Measured data from most processes are inherently multiscale in nature owing to contributions from events occurring at different locations and with different localization in time and frequency. Consequently, data analysis and modeling methods that represent the measured variables at multiple scales are better suited for extracting information from measured data than methods that represent the va...

The current special issue topic ‘‘modeling and simulation in composite materials’’ is intended to capture the recent advancements in the area of modeling and simulation in composite materials. The articles that appear under this topic describe theoretical models, molecular mechanics methods, finite-element methods, and multiscale methods for mechanical and thermal properties of composite materi...

The tensile properties of multiscale, hybrid, thermoplastic-based nanocomposites reinforced with nano-CaCO3 particles and micro–short glass fibers (SGF) were predicted by a two-step, three-dimensionalmodel using ANSYS finite element (FE) software. Cylindrical and cuboid representative volume elements were generated to obtain the effective behavior of the multiscale hybrid composites. In the fir...

Chemical Informatics lives in a twilight zone between informatics and mathematics on the one hand, and physical chemistry on the other hand. One could count numerous success stories of application in chemical and pharmaceutical industries. So far, the focus has been on correlating some molecular descriptor with measured activity. New challenges arise when one wishes to extend application into s...

We describe multiscale mortar mixed finite element discretizations for second order elliptic and nonlinear parabolic equations modeling Darcy flow in porous media. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. We discuss the construction of multiscale mo...

Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, current analysis is limited to small domains and increasing the size of the MD domain quickly presents intractable computational demands. A preferred approach to surmount this computational limitation has been to combine continuum mechanics...

Parasitic infectious diseases like malaria and certain hereditary hematologic disorders are often associated with major changes in the shape and viscoelastic properties of red blood cells. Such changes can disrupt blood flow and, possibly, brain perfusion, as in the case of cerebral malaria. In recent work on stochastic multiscale models—in conjunction with large-scale parallel computing—we wer...

We propose a deterministic two-scale tissue-cellular approach for modeling growth factor-induced angiogenesis. The bioreaction and diffusion of capillary growth factors (CGF) are modeled at a tissue scale, whereas capillary extension, branching and anastomosis are modeled at a cellular scale. The capillary indicator function is used to bridge these two scales. To solve the equation system numer...

The purpose of theses lectures is to introduce students to some of the interesting phenomena observed with stochastic processes which are evolving on two widely separated time scales. The study, and even definition of such processes involve a wide range of necessary concepts and tools from the theory of probability and stochastic processes. With the short time at our disposal, these notes are a...