arXiv subjects

Kenta Ishimoto

Publications and source records attributed to Kenta Ishimoto.

At least 19 recordsLinked to original sources

arXiv2026

Geometric formulation of state-dependent Langevin dynamics using scalar free energy

Stochastic dynamics with state-dependent diffusion arise broadly in confined, anisotropic, and hydrodynamically coupled systems. The conventional Langevin equation contains a spurious drift associated with multiplicative noise. Since the restricted free energy is generally non-scalar, the covariance is not explicit. Here, we reformulate state-dependent Langevin dynamics using a scalar free energy and a diffusion metric defined by the inverse diffusion tensor. The conventional spurious drift is then expressed as a Christoffel contribution. Although our formulation is mathematically equivalent to the conventional one through the relation between the restricted and scalar free energies, it makes coordinate covariance explicit and enables the phenomenological construction of thermodynamic potentials directly from system symmetries. We demonstrate its consistency in representative examples of state-dependent diffusion arising from coordinate transformations, geometric confinement, and projection from curved to flat spaces.

cond-mat.soft↗

arXiv2026

Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics

The Onsager principle provides a variational route to the phenomenological equations of dissipative dynamics through the minimization of the Rayleighian. We develop a covariant formulation of the Onsager principle for active and inertial systems, ensuring geometric consistency under coordinate transformations. To further incorporate thermal fluctuations, we formulate the Onsager-Machlup principle for active and inertial systems by considering the Onsager-Machlup functional and the corresponding path probability for stochastic trajectories. Requiring that the path probability obeys the detailed fluctuation theorem, we show that the extended Onsager-Machlup theory is consistent with stochastic thermodynamics. The extended OP and OMP offer a unified and useful variational framework for deriving the dynamical equations of active and inertial systems.

cond-mat.soft↗

arXiv2026

Effective roles of the head and flagellum in sperm motility

In the low Reynolds number fluid environment that microswimmers encounter, back-and-forth motion cannot lead to net displacement. In mammalian sperm, the mechanical wave propagating along their single flagellum breaks the cancellation between back-and-forth motion and, therefore, is assumed to define the movement direction. Here, we show experimentally that the sperm head movement direction is not opposite to the wave propagation direction when sperm move in a viscoelastic fluid next to a solid substrate. The oscillation of the movement direction is out of phase with the oscillation of the wave direction, and the movement has a larger amplitude than the wave direction. When we tried to reconstruct the movement direction as a linear combination of the head orientation and the wave direction, we found that the contributions from these two changed in time. Further, the last bend of the flagellum does not move in the lab frame (as observed under the microscope) on a deformable polydimethylsiloxane (PDMS) substrate, which likely results from the flagellum indenting the surface, providing a new mechanism for locomotion. Overall, our results highlight the appearance of the sperm head in steering motility and provide quantitative tests on sperm chemotaxis and flagellar bending mechanism.

physics.bio-ph↗

arXiv2026

Data-driven geometric phase in biological locomotion

Geometric phase quantifies net locomotion in dissipative media via gauge theory, but linking this theoretical quantity to noisy, sparse, and weakly periodic biological shape data is challenging. We develop a theory-guided, data-driven Koopman autoencoder to recover the limit cycle embedded in imperfect cyclic data and extract shape gaits and geometric phase from sperm and nematode data. We introduce a geometric phase sensitivity function that quantifies responses to shape perturbations and reveals mechanical information using only gauge-theoretic structure, without assuming mechanical laws.

physics.bio-ph↗

arXiv2026

Neural optimization of the most probable paths of 3D active Brownian particles

We develop a variational neural-network framework to determine the most probable path (MPP) of a 3D active Brownian particle (ABP) by directly minimizing the Onsager-Machlup integral (OMI). To obtain the OMI, we use the Onsager-Machlup variational principle for active systems and construct the Rayleighian of the ABP by including its active power. This approach reveals geometric transitions of the MPP from in-plane I- and U-shaped paths to 3D helical paths as the final time and net displacement are varied. We also demonstrate that the initial and final boundary conditions have a significant impact on the MPPs. Our results show that neural optimization combined with the Onsager-Machlup variational principle provides an efficient and versatile framework for exploring optimal transition pathways in active and nonequilibrium systems.

cond-mat.soft↗

arXiv2026

Demon's variational principle for informational active matter

The interplay between information, dissipation, and control is reshaping our understanding of thermodynamics in feedback-regulated systems. We develop the informational Onsager-Machlup principle, a generalized variational framework that unifies energetic, dissipative, and informational contributions within a single formalism. This framework introduces a conditioned Onsager-Machlup integral to quantify path entropy under specified memory states and enables the derivation of cumulant generating functions for arbitrary observables in systems with measurement and feedback. Our formulation is consistent with stochastic thermodynamics and information thermodynamics. Applying this principle to a minimal model of an information-driven swimmer, we obtain analytical expressions for the mean velocity and higher-order cumulants in the single-measurement case. For repeated measurements and the steady state, we derive approximate analytical expressions by using a Gaussian closure for the distribution of measured velocities. Our analytical expression shows good agreement with numerical results, except for cases of extreme drag asymmetry.

cond-mat.soft↗

arXiv2026

Hydrodynamic origins of symmetric swimming strategies

Efficient locomotion is important for the evolution of complex life, yet the physical principles selecting specific swimming strokes often remain entangled with biological constraints. In viscous fluids, the scallop theorem constrains the temporal organization of strokes, but no analogous principle is known for their spatial structure, leaving the prevalence of symmetric gaits across diverse organisms without a physical explanation. Here we show that spatial symmetry acts as an emergent organizing principle for efficiency in viscous fluids. By analysing deformable swimmers whose strokes are not constrained to any particular symmetry class, we identify a hydrodynamic duality: symmetric and anti-symmetric strokes are dynamically equivalent, yielding identical speeds and efficiencies, which we prove are optimal among all strokes. We validate this using numerical simulations of Stokes flow, demonstrating that these symmetry rules persist even in three-dimensional body plans. Our results suggest that the prevalence of symmetric and alternating gaits in nature reflects not merely a developmental constraint, but a physical optimality principle for locomotion in viscous environments, complementing developmental and neural constraints.

physics.bio-ph↗

arXiv2026

Most probable path and invariant sets in noise-induced transition to turbulence

Turbulence transition often arises from a subcritical transition between bistable states characterized by invariant sets of deterministic dynamical systems, and such transitions can be triggered by system noise as rare events. In this study, we employ the Onsager-Machlup (OM) formulation of stochastic dynamics to examine the Hamilton equations governing the most probable transition paths (MPPs). We introduce an effective potential function, termed the OM potential, which depends on the noise strength. Focusing on the Dauchot-Manneville model as a minimal system with an edge state, we comprehensively analyze the MPP between laminar and turbulent states for different transition times. We find that the MPPs cross the separatrix at nearly the same point regardless of the transition time, and the obtained OM action values suggest that the transition to turbulence occurs more frequently than the transition to the laminar state. Moreover, we numerically demonstrate that the noise-induced transition paths follow the OM potential landscape and its bifurcation diagram, indicating that the qualitative behavior of the MPPs is determined by the OM potential. Our methodology formulated in general dynamical systems provides a theoretical basis for predicting noise-induced transitions among invariant sets of the dynamics.

physics.flu-dyn↗

arXiv2025

Emergence of edge state in suspension of self-propelled particles

We numerically study a model convection system of a suspension of self-propelled particles, motivated by recent experimental findings of localized and bistable bioconvection pattern, being distinct from classical Rayleigh--Bénard convection. Linear stability analysis of the model system reveals that the trivial noncovection state is stabilized by an increase of self-propelled speed in the vertical direction. Through numerical simulations, we found a nonlinear convection state even when the nonconvection state is stable. Applying ideas and tools developed in wall-bounded flows, we numerically identified an edge state, which is an unstable solution on a basin boundary in the model dynamical systems.

physics.flu-dyn↗

arXiv2025

Bending-compression coupling in extensible slender microswimmers

Undulatory slender objects have been a central theme in the hydrodynamics of swimming at low Reynolds number, where the slender body is usually assumed to be inextensible, although some microorganisms and artificial microrobots largely deform with compression and extension. Here, we theoretically study the coupling between the bending and compression/extension shape modes, using a geometrical formulation of microswimmer hydrodynamics to deal with the non-commutative effects between translation and rotation. By means of a coarse-grained minimal model and systematic perturbation expansions for small bending and compression/extension, we analytically derive the swimming velocities and report three main findings. First, we revisit the role of anisotropy in the drag ratio of the resistive force theory and generally demonstrate that no motion is possible for uniform compression with isotropic drag. We then find that the bending-compression/extension coupling generates lateral and rotational motion, which enhances the swimmer's manoeuvrability, as well as changes in progressive velocity at a higher order of expansion, while the coupling effects depend on the phase difference between the two modes. Finally, we demonstrate the importance of often-overlooked Lie bracket contributions in computing net locomotion from a deformation gait. Our study sheds light on compression as a forgotten degree of freedom in swimmer locomotion, with important implications for microswimmer hydrodynamics, including understanding of biological locomotion mechanisms and design of microrobots.

physics.flu-dyn↗

arXiv2025

Motility and rotation of multi-timescale microswimmers in linear background flows

Microswimming cells and robots exhibit diverse behaviours due to both their swimming and their environment. One of the core environmental features impacting inertialess swimming is background flows. While the influence of select flows, particularly shear flows, have been extensively investigated, these are special cases. Here, we examine inertialess swimmers in more general flows, specifically general linear planar flows that may also possess rapid oscillations. Relatively weak symmetry constraints are imposed on the swimmer to ensure planarity and to reduce complexity. A further constraint reflecting common observation is imposed, namely that the swimmer is inefficient, which we suitably define. This introduces two separate timescales: a fast timescale associated with swimmer actuation, and a second timescale associated with net swimmer movement, with inefficiency dictating that this latter timescale is much slower, allowing for a multiple timescale simplification of the governing equations. With the exception of mathematically precise edge cases, we find that the behaviour of the swimmer is dictated by two parameter groupings, both of which measure balances between the angular velocity and rate of strain of the background flow. While the measures of flow angular velocity and strain rates that primarily govern the rotational dynamics are modulated by swimmer properties, the primary features of the translational motion are determined solely by a ratio of flow angular velocity to strain rate. Hence, a simple classification of the swimmer dynamics emerges. For example, this illustrates the limited extent to which, and how, microswimmers may control their orientations and trajectories in flows.

physics.flu-dyn↗

arXiv2024

Locomotion on a lubricating fluid with spatial viscosity variations

We studied locomotion of a crawler on a thin Newtonian fluid film whose viscosity varied spatially. We first derived a general locomotion velocity formula with fluid viscosity variations via the lubrication theory. For further analysis, the surface of the crawler was described by a combination of transverse and longitudinal travelling waves and we analysed the time-averaged locomotion behaviours under two scenarios: (i) a sharp viscosity interface and (ii) a linear viscosity gradient. Using the asymptotic expansions of small surface deformations and the method of multiple time-scale analysis, we derived an explicit form of the average velocity that captures nonlinear, accumulative interactions between the crawler and the spatially varying environment. (i) In the case of a viscosity interface, the time-averaged speed of the crawler is always slower than that in the uniform viscosity, for both the transverse and longitudinal wave cases. Notably, the speed reduction is most significant when the crawler's front enters a more viscous layer and the crawler's rear exits from the same layer. (ii) In the case of a viscosity gradient, the crawler's speed becomes slower for the transverse wave, while for the longitudinal wave, the corrections are of a higher order compared with the uniform viscosity case. As an application of the derived locomotion velocity formula, we also analysed the impacts of a substrate topography to the average speed. Our analysis illustrates the fundamental importance of interactions between a locomotor and its environment, and separating the time scale behind the locomotion.

physics.flu-dyn↗

arXiv2024

Inertial focusing of spherical capsule in pulsatile channel flows

We present numerical analysis of the lateral movement of spherical capsule in the steady and pulsatile channel flow of a Newtonian fluid, for a wide range of oscillatory frequency. Each capsule membrane satisfying strain-hardening characteristic is simulated for different Reynolds numbers Re and capillary numbers Ca. Our numerical results showed that capsules with high Ca exhibit axial focusing at finite Re similarly to the inertialess case. We observe that the speed of the axial focusing can be substantially accelerated by making the driving pressure gradient oscillating in time. We also confirm the existence of an optimal frequency which maximises the speed of axial focusing, that remains the same found in the absence of inertia. For relatively low Ca, on the other hand, the capsule exhibits off-centre focusing, resulting in various equilibrium radial positions depending on Re. Our numerical results further clarifies the existence of a specific Re for which the effect of the flow pulsation to the equilibrium radial position is maximum. The roles of channel size on the lateral movements of the capsule are also addressed. Throughout our analyses, we have quantified the radial position of the capsule in a tube based on an empirical expression. Given that the speed of inertial focusing can be controlled by the oscillatory frequency, the results obtained here can be utilised for label-free cell alignment/sorting/separation techniques, e.g., for circulating tumor cells in cancer patients or precious hematopoietic cells such as colony-forming cells.

physics.flu-dyn↗

arXiv2024

Statistical formulation of Onsager-Machlup variational principle

Onsager's variational principle (OVP) provides us with a systematic way to derive dynamical equations for various soft matter and active matter. By reformulating the Onsager-Machlup variational principle (OMVP), which is a time-global principle, we propose a new method to incorporate thermal fluctuations. To demonstrate the utility of the statistical formulation of OMVP (SOMVP), we obtain the diffusion constant of a Brownian particle embedded in a viscous fluid only by maximizing the modified Onsager-Machlup integral for the surrounding fluid. We also apply our formulation to a Brownian particle in a steady shear flow, which is a typical example of a non-equilibrium system. Possible extensions of our formulation to internally driven active systems are discussed.

cond-mat.soft↗

arXiv2024

Localization and bistability of bioconvection in a doubly periodic domain

A suspension of swimming microorganisms often generates a large-scale convective pattern known as bioconvection. In contrast to the thermal Rayleigh-Benard system, recent experimental studies report an emergence of steady localized convection patterns and bistability near the onset of instability in bioconvection systems. In this study, to understand the underlying mechanisms and identify the roles of particle self-propulsion in pattern formation, we theoretically and numerically investigate a model bioconvection system in a two-dimensional periodic boundary domain. In doing so, we extend a standard bioconvection model by introducing the equilibrium density profile as an independent parameter, for which the particle self-propulsion is treated as an independent dimensional parameter. Since the large-scale vertical structure dominates in this system, we are able to simplify the model by truncating the higher vertical modes. With this truncated model, we analytically derived the neutrally stable curve and found that the particle motility stabilizes the system. We then numerically analyzed the bifurcation diagram and found the bistable structure at the onset of instability. These findings, localization and bistability, are consistent with experimental observations. We further examined the global structure of the bistable dynamical system and found that the non-trivial unstable steady solution behaves as an edge state that separates the basins of attractors. These results highlight the importance of particle self-propulsion in bioconvection, and more generally our methodology based on the dynamical systems theory is useful in understanding complex flow patterns in nature.

physics.flu-dyn↗

arXiv2024

Emergence of odd elasticity in a microswimmer using deep reinforcement learning

We use the Deep Q-Network with reinforcement learning to investigate the emergence of odd elasticity in an elastic microswimmer model. For an elastic microswimmer, it is challenging to obtain the optimized dynamics due to the intricate elastohydrodynamic interactions. However, our machine-trained model adopts a novel transition strategy (the waiting behavior) to optimize the locomotion. For the trained microswimmers, we evaluate the performance of the cycles by the product of the loop area (called non-reciprocality) and the loop frequency, and show that the average swimming velocity is proportional to the performance. By calculating the force-displacement correlations, we obtain the effective odd elasticity of the microswimmer to characterize its non-reciprocal dynamics. This emergent odd elasticity is shown to be closely related to the loop frequency of the cyclic deformation. Our work demonstrates the utility of machine learning in achieving optimal dynamics for elastic microswimmers and introduces post-analysis methods to extract crucial physical quantities such as non-reciprocality and odd elasticity.

cond-mat.soft↗

arXiv2024

Robust undulatory locomotion via neuromechanical adjustments in a dissipative medium

Dissipative environments are ubiquitous in nature, from microscopic swimmers in low-Reynolds-number fluids to macroscopic animals in frictional media. In this study, motivated by various behaviours of {\it Caenorhabditis elegans} during swimming and crawling locomotion, we consider a mathematical model of a slender elastic locomotor with an internal rhythmic neural pattern generator. By analysing the dynamical systems of the model using a Poincaré section, we found that local neuromechanical adjustments to the environment can create robust undulatory locomotion. This progressive behaviour emerges as a global stable periodic orbit in a broad range of parameter regions. Further, by controlling the mechanosensation, we were able to design the dynamical systems to manoeuvre with progressive, reverse, and turning motions as well as apparently random, complex behaviours, as experimentally observed in {\it C. elegans}. The mechanisms found in this study, together with our methodologies with the dynamical systems viewpoint, are useful for deciphering complex animal adaptive behaviours and also designing adaptive robots for a wide range of dissipative environments.

nlin.AO↗

arXiv2024

Generalised Taylor dispersion of chiral microswimmers

Transport phenomena of microswimmers in fluid flows play a crucial role in various biological processes, including bioconvection and cell sorting. In this paper, we investigate the dispersion behavior of chiral microswimmers in a simple shear flow utilizing the generalized Taylor dispersion (GTD) theory, motivated by biased locomotion of bacterial swimmers known as bacterial rheotaxis. We thus focus on the influence of shear-induced torque effects due to particle chirality, employing an extended Jeffery equation for individual deterministic dynamics. We then numerically calculate macroscopic parameters including averaged swimming velocity and effective diffusion tensor using spherical harmonic expansion, and argue the obtained results based on the fixed points and their stability of the orientational dynamical systems. Our results reveal that chiral effects induce biased locomotion and we observe qualitative transitions in the orientational distribution with increasing Peclét number, aligning with previous experimental findings. The diffusion tensor analysis highlights significant reduction in the diffusion coefficient perpendicular to the flow plane due to chirality. This suggests potential applications in flow-mediated cell separation and we numerically demonstrate such chirality-induced fluid transportation. The presented methods will be useful in predicting and controlling dispersion behaviors of such chiral microswimmers.

physics.flu-dyn↗