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Jan Kierfeld

Publications and source records attributed to Jan Kierfeld.

At least 19 recordsLinked to original sources
arXiv2026

Generation of two-dimensional pulses in lipid monolayers by rapid photoswitching

We study pressure pulse generation and propagation in lipid monolayers by an experimental approach employing rapid photoisomerization of photoswitchable lipids (azoPC). This allows us to generate longitudinal surface pressure pulses by optical flash excitation in both free and constrained layer geometries. We compare the observed pulse shapes with a theoretical approach based on a nonlinear fractional wave equation for a surface displacement field, where a fractional time derivative term captures the hydrodynamics of the monolayer subphase. We explore channel geometries of different lengths and widths and find quantitative agreement between theory and experiment regarding pulse speed and pulse shapes. For narrow channels, we employ a one-dimensional version of the fractional wave equation to study pulse propagation without any fit parameters by using the pressure signal at a close pressure sensor as boundary condition to predict the pressure signal at a second far sensor. A full two-dimensional description can capture all effects arising from the channel geometry for wider channels using one common set of fit parameters for the pulse excitation that can be applied to all geometries. The nonlinearity in the fractional wave equation plays no role in explaining the observed pulse shapes because pulse amplitudes generated by azoPC photoswitching remain very small.

cond-mat.soft↗
arXiv2021

Kinetic Event-Chain Algorithm for Active Matter

We present a cluster kinetic Monte-Carlo algorithm for active matter systems of self-propelled particles with special focus on steric interactions. The kinetic event-chain algorithm is based on the event-chain Monte-Carlo method and is applied to active Brownian disks in two dimensions. The algorithm assigns Monte-Carlo moves of active disks a mean time based on a comparison between Brownian dynamics and the dynamics of the event-chain Monte-Carlo method. This time is used to perform diffusional rotation of their propulsion force. We show that the algorithm correctly and efficiently reproduces various physical results ranging from single-particle dynamics to many-body-effects. In particular, we reproduce the phase diagram of active disks and the motility-induced phase separated region with high accuracy. The kinetic event-chain algorithm is shown to be much faster - at comparable accuracy - than (event-driven) Brownian dynamics algorithms, enabling large-scale simulations up to giant systems with $10^5$ particles on standard desktop hardware.

cond-mat.soft↗
arXiv2021

Chemomechanical simulation of microtubule dynamics with explicit lateral bond dynamics

We introduce and parameterize a chemomechanical model of microtubule dynamics on the dimer level, which is based on the allosteric tubulin model and includes attachment, detachment and hydrolysis of tubulin dimers as well as stretching of lateral bonds, bending at longitudinal junctions, and the possibility of lateral bond rupture and formation. The model is computationally efficient such that we reach sufficiently long simulation times to observe repeated catastrophe and rescue events at realistic tubulin concentrations and hydrolysis rates, which allows us to deduce catastrophe and rescue rates. The chemomechanical model also allows us to gain insight into microscopic features of the GTP-tubulin cap structure and microscopic structural features triggering microtubule catastrophes and rescues. Dilution simulations show qualitative agreement with experiments. We also explore the consequences of a possible feedback of mechanical forces onto the hydrolysis process and the GTP-tubulin cap structure.

q-bio.SC↗
arXiv2021

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

We present a theory for the self-propulsion of symmetric, half spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air-water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion-advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient and Marangoni flow forces. We unravel, whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occurs for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.

physics.flu-dyn↗
arXiv2021

Surfactant-loaded capsules as Marangoni microswimmers at the air-water interface: Symmetry breaking and spontaneous propulsion by surfactant diffusion and advection

We present a realization of a fast interfacial Marangoni microswimmer by a half-spherical alginate capsule at the air-water interface, which diffusively releases water-soluble spreading molecules (weak surfactants such as polyethylene glycol (PEG)), which act as "fuel" by modulating the air-water interfacial tension. For a number of different fuels, we can observe symmetry breaking and spontaneous propulsion although the alginate particle and emission are isotropic. The propulsion mechanism is similar to soap or camphor boats, which are, however, typically asymmetric in shape or emission to select a swimming direction. We develop a theory of Marangoni boat propulsion starting from low Reynolds numbers by analyzing the coupled problems of surfactant diffusion and advection and fluid flow, which includes surfactant-induced fluid Marangoni flow, and surfactant adsorption at the air-water interface; we also include a possible evaporation of surfactant. The swimming velocity is determined by the balance of drag and Marangoni forces. We show that spontaneous symmetry breaking resulting in propulsion is possible above a critical dimensionless surfactant emission rate (Peclet number). We derive the relation between Peclet number and swimming speed and generalize to higher Reynolds numbers utilizing the concept of the Nusselt number. The theory explains the observed swimming speeds for PEG-alginate capsules, and we unravel the differences to other Marangoni boat systems based on camphor, which are mainly caused by surfactant evaporation from the liquid-air interface. The capsule Marangoni microswimmers also exhibit surfactant-mediated repulsive interactions with walls, which can be qualitatively explained by surfactant accumulation at the wall.

cond-mat.soft↗
arXiv2021

Event-Chain Monte-Carlo Simulations of Dense Soft Matter Systems

We discuss the rejection-free event-chain Monte-Carlo algorithm and several applications to dense soft matter systems. Event-chain Monte-Carlo is an alternative to standard local Markov-chain Monte-Carlo schemes, which are based on detailed balance, for example the well-known Metropolis-Hastings algorithm. Event-chain Monte-Carlo is a Markov chain Monte-Carlo scheme that uses so-called lifting moves to achieve global balance without rejections (maximal global balance). It has been originally developed for hard sphere systems but is applicable to many soft matter systems and particularly suited for dense soft matter systems with hard core interactions, where it gives significant performance gains compared to a local Monte-Carlo simulation. The algorithm can be generalized to deal with soft interactions and with three-particle interactions, as they naturally arise, for example, in bead-spring models of polymers with bending rigidity. We present results for polymer melts, where the event-chain algorithm can be used for an efficient initialization. We then move on to large systems of semiflexible polymers that form bundles by attractive interactions and can serve as model systems for actin filaments in the cytoskeleton. The event chain algorithm shows that these systems form networks of bundles which coarsen similar to a foam. Finally, we present results on liquid crystal systems, where the event-chain algorithm can equilibrate large systems containing additional colloidal disks very efficiently, which reveals the parallel chaining of disks.

cond-mat.soft↗
arXiv2020

Snapping elastic disks as microswimmers: swimming at low Reynolds numbers by shape hysteresis

We illustrate a concept for shape-changing microswimmers, which exploits the hysteresis of a shape transition of an elastic object, by an elastic disk undergoing cyclic localized swelling. Driving the control parameter of a hysteretic shape transition in a completely time-reversible manner gives rise to a non-time-reversible shape sequence and a net swimming motion if the elastic object is immersed into a viscous fluid. We prove this concept with a microswimmer which is a flat circular elastic disk that undergoes a transition into a dome-like shape by localized swelling of an inner disk. The control parameter of this shape transition is a scalar swelling factor of the disk material. With a fixed outer frame with an additional attractive interaction in the central region, the shape transition between flat and dome-like shape becomes hysteretic and resembles a hysteretic opening and closing of a scallop. Employing Stokesian dynamics simulations of a discretized version of the disk we show that the swimmer is effectively moving into the direction of the opening of the dome in a viscous fluid if the swelling parameter is changed in a time-reversible manner. The swimming mechanism can be qualitatively reproduced by a simple 9-bead model.

cond-mat.soft↗
arXiv2020

Chaining of hard disks in nematic needles: particle-based simulation of colloidal interactions in liquid crystals

Colloidal particles suspended in liquid crystals can exhibit various effective anisotropic interactions that can be tuned and utilized in self-assembly processes. We simulate a two-dimensional system of hard disks suspended in a solution of dense hard needles as a model system for colloids suspended in a nematic lyotropic liquid crystal. The novel event-chain Monte Carlo technique enables us to directly measure colloidal interactions in a microscopic simulation with explicit liquid crystal particles in the dense nematic phase. We find a directional short-range attraction for disks along the director, which triggers chaining parallel to the director and seemingly contradicts the standard liquid crystal field theory result of a quadrupolar attraction with a preferred ${45^{\circ}}$ angle. Our results can be explained by a short-range density-dependent depletion interaction, which has been neglected so far. Directionality and strength of the depletion interaction are caused by the weak planar anchoring of hard rods. The depletion attraction robustly dominates over the quadrupolar elastic attraction if disks come close. Self-assembly of many disks proceeds via intermediate chaining, which demonstrates that in lyotropic liquid crystal colloids depletion interactions play an important role in structure formation processes.

cond-mat.soft↗
arXiv2020

Pendant Drop Tensiometry: A Machine Learning Approach

Modern pendant drop tensiometry relies on numerical solution of the Young-Laplace equation and allow to determine the surface tension from a single picture of a pendant drop with high precision. Most of these techniques solve the Young-Laplace equation many times over to find the material parameters that provide a fit to a supplied image of a real droplet. Here we introduce a machine learning approach to solve this problem in a computationally more efficient way. We train a deep neural network to determine the surface tension of a given droplet shape using a large training set of numerically generated droplet shapes. We show that the deep learning approach is superior to the current state of the art shape fitting approach in speed and precision, in particular if shapes in the training set reflect the sensitivity of the droplet shape with respect to surface tension. In order to derive such an optimized training set we clarify the role of the Worthington number as quality indicator in conventional shape fitting and in the machine learning approach. Our approach demonstrates the capabilities of deep neural networks in the material parameter determination from rheological deformation experiments in general.

cond-mat.soft↗
arXiv2020

Bistability and oscillations in cooperative microtubule and kinetochore dynamics in the mitotic spindle

In the mitotic spindle microtubules attach to kinetochores via catch bonds during metaphase, and microtubule depolymerization forces give rise to stochastic chromosome oscillations. We investigate the cooperative stochastic microtubule dynamics in spindle models consisting of ensembles of parallel microtubules, which attach to a kinetochore via elastic linkers. We include the dynamic instability of microtubules and forces on microtubules and kinetochores from elastic linkers. A one-sided model, where an external force acts on the kinetochore is solved analytically employing a mean-field approach based on Fokker-Planck equations. The solution establishes a bistable force-velocity relation of the microtubule ensemble in agreement with stochastic simulations. We derive constraints on linker stiffness and microtubule number for bistability. The bistable force-velocity relation of the one-sided spindle model gives rise to oscillations in the two-sided model, which can explain stochastic chromosome oscillations in metaphase (directional instability). We derive constraints on linker stiffness and microtubule number for metaphase chromosome oscillations. Including poleward microtubule flux into the model we can provide an explanation for the experimentally observed suppression of chromosome oscillations in cells with high poleward flux velocities. Chromosome oscillations persist in the presence of polar ejection forces, however, with a reduced amplitude and a phase shift between sister kinetochores. Moreover, polar ejection forces are necessary to align the chromosomes at the spindle equator and stabilize an alternating oscillation pattern of the two kinetochores. Finally, we modify the model such that microtubules can only exert tensile forces on the kinetochore resulting in a tug-of-war between the two microtubule ensembles. Then, induced microtubule catastrophes after reaching the...

q-bio.SC↗
arXiv2019

Strong deformation of ferrofluid-filled elastic alginate capsules in inhomogenous magnetic fields

We present a new system based on alginate gels for the encapsulation of a ferrofluid drop, which allows us to create millimeter-sized elastic capsules that are highly deformable by inhomogeneous magnetic fields. We use a combination of experimental and theoretical work in order to characterize and quantify the deformation behavior of these ferrofluid-filled capsules. We introduce a novel method for the direct encapsulation of unpolar liquids by sodium alginate. The addition of polar alcohol molecules allows us to encapsulate a ferrofluid as a single phase. This encapsulation method increases the amount of encapsulated magnetic nanoparticles resulting in high deformations and offers possible applications of capsules as actuators, switches, or valves in confined spaces like microfluidic devices. We determine both elastic moduli of the capsule shell, Young's modulus and Poisson's ratio, by employing two independent mechanical methods, spinning capsule measurements and capsule compression between parallel plates. We then show that the observed magnetic deformation can be fully understood from magnetic forces exerted by the ferrofluid on the capsule shell if the magnetic field distribution and magnetization properties of the ferrofluid are known. Using an iterative solution scheme that couples a finite element / boundary element method for the magnetic field calculation to the solution of the elastic shape equations, we achieve quantitative agreement between theory and experiment for deformed capsule shapes using the Young modulus from mechanical characterization and the surface Poisson ratio as a fit parameter. This detailed analysis confirms the results from mechanical characterization that the surface Poisson ratio of the alginate shell is close to unity, that is, deformations of the alginate shell are almost area conserving.

cond-mat.soft↗
arXiv2019

Shallow shell theory of the buckling energy barrier: from the Pogorelov state to softening and imperfection sensitivity close to the buckling pressure

We study the axisymmetric response of a complete spherical shell under homogeneous compressive pressure $p$ to an additional point force. For a pressure $p$ below the classical critical buckling pressure $p_c$, indentation by a point force does not lead to spontaneous buckling but an energy barrier has to be overcome. The states at the maximum of the energy barrier represent a subcritical branch of unstable stationary points, which are the transition states to a snap-through buckled state. Starting from nonlinear shallow shell theory we obtain a closed analytical expression for the energy barrier height, which facilitates its effective numerical evaluation as a function of pressure by continuation techniques. We find a clear crossover between two regimes: For $p/p_c\ll 1$ the post-buckling barrier state is a mirror-inverted Pogorelov dimple, and for $(1-p/p_c)\ll 1$ the barrier state is a shallow dimple with indentations smaller than shell thickness and exhibits extended oscillations, which are well described by linear response. We find systematic expansions of the nonlinear shallow shell equations about the Pogorelov mirror-inverted dimple for $p/p_c\ll 1$ and the linear response state for $(1-p/p_c)\ll 1$, which enable us to derive asymptotic analytical results for the energy barrier landscape in both regimes. Upon approaching the buckling bifurcation at $p_c$ from below, we find a softening of an ideal spherical shell. The stiffness for the linear response to point forces vanishes $\propto (1-p/p_c)^{1/2}$; the buckling energy barrier vanishes $\propto (1-p/p_c)^{3/2}$. In the Pogorelov limit, the energy barrier maximum diverges $\propto (p/p_c)^{-3}$ and the corresponding indentation diverges $\propto (p/p_c)^{-2}$. Numerical prefactors for proportionalities both in the softening and the Pogorelov regime are calculated analytically.

cond-mat.soft↗
arXiv2018

Elastic capsules at liquid-liquid interfaces

We investigate the deformation of elastic microcapsules adsorbed at liquid-liquid interfaces. An initially spherical elastic capsule at a liquid-liquid interface undergoes circumferential stretching due to the liquid-liquid surface tension and becomes lens- or discus-shaped, depending on its bending rigidity. The resulting elastic capsule deformation is qualitatively similar, but distinct from the deformation of a liquid droplet into a liquid lens at a liquid-liquid interface. We discuss the deformed shapes of droplets and capsules adsorbed at liquid-liquid interfaces for a whole range of different surface elasticities: from droplets (only surface tension) deforming into liquid lenses, droplets with a Hookean membrane (finite stretching modulus, zero bending modulus) deforming into elastic lenses, to microcapsules (finite stretching and bending modulus) deforming into rounded elastic lenses. We calculate capsule shapes at liquid-liquid interfaces numerically using shape equations from nonlinear elastic shell theory. Finally, we present theoretical results for the contact angle (or the capsule height) and the maximal capsule curvature at the three phase contact line. These results can be used to infer information about the elastic moduli from optical measurements. During capsule deformation into a lens-like shape, surface energy of the liquid-liquid interface is converted into elastic energy of the capsule shell giving rise to an overall adsorption energy gain by deformation. Soft hollow capsules exhibit a pronounced increase of the adsorption energy as compared to filled soft particles and, thus, are attractive candidates as foam and emulsion stabilizers.

cond-mat.soft↗
arXiv2018

Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing

We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Kosmrlj and Nelson, Phys. Rev. X 7, 011002 (2017)]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy barrier in thermal activation to obtain our final result for the temperature-dependent critical pressure, which is significantly below the results if only parameter renormalization or only thermal activation is considered.

cond-mat.stat-mech↗
arXiv2018

Spheroidal and conical shapes of ferrofluid-filled capsules in magnetic fields

We investigate the deformation of soft spherical elastic capsules filled with a ferrofluid in external uniform magnetic fields at fixed volume by a combination of numerical and analytical approaches. We develop a numerical iterative solution strategy based on nonlinear elastic shape equations to calculate the stretched capsule shape numerically and a coupled finite element and boundary element method to solve the corresponding magnetostatic problem, and employ analytical linear response theory, approximative energy minimization, and slender-body theory. The observed deformation behavior is qualitatively similar to the deformation of ferrofluid droplets in uniform magnetic fields. Homogeneous magnetic fields elongate the capsule, and a discontinuous shape transition from a spheroidal shape to a conical shape takes place at a critical field strength. We investigate how capsule elasticity modifies this hysteretic shape transition. We show that conical capsule shapes are possible but involve diverging stretch factors at the tips, which gives rise to rupture for real capsule materials. In a slender-body approximation we find that the critical susceptibility above which conical shapes occur for ferrofluid capsules is the same as for droplets. At small fields capsules remain spheroidal, and we characterize the deformation of spheroidal capsules both analytically and numerically. Finally, we determine whether wrinkling of a spheroidal capsule occurs during elongation in a magnetic field and how it modifies the stretching behavior. We find the nontrivial dependence between the extent of the wrinkled region and capsule elongation. Our results can be helpful in order to quantitatively determine capsule or ferrofluid material properties from magnetic deformation experiments. All results also apply to elastic capsules filled with a dielectric liquid in an external uniform electric field.

cond-mat.soft↗
arXiv2017

Pendant Capsule Elastometry

We provide a C/C++ software for the shape analysis of deflated elastic capsules in a pendant capsule geometry, which is based on an elastic description of the capsule material as a quasi two-dimensional elastic membrane using shell theory. Pendant capsule elastometry provides a new in-situ and non-contact method for interfacial rheology of elastic capsules. Given an elastic model of the capsule membrane, pendant capsule elastometry determines optimal elastic moduli by fitting numerically generated axisymmetric shapes optimally to an experimental image. For each digitized image of a deflated capsule elastic moduli can be determined, if another image of its undeformed reference shape is provided. Within this paper, we focus on nonlinear Hookean elasticity because of its low computational cost its wide applicability, but also discuss and implement alternative constitutive laws. For Hookean elasticity, Young's surface modulus (or, alternatively, area compression modulus) and Poisson's ratio are determined; for Mooney-Rivlin elasticity, the Rivlin modulus and a dimensionless shape parameter are determined; for neo-Hookean elasticity, only the Rivlin modulus is determined, using a fixed dimensionless shape parameter. Comparing results for different models we find that nonlinear Hookean elasticity is adequate for most capsules. If series of images are available, these moduli can be evaluated as a function of the capsule volume to analyze hysteresis or aging effects depending on the deformation history. An additional wrinkling wavelength measurement allows the user to determine the bending modulus, from which the layer thickness can be derived. We verify the method by analyzing several materials, compare the results to available rheological measurements, and review several applications. We make the software available under the GPL license at github.com/jhegemann/opencapsule.

cond-mat.soft↗
arXiv2017

Adsorption of finite semiflexible polymers and their loop and tail distributions

We discuss the adsorption of semiflexible polymers to a planar attractive wall and focus on the questions of the adsorption threshold for polymers of {\it finite} length and their loop and tail distributions using both Monte-Carlo simulations and analytical arguments. For the adsorption threshold, we find three regimes: (i) a flexible or Gaussian regime if the persistence length is smaller than the adsorption potential range, (ii) a semiflexible regime if the persistence length is larger than the potential range, and (iii) for finite polymers, a novel crossover to a rigid rod regime if the deflection length exceeds the contour length. In the flexible and semiflexible regime, finite size corrections arise because the correlation length exceeds the contour length. In the rigid rod regime, however, it is essential how the global orientational or translational degrees of freedom are restricted by grafting or confinement. We discuss finite size corrections for polymers grafted to the adsorbing surface and for polymers confined by a second (parallel) hard wall. Based on these results we obtain a method to analyze adsorption data for finite semiflexible polymers such as filamentous actin. For the loop and tail distributions, we find power laws with an exponential decay on length scales exceeding the correlation length. We derive and confirm the loop and tail power law exponents for flexible and semiflexible polymers. This allows us to explain that, close to the transition, semiflexible polymers have significantly smaller loops and both flexible and semiflexible polymers desorb by expanding their tail length. The tail distribution allows us to extract the free energy per length of adsorption for actin filaments from experimental data [D. Welch et al., Soft Matter 11, 7507 (2015)].

cond-mat.soft↗