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

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

A sintering model for SiC(sub)w/Si3N4 composites

Presented is a model which suggests that it should be possible to pressureless sinter a SiC(sub w)/ Si3N4 composite to theoretical density. Prior failure to achieve complete densification by sintering is attributed to the use of compositions which result in a glass deficit. There is one basic premise for this model. The ratio of glass amount to surface area of nonglass constituents must be the same for both composite and sinterable monolithic Si3N4. This model suggests that whisker and grain sizes and whisker loading influence the glass amount necessary for successful sintering of composites. According to the model, a large glass amount will be necessary for successful sintering of these composites. However, grain boundary thicknesses in the composite will be less than those in the analogous monolithic materials. This suggests that good high temperature strength may still be attained. A recent report supports the predictions of the model

Slurry-pressing consolidation of silicon nitride

A baseline slurry-pressing method for a silicon nitride material is developed. The Si3N4 composition contained 5.8 wt percent SiO2 and 6.4 wt percent Y2O3. Slurry-pressing variables included volume percent solids, application of ultrasonic energy, and pH. Twenty vol percent slurry-pressed material was approximately 11 percent stronger than both 30 vol percent slurry-pressed and dry-pressed materials. The Student's t-test showed the difference to be significant at the 99 percent confidence level. Twenty volume percent (300 h) slurry-pressed test bars exhibited strengths as high as 980 MPa. Large, columnar beta-Si3N4 grains caused failure in the highest strength specimens. The improved strength correlated with better structural uniformity as determined by radiography, optical microscopy, and image analysis

Updating the Farm Bill Safety Net in an Expanding Sea of Risk

Agricultural and Food Policy, Food Consumption/Nutrition/Food Safety, H10,

Super- and subradiant emission of two-level systems in the near-Dicke limit

We analyze the stability of super- and subradiant states in a system of identical two-level atoms in the near-Dicke limit, i.e., when the atoms are very close to each other compared to the wavelength of resonant light. The dynamics of the system are studied using a renormalized master equation, both with multipolar and minimal-coupling interaction schemes. We show that both models lead to the same result and, in contrast to unrenormalized models, predict that the relative orientation of the (co-aligned) dipoles is unimportant in the Dicke limit. Our master equation is of relevance to any system of dipole-coupled two-level atoms, and gives bounds on the strength of the dipole-dipole interaction for closely spaced atoms. Exact calculations for small atom systems in the near-Dicke limit show the increased emission times resulting from the evolution generated by the strong dipole-dipole interaction. However, for large numbers of atoms in the near-Dicke limit, it is shown that as the number of atoms increases, the effect of the dipole-dipole interaction on collective emission is reduced.Comment: 14 pages, 6 figures, published versio

Multicluster growth via irreversible cooperative filling on lattices

Consider irreversible cooperative filling of sites on an infinite lattice where the filling rates ki depend on the number, i, of occupied sites adjacent to the site(s) being filled. If clustering is significantly enhanced relative to nucleation (k1/k0≡ρ≫1), then the process is thought of as a competition between nucleation, growth, and (possible) coalescence of clusters. These could be Eden clusters with or without permanent voids, Eden trees, or have modified but compact structure (depending on the ki, i≥1). Detailed analysis of the master equations in hierarchial form (exploiting an empty-site shielding property) produces results which are exact (approximate) in one (two or more) dimensions. For linear, square, and (hyper)cubic lattices, we consider the behavior of the average length of linear strings of filled sites, lav=J∞s=1 sls/J∞s=1 ls, where ls is the probability of a string of length s [lav=(1−CTHETA)−1 for random filling, at coverage CTHETA]. In one dimension, ls=ns gives the cluster size distribution, and we write lav=nav. We consider the scaling lav∼A(CTHETA)ρω as ρ→∞ (with CTHETA fixed), which is elucidated by the introduction of simpler models neglecting fluctuations in cluster growth or cluster interference. For an initially seeded lattice, there exists an upper bounding curve lav+ for lav (as a function of CTHETA), which is naturally obtained by switching off nucleation (setting k0=0). We consider scaling of lav+ as the initial seed coverage ε vanishes. The divergence, lav∼C(1−CTHETA)−1 as CTHETA→1, is also considered, focusing on the cooperativity dependence of C. Other results concerning single-cluster densities and ls behavior are discussed

Geometric phase for an adiabatically evolving open quantum system

We derive an elegant solution for a two-level system evolving adiabatically under the influence of a driving field with a time-dependent phase, which includes open system effects such as dephasing and spontaneous emission. This solution, which is obtained by working in the representation corresponding to the eigenstates of the time-dependent Hermitian Hamiltonian, enables the dynamic and geometric phases of the evolving density matrix to be separated and relatively easily calculated.Comment: 10 pages, 0 figure

Low-temperature epitaxial growth of thin metal films

We present a different mechanism to explain the occurrence of long-lived oscillations in diffraction spot intensities during epitaxial growth of metal films on fcc (100) substrates at low temperature. Rather than rely on the common picture of cyclical nucleation and growth to produce the oscillations, the model invokes ‘‘downward funneling’’ deposition dynamics to fourfold-hollow adsorption sites