. The self-consistency program is far more elegant and physically far more satisfying than the prevailing method of scattered fields guessed as to their structure and then fixed by boundary conditions.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128702248","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 consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and orientation, respectively, of a triangle with the three bodies located at the vertices. The radial variables are given by the distances between a reference body and the other two, and by the angle at the reference body between the other two. Such radial variables set the potential energy of the system, and they are reminiscent of the inter-body distance in the two-body problem. On the other hand, the angular variables are the Euler angles relative to a rigid rotation of the triangle, and they are analogous to the polar and azimuthal angle of the vector between the two bodies in the two-body problem. We show that the rotational symmetry allows us to obtain a closed set of eight Hamilton equations of motion, whose generalized coordinates are the thee radial variables and one additional angle, for which we provide the following geometrical interpretation. Given a reference body, we consider the plane through it which is orthogonal to the line between the reference and a second body. We show that the angular variable above is the angle between the plane projection of the angular-momentum vector, and the projection of the radius between the reference and the third body.
{"title":"Symmetry reduction of the three-body problem based on Euler angles","authors":"M. Castellana","doi":"10.1063/1.4990550","DOIUrl":"https://doi.org/10.1063/1.4990550","url":null,"abstract":"We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three \"radial\" and three angular variables, which determine the shape and orientation, respectively, of a triangle with the three bodies located at the vertices. The radial variables are given by the distances between a reference body and the other two, and by the angle at the reference body between the other two. Such radial variables set the potential energy of the system, and they are reminiscent of the inter-body distance in the two-body problem. On the other hand, the angular variables are the Euler angles relative to a rigid rotation of the triangle, and they are analogous to the polar and azimuthal angle of the vector between the two bodies in the two-body problem. We show that the rotational symmetry allows us to obtain a closed set of eight Hamilton equations of motion, whose generalized coordinates are the thee radial variables and one additional angle, for which we provide the following geometrical interpretation. Given a reference body, we consider the plane through it which is orthogonal to the line between the reference and a second body. We show that the angular variable above is the angle between the plane projection of the angular-momentum vector, and the projection of the radius between the reference and the third body.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"1995 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130360946","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 : 2018-02-14DOI: 10.22606/JAAM.2018.34001
F. Talamucci
The model we consider consists in a double pendulum set, where the pivot points are free to shift along a horizontal line. Moreover, the two pendula are coupled by means of a spring whose extremities connect two points of each pendulum, at a fixed distance from the corresponding pivot. The mathematical model is first written encompassing a large class of setting for the device (different sizes, different physical properties, ...). In order to carry on the problem of synchronization via analytical me-thods, we focus on the circumstance of identical pendula: in that case, some classical theorems concerning the zeroes of polynomial equations are used in order to locate the eigenvalues governing the process, so that the possibility of synchronization of the device can be better understood.
{"title":"Synchronization of a double pendulum with moving pivots: a study of the spectrum","authors":"F. Talamucci","doi":"10.22606/JAAM.2018.34001","DOIUrl":"https://doi.org/10.22606/JAAM.2018.34001","url":null,"abstract":"The model we consider consists in a double pendulum set, where the pivot points are free to shift along a horizontal line. Moreover, the two pendula are coupled by means of a spring whose extremities connect two points of each pendulum, at a fixed distance from the corresponding pivot. The mathematical model is first written encompassing a large class of setting for the device (different sizes, different physical properties, ...). In order to carry on the problem of synchronization via analytical me-thods, we focus on the circumstance of identical pendula: in that case, some classical theorems concerning the zeroes of polynomial equations are used in order to locate the eigenvalues governing the process, so that the possibility of synchronization of the device can be better understood.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129578764","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 : 2017-12-30DOI: 10.1142/S0217732318300069
I. Brevik
Recent years have witnessed a number of beautiful experiments in radiation optics. Our purpose with this mini-review is to highlight some developments of radiation pressure physics in general, and thereafter to focus on the importance of the mentioned experiments in regard to the classic Abraham-Minkowski problem. That means, what is the "correct" expression for electromagnetic momentum density in continuous matter. In our opinion one sees relatively often that authors over-interpret the importance of their experimental findings with respect to the momentum problem. Most of these experiments are actually unable to discriminate between these energy-momentum tensors at all, since they can be easily described in terms of force expressions that are common for Abraham and Minkowski. Moreover, we emphasize the inherent ambiguity in applying formal conservation principles to the radiation field in a dielectric, the reason being that the electromagnetic field in matter is only a subsystem which has to be supplemented by the mechanical subsystem to be closed. Finally, we make some suggestions regarding the connection between macroscopic electrodynamics and the Casimir effect, suggesting that there is a limit for the magnitudes of cutoff parameters in QFT related to surface tension in ordinary hydromechanics.
{"title":"Radiation Forces and the Abraham-Minkowski Problem","authors":"I. Brevik","doi":"10.1142/S0217732318300069","DOIUrl":"https://doi.org/10.1142/S0217732318300069","url":null,"abstract":"Recent years have witnessed a number of beautiful experiments in radiation optics. Our purpose with this mini-review is to highlight some developments of radiation pressure physics in general, and thereafter to focus on the importance of the mentioned experiments in regard to the classic Abraham-Minkowski problem. That means, what is the \"correct\" expression for electromagnetic momentum density in continuous matter. In our opinion one sees relatively often that authors over-interpret the importance of their experimental findings with respect to the momentum problem. Most of these experiments are actually unable to discriminate between these energy-momentum tensors at all, since they can be easily described in terms of force expressions that are common for Abraham and Minkowski. Moreover, we emphasize the inherent ambiguity in applying formal conservation principles to the radiation field in a dielectric, the reason being that the electromagnetic field in matter is only a subsystem which has to be supplemented by the mechanical subsystem to be closed. Finally, we make some suggestions regarding the connection between macroscopic electrodynamics and the Casimir effect, suggesting that there is a limit for the magnitudes of cutoff parameters in QFT related to surface tension in ordinary hydromechanics.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"23 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126154063","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 : 2017-12-20DOI: 10.1142/S0217732318300057
T. Padmanabhan
It is well known that the time dependent harmonic oscillator possesses a conserved quantity, usually called Ermakov-Lewis invariant. I provide a simple physical interpretation of this invariant as well as a whole family of related invariants. This interpretation does not seem to have been noticed in the literature before. The procedure also allows one to tackle some key conceptual issues which arise in the study of quantum fields in external, time dependent, backgrounds like in the case of particle production in an expanding universe and Schwinger effect.
{"title":"Demystifying the constancy of the Ermakov-Lewis invariant for a time dependent oscillator","authors":"T. Padmanabhan","doi":"10.1142/S0217732318300057","DOIUrl":"https://doi.org/10.1142/S0217732318300057","url":null,"abstract":"It is well known that the time dependent harmonic oscillator possesses a conserved quantity, usually called Ermakov-Lewis invariant. I provide a simple physical interpretation of this invariant as well as a whole family of related invariants. This interpretation does not seem to have been noticed in the literature before. The procedure also allows one to tackle some key conceptual issues which arise in the study of quantum fields in external, time dependent, backgrounds like in the case of particle production in an expanding universe and Schwinger effect.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131214513","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 mapping of non-extensive statistical mechanics with non-additivity parameter q ≠ 1 into Gibbs’ statistical mechanics exists (E. Vives, A. Planes, PRL 88 2, 020601 (2002)) which allows generalization to q ≠ 1 both of Einstein’s formula for fluctuations and of the ’general evolution criterion’ (P. Glansdorff, I. Prigogine, Physica 30 351 (1964)), an inequality involving the time derivatives of thermodynamical quantities. Unified thermodynamic description of relaxation to stable states with either Boltzmann ( q = 1 ) or power-law ( q ≠ 1 ) distribution of probabilities of microstates follows. If a 1D (possibly nonlinear) Fokker-Planck equation describes relaxation, then generalized Einstein’s formula predicts whether the relaxed state exhibits a Boltzmann or a power law distribution function. If this Fokker-Planck equation is associated to the stochastic differential equation obtained in the continuous limit from a 1D, autonomous, discrete, noise-affected map, then we may ascertain if a a relaxed state follows a power-law statistics—and with which exponent—by looking at both map dynamics and noise level, without assumptions concerning the (additive or multiplicative) nature of the noise and without numerical computation of the orbits. Results agree with the simulations (J. R. Sanchez, R. Lopez-Ruiz, EPJ 143.1 (2007): 241–243) of relaxation leading to a Pareto-like distribution function.
存在一个非可加性参数q≠1的非扩展统计力学映射到Gibbs统计力学(E. Vives, A. Planes, PRL 88 2, 020601(2002))，它允许将爱因斯坦涨落公式和“一般演化准则”(P. Glansdorff, I. Prigogine, Physica 30 351(1964))推广到q≠1，这是一个涉及热力学量的时间导数的不等式。用玻尔兹曼(q = 1)或幂律(q≠1)分布的微观状态概率，给出松弛到稳定状态的统一热力学描述。如果一个一维(可能是非线性的)福克-普朗克方程描述了松弛状态，那么广义爱因斯坦公式预测了松弛状态是呈现玻尔兹曼分布函数还是幂律分布函数。如果这个福克-普朗克方程与在一维、自治、离散、受噪声影响的映射的连续极限中得到的随机微分方程相关联，那么我们就可以通过观察映射动力学和噪声水平来确定松弛状态是否遵循幂律统计——以及使用哪个指数，而不需要假设噪声的(加性或乘法性)性质，也不需要对轨道进行数值计算。结果与模拟结果一致(J. R. Sanchez, R. Lopez-Ruiz, EPJ 143.1(2007): 241-243)，松弛导致Pareto-like分布函数。
{"title":"Exponential or Power Law? How to Select a Stable Distribution of Probability in a Physical System","authors":"A. D. Vita","doi":"10.3390/ecea-4-05009","DOIUrl":"https://doi.org/10.3390/ecea-4-05009","url":null,"abstract":"A mapping of non-extensive statistical mechanics with non-additivity parameter q ≠ 1 into Gibbs’ statistical mechanics exists (E. Vives, A. Planes, PRL 88 2, 020601 (2002)) which allows generalization to q ≠ 1 both of Einstein’s formula for fluctuations and of the ’general evolution criterion’ (P. Glansdorff, I. Prigogine, Physica 30 351 (1964)), an inequality involving the time derivatives of thermodynamical quantities. Unified thermodynamic description of relaxation to stable states with either Boltzmann ( q = 1 ) or power-law ( q ≠ 1 ) distribution of probabilities of microstates follows. If a 1D (possibly nonlinear) Fokker-Planck equation describes relaxation, then generalized Einstein’s formula predicts whether the relaxed state exhibits a Boltzmann or a power law distribution function. If this Fokker-Planck equation is associated to the stochastic differential equation obtained in the continuous limit from a 1D, autonomous, discrete, noise-affected map, then we may ascertain if a a relaxed state follows a power-law statistics—and with which exponent—by looking at both map dynamics and noise level, without assumptions concerning the (additive or multiplicative) nature of the noise and without numerical computation of the orbits. Results agree with the simulations (J. R. Sanchez, R. Lopez-Ruiz, EPJ 143.1 (2007): 241–243) of relaxation leading to a Pareto-like distribution function.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128545920","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}
S. Sautbekov, Sotiris Bourgiotis, A. Chrysostomou, P. Frangos
The well-known "Sommerfeld radiation problem" of a small -Hertzian- vertical dipole above flat lossy ground is reconsidered. The problem is examined in the spectral domain, through which it is proved to yield relatively simple integral expressions for the received Electromagnetic (EM) field. Then, using the Saddle Point method, novel analytical expressions for the scattered EM field are obtained, including sliding observation angles. As a result, a closed form solution for the subject matter is provided. Also, the necessary conditions for the emergence of the so-called Surface Wave are discussed as well. A complete mathematical formulation is presented, with detailed derivations where necessary.
{"title":"A Novel Asymptotic Solution to the Sommerfeld Radiation Problem: Analytic field expressions and the emergence of the Surface Waves","authors":"S. Sautbekov, Sotiris Bourgiotis, A. Chrysostomou, P. Frangos","doi":"10.2528/PIERM17082806","DOIUrl":"https://doi.org/10.2528/PIERM17082806","url":null,"abstract":"The well-known \"Sommerfeld radiation problem\" of a small -Hertzian- vertical dipole above flat lossy ground is reconsidered. The problem is examined in the spectral domain, through which it is proved to yield relatively simple integral expressions for the received Electromagnetic (EM) field. Then, using the Saddle Point method, novel analytical expressions for the scattered EM field are obtained, including sliding observation angles. As a result, a closed form solution for the subject matter is provided. Also, the necessary conditions for the emergence of the so-called Surface Wave are discussed as well. A complete mathematical formulation is presented, with detailed derivations where necessary.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116321640","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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