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We review our recent work in the area of autonomous materials research, highlighting the coupling of machine learning methods and models and more problem-aware modeling. We review the general Bayesian framework for closed-loop design…
Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g. the inviscid Burgers equation for the simple exclusion process. The physical solutions of…
Advancement in manufacturing methods enable designing so called metamaterials with a tailor-made microstructure. Microstructure affects materials response within a length-scale, where we model this behavior by using the generalized…
Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative…
To develop, calibrate and/or validate continuum models from experimental or numerical data, micro-macro transition methods are required. These methods are used to obtain the continuum fields (such as density, momentum, stress) from the…
Silicon-oxygen compounds are among the most important ones in the natural sciences, occurring as building blocks in minerals and being used in semiconductors and catalysis. Beyond the well known silicon dioxide, there are phases with…
In this contribution, we present a new Materials Knowledge System framework for microstructure-sensitive predictions of effective stress--strain responses in composite materials. The model is developed for composites with a wide range of…
An increasing variety of crystal structures has been observed in soft condensed matter over the past two decades, surpassing most expectations for the diversity of arrangements accessible through classical driving forces. Here, we survey…
Solids facing a plasma are a common situation in many astrophysical systems and laboratory setups. Moreover, many plasma technology applications rely on the control of the plasma-surface interaction. However, presently often a fundamental…
The complexities of today's materials simulations demand computer codes which are both powerful and highly flexible. A researcher should be able to readily choose different geometries, different materials and different algorithms without…
Atomistic simulations of the molecular dynamics/statics kind are regularly used to study small scale plasticity. Contemporary simulations are performed with tens to hundreds of millions of atoms, with snapshots of these configurations…
Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the…
We present a multiscale modeling approach that concurrently couples quantum mechanical, classical atomistic and continuum mechanics simulations in a unified fashion for metals. This approach is particular useful for systems where chemical…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…
The quantitative phase-field approach has been adapted to model solidification in the presence of Metal Matrix Nanocomposites (MMNCs) in a single-component liquid. Nanoparticles of fixed size and shape are represented by additional fields.…
Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an…
Heterogeneity is one important feature of complex systems, leading to the complexity of their construction and analysis. Moving the heterogeneity at model level helps in mastering the difficulty of composing heterogeneous models which…
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of…
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…