Papers by Annette Zippelius
Physics of Fluids
A fluid droplet, in general, deforms if subject to active driving, such as a finite slip velocity... more A fluid droplet, in general, deforms if subject to active driving, such as a finite slip velocity or active tractions on its interface. Starting from Stokes equations, we show that these deformations and their dynamics can be computed analytically in a perturbation theory in the inverse of the surface tension γ, by using an approach based on vector spherical harmonics. We consider squirmer models and general active tractions, such as inhomogeneous surface tensions, which may result from the Marangoni effects. In the lowest order, the deformation is of order ε∝1/γ, yet it affects the flow fields inside and outside of the droplet in order to ε0. Hence, a correct description of the flow has to allow for shape fluctuations, —even in the limit of large surface tension. We compute stationary shapes and relaxation times and compare our results to an approach, which discards all effects of deformations on surface tensions. This approach leads to the same propulsion velocity but to significa...
arXiv (Cornell University), Feb 4, 2019
We consider a liquid droplet which is propelled solely by internal flow. In a simple model, this ... more 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 Synechococcus 1 and Myxobacteria 2. 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.
Physical Review Fluids, 2019
We consider self-propelled droplets which are driven by internal flow. Tracer particles, which ar... more 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.
The European Physical Journal E, 2022
We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spheric... more We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position $$\varvec{r}_s$$ 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 $$\varvec{r}_s$$ 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 framework for the discussion of the trajectories of the composite system of drop and enclosed squirmer. Graphical Abstract
The European Physical Journal E, 2018
We discuss the flow field and propulsion velocity of active droplets, which are driven by body fo... more 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 scalethe 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. We furthermore show that there are optimal gel fractions, giving rise to maximal linear and rotational velocities. In the limit → ∞, corresponding to a very dilute gel, we recover Stokes flow. The opposite limit, → 0, corresponding to a space filling gel, is singular and not equivalent to Darcy's equation, which cannot account for self-propulsion
Physical Review Letters, 2019
The motion of active polymers in a porous medium is shown to depend critically on flexibilty, act... more 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.
Journal of Fluid Mechanics, 2017
We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming ... more We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming micro-organisms or artificial micro-swimmers. In contrast to approaches that start from active velocity fields produced by the system, we consider active interface tractions, body force densities and active stresses as the origin of autonomous swimming. For negligible Reynolds number and given activity, we compute the external and internal flow fields as well as the centre of mass velocity and angular velocity of the droplet at fixed time. To construct trajectories from single time snapshots, the evolution of active forces or stresses must be determined in the laboratory frame. Here, we consider the case of active matter, which is carried by a continuously distributed rigid but sparse (cyto)-skeleton that is immersed in the droplet interior. We calculate examples of trajectories of a droplet and its skeleton from force densities or stresses, which may be explicitly time-dependent in a fr...
Neurocomputing, 2001
A stochastic model of synaptic transmission has been designed on the basis of electrophysiologica... more A stochastic model of synaptic transmission has been designed on the basis of electrophysiological experiments. The model includes presynaptic mechanisms of recruitment and calcium related release of vesicles, transmitter dynamics in the cleft and postsynaptic receptor kinetics. Monte Carlo simulations of a single synaptic connection are performed and demonstrate that synapses depress during repetitive presynaptic stimulation due to depletion of presynaptic vesicles as well as receptor desensitization. Only for stimulation frequencies below 40 Hz depression is caused solely presynaptically by depletion of vesicles. It is shown that speci"c physiological conditions determine the frequency dependence of steady state depression currents and set limits on the range of possibly rate-coded transmission.
Physical Review A, 1978
The velocity-autocorrelation function of a tagged particle moving in a classical liquid is expres... more The velocity-autocorrelation function of a tagged particle moving in a classical liquid is expressed in terms of a characteristic oscillator frequency and a frequency-dependent relaxation kernel. The relaxation spectrum is approximated by calculating the interaction of the tagged particle with current excitations of the liquid. The interaction with the longitudinal modes is shown to be responsible for the observed peak structure of the correlation function. The results of the present theory, in particular the values for the diffusion constant, agree well with the molecular-dynamics experiments on argon and rubidium.
Statistical Physics and Thermodynamics of Nonlinear Nonequilibrium Systems, 1993
The Physics of Fluids, 1983
Internally generated vertical vorticity enters the lowest-order amplitude equations for free-slip... more Internally generated vertical vorticity enters the lowest-order amplitude equations for free-slip boundaries in an essential way when the Prandtl number P is finite and the flow three dimensional. For parallel rolls the band of stable wavenumbers is substantially modified from what was previously believed to be correct. In particular there are no stable states for P<0.301. Numerical simulations for free boundaries and larger P suggest a mechanism through which the box size determines the critical Rayleigh number for noisy time dependent convection. A stability analysis of model amplitude equations for rigid boundaries agrees qualitatively with the numerical results of Cleaver or Busse for P≲O(1). There is now considerable continuity between the stability diagrams for rigid and free boundaries.
Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spati... more Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor $S_4(q,t)$. As the fluid approaches structural arrest, i.e. for packing fractions in the range $0.6 \le \phi \le 0.805$, scaling is shown to hold: $S_4(q,t)/\chi_4(t)=s(q\xi(t))$. Both the dynamic susceptibility, $\chi_4(\tau_{\alpha})$, as well as the dynamic correlation length, $\xi(\tau_{\alpha})$, evaluated at the $\alpha$ relaxation time, $\tau_{\alpha}$, can be fitted to a power law divergence at a critical packing fraction. The largest observed correlation length amounts to 72 particle radii. The correlated regions of slow particles are neither compact nor string-like. The effects of inelasticity are probed by varying the coefficient of restitution in the range $0.7 \le \varepsilon \le 1$. Even though the strength of the dynamical heterogeneity changes dramatically with $\varepsilon$, the scaling relations are h...
We investigate dynamical heterogeneity in event driven simulations of a two-dimensional bidispers... more We investigate dynamical heterogeneity in event driven simulations of a two-dimensional bidisperse granular fluid. We study the dynamic susceptibility χ4(t) extracted from two different correlation functions Q(t) and estimate the dynamic correlation length ξ(t) obtained from the four-point structure factor S4(q,τ4), where τ4 is the time corresponding to the maximum of χ4(t). We find that the dynamic correlation length grows as the volume fraction is increased to approach the jamming transition.
Physical Review A, 1987
We study the continuous-time dynamics of a strongly diluted Hopfield model with asymmetric synapt... more We study the continuous-time dynamics of a strongly diluted Hopfield model with asymmetric synaptic connections. The model is exactly soluble for static as well as dynamic properties. The time evolution of the autocorrelation, the susceptibility, and the overlap function of two configurations are given in explicit form.
Physica A: Statistical Mechanics and its Applications, 2006
... Coulomb friction. Based on the Walton model a time evolution operator for the many particle s... more ... Coulomb friction. Based on the Walton model a time evolution operator for the many particle system is introduced, a formalism which is well suited for simple approximations. We ... particles. 2.2.4. Walton model. Tangential restitution ...
Network: Computation in Neural Systems, 1994
We investigate the effect of non-local synaptic enhancement within the framework of networks of f... more We investigate the effect of non-local synaptic enhancement within the framework of networks of formal neurons. Enhancement of nearby synapses on a common axon without simultaneous post- and presynaptic stimulation is modelled by a generalized Hebbian rule. The imprinted patterns of activity are no longer attractors of the network dynamics, but are processed instead. The network acts as a low band-pass filter for spatially uncorrelated patterns and can discriminate spatially correlated patterns, according to their degree and range of correlation. While the network is processing information, it still maintains some of the error-correcting properties of attractor neural networks.
Journal of Theoretical Biology, 2001
Patch clamp recordings of excitatory postsynaptic currents (EPSCs) in central neurons reveal larg... more Patch clamp recordings of excitatory postsynaptic currents (EPSCs) in central neurons reveal large #uctuations in amplitudes and decay times of AMPA-receptor-mediated EPSCs. By using Monte Carlo simulations of synaptic transmission in brainstem interneurons, we tested several hypothesis that could account for the observed variability. The coe$cient of variation (CV) of 0.5 for miniature amplitudes cannot be explained by #uctuations in vesicle content or receptor distribution, but is traced to variations in receptor number, which is estimated as 77$39 receptors per bouton. As the variability of rise times re#ects #uctuations in size of the post-synaptic density and heterogeneity of the receptor distribution, the relatively small CV"0.37 of experimentally determined values points to a homogeneous arrangement of receptors. Within our model the large variability of decay times (CV"0.49) can only be explained by #uctuations in the transmitter time course (mean residence times of 0.4$0.13 ms), presumably resulting from heterogeneities in synaptic morphology. Hence, our simulations indicate that di!erent noise sources control the variability of amplitudes, rise and decay times. In particular, the distribution of decay times yields information about the synaptic transmission process, which cannot be obtained from other observables.
Journal of Physics A: Mathematical and General, 1989
The author considers a Hebbian learning mechanism, which gives rise to a change in synaptic effic... more The author considers a Hebbian learning mechanism, which gives rise to a change in synaptic efficacies only if the postsynaptic neuron is active. The model is solved analytically in the limit of strong dilution. The network is shown to classify initial configurations according to their mean activity and their overlap with one of the learnt patterns. The capacity of the
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Papers by Annette Zippelius