87 citations · 1.4k across the 71 of their papers we have counts for
4 papers · 1 filter
Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity
E. Katzav, S. Nechaev, O. Vasilyev
We report some new observation concerning the statistics of Longest Increasing Subsequences (LIS). We show that the expectation of LIS, its variance, and apparently the full distri…
Fracture surfaces of heterogeneous materials: a 2D solvable model
E. Katzav, M. Adda-Bedia, B. Derrida
Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a…
Theory of dynamic crack branching in brittle materials
E. Katzav, M. Adda-Bedia, R. Arias
The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics ap…
Roughness of tensile crack fronts in heterogenous materials
E. Katzav, M. Adda--Bedia
The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysi…