We consider the Allen-Cahn equation ε∆u + u− u = 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in R such that the mean curvature is positive at each boundary point. We show that there exists a sequence εj → 0 such that the Allen-Cahn equation has a solution uεj with an interface which approaches the boundary as j → +∞.

A system of partial differential equations modeling a van der Waals fluid or an elastic medium with nonmonotone pressure-density relation is studied. As the system changes type, regularizations are considered. The existence of one-dimensional periodic travelling waves with prescribed average density in a certain range, average velocity, and wavelength is proved. They exhibit layer structure whe...

Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high densities. Starting from a continuum description of scalar active matter akin to a generalized Cahn-Hilliard equation, we give a general prescription for the mean densities of coexisting phases in flux-free steady states that amounts, at a hydrod...

Abstract. AHP is a multi-criteria decision method widely used by non-experts. We have been implementing an Intelligent Tutoring System teaching the underlying theory, in particular the construction of consistent or near consistent AHP matrices, and the calculation of priorities and consistency indexes. AHP Tutor’s architecture supports adaptable exercises and dynamic explanations of solution pa...

We studied the nonequilibrium dynamics of the q-state Potts model in the square lattice, after a quench to subcritical temperatures. By means of a continuous time Monte Carlo algorithm (nonconserved order parameter dynamics) we analyzed the long term behavior of the energy and relaxation time for a wide range of quench temperatures and system sizes. For q>4 we found the existence of different d...

Gamification means the use of various elements of game design in nongame contexts including workplace collaboration, marketing, education, military, and medical services. Gamification is effective for both improving workplace productivity and motivating employees. However, introduction of gamification is not easy because the planning and implementation processes of gamification are very complic...