Applied Mathematics Seminar

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Synopsis:

Synopsis:

Mobile robots combine sensory information with mechanical actuation to move autonomously through complex environments and perform specific tasks (e.g., a robot vacuum cleaner). The miniaturization of such robots to the size of living cells (ca. 2-40 um) is actively pursued for applications in biomedicine, materials science, and environmental sustainability. In pursuit of these “microrobots”, we seek to understand the many mechanisms underlying the self-propulsion of colloidal particles through viscous fluids. Building on this understanding, we seek to design active particles capable of autonomous behaviors such as navigation of structured environments.  In this talk, I discuss two recent efforts – on Quincke oscillators and magnetic topotaxis, respectively – that highlight these complementary aims to understand and design active colloids. In part one, I explain how static electric fields drive the oscillatory motion of micron-scale particles commensurate with the thickness of a field-induced boundary layer in nonpolar electrolytes. In part two, I describe how spatially uniform, time-periodic magnetic fields can be designed to power and direct the migration of ferromagnetic spheres up local gradients in surface topography.

 

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Ice-infiltrated sediment, known as a frozen fringe, leads to phenomena such as frost heave, ice lenses, and meters of debris-rich ice under glaciers. Understanding the dynamics of frozen fringe development is important as frost heave is responsible for damaging infrastructure at high latitudes; frozen sediments at the base of glaciers can modulate glacier flow, influencing the rate of global sea level rise; and frozen water ice exists within the sediments of the top several meters on Mars and in places on the Moon. Here we study the fluid physics of interstitial freezing water in sediments and focus on the conditions relevant for subglacial and planetary environments. We describe the thermomechanics of liquid water flow through and freezing in ice-saturated frozen sediments. The force balance that governs the frozen fringe thickness depends on the weight of the overlying material, the thermomolecular force between ice and sediments across premelted films of liquid, and the water pressure within liquid films that is required by flow according to Darcy's law. Our model accounts for premelting at ice-sediment contacts, partial ice saturation of the pore space, water flow through the fringe, the thermodynamics of the ice-water-sediment interface, and vertical force balance. We explicitly account for the formation of ice lenses, regions of pure ice that cleave the fringe at the depth where the interparticle force vanishes.

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In this talk, I will show three different experiments on live fish swimming and schooling. I will first try to bring some answers to the old fundamental question raised by fluid dynamicists: is there a hydrodynamic advantage of swimming in schools? I will then give some details about the intermittent dynamics that characterize the swimming of small and medium size fish and discuss the dependence of the global cost of transport to the parameters of the swimming. At last, I will show the role of vision in the formation of spontaneous global behavior in a large population of fish. 

 

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Synopsis:

Active matter, responsive materials and materials under time-dependent load are systems out
of thermal equilibrium. To construct coarse-grained models for such systems, one needs to integrate out a
distribution of microstates that evolves in time. This is a challenging task. In this talk, we
we review recent developments in theoretical approaches to the non-equilibrium coarse-graining problem,
in particular, time-dependent projection operator formalisms and numerical schemes to construct explicitly time-dependent memory kernels.

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magine a 1D curve, then use it to fill a 2D manifold that covers an arbitrary 3D object – this computationally intensive materials challenge has been realized in the ancient technology known as knitting. This process for making functional materials 2D materials from 1D portable cloth dates back to prehistory, with the oldest known examples dating from the 11th century CE. Knitted textiles are ubiquitous as they are easy and cheap to create, lightweight, portable, flexible and stretchy. As with many functional materials, the key to knitting’s extraordinary properties lies in its microstructure.

 

At the 1D level, knits are composed of an interlocking series of slip knots. At the most basic level there is only one manipulation that creates a knitted stitch – pulling a loop of yarn through another loop. However, there exist hundreds of books with thousands of patterns of stitches with seemingly unbounded complexity.

 

The topology of knitted stitches has a profound impact on the geometry and elasticity of the resulting fabric. This puts a new spin on additive manufacturing – not only can stitch pattern control the local and global geometry of a textile, but the creation process encodes mechanical properties within the material itself. Unlike standard additive manufacturing techniques, the innate properties of the yarn and the stitch microstructure has a direct effect on the global geometric and mechanical outcome of knitted fabrics.