On the second variation of the biharmonic Clifford torus in $$\mathbb S^4$$

Annals of Global Analysis and Geometry - The flat torus $${{\mathbb T}}=\mathbb S^1\left( \frac{1}{2} \right) \times \mathbb S^1\left( \frac{1}{2} \right) $$ admits a proper biharmonic isometric...     

Superconductivity of lanthanum and cerium at high pressures

A theoretical model involving the presence of an inner 4f shell is developed here to explain the pressure dependence of the superconducting transition temperature of lanthanum and the presence of a superconducting high pressure phase of cerium. In this model, only the conduction electrons are assumed to participate in the superconductivity mechanism, while the 4f electrons tend to inhibit superconductivity. As the 4f character decreases with increasing pressure in lanthanum, it is possible to account for the anomalous pressure dependence of the superconducting transition temperature by assuming a valency a little less than three at normal pressure. The anomalous behaviour of cerium, magnetic at room temperature and normal pressure and superconducting above 50 kbar, is also discussed here.     

Flux penetration in high-Tc superconductors: Implications for magnetic suspension and shielding

Two new effects associated with flux penetration and pinning in superconducting YBa₂Cu₃O_x are demonstrated. One of these is focussing of magnetic field lines by the superconductor and the other is magnetic suspension. The existence of stable equilibrium in suspension is shown to be related directly to hysteresis observed in the force-separation relation for a magnet and the superconductor. We also observe that the levitation height of a magnet increases with the magnet volume, contrary to results in the literature.     

Functional integral methods in the theory of the Anderson model

The use of the functional integration technique applied to the problem of local moment formation in the Anderson model is reviewed in this paper.

The different approximations are discussed, in order to clarify both their internal consistency and relations among them. Connection with the ordinary diagrammatic approach is made by summarizing and extending previous treatments done on this subject; and the difference between the one-field and the two-field approaches is explained in terms of the ‘unphysical diagrams’ generated by the first. The results for the magnetic susceptibility are presented for each approximation discussed in the paper, both in the strong magnetic and in the non-magnetic regime; while it is shown that no reliable approximation has been developed for the intermediate coupling situation.

Finally the Kondo effect is discussed within the functional integration scheme and application of the method to the study of superconducting magnetic alloys is reviewed.     

Remanent fields and critical currents in Tl2 Ba2Ca2Cu3Ox ceramic

The temperature and magnetic-field dependences of the remanent magnetization have been determined from far-field measurements for thallium ceramic samples. The current flow that gives rise to the observed magnetization is intragranular. The results are consistent with flux-creep-controlled transport with a distance between pinning centers of - 1/2/m. Using near-field measurements, the superconducting properties are found to be heterogeneous on a scale of 1 mm. Magnetic domains have been induced by pplying spatial variation in the applied field.     

Local and global uncertainty analyses of a methane flame model

Local and global uncertainty analyses of a flat, premixed, stationary, laminar methane flame model were carried out using the Leeds methane oxidation mechanism at lean (phi = 0.70), stoichiometric (phi = 1.00), and rich (phi = 1.20) equivalence ratios. Uncertainties of laminar flame velocity, maximal flame temperature, and maximal concentrations of radicals H, O, OH, CH, and CH(2) were investigated. Global uncertainty analysis methods included the Morris method, the Monte Carlo analysis with Latin hypercube sampling, and an improved version of the Sobol' method. Assumed probability density functions (pdf's) were assigned to the rate coefficients of all the 175 reactions and to the enthalpies of formation of the 37 species. The analyses provided the following answers: approximate pdf's and standard deviations of the model results, minimum and maximum values of the results at any physically realistic parameter combination, and the contribution of the uncertainty of each parameter to the uncertainty of the model result. The uncertainty of a few rate parameters and a few enthalpies of formation causes most of the uncertainty of the model results. Most uncertainty comes from the inappropriate knowledge of kinetic data, but the uncertainty caused by thermodynamic data is also significant.     

Harmonic maps with potential

Let (M,g) and (N,h) be two Riemannian manifolds, and G:N →ℝ a given function. If f:M → N is a smooth map, we set E _G (f)=12 ∫_M [∣df∣²− 2G(f)]dv _g. We establish some variational properties and some existence results for the functional E _G (f): in particular, we analyse the case of maps into a sphere. Received April 29, 1996 / Accepted May 28, 1996     

SO(2)-invariant minimal and constant mean curvature surfaces in 3-dimensional homogeneous spaces

We study SO(2)-invariant minimal and constant mean curvature surfaces in R³ endowed with a homogenous Riemannian metric whose group of isometries has dimension greater or equal to 4. Work partially supported by 40% and 60% Italian M.U.R.S.T. funds.