270 citations · 657 across the 20 of their papers we have counts for
20 papers
Variational Pattern Selection
Mark Mineev-Weinstein, Oleg Alekseev
We address pattern selection problems in nonlinear interface dynamics by maximizing the entropy of the most probable (classical) scenario associated with the processes. This variat…
Bubble dynamics in a Hele-Shaw channel and velocity selection without surface tension
Giovani L. Vasconcelos, Luan P. Cordeiro, Arthur A. Brum +1
Inviscid bubble dynamics in a viscous fluid, moving with velocity far from the bubble, is considered. The Cauchy problem of recovering the bubble evolution from its initial sha…
Statistical mechanics of stochastic growth phenomena
Oleg Alekseev, Mark Mineev-Weinstein
We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth…
Theory of stochastic Laplacian growth
Oleg Alekseev, Mark Mineev-Weinstein
We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple co…
Stochastic Laplacian growth
Oleg Alekseev, Mark Mineev-Weinstein
A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all p…
Multiple bubble dynamics and velocity selection in Laplacian growth without surface tension
Mark Mineev-Weinstein, Giovani L. Vasconcelos
A new selection phenomenon in nonlinear interface dynamics is predicted. A generic class of exact regular unsteady multi-bubble solutions in a Hele-Shaw cell is presented. These so…