Applied/ACMS

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Applied and Computational Mathematics Seminar


Fall 2024

Date Speaker Title Host(s)
Sep 13* Nan Chen (UW) Intro. to Uncertainty Quantification (UQ) (tutorial) Spagnolie
Sep 20 Katie Newhall (UNC Chapel Hill) Energy landscapes, metastability, and transition paths Rycroft
Sep 27 Indresan Govender (Mintek / Univ. of KwaZulu-Natal, South Africa) Granular flow modeling and visualization using nuclear imaging Rycroft
Oct 4* Hongfei Chen (Tulane) Investigating Hydrodynamics of Choanoflagellate Colonies: A Reduced Model Approach Jean-Luc
Oct 11 Colloquium in B239 at 4:00pm Mikaela Iacobelli (ETH/IAS) TBA Li
Oct 18 Colloquium in B239 at 4:00pm Guillaume Bal (U Chicago) Speckle formation of laser light in random media: The Gaussian conjecture Li, Stechmann
Oct 23 (Wednesday) Teresa Portone (Sandia) Beyond parametric uncertainty: quantifying model-form uncertainty in model predictions Stechmann
Oct 25 Anil Damle (Cornell) Fine-grained Theory and Hybrid Algorithms for Randomized Numerical Linear Algebra Li
Nov 1 Michael Sprague (NREL) Exascale supercomputing and predictive wind energy simulations Spagnolie
Nov 8 Miranda Holmes-Cerfon (UBC) The dynamics of particles with ligand-receptor contacts Stechmann
Nov 15* Yue Sun (UW–Madison) Rycroft
Nov 22 Ondrej Maxian (U Chicago) TBA Ohm & Spagnolie
Nov 29* Thanksgiving
Dec 6 Ido Lavi (Flatiron) TBA Spagnolie

Dates marked with an asterisk correspond to home football games of the UW–Madison Badgers. On these dates it can be difficult to get a hotel room close to campus at short notice.

Abstracts

Nan Chen (UW–Madison)

Title: Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification -- A Tutorial for Beginners

I will provide a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more about this area. The talk will exploit many elementary examples, which are understandable to graduate students and senior undergraduates, to present the ideas of UQ. Topics include characterizing uncertainties using information theory, UQ in linear and nonlinear dynamical systems, UQ via data assimilation, the role of uncertainty in diagnostics, and UQ in advancing efficient modeling. The surprisingly simple examples in each topic explain why and how UQ is essential. Both Matlab and Python codes have been made available for these simple examples.

Katie Newhall (UNC Chapel Hill)

Title: Energy landscapes, metastability, and transition paths

The concept of an energy landscape emerged in the 1930’s as a way to calculate chemical reaction rate constants via Henry Eyring’s transition state theory. Its use has expanded since then, remaining central to quantifying metastability (infrequent jumps between deterministically-stable, energy minimizing, states) that arises in noisy systems when the thermal energy is small relative to the energy barrier separating two states. In this talk, I will present extensions of this theory that I have developed and applied to physical and biological systems. The first is an infinite dimensional system for which I prove metastability is present in the absence of an energy barrier; I extend transition state theory to compute mean transition times. In the second, I derive a model for a spatially-extended magnetic system with spatially-correlated noise designed to sample the Gibbs distribution relative to a defined energy functional. In the third, I show a quasi-potential can be found and used to describe metastable transitions between stable clusters in a bead-spring polymer model of chromosome dynamics with additional stochastic binding pushing the system out of equilibrium.

Indresan Govender (Mintek / Univ. of KwaZulu Natal, South Africa)

Title: Granular flow modeling and visualization using nuclear imaging

Despite its ubiquity, a complete theory to describe the underlying rheology of granular flows remains elusive. Central to this problem is the lack of detailed, in-situ measurements of the granular flow field. To this end, we present two non-invasive imaging techniques currently employed to measure the flow of individual grains within granular flow systems that span simple mono-sized flows of plastic beads to complex industrial mixture flows of rocks and slurry. The first technique employs diagnostic X-rays operated in biplanar mode to triangulate the motion of low-density granules in simplified flow systems to within a 3D spatial accuracy of 0.15 mm at tracking frequencies up to 100 Hz. The second—arguably the workhorse of our research operation—is the nuclear imaging technique of Positron Emission Particle Tracking (PEPT) which triangulates the back-to-back gamma rays emanating from radiolabeled particles to within a millimeter in 3D space at a millisecond timing resolution. PEPT can track the motion of any particle with a diameter greater than ∼20 microns. Both techniques are well suited to studying the flow of granular materials after the data is cast into volume and time averages consistent with the continuum framework. In this talk I will explore the many interesting analysis techniques employed to mapping out the complex flow regimes found in typical granular systems, and the insights they offer towards better understanding their rheological character. Examples explored will include rotating drum flows (wet and dry), shear cells and their industrial counterpart the IsaMillTM, hydrocyclone separator flows, and the motivation for tracking of multiple particles. The validation offered to numerical schemes like the Discrete Element Method will also be explored wherein we highlight the complimentary role that measurement and simulation play in unravelling the secrets of granular flows. Finally, and deviating somewhat from the imaging world, I will present our efforts towards utilizing granular flow modeling in real-time control of complex industrial flows encountered in mineral processing.

Hongfei Chen (Tulane)

Title: Investigating Hydrodynamics of Choanoflagellate Colonies: A Reduced Model Approach

Abstract: Choanoflagellates, eukaryotes with a distinctive cellular structure consisting of a cell body, a flagellum, and a collar of microvilli, exhibit fascinating biological behavior. While many species exist as single cells, some form colonies, with the species C. Flexa standing out for its ability to dynamically transition its flagella between positions inside and outside the colony.

Modeling the hydrodynamics of these colonies ideally requires detailed representations of each cell’s flagellum, microvilli, and body. However, the computational cost of simulating colonies with hundreds of cells makes this approach very expensive. To address this, we propose a reduced modeling framework that simplifies each cell to a force dipole while retaining key hydrodynamic features.

Our force dipole model is calibrated against detailed computational simulations that account for the complete cellular structure. We show that this reduced model closely matches experimental data for non-deforming, free-swimming colonies. We further investigate how colony swimming and feeding performance depend on the flagellar position relative the colony, cell density, and overall colony shape. Finally, we explore the impact of the wall for flagella-in colonies, which are frequently observed in laboratory settings.

Guillaume Bal (Chicago)

Title: Speckle formation of laser light in random media: The Gaussian conjecture

A widely accepted conjecture in the physical literature states that classical wave-fields propagating in random media over large distances eventually follow a complex circular Gaussian distribution. In this limit, the wave intensity becomes exponentially distributed, which corroborates the speckle patterns of, e.g., laser light observed in experiments. This talk reports on recent results settling the conjecture in the weak-coupling, paraxial regime of wave propagation. The limiting macroscopic Gaussian wave-field is fully characterized by a correlation function that satisfies an unusual diffusion equation.

The paraxial model of wave propagation is an approximation of the Helmholtz model where backscattering has been neglected. It is mathematically simpler to analyze but quite accurate practically for wave-fields that maintain a beam-like structure as in the application of laser light propagating in turbulent atmospheres.

The derivation of the limiting model is first obtained in the Itô-Schrödinger regime, where the random medium is replaced by its white noise limit. The resulting stochastic PDE has the main advantage that finite dimensional statistical moments of the wave-field satisfy closed form equations. The proof of the derivation of the macroscopic model is based on showing that these moment solutions are asymptotically those of the Gaussian limit, on obtaining a stochastic continuity (and tightness) result, and on establishing that moments in the paraxial and the Itô-Schrödinger regimes are asymptotically close.

This is joint work with Anjali Nair.

Teresa Portone (Sandia)

Title: Beyond parametric uncertainty: quantifying model-form uncertainty in model predictions

Uncertainty quantification (UQ) is the science of characterizing, quantifying, and reducing uncertainties in mathematical models. It is critical for informing decisions, because it provides a measure of confidence in model predictions, given the uncertainties present in the model. While approaches to characterize uncertainties in model parameters, boundary and initial conditions are well established, it is less clear how to address uncertainties arising when the equations of a mathematical model are themselves uncertain—that is, when there is model-form uncertainty. Model-form uncertainty often arises in models of complex physical phenomena where (1) simplifications for computational tractability or (2) lack of knowledge lead to unknowns in the governing equations for which appropriate mathematical forms are unknown or may not exist. In this talk, I briefly introduce major concepts in UQ, then I discuss approaches to characterize model-form uncertainty and its impact on model predictions.

Anil Damle (Cornell)

Title: Fine-grained Theory and Hybrid Algorithms for Randomized Numerical Linear Algebra

Randomized algorithms have gained increased prominence within numerical linear algebra and they play a key role in an ever-expanding range of problems driven by a breadth of scientific applications. In this talk we will explore two aspects of randomized algorithms by (1) providing experiments and accompanying theoretical analysis that demonstrate how their performance depends on matrix structures beyond singular values (such as coherence of singular subspaces), and (2) showing how to leverage those insights to build hybrid algorithms that blend favorable aspects of deterministic and randomized methods. A focus of this talk will be on methods that approximate matrices using subsets of columns. Relevant motivating applications will be discussed and numerical experiments will illuminate directions for further research.

Miranda Holmes-Cerfon (UBC)

Title: The dynamics of particles with ligand-receptor contacts

One way to glue objects together at the nanoscale or microscale is by ligand-receptor interactions, where short sticky hair-like ligands stick to receptors on another surface, much like velcro on the nanoscale. Such interactions are common in biological systems, such as white blood cells, virus particles, cargo in the nuclear pore complex, etc, and they are also useful in materials science, where coating colloids with single-stranded DNA creates particles with programmable interactions. In these systems, the ligand-receptor interactions not only hold particles together, but also influence their dynamics. How do such particles move? Do they “roll” on each others’ surfaces, as is commonly thought? Or could they slide? And does it matter? In this talk I will introduce our modelling and experimental efforts aimed at understanding the coarse-grained dynamics of particles with ligand-receptor interactions. Our models predict these interactions can change the particles' effective diffusion by orders of magnitude. Our experiments, using DNA-coated colloids, verify this dramatic dynamical slowdown, but also show other dynamical features not yet captured by our models, which suggest new avenues for exploration.

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