The Reaction-Diffusion Front for A+B→∅A+B \to\emptyset in One Dimension

We study theoretically and numerically the steady state diffusion controlled reaction $A+B\rightarrow\emptyset$, where currents $J$ of $A$ and $B$ particles are applied at opposite boundaries. For a reaction rate $\lambda$, and equal diffusion constants $D$, we find that when $\lambda J^{-1/2} D^{-1/2}\ll 1$ the reaction front is well described by mean field theory. However, for $\lambda J^{-1/2} D^{-1/2}\gg 1$, the front acquires a Gaussian profile - a result of noise induced wandering of the reaction front center. We make a theoretical prediction for this profile which is in good agreement with simulation. Finally, we investigate the intrinsic (non-wandering) front width and find results consistent with scaling and field theoretic predictions.Comment: 11 pages, revtex, 4 separate PostScript figure

Scale-dependent variation in coral community similarity across sites, islands, and island groups

Community similarity is the proportion of species richness in a region that is shared on average among communities within that region. The slope of local richness (α diversity) regressed on regional richness (γ diversity) can serve as an index of community similarity across regions with different regional richness. We examined community similarity in corals at three spatial scales (among transects at a site, sites on an island, and islands within an island group) across a 10 000-km longitudinal diversity gradient in the west-central Pacific Ocean. When α diversity was regressed on γ diversity, the slopes, and thus community similarity, increased with scale (0.085, 0.261, and 0.407, respectively) because a greater proportion of γ diversity was subsumed within α diversity as scale increased. Using standard randomization methods, we also examined how community similarity differed between observed and randomized assemblages and how this difference was affected by spatial separation of species within habitat types and specialization of species to three habitat types (reef flats, crests, and slopes). If spatial separation within habitat types and/or habitat specialization (i.e., underdispersion) occurs, fewer species are shared among assemblages than the random expectation. When the locations of individual coral colonies were randomized within and among habitat types, community similarity was 46–47% higher than that for observed assemblages at all three scales. We predicted that spatial separation of coral species within habitat types should increase with scale due to dispersal/extinction dynamics in this insular system, but that specialization of species to different habitat types should not change because habitat differences do not change with scale. However, neither habitat specialization nor spatial separation within habitat types differed among scales. At the two larger scales, each accounted for 22–24% of the difference in community similarity between observed and randomized assemblages. At the smallest scale (transect–site), neither spatial separation within habitat types nor habitat specialization had significant effects on community similarity, probably due to the small size of transect samples. The results suggest that coral species can disperse among islands in an island group as easily as they can among sites on an island over time scales that are relevant to their establishment and persistence on reefs

Annotated Computer Output for Analyses of Unbalanced Data: SAS GLM

41 pages, 1 article*Annotated Computer Output for Analyses of Unbalanced Data: SAS GLM* (Searle, S. R.; Henderson, H. V.) 41 page

On Deriving the Inverse of a Sum of Matrices

21 pages, 1 article*On Deriving the Inverse of a Sum of Matrices* (Henderson, H. V.; Searle, S. R.) 21 page

Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction

The $A + B\to 0$ diffusion-limited reaction, with equal initial densities $a(0) = b(0) = n_0$, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimension $d > 2$ an effective theory is derived, from which the density and correlation functions can be calculated. We find the density decays in time as a,b \sim C\sqrt{\D}(Dt)^{-d/4} for $d < 4$, with \D = n_0-C^\prime n_0^{d/2} + \dots, where $C$ is a universal constant, and $C^\prime$ is non-universal. The calculation is extended to the case of unequal diffusion constants $D_A \neq D_B$, resulting in a new amplitude but the same exponent. For $d \le 2$ a controlled calculation is not possible, but a heuristic argument is presented that the results above give at least the leading term in an $\epsilon = 2-d$ expansion. Finally, we address reaction zones formed in the steady-state by opposing currents of $A$ and $B$ particles, and derive scaling properties.Comment: 17 pages, REVTeX, 13 compressed figures, included with epsf. Eq. (6.12) corrected, and a moderate rewriting of the introduction. Accepted for publication in J. Stat. Phy

Anomalous self-diffusion in the ferromagnetic Ising chain with Kawasaki dynamics

We investigate the motion of a tagged spin in a ferromagnetic Ising chain evolving under Kawasaki dynamics. At equilibrium, the displacement is Gaussian, with a variance growing as $A t^{1/2}$. The temperature dependence of the prefactor $A$ is derived exactly. At low temperature, where the static correlation length $\xi$ is large, the mean square displacement grows as $(t/\xi^2)^{2/3}$ in the coarsening regime, i.e., as a finite fraction of the mean square domain length. The case of totally asymmetric dynamics, where $(+)$ (resp. $(-)$) spins move only to the right (resp. to the left), is also considered. In the steady state, the displacement variance grows as $B t^{2/3}$. The temperature dependence of the prefactor $B$ is derived exactly, using the Kardar-Parisi-Zhang theory. At low temperature, the displacement variance grows as $t/\xi^2$ in the coarsening regime, again proportionally to the mean square domain length.Comment: 22 pages, 8 figures. A few minor changes and update

Large magnetic anisotropy in Ferrihydrite nanoparticles synthesized from reverse micelles

Six-line ferrihydrite(FH) nanoparticles have been synthesized in the core of reverse micelles, used as nanoreactors to obtain average particle sizes $$ $\approx$ 2 to 4 nm. The blocking temperatures $T_B^m$ extracted from magnetization data increased from $\approx 10$ to 20 K for increasing particle size. Low-temperature \MOS measurements allowed to observe the onset of differentiated contributions from particle core and surface as the particle size increases. The magnetic properties measured in the liquid state of the original emulsion showed that the \FH phase is not present in the liquid precursor, but precipitates in the micelle cores after the free water is freeze-dried. Systematic susceptibility \chi_{ac}(\emph{f},T) measurements showed the dependence of the effective magnetic anisotropy energies $E_{a}$ with particle volume, and yielded an effective anisotropy value of $K_{eff} = 312\pm10$ kJ/m$^3$.Comment: 8 pages, 10 figures. Nanotechnology, v17 (Nov. 2006) In pres