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Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electromigration. Both continuous and stochastic dynamics are described by generalizing conformal-mapping techniques for viscous fingering and diffusion-limited aggregation,(More)
The method of iterated conformal maps for the study of diffusion limited aggregates (DLA) is generalized to the study of Laplacian growth patterns and related processes. We emphasize the fundamental difference between these processes: DLA is grown serially with constant size particles, while Laplacian patterns are grown by advancing each boundary point in(More)
We study dense colloidal crystals under oscillatory shear using a confocal microscope. At large strains the crystals yield and the suspensions form shear bands. The pure harmonic response exhibited by the suspension rules out the applicability of nonlinear rheology models typically used to describe shear banding in other types of complex fluids. Instead, we(More)
Diffusion limited aggregation ͑DLA͒ is a model of fractal growth that had attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. We present a convergent calculation of the fractal dimension D of DLA based on a renormalization scheme for the first Laurent coefficient of the conformal map from(More)
We study the relation between stochastic and continuous transport-limited growth models. We derive a nonlinear integro-differential equation for the average shape of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation. Focusing on the advection-diffusion-limited aggregation (ADLA) model, we show that the average(More)
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of wrinkles in these problems has important implications in design and is an area of increasing interest in the fields of physics(More)
The linear dynamics of ion sputtered solids is essential to understanding the evolution of ordered and disordered surface patterns. We review the existing models of linear dynamics and point out qualitative discrepancies between theory and experimental observations that characterize the linear regime. In particular, we emphasize the importance of(More)
Colloidal silica gels are shown to stiffen with time, as demonstrated by both dynamic light scattering and bulk rheological measurements. Their elastic moduli increase as a power law with time, independent of particle volume fraction; however, static light scattering indicates that there are no large-scale structural changes. We propose that increases in(More)
Diffusion-limited aggregation (DLA) and its variants provide the simplest models of fractal patterns, such as colloidal clusters, electrodeposits, and lightning strikes. The original model involves random walkers sticking to a growing cluster, 1 but recently DLA (in the plane) has been reformu-lated in terms of stochastic conformal maps. 2 This fruitful new(More)