Scaling properties of step bunches induced by sublimation and related mechanisms: A unified perspective

This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching instability takes place when the kinetic length is larger than the average distance between the steps on the vicinal surface. In the opposite limit the instability is weak and step bunching can occur only when the magnitude of step-step repulsion is small. The central result are power law relations of the between the width, the height, and the minimum interstep distance of a bunch. These relations are obtained from a continuum evolution equation for the surface profile, which is derived from the discrete step dynamical equations for. The analysis of the continuum equation reveals the existence of two types of stationary bunch profiles with different scaling properties. Through a mathematical equivalence on the level of the discrete step equations as well as on the continuum level, our results carry over to the problems of step bunching induced by growth with a strong inverse ES effect, and by electromigration in the attachment/detachment limited regime. Thus our work provides support for the existence of universality classes of step bunching instabilities [A. Pimpinelli et al., Phys. Rev. Lett. 88, 206103 (2002)], but some aspects of the universality scenario need to be revised.Comment: 21 pages, 8 figure

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

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

Lonely adatoms in space

There is a close relation between the problems of second layer nucleation in epitaxial crystal growth and chemical surface reactions, such as hydrogen recombination, on interstellar dust grains. In both cases standard rate equation analysis has been found to fail because the process takes place in a confined geometry. Using scaling arguments developed in the context of second layer nucleation, I present a simple derivation of the hydrogen recombination rate for small and large grains. I clarify the reasons for the failure of rate equations for small grains, and point out a logarithmic correction to the reaction rate when the reaction is limited by the desorption of hydrogen atoms (the second order reaction regime)

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

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

Pattern Dynamics of Vortex Ripples in Sand: Nonlinear Modeling and Experimental Validation

Vortex ripples in sand are studied experimentally in a one-dimensional setup with periodic boundary conditions. The nonlinear evolution, far from the onset of instability, is analyzed in the framework of a simple model developed for homogeneous patterns. The interaction function describing the mass transport between neighboring ripples is extracted from experimental runs using a recently proposed method for data analysis, and the predictions of the model are compared to the experiment. An analytic explanation of the wavelength selection mechanism in the model is provided, and the width of the stable band of ripples is measured.Comment: 4 page

Persistence exponents for fluctuating interfaces

Numerical and analytic results for the exponent \theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear Langevin equations. The models are parametrized by the dynamic roughness exponent \beta, with 0 < \beta < 1; for \beta = 1/2 the time evolution is Markovian. Using simulations of solid-on-solid models, of the discretized continuum equations as well as of the associated zero-dimensional stationary Gaussian process, we address two problems: The return of an initially flat interface, and the return to an initial state with fully developed steady state roughness. The two problems are shown to be governed by different exponents. For the steady state case we point out the equivalence to fractional Brownian motion, which has a return exponent \theta_S = 1 - \beta. The exponent \theta_0 for the flat initial condition appears to be nontrivial. We prove that \theta_0 \to \infty for \beta \to 0, \theta_0 \geq \theta_S for \beta 1/2, and calculate \theta_{0,S} perturbatively to first order in an expansion around the Markovian case \beta = 1/2. Using the exact result \theta_S = 1 - \beta, accurate upper and lower bounds on \theta_0 can be derived which show, in particular, that \theta_0 \geq (1 - \beta)^2/\beta for small \beta.Comment: 12 pages, REVTEX, 6 Postscript figures, needs multicol.sty and epsf.st