Applied Mathematics Seminar

Synopsis:

In his correspondence with the poet Alfred Le Poittevin, Gustave Flaubert writes, "Anything becomes interesting if you look at it long enough." We will try to see if Flaubert is correct while looking at cycling races through the eyes of physicists. The question we will target is "How does the rider optimize his speed for a given topography and weather condition?" 

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Synopsis:

Topological states of matter have been intensively studied in crystals, leading to fascinating phenomena such as scattering-free edge current in topological insulators. However, the power of topological protection goes well beyond ordered crystal lattices. In this talk we explore how topology protects mechanical edge modes in messy, noncrystalline, systems. We will use disordered fiber networks and quasicrystals as our examples, to demonstrate how topological edge floppy modes can be induced in these structures by controlling their geometry. Fiber networks are ubiquitous in nature and especially important in bio-related materials. Establishing topological mechanics in fiber networks may shed light on understanding robust processes in mechanobiology. Quasicrystals show unusual orientational order with quasiperiodic translational order. We found that a bulk topological polarization can be defined for mechanics of quasicrystals that is unique to their non-crystallographic orientational symmetry.

References: (1) Di Zhou, Leyou Zhang, Xiaoming Mao, "Topological Edge Floppy Modes in Disordered Fiber Networks", Phys. Rev. Lett. 120, 068003 (2018); (2) Di Zhou, Leyou Zhang, Xiaoming Mao, "Topological Boundary Floppy Modes in Quasicrystals", Phys. Rev. X 9, 021054 (2019).  

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Synopsis:

Despite the complexity and diversity of modes of unsteady fluid fragmentation into secondary droplets, universality across geometry and fluid systems emerges. We discuss the role of unsteadiness in shaping a ubiquitous, yet neglected class of fluid fragmentation problems based on recent joint experimental and theoretical investigations. In particular, we reveal  how unsteadiness and multi-scale dynamics couple to select both the sizes and speeds of secondary droplets generated.

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Synopsis:

Three-dimensional structure prediction of macromolecular interaction complex is an important component in small molecular and biologics drug discovery. The search space includes the 6D rotational/translational space of mutual rigid body orientations of receptor and ligand, as well as additional degrees of freedom that represent the flexibility of the two molecules. Solving this problem requires detailed sampling and optimization of an energy-based scoring function. Since the energy function has a large number of local minima separated by high barriers, the minimization problem is extremely challenging. The search space includes the 6D rotational/translational space as well as additional degrees of freedom that represent the flexibility of the macromolecules and is a manifold. Here we present effective approaches for different steps of docking protocols, which effectively use manifold geometry to significantly speed up the search. Specifically we will describe Fast Manifold Fourier Transform (FMFT) approach for effective global  grid based sampling for macromolecular docking, and local and medium range optimization using exponential map parametrization  for docking refinement. The method enables us to calculate the approximate partition function of the system, and identify likely minima. The methods described above have been blindly validated in international docking competitions CAPRI (protein docking) and D3R (protein-ligand docking) and were among the best performers in both. The application part of the  talk will focus on modeling macromolecular  molecular interactions on the omics scale, including our effort on drug repurposing against COVID-19.

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Synopsis:

Topology enables the robust classification and characterization of complex systems, by focusing on properties that are invariant under continuous deformations. Recent  experiments have shown that topological structures play an important role in organizing various biological functions and behaviors, from signaling in the heart and brain to bacterial swarming and cell death. In the first part of this talk, I will summarize our efforts [1] to characterize and distinguish multi-cellular systems, such as bacterial biofilms and tissues, in terms of their topological architecture, by analyzing neighborhood motif distributions and computing distances between them. In the second part, we will discuss joint experimental and theoretical work that aims to understand the topological defect dynamics in the signaling waves on cell membranes [2].

[1] arXiv:2001.08788
[2] Nature Physics 16: 657, 2020

Synopsis:

COVID-19 spread across the world with a speed and intensity that laid bare the limits in our understanding of the transmission pathways of such respiratory diseases. There is, however, an emerging consensus that airborne transmission constitutes an important mode for the spread of COVID-19. Each stage in this transmission pathway is mediated by complex flow phenomena, ranging from air-mucous interaction inside the respiratory tract, turbulence in the exhaled jet/ambient flow, to inhalation and deposition of these aerosols in the lungs. Inspired by the Drake Equation that provides a framework to estimate the seemingly inestimable probability of advanced extraterrestrial life, I propose a phenomenological model for estimating the risk of airborne transmission of a respiratory infection such as COVID-19. The model incorporates simple ideas from fluid dynamics with the factors implicated in airborne transmission and is designed to serve not only as a common basis for scientific inquiry across disciplinary boundaries, but to also be understandable by a broad audience outside science and academia. Given the continuously evolving nature of the pandemic and the resurgence of infections in many communities, the importance of communicating infection risk across scientific disciplines, as well as to policy/decision makers, is more important than ever.

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Synopsis:

Plants and animals of all shapes and sizes have evolved sharp, pointed outgrowths. Their uses vary widely, from injuring predators and delivering poison to providing buoyancy and adhesion. Despite their apparent diversity, stingers have inherent similarities. In this presentation, we will argue that natural stingers exist at the threshold of stability; they're just strong enough to penetrate their targets without buckling. For straight, rigid stingers, this stability criterion translates to a linear relationship between length and base diameter that accurately describes more than 200 natural and human-made examples, including wasp stingers, cactus spines, hypodermic needles, and lances. We conclude with a discussion of implications for biomedical and engineering stinger designs.  

Synopsis:

Synopsis:

Can fish reduce their energy expenditure by schooling? We answer this long standing question by integrating Direct Numerical Simulations with deep reinforcement learning, which confers adaptive decision-making capability to simulated fish. Our results demonstrate that locomotion in coordinated groups may lead to energy savings when individual fish interact judiciously with their companions' unsteady wakes. In natural swimmers, optimal decision-making in response to an unsteady environment also requires fine-tuned sensory capabilities. By combining Navier-Stokes simulations with Bayesian experimental design, we were able to identify sensor arrangements that allow simulated swimmers to maximize the information gathered from the surrounding  flow. The resulting optimal sensor distributions resemble neuromast arrangements found in fish, and provide evidence for optimality of  sensor distribution for natural swimmers. I will also highlight recent work where we have investigated aerosol dispersal patterns for various types of facemasks and shields, which are simple yet critical tools in  the worldwide effort to combat the spread of COVID-19.

Synopsis:

An important class of fluid-structure problems involve the dynamics of ordered arrays of immersed, flexible fibers. While specialized numerical methods have been developed to study fluid-fiber systems, they become infeasible when there are many, rather than a few, fibers present, nor do these methods lend themselves to analytical calculation. Here, we introduce a coarse-grained continuum model, based on local-slender body theory, for elastic fibers immersed in a viscous Newtonian fluid. After exploring some basic properties of such ordered arrays, we use the model to study streaming flows in the fruit fly oocyte. In particular, we show that sufficiently dense microtubule arrays, forced only by molecular motors transporting cargo, undergo a "swirling transition" that is fundamentally different than the buckling transition which leads to the flapping motion of isolated filaments. The model produces streaming velocities consistent with in vivo measurements, and allows us to place bounds on the number density of kinesin-1 motors transporting cargo within the microtubule array.