Simulating the Kinematic Dynamo Forced by Heteroclinic Convective Velocity Fields

We report on the integration of the kinematic dynamo problem in a spherical domain forced by velocity fields that are convective fluid flows resulting from a bifurcation analysis of the spherical Bénard problem. We derive a code based on generalized spherical harmonics that ensures a divergence-free magnetic field. We determine the growth or decay of a magnetic field in the kinematic dynamo equation for various physically relevant velocity fields which are stationary as well as time-periodic and chaotic. Velocity signals that are produced by heteroclinic cycles are used as an input to an energy-saturated kinematic dynamo equation that limits the growth of the linearly unstable modes. Preliminary calculations indicate the possibility of reversals of the magnetic field for this case of forcing. Received 8 October 1996 and accepted 28 April 1997     

Resistance of composite flywheel rim to radial tensile stresses from centrifugal forces based on results of pure bending of a rim segment

A method is proposed for evaluating the resistance of a flywheel rim to radial stresses in free rotation. The method is based on loading a rim segment in pure bending and calculating the limiting moment and the corresponding limiting angular velocity. Applicability of the method is substantiated theoretically by investigating the similarity of the radial stress diagrams in rotation and pure bending. The method is verified experimentally for the strained state of a rim segment in pure bending.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 521–526, July–August, 1993.     

Variational principles of magnetostatics of superconductors. I

Fundamental and dual variational principles of magnetostatics of superconductors are formulated. It is shown how test fields can be expressed in terms of vector and scalar potentials. General consequences of the variational magnetostatic formulation are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 97–102, September, 1991.     

Development of the Bogolyubov-Mitropol'skii method of integral manifolds

A survey is presented of some results relating to the development of the Bogolyubov-Mitropol'skii method of integral manifolds.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 1, pp. 33–46, January, 1992.     

Hamiltonian circle actions on symplectic manifolds and the signature

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b₀(M) − b₂(M) + b₄(M) − b₆(M) + … where σ (M) is the signature of M and b_i(M) is the ith Betti number of M.     

Strings at nonzero temperature

String theory at nonzero temperature is reviewed. A bosonic string at nonzero temperature is studied and the calculation of its free energy in both the one-loop approximation and the case of arbitrary genus (multiloop analysis) is discussed. A string at nonzero temperature is compared with a string compacted on a one-dimensional torus. The properties of modular invariance and dual symmetry are discussed at both the one-loop and multiloop levels. The thermodynamics of superstrings, including also superstrings compactified on a torus, is also studied. Possible cosmological applications are briefly considered. It is shown that many features of string thermodynamics (in particular, the existence of the Hagedorn temperature and dual symmetry) also occur in the theory of noncritical strings.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–49, December, 1991.     

Estimation of the exchange constants in the Fe sublattice of the Y2Fe17 and Y2Fe17N3−δ compounds from the analysis of Mössbauer measurements

From the analysis of Mössbauer data for Y₂Fe₁₇ and Y₂Fe₁₇N_3−δ at various temperatures the hyperfine fields for 4f, 6g, 12j, 12k iron sites were estimated as a function of temperature. The reduced magnetizations calculated from the values of the hyperfine fields are fitted with a mean field model for four interacting sublattices using a computer program. The estimated exchange interaction from the fitting procedure between the 4f sites is found strongly negative (antiferromagnetic) in Y₂Fe₁₇ whereas in Y₂Fe₁₇N_3−δ it increases and becomes weak negative following a modified Slater-Néel curve. The rest of the exchange interactions are found positive or weak negative depending on the distances between the Fe atoms.