Asymptotic expansions for a remarkable class of random walks

This paper extends the research of Wiegel (J. Math. Phys. 21 (1980) 2111) on random walks which differ from free random walks through the occurrence of an extra weightfactor (−1) at every crossing of a half-line. Starting from a new closed-form expression for the weight distribution of these walks, we derive various integral representations and asymptotic expansions for the total weight of all walks

Iterative solution of a discrete axially symmetric potential problem

The Dirichlet problem for the axially symmetric potential equation in a cylindrical domain is discretized by means of a five-point difference approximation. The resulting difference equation is solved by point or line iterative methods. The rate of convergence of these methods is determined by the spectral radius of the underlying point or line Jacobi matrix. An asymptotic approximation for this spectral radius, valid for small mesh size, is derived

Random mixtures of polycyclic aromatic hydrocarbon spectra match interstellar infrared emission

The mid-infrared (IR; 5-15~$\mu$m) spectrum of a wide variety of astronomical objects exhibits a set of broad emission features at 6.2, 7.7, 8.6, 11.3 and 12.7 $\mu$m. About 30 years ago it was proposed that these signatures are due to emission from a family of UV heated nanometer-sized carbonaceous molecules known as polycyclic aromatic hydrocarbons (PAHs), causing them to be referred to as aromatic IR bands (AIBs). Today, the acceptance of the PAH model is far from settled, as the identification of a single PAH in space has not yet been successful and physically relevant theoretical models involving ``true'' PAH cross sections do not reproduce the AIBs in detail. In this paper, we use the NASA Ames PAH IR Spectroscopic Database, which contains over 500 quantum-computed spectra, in conjunction with a simple emission model, to show that the spectrum produced by any random mixture of at least 30 PAHs converges to the same 'kernel'-spectrum. This kernel-spectrum captures the essence of the PAH emission spectrum and is highly correlated with observations of AIBs, strongly supporting PAHs as their source. Also, the fact that a large number of molecules are required implies that spectroscopic signatures of the individual PAHs contributing to the AIBs spanning the visible, near-infrared, and far infrared spectral regions are weak, explaining why they have not yet been detected. An improved effort, joining laboratory, theoretical, and observational studies of the PAH emission process, will support the use of PAH features as a probe of physical and chemical conditions in the nearby and distant Universe

Response of deep-water agglutinated foraminifera to dysoxic conditions in the California Borderland basins

Analysis of agglutinated benthic foraminifera from surface samples collected in the San Pedro and Santa Catalina Basins reveals a predictable relationship between the proportions of morphogroups with decreasing bottom water oxygen levels and with the TOC content of the surficial sediment. Living (Rose Bengal stained) foraminiferal faunas from dysaerobic environments display low diversity and high dominance, suggesting stressed conditions. There is an inverse relationship between oxygen and the relative abundance of deep infaunal morphogroups. Samples collected from shallow stations above the oxygen minimum zone are comprised of epifaunal and shallow infaunal morphotypes. At intermediate depths (~500 m), there is a peak in the abundance of suspension-feeding and "climbing" forms (watchglass-shaped trochamminids attached to Rhabdammina). Specimens from intermediate stations display the largest overall size. Deeper in the San Pedro Basin the living fauna is dominated by a small, flattened, tapered, species that is interpreted as having a deep infaunal microhabitat. In the dysaerobic environments off California the greatest degree of faunal change occurs when bottom water dissolved oxygen values drop from 0.5 ml/l to 0.2 ml/l. The effect of TOC content on the benthic fauna is demonstrated at two stations from the same depth in the San Pedro Basin. The station with the higher TOC content (4.2% vs. 2.9%) contains greater proportions of the small, deep infaunal morphotype. These faunal changes may be attributed to differences in the depth of the oxygenated zone within the sediment surface layer. Agglutinated faunas from areas that experience seasonal anoxia are comprised of a large proportion of opportunistic forms such as Reophax and Psammosphaera. These are the same taxa that colonised abiotic sediment trays in a recolonisation experiment in the Panama Basin. This study further demonstrates that agglutinated foraminiferal morphotypes respond in a similar manner to calcareous benthic foraminifera in dysaerobic environments

Solution to problem 95-2 : Exciton transport

No abstract