Past Industrial and Applied Mathematics Seminar

16 November 2017
16:00
to
17:30
Giovanni Samaey
Abstract

We present a framework for the design, analysis and application of computational multiscale methods for slow-fast high-dimensional stochastic processes. We call these processes "microscopic'', and assume existence of an approximate "macroscopic'' model that captures the slow behaviour of a selected set of macroscopic state variables. The methodology combines short bursts of microscopic simulation with extrapolation at the macroscopic level. The methodology requires the careful study of a few key algorithmic ingredients. First, we need to properly initialise the microscopic system, based on a given macroscopic state and (possibly) a prior microscopic state that contains additional information about the system. Second, we need to control the variance of the noise that originates from the microscopic Monte Carlo simulation. Third, we need to analyse stability of the extrapolation step. We will discuss these aspects on two types of model problems -- scale-separated SDEs and kinetic equations -- and show the efficacity of the resulting methods in diverse applications, ranging from tumor growth to fusion energy.

  • Industrial and Applied Mathematics Seminar
2 November 2017
16:00
to
17:30
Abstract

Phytoplankton moving in the ocean, spermatozoa making their way  through the female reproductive tract and harmful bacteria that form biofilms on implanted medical devices interact with a surrounding fluid. Their length scales are small enough so that viscous effects dominate inertial effects allowing the resulting fluid dynamics to be described by the linear Stokes equations. However,  nonlinear behavior can occur because these structures are flexible and their form evolves with the flow. In addition, the fluid environment may also  be complex because of embedded microstructures that further complicate the dynamics.  We will discuss recent successes and challenges in describing these elastohydrodynamic systems.

  • Industrial and Applied Mathematics Seminar
26 October 2017
16:00
to
17:30
Abstract

Brain convolutions are specificity of mammals. Varying in intensity according to the animal species, it is measured by an index called the gyrification index, ratio between the effective surface of the cortex compared to its apparent surface. Its value is closed to 1 for rodents (smooth brain), 2.6 for new-borns and 5 for dolphins.  For humans, any significant deviation is a signature of a pathology occurring in fetal life, which can be detected now by magnetic resonance imaging (MRI). We propose a simple model of growth for a bilayer made of the grey and white matter, the grey matter being in cortical position. We analytically solved the Neo-Hookean approximation in the short and large wavelength limits. When the upper layer is softer than the bottom layer (possibly, the case of the human brain), the selection mechanism is dominated by the physical properties of the upper layer. When the anisotropy favours the growth tangentially as for the human brain, it decreases the threshold value for gyri formation. The gyrification index is predicted by a post-buckling analysis and compared with experimental data. We also discuss some pathologies in the model framework.

  • Industrial and Applied Mathematics Seminar
19 October 2017
16:00
to
17:30
Pasquale Ciarletta
Abstract

Discontinuous solutions, such as cracks or cavities, can suddenly appear in elastic solids when a limiting condition is reached. Similarly, self-contacting folds can nucleate at a free surface of a soft material subjected to a critical compression. Unlike other elastic instabilities, such as buckling and wrinkling, creasing is still poorly understood. Being invisible to linearization techniques, crease nucleation is a problem of high mathematical complexity.

In this talk, I will discuss some recent theoretical insights solving the quest for both the nucleation threshold and the emerging crease morphology.  The analytic predictions are in  agreement with experimental and numerical data. They prove a fundamental insight either for understanding the creasing onset in living matter, e.g. brain convolutions, or for guiding engineering applications, e.g. morphable meta-materials.

  • Industrial and Applied Mathematics Seminar

Pages