arXiv subjects

Lyndon Koens

Publications and source records attributed to Lyndon Koens.

At least 19 recordsLinked to original sources

arXiv2026

Hydrodynamics constrain choanoflagellate collar geometry

As the closest living relatives of animals, choanoflagellates exhibit remarkable diversity. Even their microvilli collar, used to filter and capture food, varies significantly among species. This diversity suggests either strong environmental adaptation or an insensitivity to the collar geometry. Previous hydrodynamic studies have suggested that the pressure change across the collar is similar across species. In this study, we show that hydrodynamics imposes additional geometric constraints on the choanoflagellate collar. We create a simplified, reduced-order model that neglects finite collar length to investigate how the microvillus radius and the gap between microvilli influence the flow. Comparing with biological data reveals significant variation in the pressure drop between species. Additionally, a ridge emerges in the microvilli radius-gap phase space, along which both effective flux and power dissipation are maximised. Notably, several species cluster near the flux ridge but lie away from the power dissipation ridge. These observations suggest that choanoflagellate collars do not necessarily share a similar pressure drop. Instead, their geometry is influenced by the competing demands of maximising flux and minimising power costs. The broad variation observed among species is made possible by these ridge-like structures.

physics.bio-ph↗

arXiv2025

Remember when? Deciphering Ediacaran-Cambrian Metazoan behaviour and temporal memory using fossil movement paths

Evaluating the timing and trajectory of sensory system innovations is crucial for understanding the increase in phylogenetic, behavioural, and ecological diversity during the Ediacaran-Cambrian transition. Elucidation of sensory adaptations has relied on either body-fossil evidence based on anatomical features or qualitative descriptions of trace-fossil morphology, leaving a gap in the record of sensory system innovations between the development of basic sensory capacities and that of more advanced sensory organs and brains. Here, we examine fossil movement trajectories of Ediacaran and Cambrian grazers for the presence of autocorrelation. Our analysis reveals a lack of temporal correlation in the studied Ediacaran trajectories and its presence in both analysed Cambrian trajectories, indicating time-tuned behaviours were in place by the early Cambrian. These results support the Cambrian Information Revolution hypothesis and indicates that increases in cognitive complexity and behavioural strategies were yet another important evolutionary innovation that occurred during the Ediacaran Cambrian transition.

physics.bio-ph↗

arXiv2025

Quantifying movement: Expanding the Ichnologist toolkit

The trace-fossil record serves as a rich dataset to examine fossil behaviour, ecologic interactions at community level, and evolutionary trends in behaviour across geological time. Behavioural adaptations are often invoked in a variety of evolutionary hypotheses; however, few methods to quantitatively compare fossil behaviour exist. Movement paths, such as trails and trackways, are well-studied in extant-organism research where they are discretized and mathematically analyzed for behavioural strategies and trends. Here, we reference modern movement ecology research and present a methodology to discretize horizontal movement paths in the fossil record. We then demonstrate the utility of this methodology and the spatiotemporal data it collects via an analysis of the trilobite trace fossil Cruziana semiplicata and assess our results in light of three previous assertions about its recorded behaviour. Our analysis reveals the presence of three morphotypes, interpreted as three distinct behavioural variations, which persisted across multiple geographic localities and are interpreted to reflect changes in external conditions, internal states, or a combination of the two. Our research highlights the immense potential of this methodology to test behavioural hypotheses and provides an open-source groundwork for future research.

q-bio.PE↗

arXiv2025

Spatial trends in Ediacaran Bilaterian trails

The Savannah Hypothesis and the Cambrian Information Revolution invoke the development of spatially heterogeneous resource distribution during the Ediacaran-Cambrian transition as a key driver of infaunalization and sensory evolution of mobile bilaterians, respectively. However, difficulties in detecting historical resource distribution hinders the ability to tests these theories. If external conditions crucial to organism fitness (e.g. nutrient distribution, oxygen availability) became increasingly heterogeneous across the Ediacaran-Cambrian transition, then it follows that benthic organisms dependent on these conditions would demonstrate a similar increase in the spatial variability of their movement trajectories. To investigate Ediacaran resource distribution on the seafloor we examined the morphology of Helminthoidichnites tenuis, a simple unbranched horizontal bilaterian trail, from the Ediacara Member of Southern Australia for spatial trends. Our analysis reveals a as-yet undiscovered variability in the behaviour of the Helminthoidichnites tenuis tracemaker and confirmed heterogeneity in external conditions relevant to the tracemaker in the latest Ediacaran.

q-bio.PE↗

arXiv2025

A Taylor swimming sheet under a finite Brinkman layer

An asymptotic approach is employed to study the swimming speed of a two-dimensional Taylor swimming sheet beneath a Brinkman layer of finite thickness. This configuration is representative of a swimmer confined within a porous non-Newtonian boundary and could model microscopic filter feeders like choanoflagellates and sponges or the mucociliary escalator in the lungs. When ignoring the effects of jump stress and porosity, the swimming speed of the sheet decreases as the thickness and lower boundary of the Brinkman layer increase. The same is true as the permeability of the layer decreases. Including porosity effects with a zero jump stress enhances the swimming velocity of the sheet for porosity values near unity and decreases the swimming velocity for smaller porosity values. In the absence of porosity, the swimming speed of the sheet increases for positive-valued jump stresses and decreases for negative ones. Coupling nonzero jump stress with a variable porosity establishes complex behavior, with the sheet's swimming speed attaining a maximum, surpassing that found for the Newtonian case, particularly in thin or low-permeability Brinkman layers.

physics.flu-dyn↗

arXiv2024

Slender Phoretic Loops and Knots

We present an asymptotic theory for solving the dynamics of slender autophoretic loops and knots. Our formulation is valid for non-intersecting 3D centrelines, with arbitrary chemical patterning and varying (circular) cross-sectional radius, allowing a broad class of slender active loops and knots to be studied. The theory is amenable to closed-form solutions in simpler cases, allowing us to analytically derive the swimming speed of chemically patterned tori, and the pumping strength (stresslet) of a uniformly active slender torus. Using simple numerical solutions of our asymptotic equations, we then elucidate the behaviour of many exotic active particle geometries, such as a bumpy uniformly active torus that spins and a Janus trefoil knot, which rotates as it swims forwards.

physics.flu-dyn↗

arXiv2023

Viscous tubular-body theory for plane interfaces

Filaments are ubiquitous within the microscopic world. They occur frequently in both biological and industrial environments and display varied and rich dynamics. Their wide range of applications has spurred the development of a special branch of asymptotics focused on the behaviour of filaments, called slender-body theory. Slender-body theories are typically computationally efficient and focus on the mechanics of an isolated fibre that is not too curved. However, slender-body theories that work beyond these standard limits are needed to explore more complex systems. Recently, we developed tubular-body theory for slow viscous flows, an approach similar to slender-body theory that allows the hydrodynamic traction on any isolated cable-like body in a highly viscous fluid to be determined exactly. In this paper, we extend tubular-body theory to model filaments near plane interfaces by performing an similar expansion on the single-layer boundary integral equations for bodies by a plane interface. In the derivation of the new theory, called tubular-body theory for interfaces, we established a criteria for the convergence of the tubular-body theory series representation, before comparing the result to boundary integral simulations for a prolate spheroid by a wall. The tubular-body theory for interfaces simulations are found to capture the lubrication effects when close to the plane wall. Finally we simulate the hydrodynamics of a helix beneath a free interface and a plane wall to demonstrate the broad applicability of the technique.

physics.flu-dyn↗

arXiv2023

The slow viscous flow around doubly-periodic arrays of infinite slender cylinders

The slow viscous flow through a doubly-periodic array of cylinders does not have an analytical solution. However, as a reduced model for the flow within fibrous porous media, this solution is important for many real-world systems. We asymptotically determine the flow around a doubly-periodic array of infinite slender cylinders, by placing doubly-periodic two-dimensional singularity solutions within the cylinder and expanding the no-slip condition on the cylinder's surface in powers of the cylinder radius. The asymptotic solution provides a closed-form estimate for the flow and forces as a function of the radius and the dimensions of the cell. The force is compared to results from lattice-Boltzmann simulations of low-Reynolds-number flows in the same geometry, and the accuracy of the no-slip condition on the surface of the cylinder, predicted by the asymptotic theory, is checked. Finally, the behaviour of the flow, flux, force and effective permeability of the cell is investigated as a function of the geometric parameters. The structure of the asymptotic permeability is consistent with other models for the flow parallel to an array of rods. These models could be used to help understand the flows within porous systems composed of fibres and systems involving periodic arrays such as deterministic lateral displacement.

physics.flu-dyn↗

arXiv2022

Tubular-body theory for viscous flows

Cable-like bodies play a key role in many interdisciplinary systems but are hard to simulate. Asymptotic theories, called slender-body theories, are effective but apply in specific regimes and can be hard to extend beyond leading order. In this letter we develop an exact slender-body-like theory for the surface traction of cable-like bodies in viscous flow. This theory expresses the traction as a series of solutions to a well-behaved one-dimensional Fredholm integral equation of the second kind. This process can be simply generalised to other systems.

physics.flu-dyn↗

arXiv2022

Jet-driven viscous locomotion of confined thermoresponsive microgels

We consider the dynamics of micro-sized, asymmetrically-coated thermoresponsive hydrogel ribbons (microgels) under periodic heating and cooling in the confined space between two planar surfaces. As the result of the temperature changes, the volume and thus the shape of the slender microgel change, which lead to repeated cycles of bending and elastic relaxation, and to net locomotion. Small devices designed for biomimetic locomotion need to exploit flows that are not symmetric in time (non-reciprocal) to escape the constraints of the scallop theorem and undergo net motion. Unlike other biological slender swimmers, the non-reciprocal bending of the gel centreline is not sufficient here to explain for the overall swimming motion. We show instead that the swimming of the gel results from the flux of water periodically emanating from (or entering) the gel itself due to its shrinking (or swelling). The associated flows induce viscous stresses that lead to a net propulsive force on the gel. We derive a theoretical model for this hypothesis of jet-driven propulsion, which leads to excellent agreement with our experiments.

cond-mat.soft↗

arXiv2022

Order and Information in the Patterns of Spinning Magnetic Micro-disks at the Air-water Interface

The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules hampers the ability of these systems to serve as model systems for further exploring the links between information and structures. Here, we use, as a model experimental system, hundreds of spinning magnetic micro-disks self-organizing at the air-water interface to generate various spatiotemporal patterns with varying degrees of orders. Using the neighbor distance as the information-bearing variable, we demonstrate the links among information, structure, and interactions. Most importantly, we establish a direct link between information and structure without using explicit knowledge of interactions. Finally, we show that the Shannon entropy by neighbor distances is a powerful observable in characterizing structural changes. Our findings are relevant for analyzing natural self-organizing systems and for designing collective robots.

cond-mat.soft↗

arXiv2021

Regularized Stokeslets lines suitable for slender bodies in viscous flow

Slender-body approximations have been successfully used to explain many phenomena in low-Reynolds number fluid mechanics. These approximations typically use a line of singularity solutions to represent the flow. These singularities can be difficult to implement numerically because they diverge at their origin. Hence people have regularized these singularities to overcome this issue. This regularization blurs the force over a small blob therefore removing the divergent behaviour. However it is unclear how best to regularize the singularities to minimize errors. In this paper we investigate if a line of regularized Stokeslets can describe the flow around a slender body. This is achieved by comparing the asymptotic behaviour of the flow from the line of regularized Stokeslets with the results from slender-body theory. We find that the flow far from the body can be captured if the regularization parameter is proportional to the radius of the slender body. This is consistent with what is assumed in numerical simulations and provides a choice for the proportionality constant. However more stringent requirements must be placed on the regularization blob to capture the near field flow outside a slender body. This inability to replicate the local behaviour indicates that many regularizations cannot satisfy the non-slip boundary conditions on the bodies surface to leading order, with one of the most commonly used regularizations showing an angular dependency of velocity along any cross section. This problem can be overcome with compactly supported blobs { and we construct one such example blob which could be effectively used to simulate the flow around a slender body

physics.flu-dyn↗

arXiv2021

Local drag of a slender rod parallel to a plane wall in a viscous fluid

The viscous drag on a slender rod by a wall is important to many biological and industrial systems. This drag critically depends on the separation between the rod and the wall and can be approximated asymptotically in specific regimes, namely far from, or very close to, the wall, but is typically determined numerically for general separations. In this note we determine an asymptotic representation of the local drag for a slender rod parallel to a wall which is valid for all separations. This is possible through matching the behaviour of a rod close to the wall and a rod far from the wall. We show that the leading order drag in both these regimes has been known since 1981 and that they can used to produce a composite representation of the drag which is valid for all separations. This is in contrast to a sphere above a wall, where no simple uniformly valid representation exists. We estimate the error on this composite representation as the separation increases, discuss how the results could be used as resistive-force theory and demonstrate their use on a two-hinged swimmer above a wall.

physics.flu-dyn↗

arXiv2021

Geometric phase methods with Stokes theorem for a general viscous swimmer

The geometric phase techniques for swimming in viscous flows express the net displacement of a swimmer as a path integral of a field in configuration space. This representation can be transformed into an area integral for simple swimmers using Stokes theorem. Since this transformation applies for any loop, the integrand of this area integral can be used to help design these swimmers. However, the extension of this Stokes theorem technique to more complicated swimmers is hampered by problems with variables that do not commute and by how to visualise and understand the higher dimensional spaces. In this paper, we develop a treatment for each of these problems, thereby allowing the displacement of general swimmers in any environment to be designed and understood similarly to simple swimmers. The net displacement arising from non-commuting variables is tackled by embedding the integral into a higher dimensional space, which can then be visualised through a suitability constructed surface. These methods are developed for general swimmers and demonstrated on {three} benchmark examples: Purcell's two-hinged swimmer, an axisymmetric squirmer in free space {and an axisymmetric squirmer approaching a free interface}. We show in particular that for swimmers with more than two modes of deformation, there exists an infinite set of strokes that generate each net displacement. Hence, in the absence of additional restrictions, general microscopic swimmers do not have a single stroke that maximises their displacement.

physics.flu-dyn↗

arXiv2019

Method of regularised stokeslets: Flow analysis and improvement of convergence

Since their development in 2001, regularised stokeslets have become a popular numerical tool for low-Reynolds number flows since the replacement of a point force by a smoothed blob overcomes many computational difficulties associated with flow singularities (Cortez, 2001, \textit{SIAM J. Sci. Comput.} \textbf{23}, 1204). The physical changes to the flow resulting from this process are, however, unclear. In this paper, we analyse the flow induced by general regularised stokeslets. An explicit formula for the flow from any regularised stokeslet is first derived, which is shown to simplify for spherically symmetric blobs. Far from the centre of any regularised stokeslet we show that the flow can be written in terms of an infinite number of singularity solutions provided the blob decays sufficiently rapidly. This infinite number of singularities reduces to a point force and source dipole for spherically symmetric blobs. Slowly-decaying blobs induce additional flow resulting from the non-zero body forces acting on the fluid. We also show that near the centre of spherically symmetric regularised stokeslets the flow becomes isotropic, which contrasts with the flow anisotropy fundamental to viscous systems. The concepts developed are used to { identify blobs that reduce regularisation errors. These blobs contain regions of negative force in order to counter the flows produced in the regularisation process, but still retain a form convenient for computations.

physics.flu-dyn↗

arXiv2019

A Light-Driven Microgel Rotor

The current understanding of motility through body shape deformation of microorganisms and the knowledge of fluid flows at the microscale provides ample examples for mimicry and design of soft microrobots. In this work, a two-dimensional spiral is presented that is capable of rotating by non-reciprocal curling deformations. The body of the microswimmer is a ribbon consisting of a thermo-responsive hydrogel bilayer with embedded plasmonic gold nanorods. Such a system allows fast local photothermal heating and non-reciprocal bending deformation of the hydrogel bilayer under non-equilibrium conditions. We show that the spiral acts as a spring capable of large deformations thanks to its low stiffness, which is tunable by the swelling degree of the hydrogel and the temperature. Tethering the ribbon to a freely rotating microsphere enables rotational motion of the spiral by stroboscopic irradiation. The efficiency of the rotor is estimated using resistive force theory for Stokes flow. The present research demonstrates microscopic locomotion by the shape change of a spiral and may find applications in the field of microfluidics, or soft micro-robotics.

cond-mat.mtrl-sci↗

arXiv2019

The near and far of a pair of magnetic capillary disks

Control on microscopic scales depends critically on our ability to manipulate interactions with different physical fields. The creation of micro-machines therefore requires us to understand how multiple fields, such as surface capillary or electro-magnetic, can be used to produce predictable behaviour. Recently, a spinning micro-raft system was developed that exhibited both static and dynamic self-assembly [Wang et al. (2017) Sci. Adv. 3, e1602522]. These rafts employed both capillary and magnetic interactions and, at a critical driving frequency, would suddenly change from stable orbital patterns to static assembled structures. In this paper, we explain the dynamics of two interacting micro-rafts through a combination of theoretical models and experiments. This is first achieved by identifying the governing physics of the orbital patterns, the assembled structures, and the collapse separately. We find that the orbital patterns are determined by the short range capillary interactions between the disks, while the explanations of the other two behaviours only require the capillary far field. Finally we combine the three models to explain the dynamics of a new micro-raft experiment.

cond-mat.soft↗

arXiv2018

The swimming of a deforming helix

Many microorganisms and artificial microswimmers use helical appendages in order to generate locomotion. Though often rotated so as to produce thrust, some species of bacteria such Spiroplasma, Rhodobacter sphaeroides and Spirochetes induce movement by deforming a helical-shaped body. Recently, artificial devices have been created which also generate motion by deforming their helical body in a non-reciprocal way (Mourran et al., Adv. Mater., 29, 1604825, 2017). Inspired by these systems, we investigate the transport of a deforming helix within a viscous fluid. Specifically, we consider a swimmer that maintains a helical centreline and a single handedness while changing its helix radius, pitch and wavelength uniformly across the body. We first discuss how a deforming helix can create a non-reciprocal translational and rotational swimming stroke and identify its principle direction of motion. We then determine the leading-order physics for helices with small helix radius before considering the general behaviour for different configuration parameters and how these swimmers can be optimised. Finally, we explore how the presence of walls, gravity, and defects in the centreline allow the helical device to break symmetries, increase its speed, and generate transport in directions not available to helices in bulk fluids.

physics.bio-ph↗