169 research outputs found
Filament mechanics in a half-space via regularised Stokeslet segments
We present a generalisation of efficient numerical frameworks for modelling
fluid-filament interactions via the discretisation of a recently-developed,
non-local integral equation formulation to incorporate regularised Stokeslets
with half-space boundary conditions, as motivated by the importance of
confining geometries in many applications. We proceed to utilise this framework
to examine the drag on slender inextensible filaments moving near a boundary,
firstly with a relatively-simple example, evaluating the accuracy of resistive
force theories near boundaries using regularised Stokeslet segments. This
highlights that resistive force theories do not accurately quantify filament
dynamics in a range of circumstances, even with analytical corrections for the
boundary. However, there is the notable and important exception of movement in
a plane parallel to the boundary, where accuracy is maintained. In particular,
this justifies the judicious use of resistive force theories in examining the
mechanics of filaments and monoflagellate microswimmers with planar flagellar
patterns moving parallel to boundaries. We proceed to apply the numerical
framework developed here to consider how filament elastohydrodynamics can
impact drag near a boundary, analysing in detail the complex responses of a
passive cantilevered filament to an oscillatory flow. In particular, we
document the emergence of an asymmetric periodic beating in passive filaments
in particular parameter regimes, which are remarkably similar to the power and
reverse strokes exhibited by motile 9+2 cilia. Furthermore, these changes in
the morphology of the filament beating, arising from the fluid-structure
interactions, also induce a significant increase in the hydrodynamic drag of
the filament.Comment: 21 pages, 9 figures. Supplementary Material available upon reques
Regularised non-uniform segments and efficient no-slip elastohydrodynamics
The elastohydrodynamics of slender bodies in a viscous fluid have long been
the source of theoretical investigation, being pertinent to the microscale
world of ciliates and flagellates as well as to biological and engineered
active matter more generally. Though recent works have overcome the severe
numerical stiffness typically associated with slender elastohydrodynamics,
employing both local and non-local couplings to the surrounding fluid, there is
no framework of comparable efficiency that rigorously justifies its
hydrodynamic accuracy. In this study, we combine developments in filament
elastohydrodynamics with a recent slender-body theory, affording algebraic
asymptotic accuracy to the commonly imposed no-slip condition on the surface of
a slender filament of potentially non-uniform cross-sectional radius. Further,
we do this whilst retaining the remarkable practical efficiency of contemporary
elastohydrodynamic approaches, having drawn inspiration from the method of
regularised Stokeslet segments to yield an efficient and flexible slender-body
theory of regularised non-uniform segments
Random blebbing motion: a simple model linking cell structural properties to migration characteristics
If the plasma membrane of a cell is able to delaminate locally from its actin cortex a cellular bleb can be produced. Blebs are pressure driven protrusions, which are noteworthy for their ability to produce cellular motion. Starting from a general continuum mechanics description we restrict ourselves to considering cell and bleb shapes that maintain approximately spherical forms. From this assumption we obtain a tractable algebraic system for bleb formation. By including cell-substrate adhesions we can model blebbing cell motility. Further, by considering mechanically isolated blebbing events, which are randomly distributed over the cell we can derive equations linking the macroscopic migration characteristics to the microscopic structural parameters of the cell. This multiscale modelling framework is then used to provide parameter estimates, which are in agreement with current experimental data. In summary the construction of the mathematical model provides testable relationships between the bleb size and cell motility
Systematic parameterizations of minimal models of microswimming
Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace, arising generically as the leading-order, far-field descriptions of a range of complex biological and artificial swimmers. Though many of these swimmers are associated with intricate, time varying flow fields and changing shapes, we often turn to models with constant, averaged parameters for intuition, basic understanding, and back-of-the-envelope prediction. In this brief study, via an elementary multitimescale analysis, we examine whether the standard use of a priori-averaged parameters in minimal microswimmer models is justified, asking if their behavioural predictions qualitatively align with those of models that incorporate rapid temporal variation through simple extensions. In doing so, we find that widespread, seemingly innocuous choices of parameters can give rise to qualitatively incorrect conclusions from simple models, with the potential to alter our intuition for swimming on the microscale. Further, we highlight and exemplify how a straightforward asymptotic analysis of the non-autonomous models can result in effective, systematic parametrizations of minimal models of microswimming
A hydrodynamic slender-body theory for local rotation at zero Reynolds number
Slender objects are commonplace in microscale flow problems, from soft deformable sensors to biological filaments such as flagella and cilia. While much research has focused on the local translational motion of these slender bodies, relatively little attention has been given to local rotation, even though it can be the dominant component of motion. In this study, we explore a classically motivated ansatz for the Stokes flow around a rotating slender body via superposed rotlet singularities, which leads us to pose an alternative ansatz that accounts for both translation and rotation. Through an asymptotic analysis that is supported by numerical examples, we determine the suitability of these flow ansatzes for capturing the fluid velocity at the surface of a slender body, assuming local axisymmetry of the object but allowing the cross-sectional radius to vary with arclength. In addition to formally justifying the presented slender-body ansatzes, this analysis reveals a markedly simple relation between the local angular velocity and the torque exerted on the body, which we term resistive torque theory. Though reminiscent of classical resistive force theories, this local relation is found to be algebraically accurate in the slender-body aspect ratio, even when translation is present, and is valid and required whenever local rotation contributes to the surface velocity at leading asymptotic order
The control of particles in the Stokes limit
There are numerous ways to control objects in the Stokes regime, with microscale examples ranging from the use of optical tweezers to the application of external magnetic fields. In contrast, there are relatively few explorations of theoretical controllability, which investigate whether or not refined and precise control is indeed possible in a given system. In this work, seeking to highlight the utility and broad applicability of such rigorous analysis, we recount and illustrate key concepts of geometric control theory in the context of multiple particles in Stokesian fluids interacting with each other, such that they may be readily and widely applied in this largely unexplored fluid-dynamical setting. Motivated both by experimental and abstract questions of control, we exemplify these techniques by explicit and detailed application to multiple problems concerning the control of two particles, such as the motion of tracers in flow and the guidance of one sphere by another. Further, we showcase how this analysis of controllability can directly lead to the construction of schemes for control, in addition to facilitating explorations of mechanical efficiency and contributing to our overall understanding of non-local hydrodynamic interactions in the Stokes limit
Systematic parameterisations of minimal models of microswimming
Simple models are used throughout the physical sciences as a means of
developing intuition, capturing phenomenology, and qualitatively reproducing
observations. In studies of microswimming, simple force-dipole models are
commonplace, arising generically as the leading-order, far-field descriptions
of a range of complex biological and artificial swimmers. Though many of these
swimmers are associated with intricate, time varying flow fields and changing
shapes, we often turn to models with constant, averaged parameters for
intuition, basic understanding, and back-of-the-envelope prediction. In this
brief study, via an elementary multi-timescale analysis, we examine whether the
standard use of a priori-averaged parameters in minimal microswimmer models is
justified, asking if their behavioural predictions qualitatively align with
those of models that incorporate rapid temporal variation through simple
extensions. In doing so, we highlight and exemplify how a straightforward
asymptotic analysis of these non-autonomous models can result in effective,
systematic parameterisations of minimal models of microswimming
Concentration-Dependent Domain Evolution in Reaction–Diffusion Systems
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic modelling in developmental biology. Most work to date has considered prescribed domains evolving as given functions of time, but not the scenario of concentration-dependent dynamics, which is also highly relevant in a developmental setting. Here, we study such concentration-dependent domain evolution for reaction–diffusion systems to elucidate fundamental aspects of these more complex models. We pose a general form of one-dimensional domain evolution and extend this to N-dimensional manifolds under mild constitutive assumptions in lieu of developing a full tissue-mechanical model. In the 1D case, we are able to extend linear stability analysis around homogeneous equilibria, though this is of limited utility in understanding complex pattern dynamics in fast growth regimes. We numerically demonstrate a variety of dynamical behaviours in 1D and 2D planar geometries, giving rise to several new phenomena, especially near regimes of critical bifurcation boundaries such as peak-splitting instabilities. For sufficiently fast growth and contraction, concentration-dependence can have an enormous impact on the nonlinear dynamics of the system both qualitatively and quantitatively. We highlight crucial differences between 1D evolution and higher-dimensional models, explaining obstructions for linear analysis and underscoring the importance of careful constitutive choices in defining domain evolution in higher dimensions. We raise important questions in the modelling and analysis of biological systems, in addition to numerous mathematical questions that appear tractable in the one-dimensional setting, but are vastly more difficult for higher-dimensional models
Hard Thermal Loops, Weak Gravitational Fields and The Quark Gluon Energy Momentum Tensor
We use an auxiliary field construction to discuss the hard thermal loop
effective action associated with massless thermal SU(N) QCD interacting with a
weak gravitational field. It is demonstrated that the previous attempt to
derive this effective action has only been partially successful and that it is
presently only known to first order in the graviton coupling constant. This is
still sufficient to enable a calculation of a symmetric traceless quark gluon
plasma energy momentum tensor. Finally, we comment on the conserved currents
and charges of the derived energy momentum tensor.Comment: 26, DAMTP 94-7
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