arXiv subjects

Kenta Ishimoto

Publications and source records attributed to Kenta Ishimoto.

At least 37 records · Page 2Linked to original sources

arXiv2023

Reciprocal microswimming in fluctuating and confined environments

From bacteria and sperm cells to artificial microrobots, self-propelled microscopic objects at low Reynolds numbers often perceive fluctuating mechanical and chemical stimuli and contact exterior wall boundaries both in nature and the laboratory. In this study, we theoretically investigate the fundamental features of microswimmers by focusing on their reciprocal deformation. Although the scallop theorem prohibits the net locomotion of reciprocal microswimmers, by analyzing a two-sphere swimmer model, we show that in a fluctuating and geometrically confined environment, reciprocal deformations can afford a statistically average displacement. After designing the shape gait, a reciprocal swimmer can migrate in any direction, even in the statistical sense, while the statistical average of passive rigid particles statistically diffuses in a particular direction in the presence of external boundaries. To elucidate this symmetry breakdown, by introducing an impulse response function, we derive a general formula for predicting the nonzero net displacement of a reciprocal swimmer. Using this theory, we determine the relation between the shape gait and net locomotion as well as the net diffusion constant increase and decrease owing to a reciprocal deformation. Based on these findings and a theoretical formulation, we provide a fundamental basis for environment-coupled statistical locomotion. Thus, this study is valuable for understanding biophysical phenomena in fluctuating environments, designing artificial microrobots, and conducting laboratory experiments.

cond-mat.soft↗

arXiv2023

Generalised Jeffery's equations for rapidly spinning particles. Part 2: Helicoidal objects with chirality

In this two-part study, we investigate the motion of rigid, active objects in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. In Part 2, we derive and analyse governing equations for rapidly spinning complex-shaped particles - general helicoidal objects with chirality. Using the multiscale framework we develop in Part 1 (arXiv:2301.11311), we systematically derive emergent equations of motion for the angular and translational dynamics of these chiral spinning objects. We show that the emergent dynamics due to rapid rotation can be described by effective generalised Jeffery's equations, which differ from the classic versions via the inclusion of additional terms that account for chirality and other asymmetries. Furthermore, we use our analytic results to characterise and quantify the explicit effect of rotation on the effective hydrodynamic shape of the chiral objects, significantly expanding the scope of Jeffery's seminal study.

physics.flu-dyn↗

arXiv2023

Generalised Jeffery's equations for rapidly spinning particles. Part 1: Spheroids

The observed behaviour of passive objects in simple flows can be surprisingly intricate, and is complicated further by object activity. Inspired by the motility of bacterial swimmers, in this two-part study we examine the three-dimensional motion of rigid active particles in shear Stokes flow, focusing on bodies that induce rapid rotation as part of their activity. Here, in Part 1, we develop a multiscale framework to investigate these emergent dynamics and apply it to simple spheroidal objects. In Part 2 (arXiv:2301.11032), we apply our framework to understand the emergent dynamics of more complex shapes; helicoidal objects with chirality. Via a multiple-scales asymptotic analysis for nonlinear systems, we systematically derive emergent equations of motion for long-term trajectories that explicitly account for the strong (leading-order) effects of fast spinning. Supported by numerical examples, we constructively link these effective dynamics to the well-known Jeffery's orbits for passive spheroids, deriving an explicit closed-form expression for the effective shape of the active particle, broadening the scope of Jeffery's seminal study to spinning spheroids.

physics.flu-dyn↗

arXiv2023

Odd elastohydrodynamics: non-reciprocal living material in a viscous fluid

Motility is a fundamental feature of living matter, encompassing single cells and collective behavior. Such living systems are characterized by non-conservativity of energy and a large diversity of spatio-temporal patterns. Thus, fundamental physical principles to formulate their behavior are not yet fully understood. This study explores a violation of Newton's third law in motile active agents, by considering non-reciprocal mechanical interactions known as odd elasticity. By extending the description of odd elasticity to a nonlinear regime, we present a general framework for the swimming dynamics of active elastic materials in low-Reynolds-number fluids, such as wave-like patterns observed in eukaryotic cilia and flagella. We investigate the non-local interactions within a swimmer using generalized material elasticity and apply these concepts to biological flagellar motion. Through simple solvable models and the analysis of {\it Chlamydomonas} flagella waveforms and experimental data for human sperm, we demonstrate the wide applicability of a non-local and non-reciprocal description of internal interactions within living materials in viscous fluids, offering a unified framework for active and living matter physics.

cond-mat.soft↗

arXiv2023

Odd elasticity of a catalytic micromachine

We perform numerical simulations of a model micromachine driven by catalytic chemical reactions. Our model includes a mechano-chemical coupling between the structural variables and the nonequilibrium variable describing the catalytic reactions. The time-correlation functions of the structural variables are calculated and further analyzed in terms of odd Langevin dynamics. We obtain the effective odd elastic constant that manifests the broken time-reversal symmetry of a catalytic micromachine. Within the simulation, we separately estimate the quantity called nonreciprocality and show that its behavior is similar to that of the odd elasticity.Our approach suggests a new method to extract the nonequilibrium properties of a micromachine only by measuring its structural dynamics.

cond-mat.soft↗

arXiv2023

Jeffery's orbits and microswimmers in flows: A theoretical review

In this review, we provide a theoretical introduction to Jeffery's equations for the orientation dynamics of an axisymmetric object in a flow at low Reynolds number, and review recent theoretical extensions and applications to the motions of self-propelled particles, so-called microswimmers, in external flows. Bacteria colonize human organs and medical devices even with flowing fluid, microalgae occasionally cause huge harmful toxic blooms in lakes and oceans, and recent artificial microrobots can migrate in flows generated in well-designed microfluidic chambers. The Jeffery equations, a simple set of ordinary differential equation, provide a useful building block in modeling, analyzing, and understanding these microswimmer dynamics in a flow current, in particular when incorporating the impact of the swimmer shape since the equations contain a shape parameter as a single scalar, known as the Bretherton parameter. The particle orientation forms a closed orbit when situated in a simple shear, and this non-uniform periodic rotational motion, referred to as Jeffery's orbits, is due to a constant of motion in the non-linear equation. After providing a theoretical introduction to microswimmer hydrodynamics and a derivation of the Jeffery equations, we discuss possible extensions to more general shapes, including those with rapid deformation. In the latter part of this review, simple mathematical models of microswimmers in different types of flow fields are described, with a focus on constants of motion and their relation to periodic motions in phase space, together with a breakdown of degenerate orbits, to discuss the stable, unstable, and chaotic dynamics of the system. The discussion in this paper will provide a comprehensive theoretical foundation for Jeffery's orbits and will be useful to understand the motions of microswimmers under various flows.

physics.flu-dyn↗

arXiv2023

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. Whilst much research has focussed 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.

physics.flu-dyn↗

arXiv2023

Onsager's variational principle for nonreciprocal systems with odd elasticity

Using Onsager's variational principle, we derive dynamical equations for a nonequilibrium active system with odd elasticity. The elimination of the extra variable that is coupled to the nonequilibrium driving force leads to the nonreciprocal set of equations for the material coordinates. The obtained nonreciprocal equations manifest the physical origin of the odd elastic constants that are proportional to the nonequilibrium force and the friction coefficients. Our approach offers a systematic and consistent way to derive nonreciprocal equations for active matter in which the time-reversal symmetry is broken.

cond-mat.soft↗

arXiv2022

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.

physics.flu-dyn↗

arXiv2022

Most probable path of an active Brownian particle

In this study, we investigate the transition path of a free active Brownian particle (ABP) on a two-dimensional plane between two given states. The extremum conditions for the most probable path connecting the two states are derived using the Onsager--Machlup integral and its variational principle. We provide explicit solutions to these extremum conditions and demonstrate their nonuniqueness through an analogy with the pendulum equation indicating possible multiple paths. The pendulum analogy is also employed to characterize the shape of the globally most probable path obtained by explicitly calculating the path probability for multiple solutions. We comprehensively examine a translation process of an ABP to the front as a prototypical example. Interestingly, the numerical and theoretical analyses reveal that the shape of the most probable path changes from an I to a U shape and to the $\ell$ shape with an increase in the transition process time. The Langevin simulation also confirms this shape transition. We also discuss further method applications for evaluating a transition path in rare events in active matter.

cond-mat.stat-mech↗

arXiv2022

Time-correlation functions for odd Langevin systems

We investigate the statistical properties of fluctuations in active systems that are governed by non-symmetric responses. Both an underdamped Langevin system with an odd resistance tensor and an overdamped Langevin system with an odd elastic tensor are studied. For a system in thermal equilibrium, the time-correlation functions should satisfy time-reversal symmetry and the anti-symmetric parts of the correlation functions should vanish. For the odd Langevin systems, however, we find that the anti-symmetric parts of the time-correlation functions can exist and that they are proportional to either the odd resistance coefficient or the odd elastic constant. This means that the time-reversal invariance of the correlation functions is broken due to the presence of odd responses in active systems. Using the short-time asymptotic expressions of the time-correlation functions, one can estimate an odd elastic constant of an active material such as an enzyme or a motor protein.

cond-mat.soft↗

arXiv2022

Shapes optimising grand resistance tensor entries for a rigid body in a Stokes flow

We investigate the optimal shapes of the hydrodynamic resistance of a rigid body set in motion in a Stokes flow. In this low Reynolds number regime, the hydrodynamic drag properties of an object are encoded in a finite number of parameters contained in the grand resistance tensor. Considering these parameters as objective functions to be optimised, we use calculus of variations techniques to derive a general shape derivative formula, allowing to specify how to deform the body shape to improve the objective value of any given resistance tensor entry. We then describe a practical algorithm for numerically computing the optimized shapes and apply it to several examples. Numerical results reveal interesting new geometries when optimizing the extra-diagonal inputs to the strength tensor, including the emergence of a chiral helical shape when maximising the coupling between the hydrodynamic force and the rotational motion. With a good level of adaptability to different applications, this work paves the way for a new analysis of the morphological functionality of microorganisms and for future advances in the design of microswimmer devices.

physics.flu-dyn↗

arXiv2022

Self-organized swimming with odd elasticity

We theoretically investigate self-oscillating waves of an active material, which have recently been introduced as a non-symmetric part of the elastic moduli, termed odd elasticity. Using Purcell's three-link swimmer model, we reveal that an odd-elastic filament at low Reynolds number can swim in a self-organized manner and that the time-periodic dynamics are characterized by a stable limit cycle generated by elastohydrodynamic interactions. Also, we consider a noisy shape gait and derive a swimming formula for a general elastic material in the Stokes regime with its elasticity modulus being represented by a non-symmetric matrix, demonstrating that the odd elasticity produces biased net locomotion from random noise.

cond-mat.soft↗

arXiv2022

Emergent rheotaxis of shape-changing swimmers in Poiseuille flow

A simple model for the motion of shape-changing swimmers in Poiseuille flow was recently proposed and numerically explored by Omori et al. (2022). These explorations hinted that a small number of interacting mechanics can drive long-time behaviours in this model, cast in the context of the well-studied alga Chlamydomonas and its rheotactic behaviours in such flows. Here, we explore this model analytically via a multiple-scale asymptotic analysis, seeking to formally identify the causal factors that shape the behaviour of these swimmers in Poiseuille flow. By capturing the evolution of a Hamiltonian-like quantity, we reveal the origins of the long-term drift in a single swimmer-dependent constant, whose sign determines the eventual behaviour of the swimmer. This constant captures the nonlinear interaction between the oscillatory speed and effective hydrodynamic shape of deforming swimmers, driving drift either towards or away from rheotaxis.

physics.flu-dyn↗

arXiv2021

The effects of rapid yawing on simple swimmer models and planar Jeffery's orbits

Over a sufficiently long period of time, or from an appropriate distance, the motion of many swimmers can appear smooth, with their trajectories appearing almost ballistic in nature and slowly varying in character. These long-time behaviours, however, often mask more complex dynamics, such as the side-to-side snakelike motion exhibited by spermatozoa as they swim, propelled by the frequent and periodic beating of their flagellum. Many models of motion neglect these effects in favour of smoother long-term behaviours, which are often of greater practical interest than the small-scale oscillatory motion. Whilst it may be tempting to ignore any yawing motion, simply assuming that any effects of rapid oscillations cancel out over a period, a precise quantification of the impacts of high-frequency yawing is lacking. In this study, we systematically evaluate the long-term effects of general high-frequency oscillations on translational and angular motion, cast in the context of microswimmers but applicable more generally. Via a multiple-scales asymptotic analysis, we show that rapid oscillations can cause a long-term bias in the average direction of progression. We identify sufficient conditions for an unbiased long-term effect of yawing, and we quantify how yawing modifies the speed of propulsion and the effective hydrodynamic shape when in shear flow. Furthermore, we investigate and justify the long-time validity of the derived leading-order solutions and, by direct computational simulation, we evidence the relevance of the presented results to a canonical microswimmer.

cond-mat.soft↗

arXiv2021

Squirmer hydrodynamics near a periodic surface topography

The behaviour of microscopic swimmers has previously been explored near large scale confining geometries and in the presence of very small-scale surface roughness. Here we consider an intermediate case of how a simple microswimmer, the tangential spherical squirmer, behaves adjacent to singly- and doubly-periodic sinusoidal surface topographies that spatially oscillate with an amplitude that is an order of magnitude less than the swimmer size and wavelengths within an order of magnitude of this scale. The nearest neighbour regularised Stokeslet method is used for numerical explorations after validating its accuracy for a spherical tangential squirmer that swims stably near a flat surface. The same squirmer is then introduced to the different surface topographies. The key governing factor in the resulting swimming behaviour is the size of the squirmer relative to the surface topography wavelength. When the squirmer is much larger, or much smaller, than the surface topography wavelength then directional guidance is not observed. Once the squirmer size is on the scale of the topography wavelength limited guidance is possible, often with local capture in the topography troughs. However, complex dynamics can also emerge, especially when the initial configuration is not close to alignment along topography troughs or above topography crests. In contrast to sensitivity in alignment and the topography wavelength, reductions in the amplitude of the surface topography or variations in the shape of the periodic surface topography do not have extensive impacts on the squirmer behaviour. Our findings more generally highlight that detailed numerical explorations are necessary to determine how surface topographies may interact with a given swimmer that swims stably near a flat surface and whether surface topographies may be designed to provide such swimmers with directional guidance.

physics.flu-dyn↗

arXiv2021

Control and controllability of microswimmers by a shearing flow

With the continuing rapid development of artificial microrobots and active particles, questions of microswimmer guidance and control are becoming ever more relevant and prevalent. In both the applications and theoretical study of such microscale swimmers, control is often mediated by an engineered property of the swimmer, such as in the case of magnetically propelled microrobots. In this work, we will consider a modality of control that is applicable in more generality, effecting guidance via modulation of a background fluid flow. Here, considering a model swimmer in a commonplace flow and simple geometry, we analyse and subsequently establish the efficacy of flow-mediated microswimmer positional control, later touching upon a question of optimal control. Moving beyond idealised notions of controllability and towards considerations of practical utility, we then evaluate the robustness of this control modality to sources of variation that may be present in applications, examining in particular the effects of measurement inaccuracy and rotational noise. This exploration gives rise to a number of cautionary observations, which, overall, demonstrate the need for the careful assessment of both policy and behavioural robustness when designing control schemes for use in practice.

cond-mat.soft↗

arXiv2021

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 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.

physics.flu-dyn↗