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This contribution covers the variational‐based modeling of non‐dissipative magneto‐mechanical systems using a vector potential approach and the thorough analysis and discussion of corresponding conforming finite element methods. Since the construction of divergence‐free finite element spaces explicitly enforcing the Coulomb gauge poses some major challenges, we propose some primal and mixed variational principles that ensure well posedness of the problem and allow to seek the vector potential in unconstrained function spaces. The performance of these methods is assessed in two comparative benchmark studies. The focus of both studies lies on the accurate approximation of field quantities in systems with material discontinuities and re‐entrant corners. [ABSTRACT FROM AUTHOR]

There exist two methods for finding the magnetic moment of the electron. The first method employed in quantum electrodynamics consists in calculating the energy of the electron placed in a constant magnetic field, the extra energy due to the field being proportional to the magnetic moment. It is also possible to use the second method proceeding from the fact that the asymptotic form of the vector potential at infinity is proportional to the magnetic moment. If the electron were point-like, both the methods would yield identical results. In the present paper is studied the magnetic field created by the electron in hydrogen-like ions, which enables one to find the electron magnetic moment by the second method. The electron magnetic moment in this case proves to be different in different states of the electron in the Coulomb field of the ions and, moreover, is distinct from the magnetic moment calculated by the first method. The results of the paper show that the electron is not small and is deformable under action of external fields. [ABSTRACT FROM AUTHOR]

In this paper, the bound state solutions of the radial Schrödinger equation are obtained in closed form under an improved Scarf II potential energy function (ISPEF) constrained by external magnetic and Aharonov-Bohm (AB) flux fields. By constructing a suitable Pekeris-like approximation scheme for the centrifugal barrier, approximate analytical expressions for the bound-states and thermal partition function were obtained. With the aid of the partition function, an explicit equation for magnetization at finite temperatures is developed. The obtained equations were then applied to calculate the energy levels and magnetic properties of 7Li2 (2 3Πg), K2 (X 1Σg+), Mg2 (X 1Σg+) and NaBr (X 1Σ+) diatomic molecules. The obtained numerical results of the vibrational energies for these molecules were found to be in good agreement with theoretic and experimental values reported in the existing literature. The results indicated that by turning off the magnetic and AB fields, the energy levels of the diatomic molecules degenerate. The results further revealed that an increase in the temperature of the molecules and the AB field strengths leads to a linear decrease in magnetization.

Amblyomma helvolum Koch is an Asiatic reptile-associated tick that usually inhabits tropical forests and is primarily parasitic on varanids, skinks, and snakes. In Taiwan, A. helvolum has been reported on Elaphe carinata (Taiwan stink snake) and Ptyas mucosa (Oriental rat snake). Herein, we report new host records of A. helvolum in Taiwan from the following squamate species: Diploderma swinhonis (Swinhoe's japalure), Eutropis longicaudata (Long-tailed sun skink), Oligodon formosanus (Taiwan kukri), Sphenomorphus incognitus (Brown forest skink), and Trimeresurus stejnegeri (Chinese green tree viper). In addition, we present an overview of the distribution of A. helvolum across its range and its association with reptilian microbial agents. [ABSTRACT FROM AUTHOR]

We present a strong form meshless solver for numerical solution of the nonstationary, incompressible, viscous Navier–Stokes equations in two (2D) and three dimensions (3D). We solve the flow equations in their stream function‐vorticity (in 2D) and vector potential‐vorticity (in 3D) formulation, by extending to 3D flows the boundary condition‐enforced immersed boundary method, originally introduced in the literature for 2D problems. We use a Cartesian grid, uniform or locally refined, to discretize the spatial domain. We apply an explicit time integration scheme to update the transient vorticity equations, and we solve the Poisson type equation for the stream function or vector potential field using the meshless point collocation method. Spatial derivatives of the unknown field functions are computed using the discretization‐corrected particle strength exchange method. We verify the accuracy of the proposed numerical scheme through commonly used benchmark and example problems. Excellent agreement with the data from the literature was achieved. The proposed method was shown to be very efficient, having relatively large critical time steps. [ABSTRACT FROM AUTHOR]

We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are used. Our homogenization algorithm for solving the cell problem is based on the displacement method presented in Lukkassen et al. 1995, Composites Engineering, 5(5), 519-531. We propose the use of the meridional eccentricity of the permeability tensor ellipsoid as an anisotropy index quantifying the degree of directionality in the linear magnetic response. As application problems, 2D regular and random microstructures with overlapping and nonoverlapping monodisperse disks, all of which are periodic, are considered. We show that, for the vanishing corrector function, the derived effective magnetic permeability tensor gives the (lower) Reuss and (upper) Voigt bounds with the vector and scalar potential formulations, respectively. Our results with periodic boundary conditions show an excellent agreement with analytical solutions for regular composites, whereas, for random heterogeneous materials, their convergence with volume element size is fast. Predictions for material systems with monodisperse overlapping disks for a given inclusion volume fraction provide the highest magnetic permeability with the most increased inclusion interaction. In contrast, the disk arrangements in regular square lattices result in the lowest magnetic permeability and inadequate inclusion interaction. Such differences are beyond the reach of the isotropic effective medium theories, which use only the phase volume fraction and shape as mere statistical microstructural descriptors.

We examine 3D flows x = v(x) admitting vector identity Mv = ∇ x A for a multiplier M and a potential field A. It is established that, for those systems, one can complete the vector field v into a basis fitting an sl(2) -algebra. Accordingly, in terms of covariant quantities, the structure equations determine a set of equations in Maurer-Cartan form. This realization permits one to obtain the potential field as well as to investigate the (bi-)Hamiltonian character of the system. The latter occurs if the system has a time-independent first integral. In order to exhibit the theoretical results on some concrete cases, three examples are provided, namely the Gulliot system, a system with a nonintegrable potential, and the Darboux-Halphen system in symmetric polynomials. [ABSTRACT FROM AUTHOR]

We propose to augment standard grid-based fluid solvers with pointwise divergence-free velocity interpolation, thereby ensuring exact incompressibility down to the sub-cell level. Our method takes as input a discretely divergence-free velocity field generated by a staggered grid pressure projection, and first recovers a corresponding discrete vector potential. Instead of solving a costly vector Poisson problem for the potential, we develop a fast parallel sweeping strategy to find a candidate potential and apply a gauge transformation to enforce the Coulomb gauge condition and thereby make it numerically smooth. Interpolating this discrete potential generates a point-wise vector potential whose analytical curl is a pointwise incompressible velocity field. Our method further supports irregular solid geometry through the use of level set-based cut-cells and a novel Curl-Noise-inspired potential ramping procedure that simultaneously offers strictly non-penetrating velocities and incompressibility. Experimental comparisons demonstrate that the vector potential reconstruction procedure at the heart of our approach is consistently faster than prior such reconstruction schemes, especially those that solve vector Poisson problems. Moreover, in exchange for its modest extra cost, our overall Curl-Flow framework produces significantly improved particle trajectories that closely respect irregular obstacles, do not suffer from spurious sources or sinks, and yield superior particle distributions over time. [ABSTRACT FROM AUTHOR]

Bartonella species has been validated as blood-borne bacteria in mammals and has a substantial opportunity to be harbored by a variety of hematophagous arthropod vectors. Bats, along with their ectoparasites, are recognized worldwide as one of the natural reservoir hosts for these bacteria. However, there have been few investigations of Bartonella bacteria toward a broad range of obligated bat ectoparasites in China. Here, molecular detection of Bartonella species was performed to survey the infection among bat ectoparasites and follow-up phylogenetic analyses to further characterize the evolutionary relationships of the genus. A total of 434 bat ectoparasites involving four types of arthropods, namely, bat mites, bat tick, bat fleas, and bat flies (further divided into traditionally fly-like bat flies and wingless bat flies) were collected in 10 trapping sites in Yunnan Province, southwestern China. Bartonella was detected by PCR amplification and sequencing through four gene target fragments (gltA, ftsZ, rpoB, and ITS). Accordingly, diverse Bartonella species were discovered, including both the validated species and the novel genotypes, which were characterized into several geographical regions with high prevalence. Phylogenetic analyses based on gltA and multi-locus concatenated sequences both demonstrated strong phylogeny–trait associations of Bartonella species from bats and their parasitic arthropods, suggesting the occurrence of host switches and emphasizing the potential connecting vector role of these ectoparasites. Nevertheless, the maintenance and transmission of Bartonella in both bat and hemoparasite populations have not been fully understood, as well as the risk of spillage to humans, which warrants in-depth experimental studies focusing on these mammals and their ectoparasites. [ABSTRACT FROM AUTHOR]

Psyllids (Hemiptera: Psylloidea) are herbivores that feed and reproduce on narrow subsets of hosts within a few related genera. During surveys of Solanum umbelliferum (Eschsch) (Solanaceae), we collected multiple life stages of Bactericera maculipennis (Crawford), a species exclusively associated with bindweeds (Convolvulaceae). We hypothesized that B. maculipennis has expanded its host range to include this solanaceous host. To test this, we quantified egg to adult development time on S. umbelliferum, 2 other solanaceous hosts, and Convolvulus arvensis L., the most suitable host for B. maculipennis in North America. B. maculipennis failed to develop on additional solanaceous hosts but developed significantly faster on S. umbelliferum than on C. arvensis. We also sampled for B. maculipennis at 27 S. umbelliferum populations and collected 24 individuals directly from S. umbelliferum plants. We confirmed all individuals are B. maculipennis and found that 10/24 were infected with the plant pathogen 'Candidatus Liberibacter solanacearum' (CLso), which is transmitted by the potato psyllid, B. cockerelli (Šulc). Half of infected individuals harbored CLso haplotype B, which is dominant in crops, but rare in S. umbelliferum. The other 50% harbored CLso haplotype Sumb2, previously documented in S. umbelliferum, but never in crops. Our results suggest that the host range of B. maculipennis has expanded to include a key wild host plant of B. cockerelli. This may create opportunities for exchange of multiple haplotypes of CLso between these 2 species, possibly facilitating the emergence of CLso variants as pathogens of plants in the Convolvulaceae., (© The Author(s) 2024. Published by Oxford University Press on behalf of Entomological Society of America. All rights reserved. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com.)

In this paper, the improved and the new analytical and semi-analytical expressions for calculating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air are given. The expressions are obtained either in the analytical form over the incomplete elliptic integrals of the first and the second kind or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the particular cases when the inclined circular loops are addressed. We mention that all formulas are obtained by the integral approach, except the stiffness, which is found by the derivative of the magnetic force. The novelty of this paper is the treatment of the inclined circular carting-current arc segments for which the calculations of the previously mentioned electromagnetic quantities are given.

In this paper, we will review classical electrodynamics, where our main concern will be exclusively the propagation of electromagnetic waves in the vacuum and the interaction of these waves with free charges. We will examine the reasons why the classical Maxwell's equations are not complete and consistent. We will show that there are three kinds of waves propagating in the vacuum, namely, transverse waves, longitudinal waves, and helicoidal waves. We will particularly review the theoretical and experimental aspects of longitudinal waves whose existence seems to be proven. [ABSTRACT FROM AUTHOR]

As signified by the well-known Aharanov–Bohm effect, the fields only under-describe electromagnetics and are thus not sufficient, while the potentials over-describe electromagnetics and are more than necessary with gauge redundancy. In lieu of the traditional fields and potentials, this article presents new formulations that introduce from the outset the concept and utilization of field-impulses for the fundamental equations of electromagnetics. Unlike the potentials that may or may not be real or causal depending on the gauge, the field-impulses as physical field-integrators (time-integrals) are like fields being physically real, causal, and gauge-independent. Furthermore, the single electric field-impulse/integrator alone through its second-order (wave) equation is capable of aptly describing electromagnetics in all cases of electrostatics, magnetostatics, and electrodynamics. Upon close scrutiny and comparison, the optional static–dynamic decomposition of electric field-impulse can be related to the potentials with source-incorporated gauge condition. Such source-incorporated condition is unlike other popular gauge conditions that are source-free or incorporating the source implicitly. The electric field-impulse as physical field-integrator is necessary and sufficient for many aspects of electromagnetics including field derivation, Lorentz force, momentum, interaction energy, quantum particle–electromagnetic interactions, etc. [ABSTRACT FROM AUTHOR]

A dissipation theory is proposed for the potentials-based finite-difference time-domain (FDTD) algorithm for the case of inhomogeneous lossless media. We show that under the Courant–Friedrichs–Lewy limit, the equations describing the time evolution of scalar and vector potentials can be seen as a lossless system. The developed theory provides insights into how electromagnetic energy and power flow are approximated in FDTD schemes. It can also be used to create new algorithms with guaranteed stability. [ABSTRACT FROM AUTHOR]

We consider the problem of recovering the divergence‐free velocity field U ∈ L2(Ω) of a given vorticity F=curlU on a bounded Lipschitz domain Ω⊂ℝ3. To that end, we solve the 'div–curl problem' for a given F ∈ H−1(Ω). The solution is expressed in terms of a vector potential (or stream function) A ∈ H1(Ω) such that U=curlA. After discussing existence and uniqueness of solutions and associated vector potentials, we propose a well‐posed construction for the stream function. A numerical method based on this construction is presented, and experiments confirm that the resulting approximations display higher regularity than those of another common approach. [ABSTRACT FROM AUTHOR]

The present study concerns the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and micro-rotations in the case of a harmonic dependence of the physical fields on time. The system is known from many previous discussions on the micropolar elasticity. A new analysis aimed at uncoupling the coupled vector differential equation of the linear theory of micropolar elasticity is carried out. A notion of proportionality of the vortex parts of the displacements and microrotations to a single vector, which satisfies the screw equation, is employed. Finally the problem of finding the vortex parts of the displacements and micro-rotations fields is reduced to solution of four uncoupled screw differential equations. Corresponding representation formulae are given. Obtained results can be applied to problems of the linear micropolar elasticity concerning harmonic waves propagation along cylindrical waveguides.

In this paper, the improved and the new analytical and semi-analytical expressions for calculating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air are given. The expressions are obtained either in the analytical form over the incomplete elliptic integrals of the first and the second kind or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the particular cases when the inclined circular loops are addressed. We mention that all formulas are obtained by the integral approach, except the stiffness, which is found by the derivative of the magnetic force. The novelty of this paper is the treatment of the inclined circular carting-current arc segments for which the calculations of the previously mentioned electromagnetic quantities are given. [ABSTRACT FROM AUTHOR]

Bartonella species has been validated as blood-borne bacteria in mammals and has a substantial opportunity to be harbored by a variety of hematophagous arthropod vectors. Bats, along with their ectoparasites, are recognized worldwide as one of the natural reservoir hosts for these bacteria. However, there have been few investigations of Bartonella bacteria toward a broad range of obligated bat ectoparasites in China. Here, molecular detection of Bartonella species was performed to survey the infection among bat ectoparasites and follow-up phylogenetic analyses to further characterize the evolutionary relationships of the genus. A total of 434 bat ectoparasites involving four types of arthropods, namely, bat mites, bat tick, bat fleas, and bat flies (further divided into traditionally fly-like bat flies and wingless bat flies) were collected in 10 trapping sites in Yunnan Province, southwestern China. Bartonella was detected by PCR amplification and sequencing through four gene target fragments (gltA, ftsZ, rpoB, and ITS). Accordingly, diverse Bartonella species were discovered, including both the validated species and the novel genotypes, which were characterized into several geographical regions with high prevalence. Phylogenetic analyses based on gltA and multi-locus concatenated sequences both demonstrated strong phylogeny–trait associations of Bartonella species from bats and their parasitic arthropods, suggesting the occurrence of host switches and emphasizing the potential connecting vector role of these ectoparasites. Nevertheless, the maintenance and transmission of Bartonella in both bat and hemoparasite populations have not been fully understood, as well as the risk of spillage to humans, which warrants in-depth experimental studies focusing on these mammals and their ectoparasites.

The scalar and vector potentials of the acceleration field and the pressure field are calculated for the first time for a rotating relativistic uniform system, and the dependence of the potentials on the angular velocity is found. These potentials are compared with the potentials for the non-rotating uniform system that have been found previously. The rotation leads to the appearance of vector potentials, which at each point turn out to be directed along the corresponding linear velocity of rotation. The calculation shows that for rotating stellar objects the contribution to the fields' vector potentials from the proper random motion of particles is small compared to the contribution from rotation and may not be taken into account. From the expression for the pressure field potential, a relativistic formula follows that relates the pressure, mass density, and mean square velocity of the particles. This formula in the limit of low speeds corresponds to the expression for the pressure in molecular kinetic theory. When calculating the potentials, a new method is used that takes into account the potentials of two different bodies, a cylinder and a sphere, for solving the wave equation of rotating system. [ABSTRACT FROM AUTHOR]

The time‐dependent Feinberg–Horodecki equation in the presence of a special Mie‐type pseudoharmonic potential was solved and the quantized momentum with the corresponding wave functions were obtained with the supersymmetric approach. The Fisher information for both the time and the momentum space were calculated via expectation values of time and momentum. The effect of the dissociation energy, the equilibrium time point and the quantum number respectively on the Fisher information were studied in detail. The result was applied to five molecules. The results obtained for the time‐dependent Feinberg–Horodecki equation followed the trend of the results obtained for the time‐independent Schrödinger equation. [ABSTRACT FROM AUTHOR]

Differential equations for potentials are considered that ensure the fulfillment of the basic vector differential equation of the linear theory of elasticity in the case of a harmonic dependence of the displacement field on time. An alternative scheme for splitting the vector differential equation of the linear theory of elasticity into unrelated equations is developed. It is based on the concept of a gamma vector that satisfies a screw equation. As a result, the problem of finding the vortex component of the displacement field is reduced to the sequential solution of unrelated screw first-order partial differential equations. A theorem on the completeness of the representation of the displacement field using two screw vortex vector fields is formulated and proved. [ABSTRACT FROM AUTHOR]

The features of the orientational motion and channeling of charged particles are considered. They move in a near-surface potential well whose structure is formed by the surface plane of a crystal and by the action of the vector potential of the electric current flowing through a crystal or along a conductor, near which a nonconducting crystal is located. The width of the potential well forming the near-surface channeling mode depends on the crystal thickness and the electric current density and can vary in the range from several millimeters to a few micrometers as the current density varies in the range of 1–1000 A/cm2. The process of near-surface channeling in the field of a plane conductor with current provides the abnormally weak deceleration of particles and can be used to transport particle beams along conductors with current over large distances. A similar axial channeling mode is characterized by the complete suppression of the scattering and deceleration of ion beams during their motion in free space along the surface of a cylindrical conductor with current. [ABSTRACT FROM AUTHOR]

Hybrid subdomain analysis is utilized to optimize the design of a high-speed compressor motor. Permanent magnets (PMs) are arranged in Halbach array and bounded by a carbon fiber sleeve. The stator core does not have a slot structure, so that it is advantageous in reducing the iron loss. Since the core saturation takes place, magnetic equivalent circuit (MEC) is used to find the permeability depending on the flux density of stator yoke. Furthermore, since the core is not infinitely permeable in the subdomain analysis, the solution is obtained in the whole subdomain regions: shaft, PM, air gap, coil, and stator yoke. The results of hybrid analysis are compared with those of finite-element analysis (FEA). Very close matching results are obtained in the flux density and torque even under yoke saturation. The stator yoke height is optimized against the rotor outer radius so that torque, power density, and efficiency are maximized, while stator outer radius, stack length, and coil area are fixed. [ABSTRACT FROM AUTHOR]

The properties of the eigenvalue problem of the one-dimensional Dirac operator are discussed in terms of the mutual relations between vector, scalar and pseudo-scalar contributions to the potential. Relations to the exact solubility are analyzed. [ABSTRACT FROM AUTHOR]

The article deals with the dynamic equations of the linear micropolar theory of elasticity. They are related with respect to vector fields of displacements and microrotations. Coupled equations are also obtained for vortex vector potentials of displacements and microrotations. Using (or not) calibration conditions, it is possible to formulate uncoupled equations that include the same main differential operator. Conditions for the hyperbolicity of the main operator and a condition connecting the defining constants that ensures its factorizability, that is, representation as a product of simpler differential operators commuting with each other. The actual construction of the operator factors in the factorized form is carried out. [ABSTRACT FROM AUTHOR]

Analytical solution for transient, diffusing fields inside a ring conductor with rectangular cross‐section is discussed. Some details from the paper by V. Thiagarajan with additional clarifications are presented. The comment paper on the Thiagarajan analysis by Gratkowski and Ziolkowski criticises the boundary condition used at the outer radius of the ring conductor and changes it by setting the vector potential to zero at the outer radius of the ring. It is shown that: (i) the boundary condition used by Thiagarajan is an exact analytical result from classical physics, arising from interface field continuity criterion, (ii) setting the vector potential to zero at the outer radius of the ring is not a physically valid boundary condition, and (iii) it changes the boundary value problem entirely with no comparison to the analysis commented upon (which is valid mathematically and physically). [ABSTRACT FROM AUTHOR]

A hybrid spatial–spectral method for rapid and broadband calculation of the vector potential normal modes and dyadic Green’s function (GF) inside the cavity of irregular shape is presented. In the broadband method of simulation, the normal modes of the irregular cavity, which are independent of operation frequency, are first computed through a linear eigenvalue problem based on a hybrid representation of the regular (rectangular) cavity. The method is based on the extraction of the singularity of the GF that results in a rapidly convergent hybrid spatial–spectral expansion of the GF. The method is applied to a V-grooved cavity to obtain the vector potential GF inside the cavity, and the results are shown over a broad range of frequencies. The results of the hybrid method are in good agreement with that of direct method of moment (MoM), while the hybrid method is much more efficient than direct MoM as the latter requires the computation at one frequency at a time. [ABSTRACT FROM AUTHOR]

Arch-shaped axially magnetized bodies tend to appear frequently in electrical machine analysis such as in the overhang parts of the classical radial-flux machines as well as in the main parts of the axial-flux machines. The calculation of the 3-D fields originating from these bodies is demanding. The 3-D FEA suffers from high computational burden as well as no knowledge of the field origin. Analytic techniques involve the use of elliptic integrals and complex numbers for numerical evaluation, which makes them significantly slower than the 3-D FEA. In this article, a new analytical technique is proposed to speed up the computation by a factor of 20 for the global magnetic field created by a generic magnetized body by removing complex numbers and reducing the analytic equations significantly without any loss of precision. As a result, it can compete with the conventional 3-D FEA. In addition, integral methods may contribute to the wider use of parallel processing techniques. The original expressions for the vector potential are also provided, which has its own benefits and applications. Finally, the showcased magnetized body is assessed against 3-D FEA and discussed in terms of practical applications. [ABSTRACT FROM AUTHOR]

We examine Hamiltonian analysis of three-dimensional advection flow ẋ = v (x) of incompressible nature ∇ ⋅ v = 0 assuming that the dynamics is generated by the curl of a vector potential v = ∇ × A. More concretely, we elaborate Nambu–Hamiltonian and bi-Hamiltonian characters of such systems under the light of vanishing or non-vanishing of the quantity A ⋅ ∇ × A. We present an example (satisfying A ⋅ ∇ × A ≠ 0) which can be written as in the form of Nambu–Hamiltonian and bi-Hamiltonian formulations. We present another example (satisfying A ⋅ ∇ × A = 0) which we cannot able to write it in the form of a Nambu–Hamiltonian or bi-Hamiltonian system while it can be manifested in terms of Hamiltonian one-form and yields generalized or vector Hamiltonian equations ẋ i = − 𝜖 i j k ∂ η j / ∂ x k . [ABSTRACT FROM AUTHOR]

The effect of nuclear magnetic dipole moment of hydrogen, deuterium and tritium isotopes on the electron atomic energy has been studied and analysed in this work. The electromagnetic Hamiltonian was rewritten in terms of the orbital angular momentum L e of the electron, the gyromagnetic ratio γ N of the nucleus and its total angular momentum J N . The first-order energy correction has been derived, and this correction splits each ℓ state into 2 J N + 1 states. The energy corrections and the differences between the split states of the first two lowest energy states for each isotope were calculated and it is found that these two energy states are in the radiowave range. [ABSTRACT FROM AUTHOR]