arXiv subjects

Annette Zippelius

Publications and source records attributed to Annette Zippelius.

At least 19 recordsLinked to original sources

arXiv2026

Complex nonlinear dynamics of area-preserving, active vesicles

We investigate the nonlinear shape dynamics and autonomous propulsion of actively driven quasi-spherical vesicles with locally inextensible membranes at low Reynolds number. Starting from Stokes hydrodynamics, linearized membrane elasticity, and harmonic active forcing, we derive a reduced description in terms of spherical harmonic deformation modes. The global area constraint enforced by local inextensibility is the sole source of dynamic nonlinearity. It confines the dynamics to compact manifolds in the space of possible shapes. Autonomous propulsion arises through nonlinear mode coupling and is determined geometrically by the oriented area swept by the trajectories in shape space. For two active modes, the dynamics reduces to a periodically driven phase equation exhibiting synchronization, phase slips, and mode locking. Introducing a third active mode fundamentally changes the dynamics, giving rise to quasiperiodic invariant tori and resonant periodic cycles. A recurrence diagnostic reveals the resulting resonance structure, while fluctuations of the cycle-averaged propulsion provide an experimentally accessible signature of the underlying shape dynamics. Our results demonstrate that, for actively driven vesicles, a geometric constraint is sufficient to transform an otherwise linear dynamical system into one exhibiting rich nonlinear dynamics.

cond-mat.soft↗

arXiv2026

Amoeboid swimming of active vesicles

We investigate the shape dynamics and migration of weakly deflated active vesicles driven by processes acting either directly in the membrane or transmitted by the cytoskeleton. For a force-free vesicle, local membrane incompressibility suppresses rigid-body translation, so that migration arises from time-dependent shape deformations. Assuming small excess area enables a systematic analysis of the coupled deformation and migration dynamics in free space, i.e. in the absence of substrate adhesion or confinement. Depending on the strength and frequency of the activity, the vesicle exhibits several dynamical regimes, including synchronized oscillations, quasiperiodic shape changes, transitions between non-propelling and propelling states, and intermittent motion.

cond-mat.soft↗

arXiv2025

Amoeboid propulsion of active solid bodies, vesicles and droplets: a comparison

We present a unified discussion of three types of near-spherical amoeboid microswimmers, driven by periodic, axially symmetric, achiral deformations (swim strokes): a solid deformable body, a vesicle with incompressible fluid membrane, and a droplet. Minimal models are used, which characterize the swimmer type only by boundary conditions. We calculate the swimming velocities, the dissipated power and the Lighthill efficiencies within a second order perturbation expansion in the small deformation amplitudes. %Our approach uses spherical harmonics to represent surface deformations and a system of general solutions of the Stokes equation based on vector spherical harmonics. For solid bodies, we reproduce older results by Lighthill and Blake, for vesicles and for droplets we add new results. The unified approach allows for a detailed comparison between the three types of microswimmers. We present such comparisons for swim strokes made up of spherical harmonics of adjacent orders $l$ and $l+1$, as well as for a manifold of swim strokes, made up of spherical harmonics up to order $l=4$, which respect volume- and surface-incompressibility. This manifold is two-dimensional, which allows to present swimming velocities and efficiencies in a compact graphical form. In a race in which each swimmer can choose the stroke that maximizes its speed, the droplet always comes in first, the vesicle comes in second, while the particle finishes third. However, if the three swimmers perform the same stroke, other order of rankings become possible. The maximum of the total efficiency of a droplet is greater than that of a vesicle if the internal dissipation is small. The efficiency of the solid body turns out to be typically two orders of magnitude smaller than that of vesicles and droplets. Optimizing the Lighthill efficiency and optimizing the swimming velocity result in different optimal swim strokes

cond-mat.soft↗

arXiv2023

Deformations of an active liquid droplet

A fluid droplet in general deforms, if subject to active driving, such as a finite slip velocity or active tractions on its interface. We show that these deformations and their dynamics can be computed analytically in a perturbation theory in the inverse surface tension using an approach based on vector spherical harmonics. In lowest order, the deformation is of first order, yet it affects the flow fields inside and outside of the droplet in zeroth order. Hence a correct description of the flow has to allow for shape fluctuations, even in the limit of large surface tension.

cond-mat.soft↗

arXiv2022

From viscous fluids to elastic solids: A perspective on the glass transition

A theory for the non-local stress in liquids captures the crossover from viscous to elastic correlations upon supercooling. It explains the emergence of long-ranged stress fields in glass which originate from the coupling of shear stress to transverse deformations. The Goldstone mode in colloidal glass is shown to be diffusive.

cond-mat.soft↗

arXiv2022

Simple fluid with broken time reversal invariance

We characterize a system of hard spheres with a simple collision rule that breaks time reversal symmetry, but conserves energy. The collisions lead to an a-chiral, isotropic, and homogeneous stationary state, whose properties are determined in simulations and compared to an approximate theory originally developed for elastic hard spheres. In the nonequilibrium fluid state, velocities are correlated, a phenomenon known from other nonequilibrium stationary states. The correlations are long-ranged decaying like $1/r^d$ in $d$ dimensions. Such correlations are expected on general grounds far from equilibrium and had previously been observed in driven or non-stationary systems.

cond-mat.stat-mech↗

arXiv2022

Dynamics of bacteria scanning a porous environment

It has recently been reported that bacteria, such as E.coli and P. putida, perform distinct modes of motion when placed in porous media as compared to dilute regions or free space. This has led us to suggest an efficient strategy for active particles in a disordered environment: reorientations are suppressed in locally dilute regions and intensified in locally dense ones. Thereby the local geometry determines the optimal path of the active agent and substantially accelerates the dynamics for up to two orders of magnitude. We observe a non-monotonic behavior of the diffusion coefficient in dependence on the tumbling rate and identify a localisation transition, either by increasing the density of obstacles or by decreasing the reorientation rate.

cond-mat.soft↗

arXiv2021

Mobilities of a drop and an encapsulated squirmer

We have analyzed the dynamics of a spherical, uni-axial squirmer which is located inside a spherical liquid drop at general position $\bm{r}_s$. The squirmer is subject to an external force and torque in addition to the slip velocity on its surface. We have derived exact analytical expressions for the linear and rotational velocity of the squirmer as well as the linear velocity of the drop for general, non-axisymmetric configurations. The mobilities of both, squirmer and drop, are in general anisotropic, depending on the orientation of $\bm{r}_s$, relative to squirmer axis, external force or torque. We discuss their dependence on the size of the squirmer, its distance from the center of the drop and the viscosities. Our results provide a first step towards a discussion of the trajectories of the composite system of drop and enclosed squirmer.

cond-mat.soft↗

arXiv2020

Trajectories of a droplet driven by an internal active device

We consider a liquid droplet which is propelled solely by internal flow. In a simple model, this flow is generated by an autonomous actuator, which moves on a prescribed trajectory inside the droplet. In a biological system, the device could represent a motor, carrying cargo and moving on a filamentary track. We work out the general framework to compute the self-propulsion of the droplet as a function of the actuating forces and the trajectory. The simplest autonomous device is composed of three point forces. Such a device gives rise to linear, circular or spiraling motion of the droplet, depending on whether the device is stationary or moving along a radial track. As an example of a more complex track we study in detail a spherical looped helix, inspired by recent studies on the propulsion of Synechococcus1 and Myxobacteria2. The droplet trajectories are found to depend strongly on the orientation of the device and the direction of the forces relative to the track with the posibility of unbounded motion even for time independent forcing.

cond-mat.soft↗

arXiv2020

Dynamics of a droplet driven by an internal active device

A liquid droplet, immersed into a Newtonian fluid, can be propelled solely by internal flow. In a simple model, this flow is generated by a collection of point forces, which represent externally actuated devices or model autonomous swimmers. We work out the general framework to compute the self-propulsion of the droplet as a function of the actuating forces and their positions within the droplet. A single point force, F with general orientation and position, r_0, gives rise to both, translational and rotational motion of the droplet. We show that the translational mobility is anisotropic and the rotational mobility can be nonmonotonic as a function of | r_0|, depending on the viscosity contrast. Due to the linearity of the Stokes equation, superposition can be used to discuss more complex arrays of point forces. We analyse force dipoles, such as a stresslet, a simple model of a biflagellate swimmer and a rotlet, representing a helical swimmer, driven by an external magnetic field. For a general force distribution with arbitrary high multipole moments the propulsion properties of the droplet depend only on a few low order multipoles: up to the quadrupole for translational and up to a special octopole for rotational motion. The coupled motion of droplet and device is discussed for a few exemplary cases. We show in particular that a biflagellate swimmer, modeled as a stresslet, achieves a steady comoving state, where the position of the device relative to the droplet remains fixed. In fact there are two fixpoints, symmetric with respect to the center of the droplet. A tiny external force selects one of them and allows to switch between forward and backward motion.

physics.flu-dyn↗

arXiv2020

Integration through transients for inelastic hard sphere fluids

We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalise the Integration Through Transients (\textsc{itt}) formalism to a fluid of dissipative, randomly driven granular particles. The stress relaxation function is computed approximately within a mode-coupling theory---based on the physical picture, that relaxation of shear is dominated by slow structural relaxation, as the glass transition is approached. The transient build-up of stress in steady shear is thus traced back to transient density correlations which are computed self-consistently within mode-coupling theory. The glass transition is signalled by the appearance of a yield stress and a divergence of the Newtonian viscosity, characterizing linear response. For shear rates comparable to the structural relaxation time, the stress becomes independent of shear rate and we observe shear thinning, while for the largest shear rates Bagnold scaling, i.e., a quadratic increase of shear stress with shear rate, is recovered. The rheological properties are qualitatively similar for all values of $\varepsilon$, the coefficient of restitution; however, the magnitude of the stress as well as the range of shear thinning and thickening show significant dependence on the inelasticity.

cond-mat.soft↗

arXiv2019

Chaos and mixing in self-propelled droplets

We consider self-propelled droplets which are driven by internal flow. Tracer particles, which are advected by the flow, in general follow chaotic trajectories, even though the motion of the autonomous swimmer is completely regular. The flow is mixing, and for Péclet and Batchelor numbers, which are realized e.g. in eucaryotic cells, advective mixing can substantially accelerate and even dominate transport by diffusion.

physics.flu-dyn↗

arXiv2019

Unsteady flow, clusters and bands in a model shear-thickening fluid

We analyse the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a range of stress and strainrates where no stationary flow can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between the low and high stress branches, large systems exhibit continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed large scale patterns as well as their dynamics are found to depend on strainrate: At the lower end of the unstable region, force chains merge to form giant bands that span the system in compressional direction and propagate in dilational direction. At the upper end, we observe large scale clusters which extend along the dilational direction and propagate along the compressional direction. Both patterns, bands and clusters, come in with infinite correlation length similar to the sudden onset of system-spanning plugs in impact experiments.

cond-mat.soft↗

arXiv2019

Dynamics of active filaments in porous media

The motion of active polymers in a porous medium is shown to depend critically on flexibilty, activity and degree of polymerization. For given Peclet number, we observe a transition from localisation to diffusion as the stiffness of the chains is increased. Whereas stiff chains move almost unhindered through the porous medium, flexible ones spiral and get stuck. Their motion can be accounted for by the model of a continuous time random walk with a renewal process corresponding to unspiraling. The waiting time distribution is shown to develop heavy tails for decreasing stiffness, resulting in subdiffusive and ultimately caged behaviour.

cond-mat.soft↗

arXiv2018

Linear rheology of reversibly cross-linked biopolymer networks

We suggest a simple model for reversible cross-links, binding and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the timescale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest timescale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau value, which for irreversible cross-linkers extends all the way to the static limit. This additional relaxation mechanism can be controlled by the relative weight of reversible and irreversible linkers.

cond-mat.soft↗

arXiv2018

Rheology of inelastic hard spheres at finite density and shear rate

Considering a granular fluid of inelastic smooth hard spheres we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress $σ$ to the shear rate $\dotγ$, and predictions of the yield stress complete our discussion of granular rheology derived from first principles.

cond-mat.soft↗

arXiv2018

Self propulsion of droplets driven by an active permeating gel

We discuss the flow field and propulsion velocity of active droplets, which are driven by body forces residing on a rigid gel. The latter is modelled as a porous medium which gives rise to permeation forces. In the simplest model, the Brinkman equation, the porous medium is characterised by a single length scale $\ell$ --the square root of the permeability. We compute the flow fields inside and outside of the droplet as well as the energy dissipation as a function of $\ell$. We furthermore show that there are optimal gel fractions, giving rise to maximal linear and rotational velocities. In the limit $\ell\to\infty$, corresponding to a very dilute gel, we recover Stokes flow. The opposite limit, $\ell\to 0$, corresponding to a space filling gel, is singular and not equivalent to Darcy's equation, which cannot account for self-propulsion.

cond-mat.soft↗

arXiv2017

Slow and Long-ranged Dynamical Heterogeneities in Dissipative Fluids

A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, $N_c$, and their radius of gyration, $R_G$. We show that $N_c\propto R_G^{d_f}$, providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, $d_f$, that is observed to increase with packing fraction $ϕ$. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., $ϕ\toϕ_c$. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor $S_4(q,t)$ and the dynamical susceptibility $χ_4(t)$. $S_4(q,t)$ is shown to obey scaling in the full range of packing fractions, $0.6\leqϕ\leq 0.805$, and to become increasingly long-ranged as $ϕ\toϕ_c$. Finite size scaling of $χ_4(t)$ provides a consistency check for the previously analyzed divergences of $χ_4(t)\propto (ϕ-ϕ_c)^{-γ_χ}$ and the correlation length $ξ\propto (ϕ-ϕ_c)^{-γ_ξ}$. We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for $ϕ\toϕ_c$ suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.

cond-mat.dis-nn↗