Continuum modeling of active nematics via data-driven equation discovery

Data-driven modeling seeks to extract a parsimonious model for a physical system directly from measurement data. One of the most interpretable of these methods is Sparse Identification of Nonlinear Dynamics (SINDy), which selects a relatively sparse linear combination of model terms from a large set of (possibly nonlinear) candidates via optimization. This technique has shown promise for synthetic data generated by numerical simulations but the application of the techniques to real data is less developed. This dissertation applies SINDy to video data from a bio-inspired system of mictrotubule-motor protein assemblies, an example of nonequilibrium dynamics that has posed a significant modelling challenge for more than a decade. In particular, we constrain SINDy to discover a partial differential equation (PDE) model that approximates the time evolution of microtubule orientation. The discovered model is relatively simple but reproduces many of the characteristics of the experimental data. The properties of the discovered PDE model are explored through stability analysis and numerical simulation; it is then compared to previously proposed models in the literature. Chapter 1 provides an introduction and motivation for pursuing a data driven modeling approach for active nematic systems by introducing the Sparse Identification of Nonlinear Dynamics (SINDy) modeling procedure and active nematic systems. Chapter 2 lays the foundation for modeling of active nematics to better understand the model space that is searched. Chapter 3 gives some preliminary considerations for using the SINDy algorithm and proposes several approaches to mitigate common errors. Chapter 4 treats the example problem of rediscovering a governing partial differential equation for active nematics from simulated data including some of the specific challenges that arise for discovery even in the absence of noise. Chapter 5 details the procedure for extracting data from experimental observations for use with the SINDy procedure and details tests to validate the accuracy of the extracted data. Chapter 6 presents the active nematic model extracted from experimental data via SINDy, compares its properties with previously proposed models, and provides numerical results of its simulation. Finally, Chapter 7 presents conclusions from the work and provides future directions for both active nematic systems and data-driven modeling in related systems

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios