Irradiation of a cone by a magnetic dipole

Th electromagnetic field produced by a magnetic dipole in thepresence of a perfectly conducting cone of arbitrary cross-sectionis determined. The solution is used to find out how a currenton the cone travelling towards the apex is reflected. Some valuesof the reflection coefficient are calculated. In particular,it is shown that there is a sort of resonance with the reflectionincreasing significantly as the cone approaches a plane.     

Nonlinear electrodynamic lensing of electromagnetic waves in a magnetic dipole field

We consider propagation of electromagnetic waves in magnetic dipole and gravitational fields proceeding in accordance with the nonlinear vacuum electrodynamics laws. We derive formulas describing the effect of nonlinear electrodynamic lensing of electromagnetic waves in the magnetic dipole field. We show that rotation of the magnetic dipole moment about an axis noncoincident with this moment leads to a nonlinear electrodynamic modulation of the electromagnetic radiation intensity by frequencies that are multiples of the dipole rotation frequency. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 85–94, January, 2007.     

Eddy-current braking of a translating solid bar by a magnetic dipole

The paper addresses the problem of a conducting rectangular bar of square cross-section which is moving with constant velocity in the field of an arbitrarily oriented magnetic dipole. The braking Lorentz force on the bar is obtained by FEM and compared with the analytical solution for a moving infinite plate in the field of a magnetic dipole [2]. The computation of the induced currents requires solution of a Laplace equation with mixed boundary conditions for the electric potential inside the moving bar. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Laminar magnetohydrodynamic duct flow in the presence of a magnetic dipole

We study magnetohydrodynamic flow of a liquid metal in a straight duct. The magnetic field is produced by an exterior magnetic dipole. This basic configuration is of fundamental interest for Lorentz force velocimetry (LFV), where the Lorentz force opposing the relative motion of conducting medium and magnetic field is measured to determine the flow velocity. The Lorentz force acts in equal strength but opposite direction on the flow as well as on the dipole. We are interested in the dependence of the velocity on the flow rate and on strength of the magnetic field as well as on geometric parameters such as distance and position of the dipole relative to the duct. To this end, we perform numerical simulations with an accurate finite-difference method in the limit of small magnetic Reynolds number, whereby the induced magnetic field is assumed to be small compared with the external applied field. The hydrodynamic Reynolds number is also assumed to be small so that the flow remains laminar. The simulations allow us to quantify the magnetic obstacle effect as a potential complication for local flow measurement with LFV. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct problem of calculating the magnetic dipole field in a quasilayered medium

A method is developed for calculating the electromagnetic field of a magnetic dipole in a quasilayered two-dimensional medium. The quasi-three-dimensional problem is reduced to a two-dimensional problem for the Fourier-transformed electromagnetic field. An equivalent system of integral equations on the layer boundaries is obtained. This research was partially supported by the State Scientific-Technical Program “Future Information Technologies” (grant No. 0201.06.010) and the Interuniversity Scientific Program “Russian Universities: Basic Research.” Translated from Chislennye Metody v Matematicheskoi Fizike, Moscow State University, pp. 94–110, 1998.     

Estimating the influence zone of a vertical magnetic dipole in aerial prospecting

We consider the direct problem of aerial electric sounding for a layered medium with a vertical cylindrical anomaly. We determine the minimum size of the anomaly when it is indistinguishable from an infinite layer of the same conductivity. The integral equation is solved by the integral current method. The concept of apparent conductivity is introduced for sounding problems using a magnetic dipole. The calculations support the conjecture of the locality of aerial sounding and prove the high efficiency of the integral current method for such problems.     

Relaxation transitions in polymers in the presence of magnetic fields

A method of studying the effect of magnetic fields on polymeric materials has been developed. A universal cell has been designed for measuring the loss tangent in the presence of magnetic fields at different frequencies over a broad range of temperatures. The data obtained indicate that magnetic fields have an important effect on the loss tangents of polymeric materials and the location of the loss maximum on the tan -T temperature dependence.Sumgait Branch of the Mamedaliev Institute of Petrochemical Processes, Academy of Sciences of the Azerbaidzhan SSR. Translated from Mekhanika Polimerov, No. 4, pp. 611–614, July–August, 1971.     

Mathematical modeling of the vertical magnetic dipole field in a two-dimensional nonhomogeneous medium

We consider a quasi-three-dimensional problem of remote marine sounding by a high-power stationary source located on land. A transition from the three-dimensional problem to a family of parametric two-dimensional problems is performed. The solution of the remote marine sounding problem is obtained with high accuracy after solving about 20 two-dimensional problems. The integral equations are solved by the modified integral current method, which has proved highly efficient for field computations inside a strongly conducting anomaly. The electric field amplitude is observed to increase with depth. The width of the coastal current channel is estimated by analyzing the vertical magnetic field component.     

Systematics of some beta-transitions

0⁺ excited states of even-even nuclei can arise in several ways. In order to throw some light on the mechanism of excitation of these states, the log (ft) values for beta-transitions to the 0⁺ excited state and the 0⁺ ground state of even-even nuclei have been compared. In this analysis both allowed and forbidden beta-transitions have been considered. This survey is similar to that of beta-transitions by M. Sakai. Results of the present analysis are presented and compared to that of Sakai.     

Fast computation of the field of a vertical magnetic dipole above a layered medium

We consider the direct problem of aeroelectrosounding for a layered medium. The specific feature of this problem is that its solution is representable as a Bessel transform of a function ƒ of a certain type. We have developed and implemented a method for fast computation of the Bessel transform of such functions. The method relies on the approximation of ƒ by a linear combination of exponentials with prespecified exponents. The Bessel transform of the original function ƒ is computed analytically as the Bessel transform of the approximating linear combination. Numerical computations have been carried out. __________ Translated from Prikladnaya Matematika i Informatika, No. 26, pp. 39–48, 2007.     

Electric dipole in a magnetic field: Bound states without classical turning points

We show that both rigid and nonrigid dipoles can be trapped by an uniform external magnetic field in classical mechanics. The trapped states of the dipole present a nontrivial example of classical bound states embedded in a continuum (BSEC) that can be treated as analogues of quantum BSECs. For example, the classical motion of the dipole is confined to a finite region in space although there are no classical turning points. We also examine the quantum motion of the dipole in a magnetic field and show that for the most natural choices of the parameters, no quantum BSEC solutions exist. The possibilities of experimental investigations of BSECs are discussed. Deceased. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 2, pp. 189–205, November, 1998.     

Electromagnetic interaction of a conducting cylinder with a magnetic dipole caused by steady rotation

The motion of a conductor in a magnetic field induces eddy currents whose interaction with the field produces Lorentz forces opposing the motion. One can determine the velocity of the conductor from the force on the magnet system since the latter is equal but opposite to the Lorentz force on the conductor. This contactless method is known as Lorentz force velocimetry (LFV). We study an idealized configuration of LFV, i.e. a rotating solid cylinder interacting with a point dipole. The understanding of parameter influences in this setup can be helpful for more realistic configurations. We use a purely kinematic approach appropriate for low magnetic Reynolds numbers. Numerical results for small and large distances between dipole and cylinder have been obtained with the commercial software COMSOL Multiphysics. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid

The bioelectric current dipole model is important both theoretically and computationally in the study of electrical activity in the brain and stomach due to the resemblance of the shape of these two organs to an ellipsoid. To calculate the magnetic field B due to a dipole in an ellipsoid, one must evaluate truncated series expansions involving ellipsoidal harmonics , which are products of Lamé functions. In this article, we extend a strictly analytic model (G. Dassios and F. Kariotou, J. Math. Phys. 44 (2003), 220–241), where B was computed from an ellipsoidal harmonic expansion of order 2. The present derivations show how the field can be evaluated to arbitrary order using numerical procedures for evaluating the roots of Lamé polynomials of degree 5 or higher. This can be accomplished using an optimization technique for solving nonlinear systems of equations, which allows one to acquire an understanding of the truncation error associated with the harmonic series expansion used for the calculation. Funding was provided by the National Institute of Health, Grant No. 1RO1 DK 58697 and by the Veterans’ Affairs Research Service.     

Study of relaxation transitions in polymers in the presence of magnetic fields

Infrared spectroscopy in polarized light has been used to investigate specimens of polyvinyl chloride exposed to a magnetic field. It is shown that, depending on the conditions of heat treatment, various conformational transitions of the C-Cl bond occur in the polyvinyl chloride. The orientation effects in PVC exposed to a magnetic field are associated with the preferential formation of trans isomers of the C-Cl bond.Sumgait Branch, Mamedaliev Institute of Petrochemical Processes, Academy of Sciences of the Azerbaidzhan SSR. Translated from Mekhanika Polimerov, No. 5, pp. 923–925, September–October, 1972.     

Ising model in half-space: A series of phase transitions in low magnetic fields

For the Ising model in half-space at low temperatures and for the “unstable boundary condition,” we prove that for each value of the external magnetic field μ, there exists a spin layer of thickness q(μ) adjacent to the substrate such that the mean spin is close to −1 inside this layer and close to +1 outside it. As μ decreases, the thickness of the (−1)-spin layer changes jumpwise by unity at the points μ_q, and q(μ) → ∞ as μ → +0. At the discontinuity points μ_q of q(μ), two surface phases coexist. The surface free energy is piecewise analytic in the domain Re μ > 0 and at low temperatures. We consider the Ising model in half-space with an arbitrary external field in the zeroth layer and investigate the corresponding phase diagram. We prove Antonov’s rule and construct the equation of state in lower orders with the precision of x⁷, x = e^−7ɛ. In particular, with this precision, we find the points of coexistence of the phases 0, 1, 2 and the phases 0, 2, 3, where the phase numbers correspond to the height of the layer of unstable spins over the substrate. Dedicated to Roland L’vovich Dobrushin __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 2, pp. 220–261, November, 2007.     

Systematics of some levels in even-even nuclei

Morinaga’s study of the lowest odd-parity states in even-even nuclei has been extended to even-parity odd-spin and odd-parity even-spin states. These states show good agreement with the curve E=67 A^?3/4 Mev.     

Distortion of liquid metal flow in a square duct due to the influence of a magnetic point dipole

We consider liquid metal flow in a square duct with electrically insulating walls under the influence of a magnetic point dipole using three-dimensional direct numerical simulations with a finite-difference method. The dipole acts as a magnetic obstacle. The Lorentz force on the magnet is sensitive to the velocity distribution that is influenced by the magnetic field. The flow transformation by an inhomogeneous local magnetic field is essential for obtaining velocity information from the measured forces. In this paper we present a numerical simulation of a spatially developing flow in a duct with laminar inflow and periodic boundary conditions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On an integral equation in the theory of phase transitions for a system of magnetic rods

We study a nonlinear integral equation for the orientational distribution function (ODF) describing anisotropic nematic ordering in a system of magnetic rods. For highly elongated rods, we give a classification of bifurcation points and find their asymptotic behavior in the limits of small and large magnetic moments of the rods. We develop an algorithm to construct a nearly-isotropic ODF in the vicinity of the bifurcation point. We show that for both small and large magnetic moments, the ODF obtained has a left direction of bifurcation. However, for intermediate values of the magnetic moments, solutions with a right direction of bifurcation exist along with those with the left direction.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 427–440, December, 1996.