The research on the assessment of collaborative problem solving (ColPS), as one crucial 21 Century Skill, is still in its beginnings. Using Tangible User Interfaces (TUI) for this purpose has only been marginally investigated in technology-based assessment. Our first empirical studies focused on light-weight performance measurements, usability, user experience, and gesture analysis to increase ...

In this article, Adomian decomposition method is successfully applied to find an approximate analytical solution of a Stefan problem subject to periodic boundary condition. By using initial and boundary conditions, the explicit solutions of the temperature distribution and the position of moving interface are evaluated and numerical results are depicted graphically. The method performs extremel...

In this thesis, computational interface capturing methods for mathematical models related to fluid phase change processes in porous media are studied. The mathematical models are often singular and degenerate, which contributes to the computational difficulty. An analysis of a smoothing method applied to a one dimensional free interface problem is presented. An asymptotic analysis shows the dep...

As a category of challenging flow problems, flows with moving boundaries and interfaces, includes fluid–particle, fluid–object and fluid–structure interactions; free-surface and two-fluid flows; and flows with moving mechanical components. To address the challenges involved in computation of this category of problems, we developed a number of interface-tracking and interface-capturing technique...

In this article, Adomian decomposition method is successfully applied to find an approximate analytical solution of a Stefan problem subject to periodic boundary condition. By using initial and boundary conditions, the explicit solutions of the temperature distribution and the position of moving interface are evaluated and numerical results are depicted graphically. The method performs extremel...

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unkn...

We provide an overview of some of the interface-tracking and interface-capturing techniques we developed for finite element computation of flow problems with moving boundaries and interfaces. This category of flow problems includes fluid–particle, fluid–object and fluid–structure interactions; free-surface and two-fluid flows; and flows with moving mechanical components. Both classes of techniq...

this paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. a model problem with nonlinear kinetic law is considered. the main result is an existence theorem. the mathematical effects of the kinetic term are discussed