Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential

The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" singularities in the "oil domain" of the Schwarz function are stationary, and the "physical" singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by D. Khavinson and H. S. Shapiro [17] (1989). A generalization is also given for the so-called "elliptic growth" problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how \mathbb{C}^n - techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing "globalizing families". We make three conjectures in potential theory relating to our investigation

Excited Random Walk in One Dimension

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no bias. For the 1-excited walk on the half-line (one cookie initially at each site), the probability of first returning to the starting point at time t scales as t^{-(2-p)}. Although the average return time to the origin is infinite for all p, the walk eats, on average, only a finite number of cookies until this first return when p<1/2. For the infinite line, the probability distribution for the 1-excited walk has an unusual anomaly at the origin. The positions of the leftmost and rightmost uneaten cookies can be accurately estimated by probabilistic arguments and their corresponding distributions have power-law singularities near the origin. The 2-excited walk on the infinite line exhibits peculiar features in the regime p>3/4, where the walk is transient, including a mean displacement that grows as t^{nu}, with nu>1/2 dependent on p, and a breakdown of scaling for the probability distribution of the walk.Comment: 14 pages, 13 figures, 2-column revtex4 format, for submission to J. Phys.

Toward conservational anthropology: addressing anthropocentric bias in anthropology

Anthropological literature addressing conservation and development often blames 'conservationists' as being neo-imperialist in their attempts to institute limits to commercial activities by imposing their post-materialist eco-ideology. The author argues that this view of conservationists is ironic in light of the fact that the very notion of 'development' is arguably an imposition of the (Western) elites. The anthropocentric bias in anthropology also permeates constructivist ethnographies of human-animal 'interactions,' which tend to emphasize the socio-cultural complexity and interconnectivity rather than the unequal and often extractive nature of this 'interaction.' Anthropocentrism is argued to be counteractive to reconciling conservationists' efforts at environmental protection with the traditional ontologies of the interdependency of human-nature relationship

Recent advances in the chemistry of an old enzyme, urease

Urease was the first enzyme to be crystallized and shown to be a protein. Some 50 years after its crystallization, it was shown to be the first example of the nickel metalloenzymes. Whereas urea is degraded by an elimination mechanism in aqueous solution, the enzyme urease catalyzes the hydrolysis of the substrate to carbamate and ammonia as the initial products. This change of mechanism clearly points to the involvement of nickel ion in the chemistry of the enzyme, and this has been independently established. An active-site amino acid residue undergoes a decrease in pK′a on the binding of the bidentate inhibitor, acylhydoxamate; the mechanism of this acid-strengthening is discussed in detail. The now known list of substrates is large, and special interest attaches to the derivatives of phosphoric acid which are (among others) simultaneously substrates and inhibitors of the enzyme. The mechanism of this inhibition has been elucidated. An active-site peptide from the jack bean enzyme shows very high sequence homology with that from Klebsiella oxytoca in accordance with predictions based on the involvement of nickel in the chemistry of the enzyme. A method has been developed to enable the nickel ion at the active site of the enzyme to be replaced by other bivalent metal ions. This relies on the fact that although the enzyme is very stable in 20-50 mm sulfite, the metal ion is slowly lost in very dilute sulfite; the system remains completely soluble, and the electrophoretic and ultracentrifugal properties of the nickel-depleted enzyme are the same as those of the native enzyme

The conversion of oxygen in compounds to carbon monoxide for mass-spectrometric analysis

A method by which oxygen in many organic compounds and some inorganic compounds can be converted to carbon monoxide for mass-spectrometric analysis is described. The compound is decomposed in the vapour state in the presence of excess bromine by contact with a clean or a carbon-coated platinum wire at a bright red beat. The bromine acts as a scavanger and removes hydrogen and hydrocarbons. Carbon monoxide is obtained quantitatively and may be isolated in a pure state, except when the compound contains nitrogen, by freezing out the other decomposition products using liquid air. Memory and dilution effects are very small

A low-molecular-weight acid phosphatase which contains iron

A simple, large scale purification procedure for the violet "phosphoprotein phosphatase" from beef spleen [Glomset, J. and Porath, J., Biochim. Biophys. Acta, 39, 1 (1960)] has been devised. The procedure involves a 24-hr extraction of a tissue homogenate at pH 3, ammonium sulfate fractionation, CM-cellulose chromatography, and Sephadex G-75 chromatography. The highly purified enzyme shows a constant ratio of both enzymatic activity and absorbance at 550 nm to iron concentration. The data strongly indicate that the enzyme contains iron, and moreover, support a 1:1 molar ratio of iron to enzyme