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

Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model

The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an annihilation process has not occurred at a given site has the asymptotic form $P(t) -> const + t^{-\theta}$, where $\theta$ is the persistence exponent (``type I persistence''). We argue that, for a density of particles $\rho >> 1$, this non-trivial exponent is identical to that governing the persistence properties of the one-dimensional diffusion equation, where $\theta \approx 0.1207$. In the case of an initially low density, $\rho_0 << 1$, we find $\theta \approx 1/4$ asymptotically. The probability that a site remains unvisited by any random walker (``type II persistence'') is also investigated and found to decay with a stretched exponential form, $P(t) \sim \exp(-const \rho_0^{1/2}t^{1/4})$, provided $\rho_0 << 1$. A heuristic argument for this behavior, based on an exactly solvable toy model, is presented.Comment: 11 RevTeX pages, 19 EPS figure

Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems

We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems. We first investigate the physical origin of universality in these systems, before comparing RG methods to other available analytic techniques, including exact solutions and Smoluchowski-type approximations. Starting from the microscopic reaction-diffusion master equation, we then pedagogically detail the mapping to a field theory for the single-species reaction k A -> l A (l < k). We employ this particularly simple but non-trivial system to introduce the field-theoretic RG tools, including the diagrammatic perturbation expansion, renormalization, and Callan-Symanzik RG flow equation. We demonstrate how these techniques permit the calculation of universal quantities such as density decay exponents and amplitudes via perturbative eps = d_c - d expansions with respect to the upper critical dimension d_c. With these basics established, we then provide an overview of more sophisticated applications to multiple species reactions, disorder effects, L'evy flights, persistence problems, and the influence of spatial boundaries. We also analyze field-theoretic approaches to nonequilibrium phase transitions separating active from absorbing states. We focus particularly on the generic directed percolation universality class, as well as on the most prominent exception to this class: even-offspring branching and annihilating random walks. Finally, we summarize the state of the field and present our perspective on outstanding problems for the future.Comment: 10 figures include

Sport, War and Democracy in Classical Athens

This article concerns the paradox of athletics in classical Athens. Democracy may have opened up politics to every class of Athenian but it had little impact on sporting participation. The city’s athletes continued to drawn predominantly from the upper class. It comes as a surprise then that lower-class Athenians actually esteemed athletes above every other group in the public eye, honoured them very generously when they won, and directed a great deal of public and private money to sporting competitions and facilities. In addition athletics escaped the otherwise persistent criticism of upper-class activities in the popular culture of the democracy. The research of social scientists on sport and aggression suggests this paradox may have been due to the cultural overlap between athletics and war under the Athenian democracy. The article concludes that the practical and ideological democratization of war by classical Athens legitimized and supported upper-class sport

Search for pair-produced scalar and vector leptoquarks decaying into third-generation quarks and first- or second-generation leptons in pp collisions with the ATLAS detector

Abstract A search for pair-produced scalar and vector leptoquarks decaying into quarks and leptons of different generations is presented. It uses the full LHC Run 2 (2015–2018) data set of 139 fb −1 collected with the ATLAS detector in proton–proton collisions at a centre-of-mass energy of s $$\sqrt{s}$$ = 13 TeV. Scalar leptoquarks with charge −(1/3)e as well as scalar and vector leptoquarks with charge +(2/3)e are considered. All possible decays of the pair-produced leptoquarks into quarks of the third generation (t, b) and charged or neutral leptons of the first or second generation (e, μ, ν) with exactly one electron or muon in the final state are investigated. No significant deviations from the Standard Model expectation are observed. Upper limits on the production cross-section are provided for eight models as a function of the leptoquark mass and the branching ratio of the leptoquark into the charged or neutral lepton. In addition, lower limits on the leptoquark masses are derived for all models across a range of branching ratios. Two of these models have the goal of providing an explanation for the recent B-anomalies. In both models, a vector leptoquark decays into charged and neutral leptons of the second generation with a similar branching fraction. Lower limits of 1980 GeV and 1710 GeV are set on the leptoquark mass for these two models