Past Events › Applied Mathematics Colloquium

Title: Simulating Nonlinear Faraday Waves on a Cylinder Abstract: In 1831, Faraday observed the formation of standing waves on the surface of a vibrating fluid body.  Subsequent experiments have revealed the existence of a rich tapestry of patterned states that can be accessed by varying the frequency and amplitude of the vibration and have spurred vast research in hydrodynamics and pattern formation. These include linear analyses to determine the conditions for the onset of the patterns, weakly nonlinear studies to understand pattern…

Title: Boundary-interface interaction in fluid dynamics models Abstract: The interaction between a fluid and a solid boundary  is a phenomenon not completely understood. An example is the interplay between an interface separating two fluids and the bottom of a channel: in the simplest case, when one of the two fluid is the air, the mechanism of ``drying" or  ``wetting'' some regions of the boundary seems to be  possible also in absence of the classical mechanisms  based on  surface tension or dissipation. In the…

Title: Multiscale modeling of multiphase systems Speaker: C. T. Miller, Department of Environmental Sciences and Engineering, Gillings School of Global Public Health, UNC-Chapel Hill Abstract: Two-fluid flow through porous medium systems occurs routinely in natural, engineered, and biological systems. While fundamental understanding is most advanced at the microscale, in order to model many systems of concern at the desired length scale, macroscale models are needed. Macroscale models treat systems in an averaged sense, where a point is the centroid of an averaging…

Title: Active Subspace Techniques to Construct Surrogate Models for Complex Physical and Biological Models Abstract: For many complex physical and biological models, the computational cost of high-fidelity simulation codes precludes their direct use for Bayesian model calibration and uncertainty propagation.  For example, neutronics and nuclear thermal hydraulics codes can take hours to days for a single run.  Furthermore, the models often have tens to thousands of inputs -- comprised of parameters, initial conditions, or boundary conditions -- many of which are unidentifiable…

Title: Homology Abstract: The idea of homology turns up in many different areas of mathematics, in various disguises. On the occasion of its appearance in data science (under the name of  "persistent homology" or "shape of data") in this talk we will explore the main underlying arguments and constructions in homology theory, with particular focus on persistent homology. The talk is aimed at mathematicians not familiar with homology (yet).

Title: The role of force networks in static and flowing granular materials Abstract: Granular materials are inherently heterogeneous, and continuum models of properties such as the shear modulus and sound speed often fail to quantitatively capture their dynamics. This lack of understanding has serious consequences for the engineering of both geotechnical applications, and the industrial storage and handling of granular materials. One likely reason for these difficulties is that boundary stresses are transmitted via a chain-like network of strong forces. In my…

Title: Smooth structures of convex functions and applications in Newton-type methods Abstract: In this talk, we demonstrate one way of exploiting smooth structures hidden in convex functions to develop optimization algorithms. Our key idea is to generalize a powerful concept so-called “self-concordance” introduced by Y. Nesterov and A. Nemirovskii to a broader class of convex functions. We show that this structure covers many applications in statistics and machine learning. Then, we develop a unified theory for designing numerical methods, especially proximal…