In this article we propose models and a numerical method for pattern formation on evolving curved surfaces. We formulate reaction-diffusion equations on evolving surfaces using the material transport formula, surface gradients and diffusive conservation laws. The evolution of the surface is defined by a material surface velocity. The numerical method is based on the evolving surface finite elem...

The current study examined the effect of empathy on friendship quality in the context of dyadic same-sex friendships, and how such an effect might be mediated by interpersonal competence. A special version of the actor-partner interdependence model (APIM) was used to examine this hypothesis in 146 same-sex friend dyads in 10th grade. Results showed that empathy was positively related to intimac...

In the past few decades, it has become increasingly popular and important to utilize mathematical models to understand how microscopic intercellular interactions lead to the macroscopic pattern formation ubiquitous in the biological world. Modeling methodologies come in a large variety and presently it is unclear what is their interrelationship and the assumptions implicit in their use. They ca...

A key qualitative requirement for highway traffic models is the ability to replicate a type of traffic jam popularly referred to as a phantom jam, shock wave or stop-and-go wave. Despite over 50 years of modelling, the precise mechanisms for the generation and propagation of stop-and-go waves and the associated spatio-temporal patterns are in dispute. However, the increasing availability of emp...