Universality in Bacterial Colonies

The emergent spatial patterns generated by growing bacterial colonies have been the focus of intense study in physics during the last twenty years. Both experimental and theoretical investigations have made possible a clear qualitative picture of the different structures that such colonies can exhibit, depending on the medium on which they are growing. However, there are relatively few quantitative descriptions of these patterns. In this paper, we use a mechanistically detailed simulation framework to measure the scaling exponents associated with the advancing fronts of bacterial colonies on hard agar substrata, aiming to discern the universality class to which the system belongs. We show that the universal behavior exhibited by the colonies can be much richer than previously reported, and we propose the possibility of up to four different sub-phases within the medium-to-high nutrient concentration regime. We hypothesize that the quenched disorder that characterizes one of these sub-phases is an emergent property of the growth and division of bacteria competing for limited space and nutrients.Comment: 12 pages, 5 figure

A modified Parametric Forcing Approach for modelling of roughness

Surface roughness in turbulent channel flow is effectively modelled using a modified version of the Parametric Forcing Approach introduced by Busse and Sandham (2012). In this modified approach, the model functions are determined based on the surface geometry and two model constants, whose value can be fine tuned. In addition to a quadratic forcing term, accounting for the effect of form drag due to roughness, a linear forcing term, analogous to the Darcy term in the context of porous media, is employed in order to represent the viscous drag. Comparison of the results with full-geometry resolved Direct Numerical Simulation (DNS) data for the case of dense roughness (frontal solidity ≅0.4) shows a satisfactory prediction of mean velocity profile, and hence the friction factor, by the model. The model is found to be able to reproduce the trends of friction factor with morphological properties of surface such as skewness of the surface height probability density function and coefficient of variation of the peak heights

Roughening of ion-eroded surfaces

Recent experimental studies focusing on the morphological properties of surfaces eroded by ion-bombardment report the observation of self-affine fractal surfaces, while others provide evidence about the development of a periodic ripple structure. To explain these discrepancies we derive a stochastic growth equation that describes the evolution of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters characterizing the sputtering process. Exploring the connection between the ion-sputtering problem and the Kardar-Parisi-Zhang and Kuramoto-Sivashinsky equations, we find that morphological transitions may take place when experimental parameters, such as the angle of incidence of the incoming ions or their average penetration depth, are varied. Furthermore, the discussed methods allow us to calculate analytically the ion-induced surface diffusion coefficient, that can be compared with experiments. Finally, we use numerical simulations of a one dimensional sputtering model to investigate certain aspects of the ripple formation and roughening.Comment: 20 pages, LaTeX, 5 ps figures, contribution to the 4th CTP Workshop on Statistical Physics "Dynamics of Fluctuating Interfaces and Related Phenomena", Seoul National University, Seoul, Korea, January 27-31, 199

Modelling of epitaxial film growth with a Ehrlich-Schwoebel barrier dependent on the step height

The formation of mounded surfaces in epitaxial growth is attributed to the presence of barriers against interlayer diffusion in the terrace edges, known as Ehrlich-Schwoebel (ES) barriers. We investigate a model for epitaxial growth using a ES barrier explicitly dependent on the step height. Our model has an intrinsic topological step barrier even in the absence of an explicit ES barrier. We show that mounded morphologies can be obtained even for a small barrier while a self-affine growth, consistent with the Villain-Lai-Das Sarma equation, is observed in absence of an explicit step barrier. The mounded surfaces are described by a super-roughness dynamical scaling characterized by locally smooth (faceted) surfaces and a global roughness exponent $\alpha>1$. The thin film limit is featured by surfaces with self-assembled three-dimensional structures having an aspect ratio (height/width) that may increase or decrease with temperature depending on the strength of step barrier.Comment: To appear in J. Phys. Cond. Matter; 3 movies as supplementary materia

Intermittency and roughening in the failure of brittle heterogeneous materials

Stress enhancement in the vicinity of brittle cracks makes the macro-scale failure properties extremely sensitive to the micro-scale material disorder. Therefore: (i) Fracturing systems often display a jerky dynamics, so-called crackling noise, with seemingly random sudden energy release spanning over a broad range of scales, reminiscent of earthquakes; (ii) Fracture surfaces exhibit roughness at scales much larger than that of material micro-structure. Here, I provide a critical review of experiments and simulations performed in this context, highlighting the existence of universal scaling features, independent of both the material and the loading conditions, reminiscent of critical phenomena. I finally discuss recent stochastic descriptions of crack growth in brittle disordered media that seem to capture qualitatively - and sometimes quantitatively - these scaling features.Comment: 38 pages, invited review for J. Phys. D cluster issue on "Fracture: from the Atomic to the Geophysics Scale

Optimization algorithms for the solution of the frictionless normal contact between rough surfaces

This paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half-plane using the boundary element method (BEM). After recasting the resulting Linear Complementarity Problem (LCP) as a convex quadratic program (QP) with nonnegative constraints, different optimization algorithms are compared for its solution: (i) a Greedy method, based on different solvers for the unconstrained linear system (Conjugate Gradient CG, Gauss-Seidel, Cholesky factorization), (ii) a constrained CG algorithm, (iii) the Alternating Direction Method of Multipliers (ADMM), and ($iv$) the Non-Negative Least Squares (NNLS) algorithm, possibly warm-started by accelerated gradient projection steps or taking advantage of a loading history. The latter method is two orders of magnitude faster than the Greedy CG method and one order of magnitude faster than the constrained CG algorithm. Finally, we propose another type of warm start based on a refined criterion for the identification of the initial trial contact domain that can be used in conjunction with all the previous optimization algorithms. This method, called Cascade Multi-Resolution (CMR), takes advantage of physical considerations regarding the scaling of the contact predictions by changing the surface resolution. The method is very efficient and accurate when applied to real or numerically generated rough surfaces, provided that their power spectral density function is of power-law type, as in case of self-similar fractal surfaces.Comment: 38 pages, 11 figure