I³MS - Gray Seminar
Prof. Dr. Nico Gray - Particle Size-Segregation and Rheology of Dense Granular Flows
, The University of Manchester, UK
Hazardous geophysical mass flows, such as snow avalanches, debris-flows and pyroclastic flows, often spontaneously develop large particle rich levees that channelize the flow and enhance their run-out. Large scale experiments with 10 cubic metres of water saturated sand and gravel flowing down the 80m USGS debris-flow flume indicate that a subtle segregation-mobility feedback effect is responsible for their formation. Within the flow large particles segregate to the faster moving near surface layers and are preferentially sheared towards the front. Here they may be over-run, re-segregated and recirculated, to create a coarse grained front that is more resistive to motion than the more mobile ?finer grained interior. As a result the large particles are shouldered to the side to create static levees that constrain the flow laterally. Simple models for particle segregation and the depth-averaged motion of granular avalanches are described and one of the first attempts is made to couple these two types of models together. This process proves to be non-trivial, yielding considerable complexity as well as pathologies that require additional physics to be included. Some of these difficulties can be overcome by incorporating a depth-averaged mu?(I)-rheology for granular flow into the model. However, the mu?(I)-rheology turns out to have regions of ill-posedness itself at high and low inertial numbers.
EU Regional School - McClarren Seminar
Prof. Dr. McClarren - Polynomial Chaos Expansions for Uncertainty Quantification
Texas A&M University
In computational science and engineering one often deals with computer simulations where inputs to the calculation are uncertain. A natural question to ask is how uncertain the output of a simulation is given uncertainties in the inputs. In this lecture I will give cover the application of orthogonal expansions in probability space (also known as polynomial chaos expansions) to determine the distribution of quantities of interest from a numerical simulation. I will detail how to apply these methods to a variety of input uncertainty distributions, and give concrete examples for simple functions as well as non-trivial applications. The examples will also be an opportunity to point out to students the pitfalls and common mistakes that can be made applying these techniques. Finally, I will cover more advanced ideas such as sparse quadrature and regularized regression techniques to estimate expansion coefficients.
I³MS - Helzel Seminar
Prof. Dr. Christiane Helzel
Starting point of our considerations is a coupled system consisting of a kinetic equation coupled to a macroscopic Navier-Stokes equation describing the motion of a suspension of rigid rods under the influence of gravity. A reciprocal coupling leads to the formation of clusters: The buoyancy force creates a macroscopic velocity gradient that causes the microscopic particles to align so that their sedimentation reinforces the formation of clusters of higher particle density. Since the coupled system is high-dimensional, we are interested in the derivation of simpler systems which describe the dynamics without resolving the kinetic equation. We discuss two different approaches to obtain such systems. Furthermore, we discuss the numerical methods which were used to approximate the different mathematical models and show numerical results. This is joint work with Athanasios E. Tzavaras from KAUST.
EU Regional School - Cid Seminar
Prof. Dr. Cid - Data Visualization: More than a Thousand Words
Big Data is one of the trendiest topics in the last years. It is important as it provides means to analyse large volumes of data in order to detect patterns and outliers. However, understanding data requires much more than running complex statistics and data mining processes. We need tools that let us explore the data in order to understand its complexity. Data Visualization is the discipline behind the generation of static and interactive representations of abstract data to amplify cognition. In this lecture we will understand the main goals of Data Visualization through examples that show the wide variety of representations that can be produced. We will also discuss the pros and cons of some of the most classic visualizations in order to understand the rationale we need to know to use them properly.
I³MS - Weiser Seminar
Dr. Martin Weiser - Mathematical Therapy Planning in Regional Hyperthermia
Regional hyperthermia is a cancer therapy that aims at heating large and deeply seated tumors in order to destroy them or make them susceptible to an accompanying radio or chemo therapy. Heat is induced by absorbing energy from radio waves emanating from several controllable antennas. This talk will give an overview of the mathematical tasks involved in therapy planning, covering the whole spectrum of modeling, simulation, identification, and optimization.