Eric R. Ulm

Numerical modeling of a two-coil apparatus for measuring the magnetic penetration depth in superconducting films and arrays

We determine the magnetic penetration depth λ(T) in superconducting films by measuring the mutual inductance of two coils located on opposite sides of the films. The apparatus is designed to produce an accurate value for λ(0) without any assumptions about the dependence of λ(T/Tc)/λ(0) on T/Tc. In a typical configuration of coils and a 100±10 nm thick by 6 mm radius film, λ can be measured to better than ±12% as long as λ≳1500 A. The noise level is typically ±2 A. If two films are made the same way, so that they have the same thickness d, and they are measured in the same apparatus, then the relative uncertainty in λ between the two films is only ±9%, because uncertainties in d, the coil dimensions, etc., are eliminated. This article describes the apparatus and a detailed numerical model which illustrates the induced current density in the film and establishes the sources of uncertainties. The accuracy of the model is demonstrated through comparison with measurements on 0.15 mm thick circular Pb disks.

Analytic Solution for Return of Premium and Rollup Guaranteed Minimum Death Benefit Options Under Some Simple Mortality Laws

Much attention has been focused recently on the issue of valuing guaranteed minimum death benefits embedded in annuity contracts. These benefits resemble a sequence of put options and their value should obey a differential equation similar to the Black-Scholes equation for simple put options. This paper derives a number of analytic solutions to this equation for a number of simple mortality laws.

Insurance Pricing, Reserving, and Performance Evaluation under External Constraints on Capitalization and Return on Equity

We derive formulas for calculating the premiums that should be charged on policies in a discounted cash flow model with tax reserves and required assets that are determined by regulation. We also determine the unique division of required assets into “reserves” and “capital” that allows the product profitability to be correctly evaluated. That is, the profit after capital charges is zero if the product achieves the return assumed in pricing. We illustrate the concepts using whole life insurance and guaranteed minimum death benefit examples.

Magnetic penetration depth λ(T) in Ni-doped YBa2(Cu1-xNix)3O7

Abstract We present measurements of the penetration depth λ(T) in YBa 2 (Cu 1-x Ni x ) 3 O 7 (x=.04,..06) and pure YBa 2 Cu 3 O 7 films obtained from the T dependence of the mutual inductance of two coaxial coils on opposite sides of the films. λ(0) increases by a factor of 5 with 4% Ni and a factor of 10 with 6% Ni. The data are well fitted by the function λ(T)=λ(0)/(1-T 2 /T c 2 ) 1/2 over the entire temperature range from 7K to T c , implying at low temperatures λ(T)≈λ(0)(1+αT 2 /T c 2 ) with a coefficient α that is independent of nickel concentration.

On the Interaction between Transfer Restrictions and Crediting Strategies in Guaranteed Funds

Guaranteed funds with crediting rates for fixed periods determined by a pension provider or insurance company are common features of accumulation annuity contracts. Policyholders can transfer money back and forth between these accounts and money market accounts that give them features similar to demand deposits, and yet they frequently credit a higher rate than the money market. Transfer restrictions are commonly employed to prevent arbitrage. In this article, we model the interaction between company and policyholder as a multiperiod game in which the company maximizes risk-neutral expected present value of profits and the policyholder maximizes his expected discounted utility. We find that the optimal strategy on the part of the company is to credit a rate higher than the money market rate in the first period to entice the policyholder to invest in the guaranteed fund. The company then credits the floor in the remaining periods as the policyholder transfers out the maximum amount. This does better for the policyholder in low interest rate environments and worse in high interest rate environments and acts as a type of “interest rate insurance” for the policyholder.

Fluctuation effects in the magnetic penetration depth of high-Tc films

We do not find evidence for strong fluctuation effects in the magnetic penetration depth of films of YBCO. While in YBCO crystals it has been found that (lambda) -3(T) is linear in T below Tc over a range of temperatures from 5K to 15K, (lambda) -2(T) is linear over a range of several degrees K just below Tc in YBCO and SmBCO films with very sharp transitions. At low temperatures, we find a T-linear behavior in (lambda) (T) in pure YBCO and SmBCO films. However, we do not find evidence that the T-linear behavior is due to thermal phase fluctuations which should increase in strength as (lambda) (0) increases.

The midinfrared conductivity determined from the infrared reflectance of YBa2(Cu1−xNix)3O7−δ films

Abstract We present the midinfrared conductivity of a YBa 2 (Cu 0.94 Ni 0.06 ) 3 O 7−δ film determined from fitting the measured infrared reflectance with a two-component model. To a first approximation, the “best-fit” midinfrared band conductivity is independent of T, in agreement with the midinfrared band used previously to fit the reflectances of films with ≤ 4% Ni. For the best fits, the midinfrared band at 10K and 100K has a well defined maximum at 300 cm −1 . This feature disappears at 300K and its spectral weight is redistributed up to about 1000cm −1 . Above about 1000cm −1 , the midinfrared band is independent of temperature.

Infrared reflectance of YBa2(Cu1−xNix)3O7−δ films

Abstract In this paper, we report the infrared reflectance R( v ,T) of a YBa 2 Cu 3 O 7−δ film in which 6% of the Cu atoms have been substituted by Ni. These spectra are taken with better resolution than in our earlier report of films with up to 4% Ni. The reflectance spectra for the 6% Ni-doped film are very similar to those fora 4% Ni-doped film, thus confirming our earlier conclusions about the very non-BCS gapless nature of the optical conductivity. The new spectra make evident a plateau at R = 96% for v −1 and a sharp decrease in R for v > 150cm −1 . These features imply an interesting non-Drude structure in the superconducting density of states in the infrared.