Dipole strengths in the chlorophylls

Measurements of dipole strengths of chlorophylls in solution are reviewed and correlated. The refractive index dependence is found to be expressible in a simple empirical fashion that does not rely on the concept of vacuum dipole strength. The index dependence in some respects contradicts the dependence expected on the basis of effective field theories.     

Interaction of polyvinylpyrrolidone and iodine

A nonsolvent preparation of the polyvinylpyrrolidone (PVP) complex provides new insight into the nature of the polymer-iodine interaction. The preparation is obtained by simply mixing PVP with crystalline iodine and is of interest because it provides a system in which no interfering ions are present and only one type of iodine is initially present. The iodine is shown to undergo hydrolysis with moisture in the polymer to give iodide and hypoiodite. The ionic forms of iodine appear to associate with the molecular iodine, resulting in the final stable PVP-iodine complex.     

Direct product and decomposition of certain physically important algebras

I consider the direct product algebra formed from two isomorphic Clifford algebras. More specifically, for an element x in each of the two component algebras I consider elements in the direct product space with the form x x. I show how this construction can be used to model the algebraic structure of particular vector spaces with metric, to describe the relationship between wavefunction and observable in examples from quantum mechanics, and to express the relationship between the electromagnetic field tensor and the stress-energy tensor in electromagnetism. To enable this analysis I introduce a particular decomposition of the direct product algebra.     

Hydraulic conductivity of rock fractures

The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the cubic law is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.     

Variable step size destabilizes the Störmer/leapfrog/verlet method

For fixed step-sizeh the Störmer method is stable for the standard test equationÿ= ² y,>0, if and only ifh<2. We show that for variable step sizeh _n there does not exist a (positive) limit onh which ensures stability. Nor can we guarantee stability if, in addition, we limit the step size ratioh _n/h _n–1.This work was supported in part by National Science Foundation Grant DMS 90 15533.     

Substituent effects in the fragmentation reactions of acetanilides and phenyl acetates

The mass spectra of a group of m- and p-substituted acetanilides were measured to determine the effect of the substituents, if any, on the rate of C₂H₂O expulsion (rearrangement) vs. the rate of [CH₃CO]⁺ formation (simple cleavage). Our results agree with observations of others in that substituents which raise the ionization potential of the aromatic ring appear to localize, on the average, less charge density on this locus, and conversely. The atomic composition of the substituent, however, irrespective of its position, seems to determine the relative rates of the competing reaction. Although in several cases Z_m/Z_p values were close to unity, rearrangement of isomeric molecular ions to a common species is shown not to occur.