147 citations · 706 across the 20 of their papers we have counts for
21 papers
Monte Carlo sampling for stochastic weight functions
Daan Frenkel, K. Julian Schrenk, Stefano Martiniani
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number,…
Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming
Stefano Martiniani, K. Julian Schrenk, Kabir Ramola +2
In the late 1980s, Sam Edwards proposed a possible statistical-mechanical framework to describe the properties of disordered granular materials. A key assumption underlying the the…
Structural analysis of high-dimensional basins of attraction
Stefano Martiniani, K. Julian Schrenk, Jacob D. Stevenson +2
We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the int…
Critical fragmentation properties of random drilling: How many random holes need to be drilled to collapse a wooden cube?
K. J. Schrenk, M. R. Hilário, V. Sidoravicius +4
A solid wooden cube fragments into pieces as we sequentially drill holes through it randomly. This seemingly straightforward observation encompasses deep and nontrivial geometrical…
Evidence for non-ergodicity in quiescent states of periodically sheared suspensions
K. Julian Schrenk, Daan Frenkel
We present simulations of an equilibrium statistical-mechanics model that uniformly samples the space of quiescent states of a periodically sheared suspension. In our simulations,…
Turning intractable counting into sampling: computing the configurational entropy of three-dimensional jammed packings
Stefano Martiniani, K. Julian Schrenk, Jacob D. Stevenson +2
We report a numerical calculation of the total number of disordered jammed configurations of repulsive, three-dimensional spheres in a fixed volume . To make these calcu…
Schramm-Loewner Evolution and isoheight lines of correlated landscapes
N. Pose, K. J. Schrenk, N. A. M. Araujo +1
Real landscapes are usually characterized by long-range height-height correlations, which are quantified by the Hurst exponent . We analyze the statistical properties of the iso…
Numerical evaluation of the Gauss hypergeometric function: Implementation and application to Schramm-Loewner evolution
K. J. Schrenk, J. D. Stevenson
Numerical studies of fractal curves in the plane often focus on subtle geometrical properties such as their left passage probability. Schramm-Loewner evolution (SLE) is a mathemati…
Watersheds in disordered media
N. A. M. Araújo, K. J. Schrenk, H. J. Herrmann +1
What is the best way to divide a rugged landscape? Since ancient times, watersheds separating adjacent water systems that flow, for example, toward different seas, have been used t…
Recent advances and open challenges in percolation
N. A. M. Araújo, P. Grassberger, B. Kahng +2
Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related…
Retention capacity of correlated surfaces
K. J. Schrenk, N. A. M. Araujo, R. M. Ziff +1
We extend the water retention model [C. L. Knecht et al., Phys. Rev. Lett. 108, 045703 (2012)] to correlated random surfaces. We find that the retention capacity of discrete random…
Shortest path and Schramm-Loewner Evolution
N. Posé, K. J. Schrenk, N. A. M. Araújo +1
We numerically show that the statistical properties of the shortest path on critical percolation clusters are consistent with the ones predicted for Schramm-Loewner evolution (SLE)…
Percolation with long-range correlated disorder
K. J. Schrenk, N. Pose, J. J. Kranz +3
Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as function of the Hurst exponent…
Stacked triangular lattice: Percolation properties
K. J. Schrenk, N. A. M. Araujo, H. J. Herrmann
The stacked triangular lattice has the shape of a triangular prism. In spite of being considered frequently in solid state physics and materials science, its percolation properties…
Watersheds are Schramm-Loewner Evolution curves
E. Daryaei, N. A. M. Araujo, K. J. Schrenk +2
We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter . Several numerical e…
How to share underground reservoirs
K. J. Schrenk, N. A. M. Araújo, H. J. Herrmann
Many resources, such as oil, gas, or water, are extracted from porous soils and their exploration is often shared among different companies or nations. We show that the effective s…
Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines
E. Fehr, K. J. Schrenk, N. A. M. Araújo +4
We study the corrections to scaling for the mass of the watershed, the bridge line, and the optimal path crack in two and three dimensions. We disclose that these models have numer…
Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
K. J. Schrenk, A. Felder, S. Deflorin +3
The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms, 25, 432 (2004)] and recently investigated in the framework of discontinuous percolation by Chen…
Gaussian model of explosive percolation in three and higher dimensions
K. J. Schrenk, N. A. M. Araújo, H. J. Herrmann
The Gaussian model of discontinuous percolation, recently introduced by Araújo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions,…
Fracturing ranked surfaces
K. J. Schrenk, N. A. M. Araujo, J. S. Andrade +1
Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially a…
Optimal path cracks in correlated and uncorrelated lattices
E. A. Oliveira, K. J. Schrenk, N. A. M. Araújo +2
The optimal path crack model on uncorrelated surfaces, recently introduced by Andrade et al. (Phys. Rev. Lett. 103, 225503, 2009), is studied in detail and its main percolation exp…