Epitaxy is the growth of a thin film on a substrate in which the crystal properties of the film are inherited from those of the substrate. Because of the wide range of relevant length and time scales, multiscale mathematical models have been developed to describe epitaxial growth. This presentation describes atomistic, island dynamics and continuum models. Island dynamics models are multiscale ...

This paper presents a system for modeling lichens and simulating their propagation and growth in a virtual scene. Lichens colonize almost every substrate in nature and play an important role in the visual appearance of a natural object. The propagation of lichens over the substrate is performed by an Open Diffusion Limited Aggregation model constrained by the characteristics of the environment....

9 Few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that 10 they are capable of adapting and proliferating on a food matrix. This is why any quantitative 11 health risk assessment policy must incorporate methods to accurately predict the growth of 12 bacterial populations from a small number of pathogens. In this aim, mathematical models 13 have become a p...

Many mental illnesses are thought to have their origins at early stages of development, encouraging increased research effort related to early neurodevelopment. Magnetic resonance imaging (MRI) has provided us with an unprecedented view of the brain in vivo. More recently, diffusion tensor imaging (DTI/DT-MRI), a magnetic resonance imaging technique, has enabled the characterization of the micr...

Computational plant models or 'virtual plants' are increasingly seen as a useful tool for comprehending complex relationships between gene function, plant physiology, plant development, and the resulting plant form. The theory of L-systems, which was introduced by Lindemayer in 1968, has led to a well-established methodology for simulating the branching architecture of plants. Many current arch...

Static neoclassical framework cannot be applied to model time dependent processes or increasing returns to scale in production. The dynamization of the neoclassical theory of a firm by dynamic optimization, on the other hand, assumes inconsistent profit functions with the former. As a solution to these problems, we present a dynamic theory of a firm consistent with the static neoclassical theor...

Like any other precipitation process, in supercritical water hydrothermal synthesis (SWHS), the need to improve product quality and minimize production cost requires understanding and optimization of Particle Size Distribution (PSD). In this work, using Population Balance Equation (PBE) containing nucleation and growth terms, the reactive precipitation of zirconia nanoparticles prepared by ...