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The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling exponents crucially differ from the expected KPZ values, the source of this disagreement has remained poorly understood. We have performed growth experiments with B. subtilis 168 and E. coli ATCC 25922 under conditions leading to compact colonies in the classically-alleged Eden regime, where individual motility is suppressed. Non-KPZ scaling is indeed observed for all accessible times, KPZ asymptotics being ruled out for our experiments due to the monotonic increase of front branching with time. Simulations of an effective model suggest the occurrence of transient non-universal scaling due to diffusive morphological instabilities, agreeing with expectations from detailed models of the relevant biological reaction-diffusion processes.

Cyanobacteria forming one-dimensional filaments are paradigmatic model organisms of the transition between unicellular and multicellular living forms. Under nitrogen limiting conditions, in filaments of the genus Anabaena, some cells differentiate into heterocysts, which lose the possibility to divide but are able to fix environmental nitrogen for the colony. These heterocysts form a quasi-regular pattern in the filament, representing a prototype of patterning and morphogenesis in prokaryotes. Recent years have seen advances in the identification of the molecular mechanism regulating this pattern. We use this data to build a theory on heterocyst pattern formation, for which both genetic regulation and the effects of cell division and filament growth are key components. The theory is based on the interplay of three generic mechanisms: local autoactivation, early long range inhibition, and late long range inhibition. These mechanisms can be identified with the dynamics of hetR, patS and hetN expression. Our theory reproduces quantitatively the experimental dynamics of pattern formation and maintenance for wild type and mutants. We find that hetN alone is not enough to play the role as the late inhibitory mechanism: a second mechanism, hypothetically the products of nitrogen fixation supplied by heterocysts, must also play a role in late long range inhibition. The preponderance of even intervals between heterocysts arises naturally as a result of the interplay between the timescales of genetic regulation and cell division. We also find that a purely stochastic initiation of the pattern, without a two-stage process, is enough to reproduce experimental observations.

Ion Beam Sputtering (IBS) is a cost-effective technique able to produce ordered nanopatterns on the surfaces of different materials. To date, most theoretical studies of this process have focused on systems which become amorphous under irradiation, e.g. semiconductors at room temperature. Thus, in spite of the large amount of experimental work on metals, or more recently on semiconductors at high temperatures, such experimental contexts have received relatively little theoretical attention. These systems are characterized by transport mechanisms, e.g. surface diffusion, which are anisotropic as a reflection of the crystalline structure not being overruled by the irradiation. Here, we generalize a previous continuum theory of IBS at normal incidence, in order to account for anisotropic surface diffusion. We explore systematically our generalized model in order to understand the role of anisotropy in the space ordering properties of the resulting patterns. In particular, we derive a height equation which predicts morphological transitions among hexagonal and rectangular patterns as a function of system parameters and employ an angular correlation function to assess these pattern symmetries. By suitably choosing experimental conditions, it is found that one might be able to experimentally control the type of order displayed by the patterns produced., Comment: 13 pages, 6 figures; submitted

We study the effect of advection on the aggregation and pattern formation in chemotactic systems described by Keller-Segel type models. The evolution of small perturbations is studied analytically in the linear regime complemented by numerical simulations. We show that a uniform differential flow can significantly alter the spatial structure and dynamics of the chemotactic system. The flow leads to the formation of anisotropic aggregates that move following the direction of the flow, even when the chemotactic organisms are not directly advected by the flow. Sufficiently strong advection can stop the aggregation and coarsening process that is then restricted to the direction perpendicular to the flow.

We propose and study a continuum model for the dynamics of amorphizable surfaces undergoing ion-beam sputtering (IBS) at intermediate energies and oblique incidence. After considering the current limitations of more standard descriptions in which a single evolution equation is posed for the surface height, we overcome (some of) them by explicitly formulating the dynamics of the species that transport along the surface, and by coupling it to that of the surface height proper. In this we follow recent proposals inspired by ``hydrodynamic'' descriptions of pattern formation in aeolian sand dunes and ion-sputtered systems. From this enlarged model, and by exploiting the time-scale separation among various dynamical processes in the system, we derive a single height equation in which coefficients can be related to experimental parameters. This equation generalizes those obtained by previous continuum models and is able to account for many experimental features of pattern formation by IBS at oblique incidence, such as the evolution of the irradiation-induced amorphous layer, transverse ripple motion with non-uniform velocity, ripple coarsening, onset of kinetic roughening and other. Additionally, the dynamics of the full two-field model is compared with that of the effective interface equation., Comment: 23 pages, 14 figures. Movies of figures 6, 7, and 8 available at http://gisc.uc3m.es/~javier/Movies/

The production of nanopatterns on the surfaces of targets irradiated by ion beams at low and intermediate energies has developed during the present decade to a salient degree of control over the main pattern features. However, there is still a wide experimental scatter in the type and relevance of various dynamic interfacial properties induced by this technique as a function of system type and parameters. In parallel, diverse theoretical models exist that differ in their capabilities to reproduce such a wide range of experimental features. We provide an overview of the most recent studies of nanoripple and dot production by ion-beam sputtering, with special attention to the comparison between experiments and (continuum) models, and with a focus on those issues that remain open or, at least, ambiguous. These are perhaps more evident for the case of nanodot patterns on amorphizable targets than for the case of nanoripples due, possibly, to the relative novelty of the former. The pattern properties to be considered are those of potential increased technological importance, such as the variation of nanodot size with parameters like ion energy, target temperature and sputtering time (i.e., fluence), as well as the conditions under which the quality of the pattern order is enhanced, issues such as wavelength coarsening and order enhancement becoming relevant., Comment: To appear in Lecture Notes on Nanoscale Science and Technology, edited by Z. Wang (Springer, Heidelberg)

A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell pattern develops with constant wavelength and amplitude at intermediate distances, while the profile is disordered and rough at larger distances. Moreover, for a wide range of parameters the lateral extent of ordered domains ranges up to tens of cells. This behavior is new in the context of dynamics of surfaces or interfaces with morphological instabilities. We also provide analytical estimates for the stationary pattern wavelength and mean growth velocity.

Erosion by ion-beam sputtering (IBS) of amorphous targets at off-normal incidence frequently produces a (nanometric) rippled surface pattern, strongly resembling macroscopic ripples on aeolian sand dunes. Suitable generalization of continuum descriptions of the latter allows us to describe theoretically for the first time the main nonlinear features of ripple dynamics by IBS, namely, wavelength coarsening and non-uniform propagation velocity, that agree with similar results in experiments and discrete models. These properties are seen to be the anisotropic counterparts of in-plane ordering and (interrupted) pattern coarsening in IBS experiments on rotating substrates and at normal incidence., Comment: 5 pages, 3 figures