The hydrodynamic description for emergent behavior of interacting agents is governed by Euler alignment equations, driven by different protocols of pairwise communication kernels. A main question of interest is how short- vs. long-range interactions dictate the large-crowd, long-time dynamics. 

The equations lack closure for the pressure away thermal equilibrium. We identify a distinctive feature of Euler alignment -- a reversed direction of entropy. We discuss the role of a reversed entropy inequality in selecting mono-kinetic closure for emergence of strong solutions, prove the existence of such solutions, and characterize their related invariants which extend the 1-D notion of an “e” quantity.

Structural mechanics plays a crucial role in soft matter physics, mechanobiology, metamaterials, pattern formation, active matter, and soft robotics. What unites these seemingly disparate topics is the natural balance that emerges between elasticity, geometry, and stability. This seminar will serve as a high-level overview of our work on several problems concerning the stability of structures. I will cover three topics: (1) shapeshifting shells; (2) mechanical metamaterials; and (3) elastogranular mechanics.

I will begin by discussing our development of a generalized, stimuli-responsive shell theory. (1) Non-mechanical stimuli including heat, swelling, and growth further complicate the nonlinear mechanics of shells, as simultaneously solving multiple field equations to capture multiphysics phenomena requires significant computational expense. We present a general shell theory to account for non-mechanical stimuli, in which the effects of the stimuli are
generalized into three forms: those that add mass to the shell, those that increase the area of the shell through the natural stretch, and those that change the curvature of the shell through the natural curvature. I will show how this model can capture the morphogenesis of the optic cup, the snapping of the Venus flytrap, leaf growth, and the buckling of electrically active polymer plates. (2) I will then discuss how cutting thin sheets and shells, a process
inspired by the art of kirigami, enables the design of functional mechanical metamaterials. We create linear actuators, artificial muscles, soft robotic grippers, and mechanical logic units by systematically cutting and stretching thin sheets. (3) Finally, if time permits, I will introduce our work on the interactions between elastic and granular matter, which we refer to as elastogranular mechanics. Such interactions occur across all lengths, from morphogenesis, to root growth, to stabilizing soil against erosion. We show how combining rocks and string in the absence of any adhesive we can create large, load bearing structures like columns, beams, and arches. I will finish with a general phase diagram for elastogranular behavior.

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Ever wondered how ideas from physics can used in real-world scenarios? Come to this talk to understand what is an option and how they are traded in markets. I will recall some basic notions of stochastic calculus and derive the Black-Scholes (BS) equation for plain vanilla options. The BS equation can be solved using standard path integral techniques, that also allow to price more exotic derivatives. Finally, I will discuss whether the assumptions behind Black-Scholes dynamics are reasonable in real-world markets (spoiler: they're not), volatility smiles and term structures of the implied volatility.

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

The motion of a particle suspended in a fluid flow is governed by hydrodynamic interactions. In this talk, I will present the rich nonlinear dynamics that arise from particle-fluid interactions for two different setups: (i) passive particles in 3D channel flows where fluid inertia is important, and (ii) active particles in 3D channel flows in the Stokes regime (i.e. without fluid inertia).

For setup (i), the particle-fluid interactions result in focusing of particles in the channel cross section, which has been exploited in biomedical microfluidic technologies to separate particles by size. I will offer insights on how dynamical system features of bifurcations and tipping phenomena might be exploited to efficiently separate particles of different sizes. For setup (ii), microswimmers routinely experience unidirectional flows in confined environment such as sperm cells swimming in fallopian tubes, pathogens moving through blood vessels, and microrobots programed for targeted drug delivery applications. I will show that our minimal model of the system exhibits rich nonlinear and chaotic dynamics resulting in a diverse set of active particle trajectories.

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