Sentence examples for random planar from inspiring English sources

He also has an interest in probability, and has worked on scaling limits of random planar maps.

A random planar map is a canonical model for a discrete random surface which is studied in probability, combinatorics, mathematical physics, and geometry.

The sampling is based on a vertical uniform random planar section.

Namely, we prove that the random planar map converges in the scaling limit to Liouville quantum gravity under a discrete conformal embedding which we call the Cardy embedding.

Liouville quantum gravity (LQG) is a model for a random surface which is the proven or conjectured scaling limit of discrete surfaces known as random planar maps (RPM).

In digital cartography, the automatic generation of random planar patterns and symbols is still an ongoing challenge.

The model calculations are carried out in terms of three basic molecular orientation modes, i.e. uniaxial, random, and planar orientation modes.

Olson (2008) and Olson and Dahi-Taleghani (2009) presented a pseudo-three-dimensional complex fracture network model based on the displacement discontinuity method, which considered the injection of non-Newtonian fluids, Carter filtration, random non-planar propagation and fracture height extension in three layers.

However, some have concluded this without statistical evaluations, and others have compared observed structure to globally random rather than planar models.

Fibre junctions were created in a planar random alumina fibre array by (a) sintering, (b) phosphoric acid treatment, (c) phosphoric acid/aluminium hydroxide (P/Al) treatment and (d) infiltration with alumina powder and sintering.

The numerical analysis performed here, using a finite element network model, provides a number of important results regarding the evolution of micro fractures in planar random fiber networks where the only active microscopic fracture mechanism is bond fracture.