Complex matter form an ideal platform for to the design and control of new material with improved functionality. The versatility to tailor the overall properties via (i) the individual particle properties and (ii) the properties of the suspending media makes them ubiquitous to various biological and industrial applications, e.g. food, cosmetics, paints, and pharmaceuticals. The properties of the constituent particles can vary from hard-elastic- viscoelastic, owing to the internal structure of the particle, while the solvent-mediated interactions modulate their dynamics. In this talk, I will show, using dynamic simulations and multi-scale modeling, how the internal structure of the individual particle and the hydrodynamic interactions with the suspending solvent induce arrested transitions.

I will show the importance of the many-body hydrodynamic interactions and lubrications forces on both the equilibrium and non-equilibrium solidification processes of hard particle suspensions, i.e. crystallization and vitrification, respectively, utilizing large-scale Stokesian dynamics simulation. Jumps from liquid into the solid region are executed via controlled volume-fraction, where the speed of the quench permits toggling between equilibrium and arrested states. The relative influence of many-particle hydrodynamics on aging and crystallization dynamics is studied, and I elucidate the influence of the quenching process on long-time fate of the material. I will also outline the two-scale dynamic model developed to effectively model the size- and shape-dynamics of particles that originate from their internal structure.

Using non-equilibrium thermodynamics, the macroscopic fluid-dynamics and the particle dynamics on the particle level are mutually coupled in a consistent manner, establishing the link between the macroscopic behavior, e.g. stresses, and the dynamics of the microstructure, e.g. particle shape and size. The model is cast into a form that enables modelling particles with both shape-preserving size-changes (e.g. swellable particles) and volume-preserving shape-changes (e.g. incompressible yet deformable particles). The size- shape model distinguishes itself in unifying prior knowledge of purely-shape models with that of purely-size models by appropriate choices of the Helmholtz free energy and the generalized mobility.

The presentation will focus on a simulation and computational approach to verification of the hybrid mathematical models that are formed when combining physics-based models, with discrete-transition models such as those which model software algorithms. Namely, the mathematical models that arise when for instance considering Cyberphysical Systems, or the Internet-of-Things. In many game theory, filtering problems and verification problems it is not possible to analytically obtain solutions for statistical properties of systems under study. In the first section of the talk will concentrate on system verification, and will present a new verification algorithm for continuous-time stochastic hybrid systems, whose specifications are expressed in metric interval temporal logic (MITL), by deploying a novel model reduction method. By partitioning the state space of the hybrid system and computing the optimal transition rates between partitions, we provide a procedure to both reduce the system to a continuous-time Markov chain, and the associated specification formulas. We prove that the unreduced formulas hold (or do not) if the corresponding reduced formula on the Markov chain is robustly true (or false) under certain perturbations. In addition, a stochastic algorithm to complete the verification has been developed. We have extended the approach of this algorithm, and have developed a direct stochastic algorithm for probabilistic verifying a certain hybrid system class, and applied this technique to an extensive benchmark problem with realistic dynamics. In the second part of the talk we will describe our recent work on numerical approaches to obtaining estimates of statistical properties of Markov processes, in particular mean-square estimation. Monte Carlo simulation of Markov processes allows the numerical estimation of their statistical properties from an ensemble of sample system paths. We present methods for generating reduced-variance path ensembles for the tau-leaping discrete-time simulation algorithm, which allows mean stochastic process dynamics to be estimated with substantially smaller ensemble sizes. Our methods are based on antithetic and stratified sampling of Poisson random variates, and we provide a combination of analytical proofs and numerical evidence for their performance, which can frequently be a 2-3 orders of magnitude improvement over standard Monte Carlo. Also presented will be the HoTDeC multi-vehicle, which consists of indoor airborne and ground-based vehicles.

The aortic valve interstitial cell (AVIC) is the most abundant cell type within the aortic valve and maintains the turnover of extracellular matrix (ECM) components. Under normal conditions, AVICs display a fibroblast-like, quiescent phenotype and can undergo myofibroblastic phenotypic activation in response to growth and disease which is characterized by an increase in overall cell contractility as well as an increase in ECM production and remodeling. Prolonged activation of AVICs can potentially cause drastic pathological changes in aortic valve ECM, geometry, and mechanical function and manifest into diseases such as aortic valve regurgitation or stenosis.

Cell contraction is a key component in biological processes such as wound-closure and can influence 3D tissue organization, remodeling, and function. Previous attempts to quantify cell contractility have largely relied on two dimensional assays such as traction force microscopy and micro-post assays which do not recapitulate the three dimensional complexity of native tissues. In this presentation, I will discuss our investigation of AVIC contractile behavior within 3D peptide-modified poly (ethylene glycol) (PEG) hydrogel matrices. We perform macro- and micro-level experiments to assess the contractile response of AVICs at the population- and single-cell levels, respectively. At the population-level, our results show that AVIC contraction within the PEG gel environment increases the overall stiffness of the AVIC-hydrogel construct and that AVIC contractile effects are highly dependent upon the adhesive ligand density within the PEG gel. In addition, we observed that the effects of AVIC contraction were more pronounced in lower stiffness hydrogels. At the single cell level, we used 3D traction force microscopy to assess AVIC contractile response and report that AVIC contraction is highly complex displaying contraction in one direction, expansion in an orthogonal direction, and virtually no deformation in the direction orthogonal to the previous two. In conjunction with our experimental investigations, we developed computational models of the macro- and micro-level experiments to gain a better mechanistic understanding of AVIC contractile behaviors. The macro-level model predicted that AVIC contraction causes an increase in AVIC-hydrogel construct stiffness and we observed that the Neo-Hookean material model was a good approximation of macro-level AVIC-hydrogel mechanical response. At the single-cell level, the Neo-Hookean material model is not sufficient to capture the effects of AVIC contraction on the hydrogel material, especially in regions further away from the cell surface. This discrepancy may have implications towards the complex and length-scale dependent AVIC-hydrogel interactions within our 3D culture system. The tunable and efficient techniques we have developed in this body of work will be used to quantify intrinsic differences in contractile properties between normal and diseased human AVICs to better our understanding of disease progression.

Bio
Alex Khang is a PhD candidate in the Department of Biomedical Engineering at The University of Texas at Austin. He received his BS degree in Biomedical Engineering from the University of Arkansas-Fayetteville. His doctoral project is focused on studying the mechanics and mechanobiology of heart valve interstitial cells (VIC) within a highly tunable hydrogel environment. He previously worked under the tutelage of Dr. Kartik Balachandran in the Mechanobiology and Soft Materials Laboratory. Fabricated nanofibrous scaffolds for tissue engineering applications using a novel technique called centrifugal jet spinning.

Digital Twins are one of the hottest technical trends according to Gartner, Inc.. In this talk we will shortly review the concept of Digital Twins and corresponding opportunities in the industrial context. Computational Science and Engineering is a key enabler and the impact will be highlighted along three specific examples addressing Digital Product Twins democratizing Design, Digital Production Twins enabling robots to mill and Digital Performance Twins boosting operations. In all three cases advanced mathematical algorithms make the difference and allow the “impossible”.

Bio
Dr. Hartmann is a Siemens Top Innovator, entrepreneur, and thought leader in the field of simulation and digital twins. His experience covers research, innovation, and development project oriented responsible position. Many of his innovations were showcased at top-level Siemens innovation events including the Siemens innovation day and the annual shareholder meeting. These innovations led to short term valorizations within novel products and services.

Along his professional career, he has continuously supervised students at the Technical University of Munich, as well as driven the industrial mathematics research on a national and European level within KoMSO and EU-MATHS-IN.