The sweeping rate in diffusion-mediated reactions on dust grain surfaces

A prominent chemical reaction in interstellar clouds is the formation of molecular hydrogen by recombination, which essentially takes place on dust grain surfaces. Analytical approaches to model such a system have hitherto neglected the spatial aspects of the problem by employing a simplistic version of the sweeping rate of reactants. We show how these aspects can be accounted for by a consistent definition of the sweeping rate, and calculate it exactly for a spherical grain. Two regimes can be identified: Small grains, on which two reactants almost surely meet, and large grains, where this is very unlikely. We compare the true sweeping rate to the conventional approximation and find a characteristic reduction in both regimes, most pronounced for large grains. These effects can be understood heuristically using known results from the analysis of two-dimensional random walks. We finally examine the influence of using the true sweeping rate in the calculation of the efficiency of hydrogen recombination: For fixed temperature, the efficiency can be reduced considerably, and relative to that, small grains gain in importance, but the temperature window in which recombination is efficient is not changed substantially.Comment: 10 pages, 6 figure

Symmetry analysis of magneto-optical effects: The case of x-ray diffraction and x-ray absorption at the transition metal L23 edge

A general symmetry analysis of the optical conductivity or scattering tensor is used to rewrite the conductivity tensor as a sum of fundamental spectra multiplied by simple functions depending on the local magnetization direction. Using this formalism, we present several numerical examples at the transition metal L23 edge. From these numerical calculations we can conclude that large deviations from the magneto-optical effects in spherical symmetry are found. These findings are in particular important for resonant x-ray diffraction experiments where the polarization dependence and azimuthal dependence of the scattered Bragg intensity is used to determine the local ordered magnetization direction

Magnetic coupling in highly-ordered NiO/Fe3O4(110): Ultrasharp magnetic interfaces vs. long-range magnetoelastic interactions

We present a laterally resolved X-ray magnetic dichroism study of the magnetic proximity effect in a highly ordered oxide system, i.e. NiO films on Fe3O4(110). We found that the magnetic interface shows an ultrasharp electronic, magnetic and structural transition from the ferrimagnet to the antiferromagnet. The monolayer which forms the interface reconstructs to NiFe2O4 and exhibits an enhanced Fe and Ni orbital moment, possibly caused by bonding anisotropy or electronic interaction between Fe and Ni cations. The absence of spin-flop coupling for this crystallographic orientation can be explained by a structurally uncompensated interface and additional magnetoelastic effects

Adaptation dynamics of the quasispecies model

We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen's model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a {\it quasispecies} which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.Comment: Proceedings of Statphys conference at IIT Guwahati, to be published in Praman

Morphological stability of electromigration-driven vacancy islands

The electromigration-induced shape evolution of two-dimensional vacancy islands on a crystal surface is studied using a continuum approach. We consider the regime where mass transport is restricted to terrace diffusion in the interior of the island. In the limit of fast attachment/detachment kinetics a circle translating at constant velocity is a stationary solution of the problem. In contrast to earlier work [O. Pierre-Louis and T.L. Einstein, Phys. Rev. B 62, 13697 (2000)] we show that the circular solution remains linearly stable for arbitrarily large driving forces. The numerical solution of the full nonlinear problem nevertheless reveals a fingering instability at the trailing end of the island, which develops from finite amplitude perturbations and eventually leads to pinch-off. Relaxing the condition of instantaneous attachment/detachment kinetics, we obtain non-circular elongated stationary shapes in an analytic approximation which compares favorably to the full numerical solution.Comment: 12 page

Accurate rate coefficients for models of interstellar gas-grain chemistry

The methodology for modeling grain-surface chemistry has been greatly improved by taking into account the grain size and fluctuation effects. However, the reaction rate coefficients currently used in all practical models of gas-grain chemistry are inaccurate by a significant amount. We provide expressions for these crucial rate coefficients that are both accurate and easy to incorporate into gas-grain models. We use exact results obtained in earlier work, where the reaction rate coefficient was defined by a first-passage problem, which was solved using random walk theory. The approximate reaction rate coefficient presented here is easy to include in all models of interstellar gas-grain chemistry. In contrast to the commonly used expression, the results that it provides are in perfect agreement with detailed kinetic Monte Carlo simulations. We also show the rate coefficient for reactions involving multiple species.Comment: 4 pages, 2 figure

Clonal interference and Muller's ratchet in spatial habitats

Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones. Recent theoretical studies have pointed out that the resulting fitness dynamics is analogous to a surface growth process, where new layers nucleate and spread stochastically, leading to the build up of scale-invariant roughness. This scenario differs qualitatively from the standard view of adaptation in that the speed of adaptation becomes independent of population size while the fitness variance does not. Here we exploit recent progress in the understanding of surface growth processes to obtain precise predictions for the universal, non-Gaussian shape of the fitness distribution for one-dimensional habitats, which are verified by simulations. When the mutations are deleterious rather than beneficial the problem becomes a spatial version of Muller's ratchet. In contrast to the case of well-mixed populations, the rate of fitness decline remains finite even in the limit of an infinite habitat, provided the ratio $U_d/s^2$ between the deleterious mutation rate and the square of the (negative) selection coefficient is sufficiently large. Using again an analogy to surface growth models we show that the transition between the stationary and the moving state of the ratchet is governed by directed percolation

Numerical Method for Accessing the Universal Scaling Function for a Multi-Particle Discrete Time Asymmetric Exclusion Process

In the universality class of the one dimensional Kardar-Parisi-Zhang surface growth, Derrida and Lebowitz conjectured the universality of not only the scaling exponents, but of an entire scaling function. Since Derrida and Lebowitz's original publication [PRL 80 209 (1998)] this universality has been verified for a variety of continuous time, periodic boundary systems in the KPZ universality class. Here, we present a numerical method for directly examining the entire particle flux of the asymmetric exclusion process (ASEP), thus providing an alternative to more difficult cumulant ratios studies. Using this method, we find that the Derrida-Lebowitz scaling function (DLSF) properly characterizes the large system size limit (N-->infty) of a single particle discrete time system, even in the case of very small system sizes (N <= 22). This fact allows us to not only verify that the DLSF properly characterizes multiple particle discrete-time asymmetric exclusion processes, but also provides a way to numerically solve for quantities of interest, such as the particle hopping flux. This method can thus serve to further increase the ease and accessibility of studies involving even more challenging dynamics, such as the open boundary ASEP

Statistics of turbulence in the energy-containing range of Taylor-Couette compared to canonical wall-bounded flows

Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva \textit{et al.} (\textit{J. Fluid Mech.}, vol. 823,2017, pp. 498-510) observed that remarkably the \textit{large-scale} (energy-containing range) statistics in canonical wall bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor-Couette flow. In doing so, we find that also the transversal structure function of the spanwise velocity component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached eddy contributions. By taking the effect of streamwise alignment into account, the attached eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS-framework --- both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high-Reynolds number data are currently available.Comment: accepted in J. Fluid Mec