Imperial College London

Dr Eric E Keaveny

Faculty of Natural SciencesDepartment of Mathematics

Senior Lecturer
 
 
 
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Contact

 

+44 (0)20 7594 2780e.keaveny

 
 
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Location

 

741Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

25 results found

Schoeller SF, Townsend AK, Westwood TA, Keaveny EEet al., 2019, Methods for suspensions of passive and active filaments

Flexible filaments and fibres are essential components of important complexfluids that appear in many biological and industrial settings. Directsimulations of these systems that capture the motion and deformation of manyimmersed filaments in suspension remain a formidable computational challengedue to the complex, coupled fluid--structure interactions of all filaments, thenumerical stiffness associated with filament bending, and the variousconstraints that must be maintained as the filaments deform. In this paper, weaddress these challenges by first describing filament kinematics usingquaternions to resolve both bending and twisting, applying implicittime-integration to alleviate numerical stiffness, and using quasi-Newtonmethods to obtain solutions to the resulting system of nonlinear equations. Inparticular, we employ geometric time integration to ensure that the quaternionsremain unit as the filaments move. We also show that our framework can be usedwith a variety of models and methods, including matrix-free fast methods, thatresolve low Reynolds number hydrodynamic interactions. We provide a series oftests and example simulations to demonstrate the performance and possibleapplications of our method. Finally, we provide a link to a MATLAB/Octaveimplementation of our framework that can be used to learn more about ourapproach and as a tool for filament simulation.

WORKING PAPER

Maretvadakethope S, Keaveny EE, Hwang Y, 2019, The instability of gyrotactically trapped cell layers

© 2019 Cambridge University Press. Several metres below the coastal ocean surface there are areas of high ecological activity that contain thin layers of concentrated motile phytoplankton. Gyrotactic trapping has been proposed as a potential mechanism for layer formation of bottom-heavy swimming algae cells, especially in flows where the vorticity varies linearly with depth (Durham et al.Science, vol. 323(5917), 2009, pp. 1067-1070). Using a continuum model for dilute microswimmer suspensions, we report that an instability of a gyrotactically trapped cell layer can arise in a pressure-driven plane channel flow. The linear stability analysis reveals that the equilibrium cell-layer solution is hydrodynamically unstable due to negative microswimmer buoyancy (i.e. a gravitational instability) over a range of biologically relevant parameter values. The critical cell concentration for this instability is found to be, a value comparable to the typical maximum cell concentration observed in thin layers. This result indicates that the instability may be a potential mechanism for limiting the layer's maximum cell concentration, especially in regions where turbulence is weak, and motivates the study of its nonlinear evolution, perhaps, in the presence of turbulence.

WORKING PAPER

Bao Y, Rachh M, Keaveny E, Greengard L, Donev Aet al., 2018, A fluctuating boundary integral method for Brownian suspensions, Journal of Computational Physics, Vol: 374, Pages: 1094-1119, ISSN: 0021-9991

We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for generating Brownian displacements that arise in response to the thermal fluctuations in the fluid. Our approach relies on a first-kind boundary integral formulation of a mobility problem in which a random surface velocity is prescribed on the particle surface, with zero mean and covariance proportional to the Green's function for Stokes flow (Stokeslet). This approach yields an algorithm that scales linearly in the number of particles for both deterministic and stochastic dynamics, handles particles of complex shape, achieves high order of accuracy, and can be generalized to three dimensions and other boundary conditions. We show that Brownian displacements generated by our method obey the discrete fluctuation–dissipation balance relation (DFDB). Based on a recently-developed Positively Split Ewald method Fiore et al. (2017) [24], near-field contributions to the Brownian displacements are efficiently approximated by iterative methods in real space, while far-field contributions are rapidly generated by fast Fourier-space methods based on fluctuating hydrodynamics. FBIM provides the key ingredient for time integration of the overdamped Langevin equations for Brownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of suspensions of starfish-shaped bodies using a random finite difference temporal integrator.

JOURNAL ARTICLE

Kamal A, Keaveny EE, 2018, Enhanced locomotion, effective diffusion and trapping of undulatory micro-swimmers in heterogeneous environments, JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 15, ISSN: 1742-5689

JOURNAL ARTICLE

Mingarelli L, Keaveny EE, Barnett R, 2018, Vortex lattices in binary mixtures of repulsive superfluids, PHYSICAL REVIEW A, Vol: 97, ISSN: 2469-9926

JOURNAL ARTICLE

Schoeller SF, Keaveny EE, 2018, From flagellar undulations to collective motion: predicting the dynamics of sperm suspensions, JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 15, ISSN: 1742-5689

JOURNAL ARTICLE

Delmotte B, Keaveny EE, Climent E, Plouraboué Fet al., Simulations of Brownian tracer transport in squirmer suspensions, IMA Journal of Applied Mathematics, ISSN: 0272-4960

In addition to enabling movement towards environments with favourable living conditions, swim-ming by microorganisms has also been linked to enhanced mixing and improved nutrient uptake by theirpopulations. Experimental studies have shown that Brownian tracer particles exhibit enhanced diffusiondue to the swimmers, while theoretical models have linked this increase in diffusion to the flows generated bythe swimming microorganisms, as well as collisions with the swimmers. In this study, we perform detailedsimulations based on the force-coupling method and its recent extensions to the swimming and Brownianparticles to examine tracer displacements and effective tracer diffusivity in squirmer suspensions. By iso-lating effects such as hydrodynamic or steric interactions, we provide physical insight into experimentalmeasurements of the tracer displacement distribution. In addition, we extend results to the semi-diluteregime where the swimmer-swimmer interactions affect tracer transport and the effective tracer diffusiv-ity no longer scales linearly with the swimmer volume fraction.Tracer dispersion - Squirmers - Activesuspensions - Simulations

JOURNAL ARTICLE

Li K, Javer A, Keaveny E, Brown AEXet al., 2017, Recurrent Neural Networks with Interpretable Cells Predict and Classify Worm Behaviour

An important goal in behaviour analytics is to connect disease state or genome variation with observable differences in behaviour. Despite advances in sensor technology and imaging, informative behaviour quantification remains challenging. The nematode worm C. elegans provides a unique opportunity to test analysis approaches because of its small size, compact nervous system, and the availability of large databases of videos of freely behaving animals with known genetic differences. Despite its relative simplicity, there are still no reports of generative models that can capture essential differences between even well-described mutant strains. Here we show that a multilayer recurrent neural network (RNN) can produce diverse behaviours that are difficult to distinguish from real worms' behaviour and that some of the artificial neurons in the RNN are interpretable and correlate with observable features such as body curvature, speed, and reversals. Although the RNN is not trained to perform classification, we find that artificial neuron responses provide features that perform well in worm strain classification.

CONFERENCE PAPER

Game SE, Hodes M, Keaveny EE, Papageorgiou DTet al., 2017, Physical mechanisms relevant to flow resistance in textured microchannels, PHYSICAL REVIEW FLUIDS, Vol: 2, ISSN: 2469-990X

JOURNAL ARTICLE

Keaveny EE, Brown AEX, 2017, Predicting path from undulations for C. elegans using linear and nonlinear resistive force theory, PHYSICAL BIOLOGY, Vol: 14, ISSN: 1478-3967

JOURNAL ARTICLE

Mingarelli L, Keaveny EE, Barnett R, 2016, Simulating infinite vortex lattices in superfluids, JOURNAL OF PHYSICS-CONDENSED MATTER, Vol: 28, ISSN: 0953-8984

JOURNAL ARTICLE

Delmotte B, Keaveny EE, 2015, Simulating Brownian suspensions with fluctuating hydrodynamics

© 2015 AIP Publishing LLC. Fluctuating hydrodynamics has been successfully combined with several computational methods to rapidly compute the correlated random velocities of Brownian particles. In the overdamped limit where both particle and fluid inertia are ignored, one must also account for a Brownian drift term in order to successfully update the particle positions. In this paper, we present an efficient computational method for the dynamic simulation of Brownian suspensions with fluctuating hydrodynamics that handles both computations and provides a similar approximation as Stokesian Dynamics for dilute and semidilute suspensions. This advancement relies on combining the fluctuating force-coupling method (FCM) with a new midpoint time-integration scheme we refer to as the drifter-corrector (DC). The DC resolves the drift term for fluctuating hydrodynamics-based methods at a minimal computational cost when constraints are imposed on the fluid flow to obtain the stresslet corrections to the particle hydrodynamic interactions. With the DC, this constraint needs only to be imposed once per time step, reducing the simulation cost to nearly that of a completely deterministic simulation. By performing a series of simulations, we show that the DC with fluctuating FCM is an effective and versatile approach as it reproduces both the equilibrium distribution and the evolution of particulate suspensions in periodic as well as bounded domains. In addition, we demonstrate that fluctuating FCM coupled with the DC provides an efficient and accurate method for large-scale dynamic simulation of colloidal dispersions and the study of processes such as colloidal gelation.

WORKING PAPER

Delmotte B, Keaveny EE, Plouraboué F, Climent Eet al., 2015, Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method, Journal of Computational Physics, Vol: 302, Pages: 524-547, ISSN: 0021-9991

© 2015 Elsevier Inc. We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, are considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method's ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection (10 4 -10 5 ) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models.

JOURNAL ARTICLE

Kalogirou A, Keaveny EE, Papageorgiou DT, 2015, An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol: 471, Pages: 20140932-20140932, ISSN: 1364-5021

JOURNAL ARTICLE

Keaveny EE, 2014, Fluctuating force-coupling method for simulations of colloidal suspensions, Journal of Computational Physics, Vol: 269, Pages: 61-79, ISSN: 0021-9991

JOURNAL ARTICLE

Keaveny EE, Walker SW, Shelley MJ, 2013, Optimization of Chiral Structures for Microscale Propulsion, NANO LETTERS, Vol: 13, Pages: 531-537, ISSN: 1530-6984

JOURNAL ARTICLE

Walker SW, Keaveny EE, 2013, Analysis of Shape Optimization for Magnetic Microswimmers, SIAM Journal on Control and Optimization, Vol: 51, Pages: 3093-3126, ISSN: 0363-0129

JOURNAL ARTICLE

Majmudar T, Keaveny EE, Zhang J, Shelley MJet al., 2012, Experiments and theory of undulatory locomotion in a simple structured medium., J R Soc Interface, Vol: 9, Pages: 1809-1823

Undulatory locomotion of micro-organisms through geometrically complex, fluidic environments is ubiquitous in nature and requires the organism to negotiate both hydrodynamic effects and geometrical constraints. To understand locomotion through such media, we experimentally investigate swimming of the nematode Caenorhabditis elegans through fluid-filled arrays of micro-pillars and conduct numerical simulations based on a mechanical model of the worm that incorporates hydrodynamic and contact interactions with the lattice. We show that the nematode's path, speed and gait are significantly altered by the presence of the obstacles and depend strongly on lattice spacing. These changes and their dependence on lattice spacing are captured, both qualitatively and quantitatively, by our purely mechanical model. Using the model, we demonstrate that purely mechanical interactions between the swimmer and obstacles can produce complex trajectories, gait changes and velocity fluctuations, yielding some of the life-like dynamics exhibited by the real nematode. Our results show that mechanics, rather than biological sensing and behaviour, can explain some of the observed changes in the worm's locomotory dynamics.

JOURNAL ARTICLE

Keaveny EE, Shelley MJ, 2011, Applying a second-kind boundary integral equation for surface tractions in Stokes flow, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 230, Pages: 2141-2159, ISSN: 0021-9991

JOURNAL ARTICLE

Liu D, Keaveny EE, Maxey MR, Karniadakis GEet al., 2009, Force-coupling method for flows with ellipsoidal particles, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 228, Pages: 3559-3581, ISSN: 0021-9991

JOURNAL ARTICLE

Keaveny EE, Shelley MJ, 2009, Hydrodynamic mobility of chiral colloidal aggregates, PHYSICAL REVIEW E, Vol: 79, ISSN: 1539-3755

JOURNAL ARTICLE

Keaveny EE, Maxey MR, 2008, Modeling the magnetic interactions between paramagnetic beads in magnetorheological fluids, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 227, Pages: 9554-9571, ISSN: 0021-9991

JOURNAL ARTICLE

Keaveny EE, Maxey MR, 2008, Interactions between comoving magnetic microswimmers, PHYSICAL REVIEW E, Vol: 77, ISSN: 1539-3755

JOURNAL ARTICLE

Keaveny EE, Maxey MR, 2008, Spiral swimming of an artificial micro-swimmer, JOURNAL OF FLUID MECHANICS, Vol: 598, Pages: 293-319, ISSN: 0022-1120

JOURNAL ARTICLE

Keaveny EE, Pivkin IV, Maxey M, Karniadakis GEet al., 2005, A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex-geometry flows, JOURNAL OF CHEMICAL PHYSICS, Vol: 123, ISSN: 0021-9606

JOURNAL ARTICLE

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