Irreversible reaction on a polymer chain with range two cooperative effects

We consider the kinetics of an irreversible reaction at the sites of an infinite, uniform, 1D polymer chain with first and second nearest neighbor (nn) cooperative effects. The special cases with just nn cooperative effects, and with nn blocking and general second nn cooperative effects have previously been solved exactly. For the latter case, we present several new results for highly autoinhibitory and autocatalytic rates. The general problem cannot be solved exactly but we apply the techniques of the preceding paper, which for this process exploit a shielding property of quadruples of unreacted sites, to obtain approximate solutions. Various cooperativity regimes are considered

Correlated percolation in island-forming processes: Analysis of cooperative filling on a square lattice

Percolation transitions are analyzed for correlated distributions of occupied sites created by irreversible cooperative filling on a square lattice. Filling can be either autocatalytic, corresponding to island formation, or autoinhibitory. Here percolation problems for occupied and unoccupied clusters are generally distinct. Our discussion focuses on the influence of island formation (associated with correlation lengths of many lattice vectors), and of island perimeter roughness, on percolation. We also discuss the transition to continuum percolation problems as the ratio of island growth to nucleation rates, and thus the average island size, diverges. Some direct analysis of occupied cluster structure is provided, the connection with correlated animals is made, and correlated spreading and walking algorithms are suggested for direct generation of clusters and their perimeters

Faddeev’s equations in differential form: Completeness of physical and spurious solutions and spectral properties

Faddeev type equations are considered in differential form as eigenvalue equations for non‐self‐adjoint channel space (matrix) Hamiltonians HF. For these equations in both the spatially confined and infinite systems, the nature of the spurious (nonphysical) solutions is obvious. Typically, these together with the physical solutions (given extra technical assumptions) generate a regular biorthogonal system for the channel space. This property may be used to provide an explicit functional calculus for the then real eigenvalue scalar spectral HF, to show that ±iHF generate uniformly bounded C0 semigroups and to simply relate HF to self‐adjoint Hamiltonian‐like operators. These results extend to the four‐channel Faddeev type equations where the breakup channel is included explicitly

Percolative aspects of nonequilibrium adlayer structure

For any adsorption process where all binding sites eventually fill, there exists a coverage θc at which a filled cluster (defined by linking neighboring filled sites) first spans the substrate. Such percolation features have been studied extensively for random distributions of filled sites. Here θc =0.59 monolayers for ‘‘p(1×1) ordering’’ on an infinite square lattice. Cooperative island‐forming adsorption involves competition between nucleation, growth, and coalescence or linkage of individual islands. Here clusters of linked islands eventually span the substrate. We use correlated percolation theory to provide a quantitative description of corresponding θc behavior, and of the fractal structure of the clusters of linked islands and their perimeters. Modified grain growth models, which correspond to continuum percolation problems, are also useful here. We show how percolation theoretic ideas can be extended to analyze nonpercolating c(2×2) ordering. Even for the essentially random adsorption mechanisms of H2O on Fe(001), and oxygen on Pd(100), such nonequilibrium c(2×2) ordering is significant. We also discuss how island‐forming cooperativity here affects the c(2×2) ordering

Hazards to golden-mantled ground squirrels and associated secondary hazard potential from strychnine baiting for forest pocket gophers

Radio telemetry and capture-recapture techniques were used to evaluate the hazards to golden-mantled ground squirrels (Spermophilus lateralis) from hand baiting with 0.5% strychnine-treated oats for western pocket gophers (Thomomys mazama) on conifer plantations in eastern Oregon. Toxicology data were collected on field-killed and caged ground squirrels and on caged mink (Mustela vison), great horned owls (Bubo virginianus), and red-tailed hawks (Buteo jamaicensis). Ground squirrel populations were reduced 50 to 75% following underground baiting for pocket gophers. Maximum amount of strychnine alkaloid found in cheek pouches and carcass of a field-killed golden-mantled ground squirrel was 2.88 mg. Mean amount of strychnine in carcasses was 0.35 mg; almost all occurred in the gut. The estimated LD50 for mink was 0.6 mg/kg. The lowest lethal dose for great horned owls and red-tailed hawks was 7.7 mg/kg and 10.2 mg/kg, respectively. The LD50 for owls and hawks was not determined. Long-term effects on golden-mantled ground squirrel populations and secondary hazard potential to owls and hawks were judged to be minimal. Wild mustelids as large as mink could be adversely affected by consuming the gut content of strychnine-killed golden-mantled ground squirrels

The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

This paper considers the outcome of a formal sensitivity analysis on a series of epidemic model structures developed to study the population level effects of maternal antibodies. The analysis is used to compare the potential influence of maternally acquired immunity on various age and time domain observations of infection and serology, with and without seasonality. The results of the analysis indicate that time series observations are largely insensitive to variations in the average duration of this protection, and that age related empirical data are likely to be most appropriate for estimating these characteristics

Factorization relations and consistency conditions in the sudden approximation

Linear factorization relations are derived for the matrix elements of quantum mechanical operators defined on some space H = H1⊕⋅2 which are diagonalizable on H1. The coefficients in these relationships do not depend on the operators per se but do depend on the representations in which the operators are diagonal. The formulation is very general with regard to the nature of the ’’input’’ information in the factorization. With each choice of input information there are associated consistency conditions. The consistency conditions, in turn, give rise to a flexibility in the form of the factorization relations. These relations are examined in detail for the operators of scattering theory which are local in the internal molecular coordinates. In particular, this includes S and T matrices in the energy sudden (ES) approximation. A similar development is given for the square of the magnitude of operator matrix elements appropriately averaged over ’’symmetry classes.’’ In the ES these relations apply to transition cross sections between symmetry classes. In particular, they apply to degeneracy averaged cross sections in situations where the symmetry classes correspond to energy levels