Related papers: Coarsening versus pattern formation
Two very basic constructions involving experimental procedures are the formation of coarse-grained versions of experiments, and the formation of branching sequential experiments. The latter allow for the conditioning of states on the…
We study spinodal decomposition and coarsening when initiated by localized disturbances in the Cahn-Hilliard equation. Spatio-temporal dynamics are governed by multi-stage invasion fronts. The first front invades a spinodal unstable…
Many two-phase materials suffer from grain-growth due to the energy cost which is associated with the interface that separates both phases. While our understanding of the driving forces and the dynamics of grain growth in different…
A hierarchical system of equations is introduced to describe dynamics of `sizes' of infinite clusters which coagulate and fragmentate with homogeneous rates of certain form. We prove that this system of equations is solved weakly by…
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
Microcanonical Monte Carlo simulations of a polydisperse soft-spheres model for liquids and colloids have been performed for very large polydispersity, in the region where a phase-separation is known to occur when the system (or part of it)…
Patterns are quotidian in nature. Distinct multiscale patterns are generally a consequence of nonequilibrium dynamical processes associated with mechanical or hydrodynamic instabilities. In this thesis, I report experimental investigations…
In many systems we can describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization…
We studied interplay between kinetic roughening and phase ordering in 1+1 dimensional single-step solid-on-solid growth model with two kinds of particles and Ising-like interaction. Evolution of both geometrical and compositional properties…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the commutativity of a larger class of diagrams. In the…
The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial…
This Article presents a nonequilibrium thermodynamic theory for the mean-field precipitation, aggregation and pattern formation of colloidal clusters. A variable gradient energy coefficient and the arrest of particle diffusion upon…
Normal modes provide a fundamental basis for understanding crucial properties of solids, such as the thermal conductivity, the heat capacity and the sound propagation. While the normal modes are excellently described by plane waves in…
The spontaneous emergence of heterogeneous dislocation patterns is a conspicuous feature of plastic deformation and strain hardening of crystalline solids. Despite long-standing efforts in the materials science and physics of defect…
We introduce a simple model of heterogeneous catalysis on a disordered surface which consists of two types of randomly distributed sites with different adsorption rates. Disorder can create a reactive steady state in situations where the…
The rate of curvature-driven grain growth in polycrystalline materials is well-known to be limited by interface dissipation. We show analytically and by simulations that, for systems forming modulated phases or non-equilibrium patterns with…
The adhesion dynamics of a membrane confined between two permeable walls is studied using a two-dimensional hydrodynamic model. The membrane morphology decomposes into adhesion patches on the upper and the lower walls and obeys a nonlinear…
This paper presents a theoretical model for studying the dynamics of ordering in alloys which exhibit modulated phases. The model is different from the standard time-dependent Ginzburg-Landau description of the evolution of a non-conserved…