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In deposition with a poisoning species, we show that the transition to a blocked or pinned phase may be viewed as an absorbing transition in the directed percolation (DP) class. We consider a ballistic-like deposition model with an active…
Recent experiments have illuminated a remarkable growth mechanism of rod-shaped bacteria: proteins associated with cell wall extension move at constant velocity in circles oriented approximately along the cell circumference (Garner et al.,…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
Bootstrap percolation is a wide class of monotone cellular automata with random initial state. In this work we develop tools for studying in full generality one of the three `universality' classes of bootstrap percolation models in two…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
The main contribution of this paper is the development of a novel approach to multi-scale analysis that we believe can be used to analyse processes with non-equilibrium dynamics. Our approach will be referred to as \emph{multi-scale…
We investigate the time evolution of an initial step profile separating a bare substrate region from the rest of the compressively strained adsorbate layer near a commensurate to incommensurate transition. The rate of profile evolution as a…
As an introductory lecture to the workshop an overview is given over continuum models for homoepitaxial surface growth using partial differential equations (PDEs). Their {\em heuristic derivation} makes use of inherent symmetries in the…
Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a…
Next to the directed percolation (DP) universality class, parity conserving directed percolation (pcDP; also called parity conserving branching annihilating random walks, pcBARW) is the second-most important model with an absorbing state…
The transition to turbulence is characterized by an abrupt loss of order and predictability, featuring the intermittent proliferation and decay of localized turbulent structures. En-route to becoming fully turbulent, surprisingly order…
Replacement reactions during fluid infiltration into porous media, rocks and buildings are known to have important implications for reservoir development, ore formation as well as weathering. Natural observations and experiments have shown…
We consider a lattice of coupled circle maps, a model arising naturally in descriptions of solid state phenomena such as Josephson junction arrays. We find that the onset of spatiotemporal intermittency (STI) in this system is analogous to…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
We analyze the properties of Degree-Ordered Percolation (DOP), a model in which the nodes of a network are occupied in degree-descending order. This rule is the opposite of the much studied degree-ascending protocol, used to investigate…
We study the implications of coupling Langmuir kinetics (LK) process with the dynamics of an extending lattice. The model that we consider couples dynamically extending exclusion process (DEEP) with the process of random attachment and…
Understanding plastic deformation of crystals in terms of the fundamental physics of dislocations has remained a grand challenge in materials science for decades. To overcome this, the Discrete Dislocation Dynamics (DDD) method has been…
We study a class of minimal geometric partial differential equations that serves as a framework to understand the evolution of boundaries between states in different pattern forming systems. The framework combines normal growth, curvature…
We have studied the percolation behaviour of deposits for different (2+1)-dimensional models of surface layer formation. The mixed model of deposition was used, where particles were deposited selectively according to the random (RD) and…
The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an…