arXiv subjects

Holger Stark

Publications and source records attributed to Holger Stark.

At least 55 records · Page 3Linked to original sources

arXiv2018

Dissipative systems with nonlocal delayed feedback control

We present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a measurement point is captured by an inherent delay time (or latency). A detailed linear stability analysis demonstrates that a non-zero system delay acts destabilizing on the otherwise stable fixed point for sufficiently large feedback strengths. The imaginary part of the dominant eigenvalue is bounded by twice the feedback strength. In the relevant parameter space it changes discontinuously along specific lines when switching between branches of eigenvalues. When the feedback control force is bounded by a sigmoid function, a supercritical Hopf bifurcation occurs at the stability-instability transition. The frequency and amplitude of the resulting limit cycles respond to parameter changes like the dominant eigenvalue. In particular, they show similar discontinuities along specific lines. These results are largely independent of the exact shape of the sigmoid function. Our findings match well with previously reported results on a feedback-induced instability of vortex diffusion in a rotationally driven Newtonian fluid [M. Zeitz, P. Gurevich, and H. Stark, Eur. Phys. J. E 38, 22 (2015)]. Thus, our model captures the essential features of nonlocal delayed feedback control in spatially extended dissipative systems.

nlin.AO↗

arXiv2018

A flowing pair of particles in inertial microfluidics

A flowing pair of particles in inertial microfluidics gives important insights into understanding and controlling the collective dynamics of particles like cells or droplets in microfluidic devices. They are applied in medical cell analysis and engineering. We study the dynamics of a pair of solid particles flowing through a rectangular microchannel using lattice Boltzmann simulations. We determine the inertial lift force profiles as a function of the two particle positions, their axial distance, and the Reynolds number. Generally, the profiles strongly differ between particles leading and lagging in flow and the lift forces are enhanced due to the presence of a second particle. At small axial distances, they are determined by viscous forces, while inertial forces dominate at large separations. Depending on the initial conditions, the two-particle lift forces in combination with the Poiseuille flow give rise to three types of unbound particle trajectories, called moving-apart, passing, and swapping, and one type of bound trajectories, where the particles perform damped oscillations. The damping rate scales with Reynolds number squared, since inertial forces are responsible for driving the particles to their steady-state positions.

physics.flu-dyn↗

arXiv2018

Statistical parameter inference of bacterial swimming strategies

We provide a detailed stochastic description of the swimming motion of an E.coli bacterium in two dimension, where we resolve tumble events in time. For this purpose, we set up two Langevin equations for the orientation angle and speed dynamics. Calculating moments, distribution and autocorrelation functions from both Langevin equations and matching them to the same quantities determined from data recorded in experiments, we infer the swimming parameters of E.coli . They are the tumble rate $λ$, the tumble time $r^{-1}$ , the swimming speed $v_0$ , the strength of speed fluctuations $σ$, the relative height of speed jumps $η$, the thermal value for the rotational diffusion coefficient $D_0$ , and the enhanced rotational diffusivity during tumbling $D_T$ . Conditioning the observables on the swimming direction relative to the gradient of a chemoattractant, we infer the chemotaxis strategies of E.coli . We confirm the classical strategy of a lower tumble rate for swimming up the gradient but also a smaller mean tumble angle (angle bias). The latter is realized by shorter tumbles as well as a slower diffusive reorientation. We also find that speed fluctuations are increased by about 30% when swimming up the gradient compared to the reversed direction.

physics.bio-ph↗

arXiv2018

Simulating squirmers with multiparticle collision dynamics

Multiparticle collision dynamics is a modern coarse-grained simulation technique to treat the hydrodynamics of Newtonian fluids by solving the Navier-Stokes equations. Naturally, it also includes thermal noise. Initially it has been applied extensively to spherical colloids or bead-spring polymers immersed in a fluid. Here, we review and discuss the use of multiparticle collision dynamics for studying the motion of spherical model microswimmers called squirmers moving in viscous fluids.

cond-mat.soft↗

arXiv2017

Gravity-induced dynamics of a squirmer microswimmer in wall proximity

We perform hydrodynamic simulations using the method of multi-particle collision dynamics and a theoretical analysis to study a single squirmer microswimmer at high Péclet number, which moves in a low Reynolds number fluid and under gravity. The relevant parameters are the ratio $α$ of swimming to bulk sedimentation velocity and the squirmer type $β$. The combination of self-propulsion, gravitational force, hydrodynamic interactions with the wall, and thermal noise leads to a surprisingly diverse behavior. At $α> 1$ we observe cruising states, while for $α<1$ the squirmer resides close to the bottom wall with the motional state determined by stable fixed points in height and orientation. They strongly depend on the squirmer type $β$. While neutral squirmers permanently float above the wall with upright orientation, pullers float for $α$ larger than a threshold value $α_{\mathrm{th}}$ and are pinned to the wall below $α_{\mathrm{th}}$. In contrast, pushers slide along the wall at lower heights, from which thermal orientational fluctuations drive them into a recurrent floating state with upright orientation, where they remain on the timescale of orientational persistence.

physics.flu-dyn↗

arXiv2017

Feedback-Control of Photoresponsive Fluid Interfaces

Photoresponsive surfactants provide a unique microfluidic driving mechanism. Since their molecular shapes change under illumination and thereby affect surface tension of fluid interfaces, Marangoni flow along the interface occurs. To describe the dynamics of the surfactant mixture at a planar interface, we formulate diffusion-advection-reaction equations for both surfactant densities. They also include adsorption from and desorption into the neighboring fluids and photoisomerization by light. We then study how the interface responds when illuminated by spots of light. Switching on a single light spot, the density of the switched surfactant spreads in time and assumes an exponentially decaying profile in steady state. Simultaneously, the induced radial Marangoni flow reverses its flow direction from inward to outward. We use this feature to set up specific feedback rules, which couple the advection velocities sensed at the light spots to their intensities. As a result two neighboring spots switch on and off alternately. Extending the feedback rule to light spots arranged on the vertices of regular polygons, we observe periodic switching patterns for even-sided polygons, where two sets of next-nearest neighbors alternate with each other. A triangle and pentagon also show regular oscillations, while heptagon and nonagon exhibit irregular oscillations due to frustration. While our findings are specific to the chosen set of parameters, they show how complex patterns at photoresponsive fluid interfaces emerge from simple feedback coupling.

cond-mat.soft↗

arXiv2017

Collective Sedimentation of Squirmers under Gravity

Active particles, which interact hydrodynamically, display a remarkable variety of emergent collective phenomena. We use squirmers to model spherical microswimmers and explore the collective behavior of thousands of them under the influence of strong gravity using the method of multi-particle collision dynamics for simulating fluid flow. The sedimentation profile depends on the ratio of swimming to sedimentation velocity as well as on the squirmer type. It shows close packed squirmer layers at the bottom and a highly dynamic region with exponential density dependence towards the top. The mean vertical orientation of the squirmers strongly depends on height. For swimming velocities larger than the sedimentation velocity, squirmers show strong convection in the exponential region. We quantify the strength of convection and the extent of convection cells by the vertical current density and its current dipole, which are large for neutral squirmers as well as for weak pushers and pullers.

physics.flu-dyn↗

arXiv2017

Self-Organized Velocity Pulses of Dense Colloidal Suspensions in Microchannel Flow

We present a numerical study of dense colloidal suspensions in pressure-driven microchannel flow in two dimensions. The colloids are modeled as elastic and frictional spheres suspended in a Newtonian fluid, which we simulate using the method of multi-particle collision dynamics. The model reproduces periodic velocity and density pulse trains, traveling upstream in the microchannel, which are found in experiments conducted by L. Isa et al. [Phys. Rev. Lett. 102, 058302 (2009)]. We show that colloid-wall friction and the resultant force chains are crucial for the formation of these pulses. With increasing colloid density first solitary jams occur, which become periodic pulse trains at intermediate densities and unstable solitary pulses at high densities. We formulate a phenomenological continuum model and show how these spatio-temporal flow and density profiles can be understood as homoclinic and periodic orbits in traveling-wave equations.

cond-mat.soft↗

arXiv2017

Model microswimmers in channels with varying cross section

We study different types of microswimmers moving in channels with varying cross section and thereby interacting hydrodynamically with the channel walls. Starting from the Smoluchowski equation for a dilute suspension, for which interactions among swimmers can be neglected, we derive analytic expressions for the lateral probability distribution between plane channel walls. For weakly corrugated channels we extend the Fick--Jacobs approach to microswimmers and thereby derive an effective equation for the probability distribution along the channel axis. Two regimes arise dominated either by entropic forces due to the geometrical confinement or by the active motion. In particular, our results show that the accumulation of microswimmers at channel walls is sensitive to both, the underlying swimming mechanism and the geometry of the channels. Finally, for asymmetric channel corrugation our model predicts a rectification of microswimmers along the channel, the strength and direction of which strongly depends on the swimmer type.

cond-mat.soft↗

arXiv2017

Diffusion in systems crowded by active force-dipole molecules

Experimental studies of systems containing active proteins that undergo conformational changes driven by catalytic chemical reactions have shown that the diffusion coefficients of passive tracer particles and active molecules are larger than the corresponding values when chemical activity is absent. Various mechanisms have been proposed for such behavior, including, among others, force dipole interactions of molecular motors moving on filaments and collective hydrodynamic effects arising from active proteins. Simulations of a multi-component system containing active dumbbell molecules that cycle between open and closed states, a passive tracer particle and solvent molecules are carried out. Consistent with experiments, it is shown that the diffusion coefficients of both passive particles and the dumbbells themselves are enhanced when the dumbbells are active. The dependence of the diffusion enhancement on the volume fraction of dumbbells is determined, and the effects of crowding by active dumbbell molecules are shown to differ from those due to inactive molecules.

cond-mat.soft↗

arXiv2017

Inertial migration and axial control of deformable capsules

The mechanical deformability of single cells is an important indicator for various diseases such as cancer, blood diseases and inflammation. Lab-on-a-chip devices allow to separate such cells from healthy cells using hydrodynamic forces. We perform hydrodynamic simulations based on the lattice-Boltzmann method and study the behavior of an elastic capsule in a microfluidic channel flow in the inertial regime. While inertial lift forces drive the capsule away from the channel center, its deformability favors migration in the opposite direction. Balancing both migration mechanisms, a deformable capsule assembles at a specific equilibrium distance depending on its size and deformability. We find that this equilibrium distance is nearly independent of the channel Reynolds number and falls on a single master curve when plotted versus the Laplace number. We identify a similar master curve for varying particle radius. In contrast, the actual deformation of a capsule strongly depends on the Reynolds number. The lift-force profiles behave in a similar manner as those for rigid particles. Using the Saffman effect, the capsule's equilibrium position can be controlled by an external force along the channel axis. While rigid particles move to the center when slowed down, very soft capsules show the opposite behavior. Interestingly, for a specific control force particles are focused on the same equilibrium position independent of their deformability.

physics.flu-dyn↗

arXiv2016

Active Brownian particles moving in a random Lorentz gas

Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study non-interacting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the critical obstacle density $η_c$ the ABPs are trapped, their long-time diffusion below $η_c$ is strongly influenced by the propulsion speed $v_0$. With increasing $v_0$, ABPs are stuck at the obstacles for longer times. Thus, for large propulsion speed, the long-time diffusion constant decreases more strongly in a denser obstacle environment than for passive particles. This agrees with the behavior of an effective swimming velocity and persistence time, which we extract from the velocity autocorrelation function.

cond-mat.soft↗

arXiv2016

Active Brownian particles and run-and-tumble particles separate inside a maze

A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily. According to our simulations and a rate theory, which we developed, ABPs in steady state accumulate in the outermost region of the Matryoshka-like mazes, while RTPs occupy all locations within the maze with nearly equal probability. These results suggest a novel technique for separating different types of self-propelled particles by designing appropriate confining geometries without using chemical or biological agents.

cond-mat.soft↗

arXiv2016

Phase Separation and Coexistence of Hydrodynamically Interacting Microswimmers

A striking feature of the collective behavior of spherical microswimmers is that for sufficiently strong self-propulsion they phase-separate into a dense cluster coexisting with a low-density dis- ordered surrounding. Extending our previous work, we use the squirmer as a model swimmer and the particle-based simulation method of multi-particle collision dynamics to explore the influence of hydrodynamics on their phase behavior in a quasi-two-dimensional geometry. The coarsening dynamics towards the phase-separated state is diffusive in an intermediate time regime followed by a final ballistic compactification of the dense cluster. We determine the binodal lines in a phase diagram of Péclet number versus density. Interestingly, the gas binodals are shifted to smaller densities for increasing mean density or dense-cluster size, which we explain using a recently introduced pressure balance [S. C. Takatori et al., Phys. Rev. Lett. 113, 028103 (2014)] extended by a hydrodynamic contribution. Furthermore, we find that for pushers and pullers the binodal line is shifted to larger Péclet numbers compared to neutral squirmers. Finally, when lowering the Péclet number, the dense phase transforms from a hexagonal "solid" to a disordered "fluid" state.

cond-mat.soft↗

arXiv2016

Active Brownian motion of emulsion droplets: Coarsening dynamics at the interface and rotational diffusion

A micron-sized droplet of bromine water immersed in a surfactant-laden oil phase can swim (S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13 073021 (2011)). The bromine reacts with the surfactant at the droplet interface and generates a surfactant mixture. It can spontaneously phase-separate due to solutocapillary Marangoni flow, which propels the droplet. We model the system by a diffusion-advection-reaction equation for the mixture order parameter at the interface including thermal noise and couple it to fluid flow. Going beyond previous work, we illustrate the coarsening dynamics of the surfactant mixture towards phase separation in the axisymmetric swimming state. Coarsening proceeds in two steps: an initially slow growth of domain size followed by a nearly ballistic regime. On larger time scales thermal fluctuations in the local surfactant composition initiates random changes in the swimming direction and the droplet performs a persistent random walk, as observed in experiments. Numerical solutions show that the rotational correlation time scales with the square of the inverse noise strength. We confirm this scaling by a perturbation theory for the fluctuations in the mixture order parameter and thereby identify the active emulsion droplet as an active Brownian particle.

cond-mat.soft↗

arXiv2016

Taylor line swimming in microchannels and cubic lattices of obstacles

Microorganisms naturally move in microstructured fluids. Using the simulation method of multi-particle collision dynamics, we study an undulatory Taylor line swimming in a two-dimensional microchannel and in a cubic lattice of obstacles, which represent simple forms of a microstructured environment. In the microchannel the Taylor line swims at an acute angle along a channel wall with a clearly enhanced swimming speed due to hydrodynamic interactions with the bounding wall. While in a dilute obstacle lattice swimming speed is also enhanced, a dense obstacle lattice gives rise to geometric swimming. This new type of swimming is characterized by a drastically increased swimming speed. Since the Taylor line has to fit into the free space of the obstacle lattice, the swimming speed is close to the phase velocity of the bending wave traveling along the Taylor line. While adjusting its swimming motion within the lattice, the Taylor line chooses a specific swimming direction, which we classify by a lattice vector. When plotting the swimming velocity versus the magnitude of the lattice vector, all our data collapse on a single master curve. Finally, we also report more complex trajectories within the obstacle lattice.

cond-mat.soft↗

arXiv2016

Dynamics of a bacterial flagellum under reverse rotation

To initiate tumbling of an E. coli, one of the helical flagella reverses its sense of rotation. It then transforms from its normal form first to the transient semicoiled state and subsequently to the curly-I state. The dynamics of polymorphism is effectively modeled by describing flagellar elasticity through an extended Kirchhoff free energy. However, the complete landscape of the free energy remains undetermined because the ground state energies of the polymorphic forms are not known. We investigate how variations in these ground state energies affect the dynamics of a reversely rotated flagellum of a swimming bacterium. We find that the flagellum exhibits a number of distinct dynamical states and comprehensively summarize them in a state diagram. As a result, we conclude that tuning the landscape of the extended Kirchhoff free energy alone cannot generate the intermediate full-length semicoiled state. However, our model suggests an ad hoc method to realize the sequence of polymorphic states as observed for a real bacterium. Since the elastic properties of bacterial flagella are similar, our findings can easily be extended to other peritrichous bacteria.

physics.bio-ph↗

arXiv2016

Kinetic Monte Carlo Simulations for Birefringence Relaxation of Photo-Switchable Molecules on a Surface

Recent experiments have demonstrated that in a dense monolayer of photo-switchable dye Methyl-Red molecules the relaxation of an initial birefringence follows a power-law decay, typical for glass-like dynamics. The slow relaxation can efficiently be controlled and accelerated by illuminating the monolayer with circularly polarized light, which induces trans-cis isomerization cycles. To elucidate the microscopic mechanism, we develop a two-dimensional molecular model in which the trans and cis isomers are represented by straight and bent needles, respectively. As in the experimental system, the needles are allowed to rotate and to form overlaps but they cannot translate. The out-of-equilibrium rotational dynamics of the needles is generated using kinetic Monte Carlo simulations. We demonstrate that, in a regime of high density and low temperature, the power-law relaxation can be traced to the formation of spatio-temporal correlations in the rotational dy- namics, i.e., dynamic heterogeneity. We also show that the nearly isotropic cis isomers can prevent dynamic heterogeneity from forming in the monolayer and that the relaxation then becomes exponential.

cond-mat.soft↗