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  • 1.
    Enflo, Bengt Olof
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Hedberg, Claes M.Blekinge Institute of Technology.Kari, LeifKTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
    Non-Linear Acoustics: Fundamentals and Applications2008Conference proceedings (editor) (Refereed)
  • 2.
    Essen, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas2011In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 94, no 4, p. 47003-Article in journal (Refereed)
    Abstract [en]

    The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position-dependent interactions but this is not required by classical physics. Since the work of Darwin in 1920 it has been known that the magnetism due to classical charged point particles can only be described by allowing velocity-dependent interactions in the Lagrangian. Legendre transformation to an approximate Hamiltonian can give an estimate of the Darwin diamagnetism for a system of charged point particles. Comparison with experiment, however, requires knowledge of the number of classically behaving electrons in the sample. A new repulsive effective many-body force, which should be relevant in plasmas, is predicted by the Hamiltonian.

  • 3.
    Essen, Hanno
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Fiolhais, Miguel C. N.
    Meissner effect, diamagnetism, and classical physics-a review2012In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 80, no 2, p. 164-169Article in journal (Refereed)
    Abstract [en]

    We review the literature on what classical physics says about the Meissner effect and the London equations. We discuss the relevance of the Bohr-van Leeuwen theorem for the perfect diamagnetism of superconductors and conclude that the theorem is based on invalid assumptions. We also point out results in the literature that show how magnetic flux expulsion from a sample cooled to superconductivity can be understood as an approach to the magnetostatic energy minimum. These results have been published several times but many textbooks on magnetism still claim that there is no classical diamagnetism, and virtually all books on superconductivity repeat Meissner's 1933 statement that flux expulsion has no classical explanation.

  • 4.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    From least action in electrodynamics to magnetomechanical energy-a review2009In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 30, no 3, p. 515-539Article, review/survey (Refereed)
    Abstract [en]

    The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative and one can study them in a Hamiltonian formalism. The central concepts of generalized capacitance and inductance coefficients are introduced and explained. The problem of gauge independence of self-inductance is considered. Our main interest is in magnetomechanics, i.e. the study of systems where there is exchange between mechanical and magnetic energy. This throws light on the concept of magnetic energy, which according to the literature has confusing and peculiar properties. We apply the theory to a few simple examples: the extension of a circular current loop, the force between parallel wires, interacting circular current loops and the rail gun. These show that the Hamiltonian, phase space, form of magnetic energy has the usual property that an equilibrium configuration corresponds to an energy minimum.

  • 5.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Matrix analysis of coupled damped vibrations: two degree-of-freedom analytic solution2007In: International journal of pure and applied mathematics, ISSN 1311-8080, E-ISSN 1314-3395, Vol. 36, p. 115-146Article in journal (Refereed)
    Abstract [en]

    The linear coupled damped free oscillator problem is solved bymeans of matrix analysis. The solution can be written by means of exponentialsof time evolution matrices multiplied by time. These time evolution matricesare determined as the solutions of quadratic matrix equations. The intricaciesof non-proportional damping become particularly clear in this treatment. Forthe two degree-of-freedom problem an explicit analytic solution is given in termsof a root of a cubic equation. The existence of an algebraically simpler specialcase (other than proportional damping) is pointed out.

  • 6.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Mechanics, cosmology and Mach's principle2013In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 34, no 1, p. 139-145Article in journal (Refereed)
    Abstract [en]

    It is pointed out that recent cosmological findings seem to support the view that the mass/energy distribution of the universe defines the Newtonian inertial frames, as originally suggested by Mach. The background concepts of inertial frame, Newton's second law and fictitious forces are clarified. A precise definition of Mach's principle is suggested. Then, an approximation to general relativity discovered by Einstein, Infeld and Hoffmann is used and it is found that this precise formulation of Mach's principle is realized provided the mass/energy density of the universe has a specific value. This value turns out to be twice the critical density. The implications of this approximate result are put into context.

  • 7.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Periodiska systemets rätta form1989In: Elementa : tidskrift för matematik, fysik och kemi, ISSN 0013-5933, Vol. 72, no 1, p. 17-20Article in journal (Refereed)
  • 8.
    Essén, Hanno
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Fiolhais, M. C. N.
    The darwin-breit magnetic interaction and superconductivity2013In: PIERS Proceedings, Stockholm, Sweden, Aug. 12-15, 2013, Electromagnetics Academy , 2013, p. 1198-1202Conference paper (Refereed)
    Abstract [en]

    A number of facts indicating the relevance of the Darwin magnetic interaction energy in the superconducting phase are pointed out. The magnetic interaction term derived by Darwin is the same as the, so called, Breit term in relativistic quantum mechanics. While this term always is a small perturbation in few body systems it can be shown to be potentially dominating in systems of large numbers of electrons. It is therefore a natural candidate in the explanation of emergent phenomena - phenomena that only occur in sufficiently large systems. The dimensionless parameter that indicates the importance of the magnetic energy is the number of electrons times the classical electron radius divided by the size of the system. The number of electrons involved are only the electrons at the Fermi surface; electrons with lower energy cannot contribute to current density and thus not to the magnetic field. The conventional understanding of superconductivity has always been problematic and no really reductionistic derivation exists. The idea that the inductive inertia, due to magnetism, is important in the explanation of superconductivity was first advanced by Frenkel and later brought up by Welker before it was prematurely discarded. So were theories involving Wigner crystallization. We speculate that the answer requires the combination of a Wigner lattice and the Darwin interaction. We point out that the Darwin interaction can be shown to have the right order of magnitude to explain the energy scales involved in normal superconductors. The London magnetic moment of rotating superconductors and the Meissner effect and their connection are discussed next. The London moment is shown to indicate that the number of electrons involved in the superconducting condensate is such that the Darwin interaction cannot be neglected.

  • 9.
    Essén, Hanno
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Static deformation of a heavy spring due to gravity and centrifugal force2010In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 31, no 3, p. 603-609Article in journal (Refereed)
    Abstract [en]

    The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases: first for a spring hanging in a constant gravitational field, and then for a spring which is at rest in a rotating system where it is stretched by the centrifugal force. Two different models are considered: first a discrete model assuming a finite number of point masses connected by springs of negligible weight, and then the continuum limit of this model. In the second case, the differential equation for the deformation is obtained by demanding that the potential energy is minimized. In this way a simple application of the variational calculus is obtained.

  • 10.
    Essén, Hanno
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Sten, J. C. -E
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics, Structural Mechanics.
    Magnetic energy of surface currents on a torus2013In: Progress in Electromagnetics Research B, ISSN 1937-6472, E-ISSN 1937-6472, no 46, p. 357-378Article in journal (Refereed)
    Abstract [en]

    The magnetic energy and inductance of current distribu-tions on the surface of a torus are considered. Specifically, we investigate the influence of the aspect ratio of the torus, and of the pitch angle for helical current densities, on the energy. We show that, for a fixed surface area of the torus, the energy experiences a minimum for a certain pitch angle. New analytical relationships are presented as well as a review of results scattered in the literature. Results for the ideally conducting torus, as well as for thin rings are given.

  • 11. Fiolhais, M. C. N.
    et al.
    Essen, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Electromagnetic wave scattering by a superconductor2012In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 97, no 4, p. 44006-Article in journal (Refereed)
    Abstract [en]

    The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in cylindrical coordinates. Numerical results computed up to O(77) of Bessel functions are presented for different wavelengths showing the appearance of a diffraction pattern.

  • 12. Fiolhais, M. C. N.
    et al.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Magnetic field expulsion in perfect conductors - The magnetic equivalent of Thomson's theorem2013In: Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013, Electromagnetics Academy , 2013, p. 1193-1197Conference paper (Refereed)
    Abstract [en]

    Thomson's theorem states that electric charge density on metal conductors, at static equilibrium, is distributed on the surface of the conductors in such a way that the interior electric field is zero, and the electric field on the surface must be perpendicular to the surface. In this paper, we present a theorem for static magnetic fields, analogous of the Thomson's theorem of electrostatics. We prove, by making use of a variational principle, that the minimization of the magnetic field energy corresponds to the magnetic field expulsion of perfect conductive systems through surface currents. As a result, the current density distributes itself on the surface of the ideal conductor so that the interior magnetic field becomes zero, and all current flows on its surface. This result is put into the context of superconductivity, and leads us to conclude the Meissner effect is not a pure quantum effect, restricted to superconductors, but rather a magnetostatic equilibrium state as a consequence of zero resistivity. In addition, the London equations are derived following an approach by Pierre-Gilles de Gennes where "the superconductor finds an equilibrium state where the sum of the kinetic and magnetic energies is minimum, and this state, for macroscopic samples, corresponds to the expulsion of magnetic flux". For further confirmation, the same result is also derived in the classical limit of the Coleman-Weinberg model, the most successful quantum macroscopic theory of superconductivity. A specific example is presented to corroborate the result of our theorem. In particular, an explicit solution for a minimal energy magnetic field configuration is analyzed, and found to be in agreement with our statement.

  • 13. Fiolhais, Miguel C. N.
    et al.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Electrodynamics of Perfect Conductors2013In: International journal of theoretical physics, ISSN 0020-7748, E-ISSN 1572-9575, Vol. 52, no 5, p. 1701-1705Article in journal (Refereed)
    Abstract [en]

    The most general electrodynamic equations of a perfect conducting state are obtained using a variational principle in a classical framework, following an approach by Pierre-Gilles de Gennes. London equations are derived as the time-independent case of these equations, corresponding to the magnetostatic minimal energy state of the perfect conducting system. For further confirmation, the same equations are also derived in the classical limit of the Coleman-Weinberg model, the most successful quantum macroscopic theory of superconductivity. The magnetic field expulsion is, therefore, a direct consequence of zero resistivity and not an exclusive property of superconductors.

  • 14. Fiolhais, Miguel
    et al.
    Essén, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Providencia, Constanta
    Nordmark, Arne
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
    Magnetic field and current are zero inside ideal conductors2011In: Progress in Electromagnetics Research B, ISSN 1937-6472, E-ISSN 1937-6472, Vol. 27, p. 187-212Article in journal (Refereed)
    Abstract [en]

    We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomson's theorem on the equilibrium electric field and charge distribution in a system of conductors. We first prove Thomson's theorem using a variational principle. Our new theorem is then derived by similar methods. We find that magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic field; perfect conductors are perfectly diamagnetic. The results agree with currents in superconductors being confined near the surface. The theorem implies a generalized force that expels current and magnetic field from the interior of a conductor that loses its resistivity. Examples of solutions that obey the theorem are presented.

  • 15.
    Nordmark, Arne B.
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Essen, Hanno
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    The comfortable roller coaster-on the shape of tracks with a constant normal force2010In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 31, no 6, p. 1307-1317Article in journal (Refereed)
    Abstract [en]

    A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is, what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.

  • 16. Oluwadare, O. J.
    et al.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Oyewumi, K. J.
    Non-Relativistic Phase Shifts for Scattering on Generalized Radial Yukawa Potentials2016In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 65, no 4, p. 434-440Article in journal (Refereed)
    Abstract [en]

    Non-relativistic phase shifts for a generalized Yukawa potential V(r) = -Vo(e(-alpha r)/r) Vi(e(-2 alpha r)/r(2)) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms. Small variations of V-1 seem to have marginal effects on the effective potential and on exact phase shifts. However, as pointed out in this study, a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts. The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.

  • 17.
    Thylwe, Karl-Erik
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    Semi-Relativistic Two-Body States of Spinless Particles with a Scalar-Type Interaction Potential2018In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 69, no 2, p. 127-130Article in journal (Refereed)
    Abstract [en]

    A semi-relativistic quantum approximation for mutual scalar interaction potentials is outlined and discussed. Equations are consistent with two-body Dirac equations for bound states of zero total angular momentum. Two-body effects near the non-relativistic limit for a linear scalar potential is studied in some detail.

  • 18.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    McCabe, Patrick
    Near/far-side angular decompositions of Legendre polynomials using the amplitude-phase method2017In: Journal of Mathematical Chemistry, ISSN 0259-9791, E-ISSN 1572-8897, Vol. 55, no 8, p. 1638-1648Article in journal (Refereed)
    Abstract [en]

    A decomposition of Legendre polynomials into propagating angular waves is derived with the aid of an amplitude-phase method. This decomposition is compared with the 'Nussenzveig/Fuller' so called near/far-side decomposition of Legendre polynomials. The latter decomposition requires the Legendre function of the second kind. This is not the case with the amplitude-phase decomposition. Both representations have the same asymptotic expressions for large values of , where l and are the polynomial degree and the angle respectively. Furthermore, both components of both representations satisfy the Legendre differential equation. However, we show the two representations are not identical.

  • 19.
    Thylwe, Karl-Erik
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
    McCabe, Patrick
    On Calculations of Legendre Functions and Associated Legendre Functions of the First Kind of Complex Degree2015In: Communications in Theoretical Physics, ISSN 0253-6102, E-ISSN 1572-9494, Vol. 64, no 1, p. 9-12Article in journal (Refereed)
    Abstract [en]

    Formulas for calculating Legendre functions and associated Legendre functions of the first kind of complex degree using an Ermakov-Lewis invariant are presented. These formulas are straight-forward to implement numerically and are motivated by the lack of computational routines in standard university tools like those of Mat Lab and Maple. Angular waves propagating in opposite directions are also obtained. The results are particularly useful in complex angular momentum theories and nearside/farside analysis of spin-dependent angular scattering from central potentials.

1 - 19 of 19
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