Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Magnetic irreversibility and metastability in a CuMn alloy

Our magnetic measurements on a CuMn alloy reveal that T_m, the temperature of the susceptibility peak, is marked by a qualitative change in the magnetization-vs.-field behavior. The magnetization process at and above T_m is reversible at all fields, whereas below T_m an irreversibility sets in at a threshold field H₁ and persists up to a second threshold field H₂. The irreversibility results in an isothermal remanence whose saturation value (attained when the field removed exceeds H₂) equals the saturation value of the thermoremanence (attained after cooling from above T_m in a field larger than H₂). Both states of remenence are characterized by a magnetization which is completely reversed by a small reverse field but returns to its original polarity when the field is removed. The hysteresis loop remains thus displaced as long as the cycling field is less than H₁.     

Vortex pinning in polycrystalline Eu1.5Ce0.5Sr2Cu2NbO10 from rotational magnetic measurements

Rotational magnetization-vector measurements were carried out on a superconducting polycrystalline disk of EuCSCNO. The results at 4.2 K and low fields resemble recent results for YBa₂Cu₃O_7−δ (YBCO) and Ba_0.57K_0.43BiO₃ (BKBO) in revealing a broad distribution in the strength of the vortex pinning torques. This resemblance extends to higher fields, where it was found that the average pinning torque per vortex (τ_p), which is directly related to the critical current density, decreases steadily with increasing field in a manner consistent with vortex bundling. Quantitatively, however, the values of τ_p for EuCSCNO are smaller by an order of magnitude than those for YBCO but are only moderately smaller than those for BKBO. This comparison supports the notion that the vortex pinning may derive in part from deviations from oxygen stoichiometry, which are normally present in YBCO but are essentially absent in EuCSCNO and BKBO. Moreover, as in YBCO and BKBO, the τ_p in EuCSCNO at fixed field is found to diminish rapidly as the temperature rises towards T_c.