Zero tension Kardar-Parisi-Zhang equation in (d+1)- Dimensions

Abstract

The joint probability distribution function (PDF) of the height and its gradients is derived for a zero tension $d+1$-dimensional Kardar-Parisi-Zhang (KPZ) equation. It is proved that the height`s PDF of zero tension KPZ equation shows lack of positivity after a finite time $t_c$. The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale $t_c$ and the singularity time scale $t_{c,\nu \to 0}$ of the KPZ equation with an infinitesimal surface tension is investigated.

18 pages, 8 figures

References in corpus (4)

• Percolation, Morphogenesis, and Burgers Dynamics in Blood Vessels Formation
• Reconstruction of the early Universe as a convex optimization problem
• Topological Shocks in Burgers Turbulence
• Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension

Cited by in corpus (4)

• Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation
• Level Crossing Analysis of Burgers Equation in 1+1 Dimensions
• Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces
• Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree