Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes

Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various nonellipsoidal shapes. The procedure is based on calculating the total magnetic moment by integrating the magnetic induction obtained from a full three-dimensional (3D) solution of the Maxwell equations using an adaptive mesh. The results are relevant for superconductors (and conductors in ac fields) when the London penetration depth (or the skin depth) is much smaller than the sample size. Simple but reasonably accurate approximate formulas are given for practical shapes including rectangular cuboids, finite cylinders in axial and transverse fields, as well as infinite rectangular and elliptical cross-section strips

No Child Left Behind’s school performance metrics may bepunishing disadvantaged school districts and students

In 2001, Congress enacted the No Child Left Behind Act, with the aims of improving student’s academic achievement and closing the achievement gap between high and low achieving students. In new research, Vladimir Kogan, Stéphane Lavertu and Zachary Peskowitz assess the impact of the measure’s school and district performance metrics. They find that changes in the measure’s ‘adequate yearly progress’ metric meant that disadvantaged schools districts which had actually seen improvements in student achievement were less likely to pass a school tax levy, starving these districts of the resources needed to educate low achieving students

On the Effects of a Finite Aperture on the Inverse Born Approximation

One of the most important effects of complex part geometry is that the available entrance and exit angles for ultrasound are limited. We will present a study of the Inverse Born Approximation in which we have data for incident (and exit) directions confined to a conical aperture. Modeling the direct problem by the Born Approximation, we obtained analytical results for (1) a weak spherical inclusion, and (2) a penny shaped crack (modeled by an oblate spheroid). General results are: (a) the value of the characteristic function γ is constant in the interior of the flaw, but reduced in value; (b) the discontinuity at the boundary of the flaw occurs over the “lighted” portion of the flaw; (c) this discontinuity is contrasted by a region where γ is negative; and (d) new non-physical discontinuities and non-analyticities appear in the reconstructed characteristic function. These general features also appear in numerical calculations which use as input strong scattering data from a spherical void and a flat penny shaped crack in Titanium. The numerical results can be straightforwardly interpreted in terms of the analytical calculation mentioned above, indicating that they will be useful in the study of realistic flaws. We conclude by discussing the stabilization of the aperture limited inversion problem and the removal of non-physical features in the reconstruction

Josephson junction between anisotropic superconductors

The sin-Gordon equation for Josephson junctions with arbitrary misaligned anisotropic banks is derived. As an application, the problem of Josephson vortices at twin planes of a YBCO-like material is considered. It is shown that for an arbitrary orientation of these vortices relative to the crystal axes of the banks, the junctions should experience a mechanical torque which is evaluated. This torque and its angular dependence may, in principle, be measured in small fields, since the flux penetration into twinned crystals begins with nucleation of Josephson vortices at twin planes.Comment: 6 page

London penetration depth at zero temperature and near the superconducting transition

A simple relation is established between the zero-T penetration depth λ(0) and the slope of λ−2(T) near Tc, similar to Helfand-Werthamer\u27s relation for Hc2(0) and the slope of Hc2(T) at Tc for the isotropic s-wave case with nonmagnetic scattering [E. Helfand and N. R. Werthamer, Phys. Rev. 147, 288 (1966)]. When the scattering parameter ρ=ℏv/2πTcℓ (v is the Fermi velocity and ℓ is the mean free path) varies from 1 to 10, the coefficient of proportionality between λ−2(0) and Tc(dλ−2/dT)Tc changes from 0.43 to 0.38. Combining this relation with the Rutgers thermodynamic identity, one can express λ(0) in terms of the slope (dHc2/dT)Tc and the density of states