A general review of the extended finite element method and its application to the simulation of first-order phase transitions is provided. Detailed numerical investigations are then performed by focusing on the one-dimensional case and studying: (i) spatial and temporal discretisations, (ii) different numerical techniques for the interface-condition enforcement, and (iii) different treatments f...

Fully relativistic four-component density functional theory with the general gradient approximation calculations have been performed to determine the adsorption energy and position of the superheavy element 112 on a Au surface. Extended cluster as well as embedded cluster calculations were used to simulate the surface which allow for the top, bridge, and hollow adsorption sites without losing t...

We construct finite element projectors that can be applied to functions with low regularity. These projectors are continuous in a weighted norm arising naturally when modeling devices with axial symmetry. They have important commuting diagram properties needed for finite element analysis. As an application, we use the projectors to prove quasioptimal convergence for the edge finite element appr...

The human visual system has specialised mechanisms for encoding mirror-symmetry and for detecting symmetric motion-directions for objects that loom or recede from the observers. The contribution of motion to mirror-symmetry perception has never been investigated. Here we examine symmetry detection thresholds for stationary (static and dynamic flicker) and symmetrically moving patterns (inwards,...

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...

Symmetry is treated as a continuous property and a Continuous Symmetry Measure (CSM) of structures is de ned. The CSM of a structure is de ned to be the minimummean squared distance required to move points of the original structure and change it to a symmetrical structure. This general de nition of a symmetrymeasure enables a comparison of the amount of symmetry of di erent shapes and the amoun...

Symmetry is treated as a continuous property and a Continuous Symmetry Measure (CSM) of structures is de ned. The CSM of a structure is de ned to be the minimummean squared distance required to move points of the original structure and change it to a symmetrical structure. This general de nition of a symmetrymeasure enables a comparison of the amount of symmetry of di erent shapes and the amoun...