TY - JOUR

T1 - Stochastic interface dynamics in the Hele-Shaw cell

AU - Alekseev, Oleg

PY - 2019/7/22

Y1 - 2019/7/22

N2 - A one-parametric stochastic regularized dynamics of the interface in the Hele-Shaw cell is introduced. The short-distance regularization suggested by the aggregation model stabilizes the growth by preventing the formation of cusps at the interface and makes the interface dynamics chaotic. The introduced stochastic growth process generates universal complex patterns with the well-developed fjords of oil separating the fingers of water. In a long time asymptotic, by coupling a conformal field theory to the stochastic growth process, we introduce a set of observables (the martingales), whose expectation values are constant in time. The martingales are closely connected to degenerate representations of the Virasoro algebra and can be written in terms of conformal correlation functions. A direct link between Laplacian growth and conformal Liouville field theory with the central charge c≥25 is proposed.

AB - A one-parametric stochastic regularized dynamics of the interface in the Hele-Shaw cell is introduced. The short-distance regularization suggested by the aggregation model stabilizes the growth by preventing the formation of cusps at the interface and makes the interface dynamics chaotic. The introduced stochastic growth process generates universal complex patterns with the well-developed fjords of oil separating the fingers of water. In a long time asymptotic, by coupling a conformal field theory to the stochastic growth process, we introduce a set of observables (the martingales), whose expectation values are constant in time. The martingales are closely connected to degenerate representations of the Virasoro algebra and can be written in terms of conformal correlation functions. A direct link between Laplacian growth and conformal Liouville field theory with the central charge c≥25 is proposed.

KW - DIFFUSION-LIMITED AGGREGATION

KW - FLOWS

UR - http://www.scopus.com/inward/record.url?scp=85069804470&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.100.012130

DO - 10.1103/PhysRevE.100.012130

M3 - Article

C2 - 31499909

AN - SCOPUS:85069804470

VL - 100

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

M1 - 012130

ER -