We study the entanglement properties of the shape phase transitions between different geometric limits of two coupled equivalent molecular benders modeled with the two-dimensional limit of the vibron model. This system has four possible geometric configurations: linear, cis-bent, trans-bent, and nonplanar. We show how the entanglement, accessed through the calculation of the linear entropy, bet...

The Universal B-tree is a data structure for multidimensional data indexing. In this paper we introduce a new algorithm of processing the range query in UB-trees. This algorithm performs very well, especially in high-dimensional indexes and thus significantly reduces influence of the ”curse of dimensionality”. We explain the algorithm using a geometric model giving the reader understandable ins...

We study the richness of ensemble graphical structures (i.e., unlabeled graphs) one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in [0, 1] that connect if they are within connection range notation="...

This work presents two unsplit geometric VOF schemes that extend the two-dimensional cellwise conservative (CCU) scheme (Comminal et al. (2015) [49]) to three dimensions. The novelty of 3D-CCU lies in representation streaksurfaces donating regions by polyhedral surfaces whose vertices are calculated with 4th order Runge-Kutta scheme. Moreover, advected liquid volumes computed using a truncation...