Turbulent coherent structures and the origin of life

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Life, as we know it, consists of replicating strings of nucleic acids. If life originated with such strings, it is reasonable to assume that they were quite short, slowly increasing in length and complexity over time. Pioneering work by Eigen and Schuster demonstrated that self-replication would have been constrained by an “error threshold”, a critical number of base-pair nucleotides above which it is unreasonable to assume a particular string could replicate itself faithfully enough to sustain an exact lineage for long times. As a consequence, more complicated replication machineries — metabolisms involving more than one string, such as primitive replicases and cooperative hypercycles — would have been necessary to avoid the error threshold. However, these metabolisms are susceptible to defection, i.e. metabolic collapse due to malfunction of one or more of the components. Two proposed mechanisms to avoid defectors are primitive cell membranes and spatial distributions which allow healthy metabolisms to evade defective elements. Membranes provide additional benefits, which can be defined by algorithmic procedures such as concentrating, splitting and merging, which make them more appealing than spatial structures. Here we show that naturally-occurring spatial structures in fluid flows can actually incorporate the benefits of both the membrane and spatialization theories, allowing for algorithmic processes to redistribute genetic material without any kind of physical membrane.

arXiv, PDF


Large-scale quantitative profiling of the Old English verse tradition

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The corpus of Old English (OE) verse is an indispensable source for scholars of the Indo-European tradition, early Germanic culture, and English literary history. Although the focus of sustained literary scholarship for over two centuries, OE poetry has not been subjected to corpus-wide computational profiling, in part because of the sparseness and extreme fragmentation of the surviving material. Here we report a detailed quantitative analysis of the whole corpus that considers a broad range of features reflective of sound, meter, and diction. This integrated examination of fine-grained features enabled us to identify salient stylistic patterns despite the inherent limitations of the corpus. In particular, we provide quantitative evidence in support of the unitary authorship of Beowulf and the Cynewulfian authorship of Andreas, shedding new light on two longstanding questions in OE philology. Our results demonstrate the usefulness of high-dimensional stylometric profiling for fragmentary literary traditions and lay the foundation for future studies of the cultural evolution of English literature


Neidorf, L., M. S. Krieger, M. Yakubek, P. Chaudhuri, and J. P. Dexter (2018). Large- scale quantitative profiling of the Old English verse tradition. Nature Human Behaviour (in press)


Swimming in a confined liquid crystal


Microscopic lifeforms rarely locomote in an unconfined liquid. Solid boundaries representing biological membranes, other swimmers, or filaments much larger than the swimmer can represent elements of confinement. Due to the long range of hydrodynamic forces at this scale, the boundaries often have a dominant impact on the physics of locomotion. Here we extend previous work on locomotion of a swimmer with a prescribed stroke in confined isotropic fluids to anisotropic fluids, using the model of a nematic liquid crystal. The competition between elasticity, hydrodynamics, and anchoring conditions leads to a complex locomotion problem with unique transport properties. We examine this problem analytically and numerically for a model swimmer near a bounding wall which can itself also be elastic. For strong planar anchoring at a rigid wall, we find that the swimming speed goes to the isotropic Newtonian limit as the swimmer gets close to the wall, although the power required to maintain the swimmer’s speed depends on liquid crystal properties. We also report new findings on the swimming speed due to large-amplitude waveforms in unbounded liquid crystals.

Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Swimming in a confined liquid crystal”, arXiv, PDF


Effects of motion in structured populations


In evolutionary processes, population structure has a substantial effect on natural selection. Here, we analyze how motion of individuals affects constant selection in structured populations. Motion is relevant because it leads to changes in the distribution of types as mutations march toward fixation or extinction. We describe motion as the swapping of individuals on graphs, and also more generally as the shuffling of individuals between reproductive updates. Beginning with a one-dimensional graph, the cycle, we prove that motion suppresses natural selection for death-birth updating or for any process that combines birth-death and death-birth updating. If the rule is purely birth-death updating, no change in fixation probability appears in the presence of motion. We further investigate how motion affects evolution on the square lattice and on weighted graphs. In the latter case, we find that motion can be either an amplifier or a suppressor of natural selection. In some cases, whether it is one or the other can be a function of the relative reproductive rate, indicating that motion is a subtle and complex attribute of evolving populations.

Madison S. Krieger, A. McAvoy and M. A. Nowak, “Effects of motion in structured populations”, J. Roy. Soc. Interface 14(135), Arxiv, PDF

Microscale locomotion in a nematic liquid crystal


Microorganisms often encounter anisotropy, for example in mucus and biofilms. We study how anisotropy and elasticity of the ambient fluid affects the speed of a swimming microorganism with a prescribed stroke. Motivated by recent experiments on swimming bacteria in anisotropic environments, we extend a classical model for swimming microorganisms, the Taylor swimming sheet, actuated by small-amplitude traveling waves in a three-dimensional nematic liquid crystal without twist. We calculate the swimming speed and entrained volumetric flux as a function of the swimmer’s stroke properties as well as the elastic and rheological properties of the liquid crystal. These results are then compared to previous results on an analogous swimmer in a hexatic liquid crystal, indicating large differences in the cases of small Ericksen number and in a nematic fluid when the tumbling parameter is near the transition to a shear-aligning nematic. We also propose a novel method of swimming in a nematic fluid by passing a traveling wave of director oscillation along a rigid wall.

Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Microscale locomotion in a nematic liquid crystal”, Soft Matter, 2015, 11, 9115 – 9125, arXiv, PDF

Minimal model for transient swimming in a liquid crystal


When a microorganism begins swimming from rest in a Newtonian fluid such as water, it rapidly attains its steady-state swimming speed since changes in the velocity field spread quickly when the Reynolds number is small. However, swimming microorganisms are commonly found or studied in complex fluids. Because these fluids have long relaxation times, the time to attain the steady-state swimming speed can also be long. In this article we study the swimming startup problem in the simplest liquid crystalline fluid: a two-dimensional hexatic liquid crystal film. We study the dependence of startup time on anchoring strength and Ericksen number, which is the ratio of viscous to elastic stresses. For strong anchoring, the fluid flow starts up immediately but the liquid crystal field and swimming velocity attain their sinusoidal steady-state values after a time proportional to the relaxation time of the liquid crystal. When the Ericksen number is high, the behavior is the same as in the strong anchoring case for any anchoring strength. We also find that the startup time increases with the ratio of the rotational viscosity to the shear viscosity, and then ultimately saturates once the rotational viscosity is much greater than the shear viscosity.

Madison S. Krieger, Marcelo A. Dias and Thomas R. Powers, “Transient swimming in a hexatic liquid crystal”,  Eur. Phys. J. E. 38, 94, arXiv, PDF

Locomotion and Transport in a Hexatic Liquid Crystal



The swimming behavior of bacteria and other microorganisms is sensitive to the physical properties of the fluid in which they swim. Mucus, biofilms, and artificial liquid-crystalline solutions are all examples of fluids with some degree of anisotropy that are also commonly encountered by bacteria. In this article, we study how liquid-crystalline order affects the swimming behavior of a model swimmer. The swimmer is a one-dimensional version of G. I. Taylor’s swimming sheet: an infinite line undulating with small-amplitude transverse or longitudinal traveling waves. The fluid is a two-dimensional hexatic liquid-crystalline film. We calculate the power dissipated, swimming speed, and flux of fluid entrained as a function of the swimmer’s waveform as well as properties of the hexatic film, such as the rotational and shear viscosity, the Frank elastic constant, and the anchoring strength. The departure from isotropic behavior is greatest for large rotational viscosity and weak anchoring boundary conditions on the orientational order at the swimmer surface. We even find that if the rotational viscosity is large enough, the transverse-wave swimmer moves in the opposite direction relative to a swimmer in an isotropic fluid.

Madison S. Krieger, Saverio E. Spagnolie and Thomas R. Powers, “Locomotion and transport in a hexatic liquid crystal”, Phys. Rev. E 90, 052503, arXiv, PDF