Thu, 12 Jun 2025

12:00 - 13:00
L3

Microfluidic model of haemodynamics in complex media

Anne Juel
(University of Manchester)
Further Information

Short Bio
Anna Juel is a physicist whose research explores the complex dynamics of material systems, particularly in two-phase flows and wetting phenomena. Her group focuses on microfluidics, fluid-structure interactions, and complex fluid flows, with applications ranging from chocolate moulding to airway reopening and flexible displays. Based at the Manchester Centre for Nonlinear Dynamics, her experimental work often uncovers surprising behaviour, driving new insights through combined experimentation and modelling.

Abstract
The flow of red blood cells (RBCs) in heterogeneous biological porous tissues such as the human placenta, remains poorly understood despite the essential role the microvasculature plays in maintaining overall health and functionality of tissues, blood flow and transport mechanisms. This is in great part because the usual description of blood as a simple fluid breaks down when the size of RBCs is similar to that of the vessel. In this study, we use a bespoke suspension of ultra-soft microcapsules with a poroelastic membrane, which have been previously shown to mimic the motion and large deformations of RBCs in simple conduits [1], in order to explore soft suspension flows in planar porous media. Our planar porous devices are Hele-Shaw channels, where the capsules are slightly confined within the channel depth, and in which we increase confinement by adding regular or disordered arrays of pillars. We perform experiments that relate the global resistance of the suspension flow through the porous media to the local distributions of capsule concentration and velocity as a function of volume fraction, capillary number Ca, the ratio of viscous to elastic forces, and geometry. We find that the flow patterns in Hele-Shaw channels and ordered porous media differ significantly from those in disordered porous media, where the presence of capsules promotes preferential paths and supports anomalous capsule dispersion. In contrast, the flows in ordered geometries develop intriguing shear-banding patterns as the volume fraction increases. Despite the complex microscopic dynamics of the suspension flow, we observe the emergence of similar scaling laws for the global flow resistance in both regular and disordered porous media as a function of Ca. We find that the scaling exponent decreases with increasing volume fraction because of cooperative capsule mechanisms, which yield relative stiffening of the system for increasing Ca.
 
[1] Chen et al. Soft Matter 19, 5249- 5261.
 
Thu, 05 Jun 2025

12:00 - 13:00
L3

Constitutive Modeling of the Microstructure of Arterial Walls Including Collagen Cross-Linking

Gerhard Holzapfel
(TU Graz)
Further Information

Extended Bio
Gerhard A. Holzapfel is a world-leading figure in biomechanics, currently serving as Professor and Head of the Institute of Biomechanics at Graz University of Technology (TUG), Austria. He also holds appointments as Adjunct Professor at the Norwegian University of Science and Technology (NTNU) in Trondheim and Visiting Professor at the University of Glasgow. From 2004 to 2013, he was Professor of Biomechanics at the Royal Institute of Technology (KTH) in Stockholm.

Following a PhD in Mechanical Engineering from Graz, Professor Holzapfel was awarded an Erwin Schrödinger Scholarship, enabling him to conduct research at Stanford University. He achieved his Habilitation at TU Vienna in 1996 and was the recipient of Austria’s prestigious START Award in 1997. Over subsequent decades, he has led pioneering work in computational biomechanics, including as Head of the Computational Biomechanics research group at TUG (1998–2004).

Professor Holzapfel has received numerous accolades, including the Erwin Schrödinger Prize of the Austrian Academy of Sciences (2011), listings among “The World’s Most Influential Scientific Minds” (Thomson Reuters, 2014), the William Prager Medal and Warner T. Koiter Medal (2021), an honorary doctorate from École des Mines de Saint-Étienne (2024), and election to the U.S. National Academy of Engineering (2025). In 2024, he was awarded a prestigious Synergy Grant from the European Research Council (ERC).

His research spans experimental and computational biomechanics and mechanobiology, with a particular focus on soft biological tissues and the cardiovascular system in both health and disease. His expertise includes nonlinear continuum mechanics, constitutive modelling, growth and remodeling, imaging and image-based modeling, and the mechanics of therapeutic interventions such as angioplasty and stenting.

Professor Holzapfel is the author of the widely adopted graduate textbook Nonlinear Solid Mechanics (Wiley), has co-edited seven additional books, and contributed chapters to over 30 volumes. He has published more than 300 peer-reviewed journal articles. He is also the co-founder and co-editor of the journal Biomechanics and Modeling in Mechanobiology (Springer). His work has been funded by numerous national and international agencies, including the Austrian Science Fund, NIH, the European Commission, and industry collaborators.

Abstract

Nowadays, the 3D ultrastructure of a fibrous tissue can be reconstructed in order to visualize the complex nanoscale arrangement of collagen fibrils including neighboring proteoglycans even in the stretched loaded state [1]. In particular, experimental data of collagen fibers in human artery layers have shown that the f ibers are not symmetrically dispersed [2]. In addition, it is known that collagen f ibers are cross-linked and the density of cross-links in arterial tissues has a stiffening effect on the associated mechanical response. A first attempt to characterize this effect on the elastic response is presented and the influence of the cross-link density on the mechanical behavior in uniaxial tension is shown [3]. A recently developed extension of the model that accounts for dispersed fibers connected by randomly distributed cross-links is outlined [4]. A simple shear test focusing on the sign of the normal stress perpendicular to the shear planes (Poynting effect) is analyzed. In [5] it was experimentally observed that, in contrast to rubber, semi-flexible biopolymer gels show a tendency to approach the top and bottom faces under simple shear. This so-called negative Poynting effect and its connection with the cross-links as well as the fiber and crosslink dispersion is also examined. 

References 

[1]A. Pukaluk et al.: An ultrastructural 3D reconstruction method for observing the arrangement of collagen fibrils and proteoglycans in the human aortic wall under mechanical load. Acta Biomaterialia, 141:300-314, 2022. 

 [2] G.A. Holzapfel et al.: Modelling non-symmetric collagen fibre dispersion in arterial walls. Journal of the Royal Society Interface, 12:20150188, 2015. 

 [3] G.A. Holzapfel and R.W. Ogden: An arterial constitutive model accounting for collagen content and cross-linking. Journal of the Mechanics and Physics of Solids, 136:103682, 2020. 

 [4] S. Teichtmeister and G.A. Holzapfel: A constitutive model for fibrous tissues with cross-linked collagen fibers including dispersion – with an analysis of the Poynting effect. Journal of the Mechanics and Physics of Solids, 164:104911, 2022. 

[5] P.A. Janmey et al.: Negative normal stress in semiflexible biopolymer gels. Nature Materials, 6:48–51, 2007.

 

Thu, 29 May 2025

12:00 - 13:00
L3

Pressure-driven fracture in elastic continuum materials

Peter Stewart
(University of Glasgow)
Further Information

Short Bio
Peter S. Stewart is a Professor of Applied Mathematics at the University of Glasgow. His research applies continuum mechanics to physiological and industrial problems. He previously held postdoctoral positions at the University of Oxford and Northwestern University, and earned his PhD from the University of Nottingham with a thesis on flows in flexible channels and airways. http://www.maths.gla.ac.uk/~pstewart

Abstract
Experiments indicate that a monolayer of gas-liquid foam confined within a Hele-Shaw cell can exhibit brittle fracture when subject to an applied driving pressure. In this talk we characterise this brittle fracture mode by considering the propagation of an internally pressurised crack though a slab of elastic continuum material with low resistance to shear, extending the classical description of pressure-driven fracture in a linearly elastic material to a slab of finite-width. We employ a novel matched eigenfunction expansion approach to formulate the stress field, incorporating a global penalty term which we isolate by solving a Fredholm integral equation. We recover the well-known stress singularity in the neighbourhood of the crack tip, but demonstrate that the spatial extent of this stress field in the direction of the crack is set by the domain width irrespective of the shear modulus of the material. The versatility of this approach allows for considerable modifications in the physical properties of the fracturing material, including those characteristic of foams, where out-of-plane deflection of the structural elements and accompanying viscous resistance to motion over the plates of the Hele-Shaw cell are important. These modifications facilitate a solution of the continuum model in the limit of zero shear modulus, where the stress singularity is entirely absent and the lengthscale of the stress-field in the direction of the crack is instead set by the dissipation coefficients. We exploit this mis-match in lengthscales to construct an asymptotic description for a slender domain, analytically characterising the critical conditions for crack propagation as a function of the driving pressure and the domain width. Furthermore, we show that this outer asymptotic solution can be extended to describe materials with low but finite shear modulus, where the accompanying stress singularity around the crack tip is confined within a boundary layer adjacent to the crack surface.
 
 
 
 
Thu, 22 May 2025

12:00 - 13:00
L3

Accelerating Predictions of Turbulent Combustion and Nonequilibrium Flows Using Solver-Embedded Deep Learning

Jonathan MacArt
(Univ. of Notre Dame)
Further Information

Short Bio
Jonathan MacArt leads the Reacting Turbulence Lab, where he and his team develop high-performance computational tools to study how flow physics interact with phenomena like chemical heat release and plasma kinetics. Their work includes large-scale DNS, LES, RANS simulations, and physics-informed machine learning, with applications ranging from gas turbines to hypersonic propulsion systems.

Abstract

Predictions of complex flows remain a significant challenge for engineering systems. Computationally affordable predictions of turbulent flows generally require Reynolds-Averaged Navier–Stokes (RANS) simulations and Large-Eddy Simulation (LES), the predictive accuracy of which can be insufficient due to non-Boussinesq turbulence and/or unresolved multiphysics that preclude qualitative fidelity in certain regimes. For example, in turbulent combustion, flame–turbulence interactions can lead to inverse-cascade energy transfer, which violates the assumptions of many RANS and LES closures. We present an adjoint-based, solver-embedded data assimilation method to augment the RANS and LES equations using trusted data. This is accomplished using Python-native flow solvers that leverage differentiable programming techniques to construct the adjoint equations needed for optimization. We present applications to shock-tube ignition delay predictions, turbulent premixed jet flames, and shock-dominated nonequilibrium flows and discuss the potential of adjoint-based approaches for future machine learning applications.

 

Thu, 08 May 2025

12:00 - 13:00
L3

Low-rank methods for discovering structure in data tensors in neuroscience

Alex Cayco-Gajic
(École Normale Supérieure Paris)
Further Information

Short Bio

Alex Cayco Gajic is a Junior Professor in the Department of Cognitive Studies at ENS, with a background in applied mathematics and a PhD from the University of Washington. Her research bridges computational modelling and data analysis to study cerebellar function, exploring its roles beyond motor control in collaboration with experimental neuroscientists.

Abstract

A fundamental question in neuroscience is to understand how information is represented in the activity of  tens of thousands of neurons in the brain. Towards this end, low-rank matrix and tensor decompositions are commonly used to identify correlates of behavior in high-dimensional neural data. In this talk I will first present a novel tensor decomposition based on the slice rank which is able to disentangle mixed modes of covarying patterns in data tensors. Second, to compliment this statistical approach, I will present our recent dynamical systems modelling of neural activity over learning. Rather than factorizing data tensors themselves, we instead fit a dynamical system to the data, while constraining the tensor of parameters to be low rank. Together these projects highlight how applications in neural data can inspire new classes of low-rank models.

Thu, 01 May 2025

12:00 - 13:00
L3

Do Plants Know Math?: Adventures of a Mathematician in Science Writing

Christophe Golé
(Smith College)
Further Information

Short Bio
Christophe Golé is a mathematician originally from France, with academic positions held at institutions including ETH Zurich and UC Santa Cruz. He is the author of Symplectic Twist Maps, a book on dynamical systems, and coined the term “ghost tori” in this context. His recent work focuses on mathematical biology, particularly plant pattern formation (phyllotaxis) and the occurrence of Fibonacci numbers in nature. He co-founded the NSF-funded 4 College Biomath Consortium, which led to the Five College Biomathematical Sciences Certificate Program.

Abstract

"Do Plants Know Math?" is the title of a book I co-authored with physicist Stéphane Douady, biologist Jacques Dumais, and writer Nancy Pick. Written for a general audience with a historical perspective, the book primarily explores phyllotaxis—the arrangement of leaves and other organs around plant stems—while also examining plant fractals, kirigami models of leaf formation, and related phenomena.

To our knowledge, phyllotaxis represents the first historical intersection of biological and mathematical research. Delving into its history uncovers remarkable treasures: phyllotaxis studies led to the first formulation of renormalization (van Iterson, 1907) and inspired one of the earliest computer programs (developed by Turing in the last years of his life).

In this talk, I will highlight several of these hidden historical gems while discussing the productive symbiosis between our scientific research on phyllotaxis and the creation of our book.

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Summer school looking for tutors

Reach run Summer Schools in Oxford. You know, the ones where 100s of international kids loll around in the University Parks for hour after hour. On a serious note, they are looking for DPhil-level tutors and pay okay. Below is their blurb: 

Jan in front of a whiteboard

Information Theory and Martingales

Information Theory, formalised by Claude Shannon in the 1940s, is one of the planks of 20th and 21st century science. You can now watch eight lectures we're showing from Sam Cohen's popular 3rd year Oxford Mathematics course, part of our aim of making more of our teaching visible to a wider audience.

Exact identifiability analysis for a class of partially observed
near-linear stochastic differential equation models
 Browning, A Chappell, M Rahkooy, H Loman, T Baker, R (25 Mar 2025) http://arxiv.org/abs/2503.19241v2
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