L3

In this talk, we will explore three flow configurations that illustrate the behaviour of slow-moving viscous fluids in confined geometries: viscous gravity currents, fracturing of shear-thinning fluids in a Hele-Shaw cell, and rectangular channel flows of non-Newtonian fluids. We will first develop simple mathematical models to describe each setup, and then we will compare the theoretical predictions from these models with laboratory experiments. As is often the case, we will see that even models that are grounded in solid physical principles often fail to accurately predict the real-world flow behaviour. Our aim is to identify the primary physical mechanisms absent from the model using laboratory experiments. We will then refine the mathematical models and see whether better agreement between theory and experiment can be achieved.

When a specimen of non-trivial shape undergoes deformation under a dead load or during an active process, finite element simulations are the only technique for evaluating the deformation. Classical books describe complicated techniques for evaluating stresses and strains in semi-infinite, circular or cylindrical objects.  However, the results obtained are limited, and it is well known that elasticity (linear or nonlinear) is strongly intertwined with geometry. For the simplest geometries, it is possible to determine the exact deformation, essentially for low loading values, and prove that there is a threshold above which the specimen loses stability. The next step is to apply perturbation techniques (linear and nonlinear bifurcation theory).
 

In this talk, I will demonstrate how many aspects can be simplified or revealed through the use of complex analysis and conformal mapping techniques for shapes, strains, and active stresses in thin samples. Examples include leaves and embryonic jellyfish.

In this talk, we will explore three flow configurations that illustrate the behaviour of slow-moving viscous fluids in confined geometries: viscous gravity currents, fracturing of shear-thinning fluids in a Hele-Shaw cell, and rectangular channel flows of non-Newtonian fluids. We will first develop simple mathematical models to describe each setup, and then we will compare the theoretical predictions from these models with laboratory experiments. As is often the case, we will see that even models that are grounded in solid physical principles often fail to accurately predict the real-world flow behaviour. Our aim is to identify the primary physical mechanisms absent from the model using laboratory experiments. We will then refine the mathematical models and see whether better agreement between theory and experiment can be achieved.

 I will present a new framework for determining effectively the spectrum and stability of traveling waves on networks with symmetries, such as rings and lattices, by computing master stability curves (MSCs). Unlike traditional methods, MSCs are independent of system size and can be readily used to assess wave destabilization and multi-stability in small and large networks.

I am going to start by reviewing axioms of quantum mechanics, which in fact give a description of a Hilbert space. I will argue that the language that Dirac and his followers developed is that of continuous logic and the form of axiomatisation is that of "algebraic logic" in the sense of A. Tarski's cylindric algebras. In fact, Hilbert spaces can be seen as a continuous model theory version of cylindric algebras.

This talk will focus on systems-theoretic and control theory tools that help characterize the responses of nonlinear systems to external inputs, with an emphasis on how network structure “motifs” introduce constraints on finite-time, transient behaviors.  Of interest are qualitative features that are unique to nonlinear systems, such as non-harmonic responses to periodic inputs or the invariance to input symmetries. These properties play a key role as tools for model discrimination and reverse engineering in systems biology, as well as in characterizing robustness to disturbances. Our research has been largely motivated by biological problems at all scales, from the molecular (e.g., extracellular ligands affecting signaling and gene networks), to cell populations (e.g., resistance to chemotherapy due to systemic interactions between the immune system and tumors; drug-induced mutations; sensed external molecules triggering activations of specific neurons in worms), to interactions of individuals (e.g., periodic or single-shot non-pharmaceutical “social distancing'” interventions for epidemic control). Subject to time constraints, we'll briefly discuss some of these applications.