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Graphical abstract Highlights • Energetically inaccessible conical intersections strongly affect standard single adiabatic state descriptions of nonadiabatic tunneling. • Linked intersections limit the validity of standard treatments of nonadiabatic dynamics involving more than two adiabatic electronic states. • The geometric phase and vector potential needed to describe the Molecular Aharonov Bohm effect can determined from a two state diabatization. • Some properties based diabatizations produce spurious singularities in the derivative couplings. Abstract In this Viewpoint issues in the construction and use of adiabatic and diabatic representations in describing spin-conserving electronically nonadiabatic processes using the Born-Huang ansatz are reviewed and illustrated. We address issues which limit the accuracy of commonly used approximate equations of motion. The following caveats are discussed. (i) The use of adiabatic states for Nstate > 2 is complicated by the fact that if states (I , J) and (J , K) have conical intersections then the derivative coupling f (a),I,J (R) may well be double-valued, rendering it inappropriate for nuclear dynamics. (ii) In the nonadiabatic tunneling regime, nuclear motion can be restricted to a single adiabatic potential energy surface on the basis of total energy. However, energetically inaccessible conical intersections make it necessary to take into account the geometric phase and the induced vector potential when formulating the nuclear Schrödinger equation. We review how a diabatization approach which takes explicit account of the derivative couplings can be used to accurately include these factors. (iii) Finally, we review how a commonly used class of two-state diabatizations based on smooth molecular properties can be subject to ruinous singularities inherent in equations defining the diabatization. [ABSTRACT FROM AUTHOR]

Abstract Many codes have been developed to study highly relativistic, magnetized flows around and inside compact objects. Depending on the adopted formalism, some of these codes evolve the vector potential A , and others evolve the magnetic field B = ∇ × A directly. Given that these codes possess unique strengths, sometimes it is desirable to start a simulation using a code that evolves B and complete it using a code that evolves A. Thus transferring the data from one code to another would require an inverse curl algorithm. This paper describes two new inverse curl techniques in the context of Cartesian numerical grids: a cell-by-cell method, which scales approximately linearly with the numerical grid, and a global linear algebra approach, which has worse scaling properties but is generally more robust (e.g., in the context of a magnetic field possessing some nonzero divergence). We demonstrate these algorithms successfully generate smooth vector potential configurations in challenging special and general relativistic contexts. Highlights • Our solution consists of a numerical implementation of the "inverse curl" operator. • We use two different methods that have different strengths and weaknesses. • The cell-by-cell technique is very fast and scales with the number of gridpoints. • The global linear algebra method is slower but has better symmetry properties. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we deal with the solenoidal conservative Lie algebra associated to the classical normal form of Hopf-zero singular system. We concentrate on the study of some representations and Z 2 -equivariant normal form for such singular differential equations. First, we list some of the representations that this Lie algebra admits. The vector fields from this Lie algebra could be expressed by the set of ordinary differential equations where the first two of them are in the canonical form of a one-degree of freedom Hamiltonian system and the third one depends upon the first two variables. This representation is governed by the associated Poisson algebra to one sub-family of this Lie algebra. Euler's form, vector potential, and Clebsch representation are other representations of this Lie algebra that we list here. We also study the non-potential property of vector fields with Hopf-zero singularity from this Lie algebra. Finally, we examine the unique normal form with non-zero cubic terms of this family in the presence of the symmetry group Z 2. The theoretical results of normal form theory are illustrated with the modified Chua's oscillator. Highlights • Constructing the Poisson algebra for a Lie subalgebra of Hopf-zero singularities. • Significant representations of solenoidal family of Hopf-zero singularities. • Unique normal form classification of solenoidal family of Hopf-pitchfork singularities. • Z 2 -equivariant normal form of modified Chua's oscillator. [ABSTRACT FROM AUTHOR]

The magnetic field of different geometry of the permanent magnet is analytically calculated by using basic principles of the magnetism in very easier approach. Concept of origin shifting and geometrical shape transformation are used to formulate the formula for cuboidal, cubical and cylindrical permanent magnets. This concept can be used for the analysis of magnetic field distribution in space around for permanent magnet as well as electromagnet in a very easier approach. Handy and simplified software is made to calculate the magnetic field due to permanent magnet and electromagnet at any desired position on space. Magnetic field visualization is also done in both magnitude and direction by using MATLAB. [ABSTRACT FROM AUTHOR]

It is discovered that a change of a vector potential by means of a laboratory device effects on antigen-antibody reaction in lymphocytes suspension. The effect decreases lysis of lymphocytes in anti-CD3 antibodies presence and increases the destruction in anti-HLA antibodies presence. Authors propose that these effects are due to changes of antigen-antibody complexes lateral mobility and to changes of complexes aggregates biochemical activity.

Abstract Ticks, as obligate blood-sucking ectoparasites, attack a broad range of vertebrates and transmit a great diversity of pathogenic microorganisms. They are considered second only to mosquitoes as vectors of human disease, and the most important vector of pathogens of domestic and wild animals. Of the 117 described species in the Chinese tick fauna, 60 are known to transmit one or more diseases: 36 species isolated within China and 24 species isolated outside China. Moreover, 38 of these species carry multiple pathogens, indicating the potentially vast role of these vectors in transmitting pathogens. Spotted fever is the most common tick-borne disease, and is carried by at least 27 tick species, with Lyme disease and human granulocytic anaplasmosis ranked as the second and third most widespread tick-borne diseases, carried by 13 and 10 species, respectively. Such knowledge provides us with clues for the identification of tick-associated pathogens and suggests ideas for the control of tick-borne diseases in China. However, the numbers of tick-associated pathogens and tick-borne diseases in China are probably underestimated because of the complex distribution and great diversity of tick species in this country.

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 7 Li 2 (2 3 Π g ), K 2 (X 1 Σ g + ), Mg 2 (X 1 Σ g + ) and NaBr (X 1 Σ + ) 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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (©2023PublishedbyElsevierLtd.)

The theory, modeling, measurement, and analysis of the radiation characteristics of bond wire antennas (BWAs) is presented in this paper. We commence with rigorous formulations and derivations of analytical models for calculating the vector potential, radiated electromagnetic fields, and directivity of full-loop BWAs (FL-BWAs), considering nonconstant current distribution along the BWAs. Based on the image theory, we derive an analytical model for calculating the directivity of half-loop BWAs (HL-BWAs) from that of FL-BWAs. Very good correlation is obtained between the directivities calculated analytically using the derived models, and numerically using commercial full-wave solvers, thus validating our analytical approach. We apply the verified models to thoroughly analyze the radiation characteristics of FL-BWAs and HL-BWAs. The radiation characteristics of an HL-BWA are based on the assumption that its reference plane is infinitely large and perfectly conducting. However, for the development of wireless systems, reference planes of finite sizes are required. Therefore, we investigate the impact of realistic planes sizes. Our results reveal that the radiation characteristics of BWAs referred to as “HL-BWAs” in published literature differ significantly from those of true HL-BWAs. Therefore, we introduce the term “quasi-half-loop BWA (QHL-BWA)” to describe BWAs with small reference planes. For experimental verification, QHL-BWAs which operate in the 60 GHz band were fabricated using the wedge–wedge bonding process. Both S-parameter and radiation pattern measurements were performed. Very good correlation was obtained between measurement and simulation results. [ABSTRACT FROM AUTHOR]

In this article, we discuss how a combination of electrodynamics and quantum mechanics makes interference measurements of the quantum phase possible in terms of the vector potential, neither of which is detectable independently. This effect, predicted by Aharonov and Bohm, is of great significance in the contemporary interesting topic of nanoscopic physics. We also indicate how the effect can be incorporated in a solid state device by employing the tight-binding (TB) model. The TB model can be realized in a mesoscopic ring which allows the measurement of the bond current and the associated diamagnetism. An exactly solvable case of a threesite ring is presented that serves as a pedagogic example providing further insights into the phenomenon. [ABSTRACT FROM AUTHOR]

In this paper, we propose a potential-based integral equation solver for low-frequency electromagnetic (EM) problems. In this formulation, the scalar potential ( \Phi ) equation is solved in tandem with the vector potential ( \textbf {A} ) equation. The resulting system is immune to low-frequency catastrophe and accurate in capturing the electrostatic and magnetostatic physics. The fast convergence of the new \textbf {A}$ - $\Phi $ system, which is a typical symmetric saddle point problem, is made possible through the design of an appropriate left constraint preconditioner. Numerical examples validate the efficiency and stability of the novel formulation in solving both EM scattering and circuit problems over a wide frequency range up to very low frequencies. [ABSTRACT FROM PUBLISHER]

This paper deals with the investigation of braking forces induced by eddy currents, which have effects on the permanent magnet moving at a constant speed in the direction of the conductive tube axis. The analysis is based on calculation of an action of a force between the current density, representing the magnet, and the eddy currents. The chosen solution is based on classical electrodynamics and can serve as a guide for the calculation of other cases, where braking forces are created between the moving cell, which is a source of the magnetic field, and a close conductive subject. The obtained results indicate the braking force affecting the magnet and the dependence of this force on the current. The graphical representation of the results shows that the balancing velocity of the magnet fall is inversely proportional to the quadrant of its magnetic moment. This work may be useful for experts in the area of the design of electromagnetic clutches, brakes, and actuators and for university teachers dealing with electrodynamics. Moreover, it can serve as a demonstration of a calculation of the field by vector potential, which is an appropriate quantity used for the description of magnetic fields. [ABSTRACT FROM AUTHOR]

An analytical solution was obtained for a stationary axisymmetric motion equation for a flow caused by an inhomogeneous electric current propagating through an electrically conducting liquid. The problem was solved in the variables for vorticity and velocity vector potential in hemispherical geometry with the finite size electrodes. Stokes and electrodynamic approximations were used. [ABSTRACT FROM AUTHOR]

We address the non-uniqueness of the vector potential for the Sommerfeld half-space problem with a horizontal Hertzian dipole. In contrast to the classical solution, which utilizes horizontal and vertical components of the vector potential, the formulation presented here employs two horizontal components. In this approach, unlike in the traditional one, the scalar potentials of single-point charges associated with the vertical and horizontal Hertzian dipoles are identical. [ABSTRACT FROM AUTHOR]