James E. Kiefer

Photon migration in layered media

Surface emission profiles and related functions are computed for particles (photons) migrating within a semiinfinite medium containing a surface layer whose absorbance differs from that of the underlying layer. Photons are assumed to be inserted at a single point on the surface. In certain cases distinct features appear in the emission profiles which enable determination of the thickness of the top layer and of the absorption coefficients of both layers. Computations are performed to provide estimates of parameter ranges for which the presence of one layer distorts photon emission profiles from the other. Several ancillary functions are calculated, including the absorbance profile as a function of depth, the expected path length of photons that are reemitted at a distance rho from the point of insertion, and the average depth probed by those reemitted photons.

Some Properties of the A + B C Reaction-Diffusion System with Initially Separated Components

We study some properties of the A+B→C reaction-diffusion system with initially separated components, first analyzed by means of an asymptotic scaling argument by Gàlfi and Ràcz. We show that, in contrast to the asymptotic result that predicts that the rate of production of C goes liket−1, at early times it is shown to increase ast1/2. Deviations from this behavior appear at times inversely proportional to the reaction constant. Analogous crossover properties appear in the kinetic behavior of the reaction front. A second part of the study is concerned with the same chemical reaction on a fractal surface. When the substrate is a percolation cluster at criticality, both the maximum production rate and the width of the reaction zone differ considerably from those for the homogeneous space.

Exact enumeration of random walks with traps

A new useful method of exact enumeration of random walks with traps is presented. The method is applied to the one-dimensional case and is shown to yield excellent agreement with an exact solution. The advantage of the method is that it can be applied in higher dimensions. Numerical results confirm the known asymptotic solution and can be used to estimate the time and concentration needed to approach this limit.

A Truncated Test for Choosing the Better of Two Binomial Populations

Abstract It is shown that a test suggested by Bechhofer, Kiefer, and Sobel [1], for selecting the better of two binomial populations, can be formulated and solved when a maximum number of tests is specified. It is assumed that the probability of correctly selecting the better population is specified to be better than P* when the difference in success probabilities exceeds a specified Δ*. The populations are sampled equally and it is assumed that the trial ends either when the difference in the number of successes exceeds a calculated value of s, or when N tests have been made, whichever is sooner.

Numerical method for studying the detectability of inclusions hidden in optically turbid tissue

We introduce an efficient numerical method for studying the detectability of absorptive inclusions in a multiple-scattering optical medium. Use of the method is demonstrated by the forward calculation of integrated and time-gated photon intensities. Schemes for positioning the light source above an inclusion and otherwise determining the location of a hidden object, involving either reflected or transmitted reemissions, are discussed as examples. They are investigated for several illustrative models, and images are calculated as a function of the size and shape of the inclusion.

Accuracy and precision in the estimation of internuclear distances for structure determinations

Abstract We investigate systematic digitization errors in the estimation of peak areas in one-dimensional, and peak volumes in two-dimensional NMR spectra. These errors are due to the availability of data at discrete frequencies only, rather than as a continuous function of frequency. Under unfavorable but not unreasonable experimental conditions, these errors in one-dimensional experiments can be as large as 100%. With typical experimental parameters errors due to digitization are estimated to be around 10%. In two-dimensional experiments the corresponding errors in peak-volume estimates due to limited digital resolution can easily exceed 100%.

A study of precision in the measurement of chemical shifts

Abstract This paper contains an investigation by simulation of several methods for processing data from chemical shift experiments. On the assumption that the data are obtained digitally as free-induction decays and then Fourier transformed, we analyze the error in estimating the peak position, ω 0 . Two sources of error are considered, one resulting from instrumental noise, the second attributable to taking digital rather than continuous data. We show that the error resulting from noise is approximately Gaussian, while the digitization error may have a more complicated form depending on the technique used to estimate ω 0 from the data. There is some evidence indicating that the two types of error are additive. Several methods of estimating ω 0 were compared. The comparison showed that it is always desirable to use some form of curve fitting the peak rather than using the position of the maximum as an estimate of ω 0 . We conclude that it would be useful to be able to choose the number of points around the peak, for curve fitting. Finally we examined the use of both filtering and data smoothing on precision.

Some convenient bounds and approximations for the many body Van der Waals attraction between two spheres

Abstract We derive an accurate approximation to Langbeins exact expression [J. Phys. Chem. Sol. 32, 1657 (1971)] for the Van der Waals force between two spheres. The resulting formula is comparatively easy to use for computation and appears to have better than 2% accuracy.

A method for eliminating error due to phase imperfection in NOE measurements

Abstract Several schemes for estimating peak areas and their associated errors in nuclear Overhauser effect studies are investigated. The performance of these schemes is considered from the point of view of minimizing effects of errors due to phase. The assumptions made are (1) that random instrumental and digital noise are the only sources of error and (2) that adequate signal to noise to measure peak heights and linewidths can be attained. For the conditions considered it is found that taking the product of peak height times the width of the peak at one-half peak height is an efficient procedure for minimizing effects of phase error.

Effects of dielectric inhomogeneity on the magnitude of van der Waals interactions

Abstract We develop a formalism for calculating van der Waals forces between bodies with inhomogeneous dielectric properties in the nonretarded limit. The result obtained by pairwise summation of forces is given and is shown to yield good agreement with more exact calculations when the variations in dielectric properties are not too great. Finally, we calculate the magnitude of the free energy of interaction for spatial variation of the form ( α + βz ) n where z is the spatial coordinate, α and β can depend on frequency, and n is a constant. By varying n we study the effects of different profile shapes on van der Waals interactions. These effects are found to be substantial in some of the cases studied.