Coastal change and hypoxia in the northern Gulf of Mexico: Part I

International audienceThe Committee on Environment and Natural Resources (CENR) has identified the input of nutrient-rich water from the Mississippi/Atchafalaya River Basin (MARB) as the prime cause of hypoxia in the northern Gulf of Mexico and the prime means for its control. A Watershed Nutrient Task Force was formed to solve the hypoxia problem by managing the MARB catchment. However, the hypoxic zone is also experiencing massive physical, hydrological, chemical and biological changes associated with an immense river-switching and delta-building event that occurs here about once a millennium. Coastal change induced hypoxia in the northern Gulf of Mexico prior to European settlement. It is recommended that for further understanding and control of Gulf hypoxia the Watershed Nutrient Task Force adopt a truly holistic environmental approach which includes the full effects of this highly dynamic coastal area

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

Records and sequences of records from random variables with a linear trend

We consider records and sequences of records drawn from discrete time series of the form $X_{n}=Y_{n}+cn$, where the $Y_{n}$ are independent and identically distributed random variables and $c$ is a constant drift. For very small and very large drift velocities, we investigate the asymptotic behavior of the probability $p_n(c)$ of a record occurring in the $n$th step and the probability $P_N(c)$ that all $N$ entries are records, i.e. that $X_1 < X_2 < ... < X_N$. Our work is motivated by the analysis of temperature time series in climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure

Linear theory of unstable growth on rough surfaces

Unstable homoepitaxy on rough substrates is treated within a linear continuum theory. The time dependence of the surface width $W(t)$ is governed by three length scales: The characteristic scale $l_0$ of the substrate roughness, the terrace size $l_D$ and the Ehrlich-Schwoebel length $l_{ES}$. If $l_{ES} \ll l_D$ (weak step edge barriers) and $l_0 \ll l_m \sim l_D \sqrt{l_D/l_{ES}}$, then $W(t)$ displays a minimum at a coverage $\theta_{\rm min} \sim (l_D/l_{ES})^2$, where the initial surface width is reduced by a factor $l_0/l_m$. The r\^{o}le of deposition and diffusion noise is analyzed. The results are applied to recent experiments on the growth of InAs buffer layers [M.F. Gyure {\em et al.}, Phys. Rev. Lett. {\bf 81}, 4931 (1998)]. The overall features of the observed roughness evolution are captured by the linear theory, but the detailed time dependence shows distinct deviations which suggest a significant influence of nonlinearities

Kinetic roughening of surfaces: Derivation, solution and application of linear growth equations

We present a comprehensive analysis of a linear growth model, which combines the characteristic features of the Edwards--Wilkinson and noisy Mullins equations. This model can be derived from microscopics and it describes the relaxation and growth of surfaces under conditions where the nonlinearities can be neglected. We calculate in detail the surface width and various correlation functions characterizing the model. In particular, we study the crossover scaling of these functions between the two limits described by the combined equation. Also, we study the effect of colored and conserved noise on the growth exponents, and the effect of different initial conditions. The contribution of a rough substrate to the surface width is shown to decay universally as $w_i(0) (\xi_s/\xi(t))^{d/2}$, where $\xi(t) \sim t^{1/z}$ is the time--dependent correlation length associated with the growth process, $w_i(0)$ is the initial roughness and $\xi_s$ the correlation length of the substrate roughness, and $d$ is the surface dimensionality. As a second application, we compute the large distance asymptotics of the height correlation function and show that it differs qualitatively from the functional forms commonly used in the intepretation of scattering experiments.Comment: 28 pages with 4 PostScript figures, uses titlepage.sty; to appear in Phys. Rev.

Coarsening of Sand Ripples in Mass Transfer Models with Extinction

Coarsening of sand ripples is studied in a one-dimensional stochastic model, where neighboring ripples exchange mass with algebraic rates, $\Gamma(m) \sim m^\gamma$, and ripples of zero mass are removed from the system. For $\gamma < 0$ ripples vanish through rare fluctuations and the average ripples mass grows as \avem(t) \sim -\gamma^{-1} \ln (t). Temporal correlations decay as $t^{-1/2}$ or $t^{-2/3}$ depending on the symmetry of the mass transfer, and asymptotically the system is characterized by a product measure. The stationary ripple mass distribution is obtained exactly. For $\gamma > 0$ ripple evolution is linearly unstable, and the noise in the dynamics is irrelevant. For $\gamma = 1$ the problem is solved on the mean field level, but the mean-field theory does not adequately describe the full behavior of the coarsening. In particular, it fails to account for the numerically observed universality with respect to the initial ripple size distribution. The results are not restricted to sand ripple evolution since the model can be mapped to zero range processes, urn models, exclusion processes, and cluster-cluster aggregation.Comment: 10 pages, 8 figures, RevTeX4, submitted to Phys. Rev.

Evolutionary trajectories in rugged fitness landscapes

We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the most populated genotype \textit{jumps} from a local fitness maximum to another and eventually reaches the global maximum. We use a strong selection limit, which reduces the dynamics beyond the first time step to the competition between independent mutant subpopulations, to study the dynamics of this model and of a simpler one-dimensional model which ignores the geometry of the sequence space. We find that the fit genotypes that appear along a trajectory are a subset of suitably defined fitness \textit{records}, and exploit several results from the record theory for non-identically distributed random variables. The genotypes that contribute to the trajectory are those records that are not \textit{bypassed} by superior records arising further away from the initial population. Several conjectures concerning the statistics of bypassing are extracted from numerical simulations. In particular, for the one-dimensional model, we propose a simple relation between the bypassing probability and the dynamic exponent which describes the scaling of the typical evolution time with genome size. The latter can be determined exactly in terms of the extremal properties of the fitness distribution.Comment: Figures in color; minor revisions in tex

Records in a changing world

In the context of this paper, a record is an entry in a sequence of random variables (RV's) that is larger or smaller than all previous entries. After a brief review of the classic theory of records, which is largely restricted to sequences of independent and identically distributed (i.i.d.) RV's, new results for sequences of independent RV's with distributions that broaden or sharpen with time are presented. In particular, we show that when the width of the distribution grows as a power law in time $n$, the mean number of records is asymptotically of order $\ln n$ for distributions with a power law tail (the \textit{Fr\'echet class} of extremal value statistics), of order $(\ln n)^2$ for distributions of exponential type (\textit{Gumbel class}), and of order $n^{1/(\nu+1)}$ for distributions of bounded support (\textit{Weibull class}), where the exponent $\nu$ describes the behaviour of the distribution at the upper (or lower) boundary. Simulations are presented which indicate that, in contrast to the i.i.d. case, the sequence of record breaking events is correlated in such a way that the variance of the number of records is asymptotically smaller than the mean.Comment: 12 pages, 2 figure

Dynamic Scaling in a 2+1 Dimensional Limited Mobility Model of Epitaxial Growth

We study statistical scale invariance and dynamic scaling in a simple solid-on-solid 2+1 - dimensional limited mobility discrete model of nonequilibrium surface growth, which we believe should describe the low temperature kinetic roughening properties of molecular beam epitaxy. The model exhibits long-lived ``transient'' anomalous and multiaffine dynamic scaling properties similar to that found in the corresponding 1+1 - dimensional problem. Using large-scale simulations we obtain the relevant scaling exponents, and compare with continuum theories.Comment: 5 pages, 4 ps figures included, RevTe