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Showing papers on "Electromagnetic field published in 2010"


Journal ArticleDOI
10 Dec 2010-Science
TL;DR: Electromagnetically induced transparency in an optomechanical system whereby the coupling of a cavity to a light pulse is used to control the transmission of light through the cavity may help to allow the engineering of light storage and routing on an optical chip.
Abstract: Electromagnetically induced transparency is a quantum interference effect observed in atoms and molecules, in which the optical response of an atomic medium is controlled by an electromagnetic field. We demonstrated a form of induced transparency enabled by radiation-pressure coupling of an optical and a mechanical mode. A control optical beam tuned to a sideband transition of a micro-optomechanical system leads to destructive interference for the excitation of an intracavity probe field, inducing a tunable transparency window for the probe beam. Optomechanically induced transparency may be used for slowing and on-chip storage of light pulses via microfabricated optomechanical arrays.

1,316 citations


Journal ArticleDOI
TL;DR: A measure of the local density of chirality of the electromagnetic field determines the asymmetry in the rates of excitation between a small chiral molecule and its mirror image, and applies to molecules in electromagnetic fields with arbitrary spatial dependence.
Abstract: We introduce a measure of the local density of chirality of the electromagnetic field. This optical chirality determines the asymmetry in the rates of excitation between a small chiral molecule and its mirror image, and applies to molecules in electromagnetic fields with arbitrary spatial dependence. A continuity equation for optical chirality in the presence of material currents describes the flow of chirality, in a manner analogous to the Poynting theorem for electromagnetic energy. ``Superchiral'' solutions to Maxwell's equations show larger chiral asymmetry, in some regions of space, than is found in circularly polarized plane waves.

878 citations


Journal ArticleDOI
12 Feb 2010-Science
TL;DR: The behavior of the artificial atom, a superconducting macroscopic two-level system, is in a quantitative agreement with the predictions of quantum optics for a pointlike scatterer interacting with the electromagnetic field in one-dimensional open space.
Abstract: An atom in open space can be detected by means of resonant absorption and reemission of electromagnetic waves, known as resonance fluorescence, which is a fundamental phenomenon of quantum optics. We report on the observation of scattering of propagating waves by a single artificial atom. The behavior of the artificial atom, a superconducting macroscopic two-level system, is in a quantitative agreement with the predictions of quantum optics for a pointlike scatterer interacting with the electromagnetic field in one-dimensional open space. The strong atom-field interaction as revealed in a high degree of extinction of propagating waves will allow applications of controllable artificial atoms in quantum optics and photonics.

599 citations



Journal ArticleDOI
TL;DR: In this article, the authors summarized the rapid development in this field and discussed several experimental demonstrations and approaches for enhancing the strength of the optical gradient force, and some of the possible applications of the effect are reviewed.
Abstract: Optical forces are widely used to manipulate microparticles such as living cells, DNA and bacteria. The forces used in these 'optical tweezers' originate from the strongly varying electromagnetic field in the focus of a high-power laser beam. This field gradient polarizes the particle, causing the positively and negatively charged sides of the dipole to experience slightly different forces. It was recently realized that the strong field gradient in the near-field of guided wave structures can also be exploited for actuating optomechanical devices, and initial theoretical work in this area was followed rapidly by several experimental demonstrations. This Review summarizes the rapid development in this field. First, the origin of the optical gradient force is discussed in detail. Several experimental demonstrations and approaches for enhancing the strength of the effect are then discussed. Finally, some of the possible applications of the effect are reviewed.

334 citations


Journal ArticleDOI
TL;DR: The origin and significance of the self-interaction force between both dipoles is discussed in connection with that of the angular distribution of scattered light and of the extinction cross section.
Abstract: We present a study of the optical force on a small particle with both electric and magnetic response, immersed in an arbitrary non-absorbing medium, due to a generic incident electromagnetic field. Expressions for the gradient force, radiation pressure and curl components are obtained for the force due to both the electric and magnetic dipoles excited in the particle. In particular, for the magnetic force we tentatively introduce the concept of curl of the spin angular momentum density of the magnetic field, also expressed in terms of 3D generalizations of the Stokes parameters. From the formal analogy between the conservation of momentum and the optical theorem, we discuss the origin and significance of the self-interaction force between both dipoles; this is done in connection with that of the angular distribution of scattered light and of the extinction cross section.

299 citations


Journal ArticleDOI
TL;DR: In this paper, a general mesh-free description of the magnetic field distribution in various electromagnetic machines, actuators, and devices is presented, based on transfer relations and Fourier theory.
Abstract: We present a general mesh-free description of the magnetic field distribution in various electromagnetic machines, actuators, and devices. Our method is based on transfer relations and Fourier theory, which gives the magnetic field solution for a wide class of two-dimensional (2-D) boundary value problems. This technique can be applied to rotary, linear, and tubular permanent-magnet actuators, either with a slotless or slotted armature. In addition to permanent-magnet machines, this technique can be applied to any 2-D geometry with the restriction that the geometry should consist of rectangular regions. The method obtains the electromagnetic field distribution by solving the Laplace and Poisson equations for every region, together with a set of boundary conditions. Here, we compare the method with finite-element analyses for various examples and show its applicability to a wide class of geometries.

280 citations


Journal ArticleDOI
TL;DR: In this paper, an algorithm for calculating the electromagnetic field distribution in multilayer structure is developed relying on Abeles matrices method for wave propagation in isotropic stratified media.
Abstract: The performance of surface plasmon resonance (SPR) sensors depends on the design parameters. An algorithm for calculating the electromagnetic fields distribution in multilayer structure is developed relying on Abeles matrices method for wave propagation in isotropic stratified media. The correlation between field enhancement and sensitivity enhancement is examined and found to agree with the overlap integral in the analyte region. This correlation was verified in the conventional SPR sensor based on Kretschmann configuration, and in the improved SPR sensor with high refractive index dielectric top layer for several cases, e.g. field enhancement due to resonance, the sensitivity dependence on the wavelength, the influence of prism refractive index on sensitivity, and the effect of the layers materials and thicknesses.

280 citations


Journal ArticleDOI
TL;DR: In this article, the authors reported the first experimental demonstration of an omnidirectional electromagnetic absorber in the microwave frequency, composed of non-resonant and resonant metamaterial structures, which can trap and absorb electromagnetic waves coming from all directions spirally inwards without any reflections due to the local control of electromagnetic fields.
Abstract: In a recent theoretical work by Narimanov and Kildishev (2009 Appl. Phys. Lett. 95 041106) an optical omnidirectional light absorber based on metamaterials was proposed, in which theoretical analysis and numerical simulations showed that all optical waves hitting the absorber are trapped and absorbed. Here we report the first experimental demonstration of an omnidirectional electromagnetic absorber in the microwave frequency. The proposed device is composed of non-resonant and resonant metamaterial structures, which can trap and absorb electromagnetic waves coming from all directions spirally inwards without any reflections due to the local control of electromagnetic fields. It is shown that the absorption rate can reach 99 per cent in the microwave frequency. The all-directional full absorption property makes the device behave like an 'electromagnetic black body', and the wave trapping and absorbing properties simulate, to some extent, an 'electromagnetic black hole.' We expect that such a device could be used as a thermal emitting source and to harvest electromagnetic waves.

267 citations


Journal ArticleDOI
17 Dec 2010-Science
TL;DR: The recent development of advanced fabrication techniques being applied to metamaterials and photonic crystals may lead to realization of such designer materials.
Abstract: Usually, investigators in materials science have asked: “What properties does a certain new material or structure have?” Now, the inverse problem arises: “I want to achieve certain—possibly unheard-of—material properties. How should the corresponding micro- or nanostructure look?” Examples could be: efficiently blocking acoustic noise due to a highway from a nearby village by a tailored wall, concentrating electromagnetic energy into as-tight-as-possible spaces, or avoiding reflections from a material's surface. The underlying common scheme is wave physics. Material properties that were otherwise unachievable, e.g., negative refraction and cloaking, may eventually be designed into optical metamaterials and photonic crystals. Both require tailoring of the properties (i.e., phase velocity and impedance) of an electromagnetic wave moving through the substance at the local level. In photonic crystals, the phase velocity of an electromagnetic wave moving through the crystal is controlled by tuning the photonic band structure; the impedance is determined by the electromagnetic field distributions throughout the material. In metamaterials, this amounts to tailoring the effective electric permittivity and magnetic permeability. In either case, introducing resonances is the key to controlling the local wave properties. The recent development of advanced fabrication techniques being applied to metamaterials and photonic crystals may lead to realization of such designer materials.

252 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived an analytical expression for the dipole-field coupling strength and the Purcell factor and showed that simple semiclassical theory fails to predict the correct scattered field spectrum even in the weak-field limit.
Abstract: We derive a full quantum optical model of interactions between a dipole and a metal nanoparticle. The electromagnetic field of the nanoparticle is quantized from the time-harmonic solution to the wave equation. We derive an analytical expression for the dipole-field coupling strength and the Purcell factor. The semiclassical theory, derived from the Maxwell-Bloch equations, is compared to the full quantum calculations based on numerical solution of the master equation. The metal nanoparticle-dipole system is found to be in an interesting regime of cavity quantum electrodynamics where dipole decay is dominated by dephasing, but the dipole-field coupling strength is still strong enough to achieve large cooperativity. In the presence of large dephasing, we show that simple semiclassical theory fails to predict the correct scattered field spectrum even in the weak-field limit. We reconcile this discrepancy by applying the random-phase-jump approach to the cavity photon number instead of the dipole operator. We also investigate the quantum fluctuations of the scattered field and show that they are significantly dependent on the dephasing rate.

Journal ArticleDOI
TL;DR: In this article, the reactive energy stored in the electromagnetic field surrounding an electromagnetic device is calculated using new expressions, completely general, explicit and without approximations in terms of the currents flowing on the device.
Abstract: New expressions are derived to calculate the reactive energy stored in the electromagnetic field surrounding an electromagnetic device. The resulting expressions are very simple to interpret, completely general, explicit and without approximations in terms of the currents flowing on the device. They are also fast since they involve integrals solely over the device generating the field. The new technique is very feasible to be used in cases where the electric and magnetic reactive energies are important in practice, especially in the case of radiating structures. Used there, they allow to study the effect of the shape of the device on the amount of reactive energy, and thus on the Q of the device. The implementation of the new expressions in numerical CAD tools is extremely simple and straightforward.

Journal ArticleDOI
TL;DR: In this paper, an analytical method for magnetic field calculation in the air gap of cylindrical electrical machines including slotting effects is presented. But this method does not take into account the mutual influence of slots on the air-gap magnetic field.
Abstract: This paper deals with an analytical method for magnetic field calculation in the air gap of cylindrical electrical machines including slotting effects. The analytical method is based on the resolution of the two-dimensional Laplace's equation in polar coordinates by the separation of variables technique. The originality of the proposed model is to take into account the mutual influence of slots on the air-gap magnetic field. The proposed method is sufficiently general to be used as a tool for air-gap magnetic field calculation of slotted electrical machines as reluctance or permanent magnet motors or actuators. Magnetic field and electromagnetic torque computed with the proposed analytical method are validated through finite-element analysis.

Journal ArticleDOI
TL;DR: A simple analysis of the problems involved in defining spin and orbital angular momenta for electromagnetic fields is presented and some of the remaining challenges are discussed.
Abstract: The association of spin and orbital angular momenta of light with its polarization and helical phase fronts is now well established The problems in linking this with electromagnetic theory, as expressed in Maxwell's equations, are rather less well known We present a simple analysis of the problems involved in defining spin and orbital angular momenta for electromagnetic fields and discuss some of the remaining challenges Crucial to our investigation is the duplex symmetry between the electric and magnetic fields

Journal ArticleDOI
TL;DR: Numerical simulations of the graded photonic crystal based Luneburg lens and electromagnetic beam bend show that the homogenization based on Maxwell-Garnett theory gives very good results for implementation of devices intended to steer and focus electromagnetic fields.
Abstract: Engineering of a refractive index profile is a powerful method for controlling electromagnetic fields. In this paper, we investigate possible realization of isotropic gradient refractive index media at optical frequencies using two-dimensional graded photonic crystals. They consist of dielectric rods with spatially varying radii and can be homogenized in broad frequency range within the lowest band. Here they operate in metamaterial regime, that is, the graded photonic crystals are described with spatially varying effective refractive index so they can be regarded as low-loss and broadband graded dielectric metamaterials. Homogenization of graded photonic crystals is done with Maxwell-Garnett effective medium theory. Based on this theory, the analytical formulas are given for calculations of the rods radii which makes the implementation straightforward. The frequency range where homogenization is valid and where graded photonic crystal based devices work properly is discussed in detail. Numerical simulations of the graded photonic crystal based Luneburg lens and electromagnetic beam bend show that the homogenization based on Maxwell-Garnett theory gives very good results for implementation of devices intended to steer and focus electromagnetic fields.

Journal ArticleDOI
TL;DR: In this article, lower bounds on the quality factor (Q) of small electric and magnetic-dipole antennas were obtained for arbitrarily shaped volumes and excited by general sources or by global electric-current sources alone.
Abstract: General expressions are obtained for the lower bounds on the quality factor (Q) of electrically small electric- and magnetic-dipole antennas confined to an arbitrarily shaped volume V and excited by general sources or by global electric-current sources alone. The lower-bound expressions depend only on the direction of the dipole moment with respect to V , the electrical size of V , and the static electric and magnetic polarizabilities per unit volume of hypothetical perfectly electrically conducting and perfectly magnetically conducting volumes V . The lower bounds are obtained directly from the electromagnetic field expressions for Q with the help of current equivalence principles and the uncoupling of Maxwell's equations for electrically small volumes into quasi-electrostatic and quasi-magnetostatic fields.

Journal ArticleDOI
TL;DR: This work compute this current in the presence of a color-flux tube possessing topological charge, with a magnetic field applied perpendicular to it, and argues that this situation is realized at the early stage of relativistic heavy-ion collisions.
Abstract: In quantum chromodynamics, a gauge field configuration with nonzero topological charge generates a difference between the number of left- and right-handed quarks. When a (electromagnetic) magnetic field is added to this configuration, an electromagnetic current is induced along the magnetic field; this is called the chiral magnetic effect. We compute this current in the presence of a color-flux tube possessing topological charge, with a magnetic field applied perpendicular to it. We argue that this situation is realized at the early stage of relativistic heavy-ion collisions.

Journal ArticleDOI
TL;DR: This work calculated electric field generated by axial longitudinal vibration modes of microtubules for random, and coherent excitation of vibrations, and found that the electric field intensity is highest at the end of micro Tubule.
Abstract: Microtubules are electrically polar structures fulfilling prerequisites for generation of oscillatory electric field in the kHz to GHz region. Energy supply for excitation of elasto-electrical vibrations in microtubules may be provided from GTP-hydrolysis; motor protein-microtubule interactions; and energy efflux from mitochondria. We calculated electric field generated by axial longitudinal vibration modes of microtubules for random, and coherent excitation. In case of coherent excitation of vibrations, the electric field intensity is highest at the end of microtubule. The dielectrophoretic force exerted by electric field on the surrounding molecules will influence the kinetics of microtubule polymerization via change in the probability of the transport of charge and mass particles. The electric field generated by vibrations of electrically polar cellular structures is expected to play an important role in biological self-organization.

Journal ArticleDOI
TL;DR: In this paper, the Abraham-Minkowski controversy was resolved within the framework of the classical theory of electrodynamics, without resorting to such complicating and ultimately unnecessary factors as pseudo-momentum, special surface forces, alternative energymomentums tensors, and hidden momenta, that have caused so much confusion for such a long period of time.

Journal ArticleDOI
TL;DR: In this paper, a finite-element time-domain FETD approach for the simulation of 3D electromagnetic EM diffusion phenomena is presented, which efficiently simulates transient electric fields and the time derivatives of magnetic fields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms.
Abstract: We present a finite-element time-domain FETD approach for the simulation of 3D electromagnetic EM diffusion phenomena. The finite-element algorithm efficiently simulates transient electric fields and the time derivatives of magneticfields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms. To compute transient electromagnetic fields,theelectricfielddiffusionequationistransformedinto asystemofdifferentialequationsviaGalerkin’smethodwith homogeneous Dirichlet boundary conditions. To ensure numerical stability and an efficient time step, the system of the differential equations is discretized in time using an implicit backward Euler scheme. The resultant FETD matrix-vector equation is solved using a sparse direct solver along with a fill-inreducedorderingtechnique.Whenadvancingthesolution in time, the FETD algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution. To simulate a step-off source waveform, the 3D FETD algorithm also incorporates a 3D finite-element direct current FEDCalgorithmthatsolvesPoisson’sequationusingasecondarypotentialmethodforageneralanisotropicearthmodel. Examples of controlled-source FETD simulations are compared with analytic and/or 3D finite-difference time-domain solutions and are used to confirm the accuracy and efficiencyofthe3DFETDalgorithm.

Journal ArticleDOI
TL;DR: In this paper, a matterless double-slit scenario is proposed, in which photons generated from head-on collisions between a probe laser field and two ultraintense laser beams form a doubleslit interference pattern.
Abstract: Double slits provide incoming particles with a choice. Those that survive passage through the slits have chosen from two possible paths, which interfere to distribute them in a wave-like manner. Such wave–particle duality1 continues to be challenged2,3,4,5 and investigated in a broad range of disciplines with electrons6, neutrons7, helium atoms8, C60 fullerenes9, Bose–Einstein condensates10 and biological molecules11. All variants have hitherto involved material constituents. We present a matterless double-slit scenario in which photons generated from virtual electron–positron pair annihilation in head-on collisions of a probe laser field with two ultra-intense laser beams form a double-slit interference pattern. Such electromagnetic fields are predicted to induce material-like behaviour in vacuum, supporting elastic scattering between photons12,13. Our double-slit scenario presents, on the one hand, a realizable method with which to observe photon–photon scattering and, on the other hand, demonstrates the possibility of both controlling light with light and non-locally investigating features of the quantum vacuum structure. A matterless double-slit scenario is proposed, in which photons generated from head-on collisions between a probe laser field and two ultraintense laser beams form a double-slit interference pattern. Such electromagnetic fields are predicted to induce material-like behaviour in a vacuum, supporting elastic scattering between photons.

Journal ArticleDOI
TL;DR: In this article, it was shown that CPT-even aether-like Lorentz-breaking actions, for the scalar and electromagnetic fields, can be generated via their appropriate aetherlike coupling to spinor fields, in three, four, and five space-time dimensions.
Abstract: We show that CPT-even aetherlike Lorentz-breaking actions, for the scalar and electromagnetic fields, are generated via their appropriate Lorentz-breaking coupling to spinor fields, in three, four, and five space-time dimensions. Besides, we also show that aetherlike terms for the spinor field can be generated as a consequence of the same couplings. We discuss the dispersion relations in the theories with aetherlike Lorentz-breaking terms and find the tree-level effective (Breit) potential for fermion scattering and the one-loop effective potential corresponding to the action of the scalar field.

Journal ArticleDOI
TL;DR: In this article, the Gauss-Bonnet gravity in the presence of a new class of nonlinear electromagnetic field, namely, power Maxwell invariant, was considered and a suitable transformation was obtained to obtain a class of real rotating solutions with k rotation parameters.

Journal ArticleDOI
TL;DR: A generic classification scheme of torque transducers in terms of axial or polar output is provided, within which the results from behavioural experiments conducted under altered field conditions or with pulsed fields are discussed.
Abstract: Although ferrimagnetic material appears suitable as a basis of magnetic field perception in animals, it is not known by which mechanism magnetic particles may transduce the magnetic field into a nerve signal. Provided that magnetic particles have remanence or anisotropic magnetic susceptibility, an external magnetic field will exert a torque and may physically twist them. Several models of such biological magnetic-torque transducers on the basis of magnetite have been proposed in the literature. We analyse from first principles the conditions under which they are viable. Models based on biogenic single-domain magnetite prove both effective and efficient, irrespective of whether the magnetic structure is coupled to mechanosensitive ion channels or to an indirect transduction pathway that exploits the strayfield produced by the magnetic structure at different field orientations. On the other hand, torque-detector models that are based on magnetic multi-domain particles in the vestibular organs turn out to be ineffective. Also, we provide a generic classification scheme of torque transducers in terms of axial or polar output, within which we discuss the results from behavioural experiments conducted under altered field conditions or with pulsed fields. We find that the common assertion that a magnetoreceptor based on single-domain magnetite could not form the basis for an inclination compass does not always hold.

Proceedings ArticleDOI
25 Jul 2010
TL;DR: In this article, the On-line Electric Vehicle (OLEV) system and its noncontact power transfer mechanism were introduced and some techniques for the reduction of electromagnetic fields (EMFs) from the power line and the vehicle itself were proposed.
Abstract: In this paper, we introduce the On-line Electric Vehicle (OLEV) system and its non-contact power transfer mechanism and propose some techniques for the reduction of electromagnetic fields (EMFs) from the power line and the vehicle itself. By applying a metallic plate shield, horizontal/vertical shield, and connecting wire for loop cancellation, the low frequency EMFs have been significantly reduced. Simulation and measurement results for application to vehicles currently in service are also given.

Journal ArticleDOI
TL;DR: In this article, the authors study the generation of helical magnetic fields during single field inflation induced by an axial coupling of the electromagnetic field to the inflaton and find that such a coupling always leads to a blue spectrum with $B^2(k) \propto k$ as long as the theory is treated perturbatively.
Abstract: We study the generation of helical magnetic fields during single field inflation induced by an axial coupling of the electromagnetic field to the inflaton. During slow roll inflation, we find that such a coupling always leads to a blue spectrum with $B^2(k) \propto k$, as long as the theory is treated perturbatively. The magnetic energy density at the end of inflation is found to be typically too small to backreact on the background dynamics of the inflaton. We also show that a short deviation from slow roll does not result in strong modifications to the shape of the spectrum. We calculate the evolution of the correlation length and the field amplitude during the inverse cascade and viscous damping of the helical magnetic field in the radiation era after inflation. We conclude that except for low scale inflation with very strong coupling, the magnetic fields generated by such an axial coupling in single field slow roll inflation with perturbative coupling to the inflaton are too weak to provide the seeds for the observed fields in galaxies and clusters.

Journal ArticleDOI
TL;DR: In this article, a subwavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media is considered and it is shown that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials.
Abstract: We consider a subwavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small, thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. The behavior of the electromagnetic field in the extreme nonlinear regime is very peculiar and characterized by interesting features such as the transverse power flow reversing. In order to probe this regime, we consider a class of fields (transverse magnetic nonlinear guided waves) admitting full analytical description and show that these waves are allowed to propagate even in media with $\ensuremath{\epsilon}l0$ and $\ensuremath{\mu}g0$ since the nonlinear polarization produces a positive overall effective permittivity. The considered nonlinear waves exhibit, in addition to the mentioned features, a number of interesting properties like hyperfocusing induced by the phase difference between the field components.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate the case of a rotating black hole immersed in a weak, asymptotically uniform magnetic field and find that the role of the black hole spin in setting the chaos is more complicated than initially thought.
Abstract: Accretion onto black holes and compact stars brings material in a zone of strong gravitational and electromagnetic fields. We study dynamical properties of motion of electrically charged particles forming a highly diluted medium (a corona) in the regime of strong gravity and large-scale (ordered) magnetic field. We start our work from a system that allows regular motion, then we focus on the onset of chaos. To this end, we investigate the case of a rotating black hole immersed in a weak, asymptotically uniform magnetic field. We also consider a magnetic star, approximated by the Schwarzschild metric and a test magnetic field of a rotating dipole. These are two model examples of systems permitting energetically bound, off-equatorial motion of matter confined to the halo lobes that encircle the central body. Our approach allows us to address the question of whether the spin parameter of the black hole plays any major role in determining the degree of the chaoticness. To characterize the motion, we construct the recurrence plots (RPs) and we compare them with Poincare surfaces of section. We describe the RPs in terms of the recurrence quantification analysis, which allows us to identify the transition between different dynamical regimes. We demonstrate that this new technique is able to detect the chaos onset very efficiently and provide its quantitative measure. The chaos typically occurs when the conserved energy is raised to a sufficiently high level that allows the particles to traverse the equatorial plane. We find that the role of the black hole spin in setting the chaos is more complicated than initially thought.

Journal ArticleDOI
TL;DR: In this article, the generalized field equation of dyons was reformulated in terms of octonion variables, and the generalized potential and current equations were discussed in a consistent manner, and it has been shown that due to the non associativity of OCTI variables it is necessary to impose certain constraints to describe generalized OCTI electrodynamics in a manifestly covariant and consistent manner.
Abstract: We have made an attempt to reformulate the generalized field equation of dyons in terms of octonion variables. Octonion forms of generalized potential and current equations are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion electrodynamics in manifestly covariant and consistent manner.

Journal ArticleDOI
TL;DR: The new multi- coil approach provides the framework for the integration of conventional imaging and shim coils into a single multi-coil system in which shape, strength, accuracy and spatial coverage of the magnetic field can be specifically optimized for the application at hand.