arXiv subjects

Reiner Kree

Publications and source records attributed to Reiner Kree.

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↗

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↗

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↗

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↗

arXiv2016

Dynamical Transitions in a Dragged Growing Polymer Chain

We extend the Rouse model of polymer dynamics to situations of non-stationary chain growth. For a dragged polymer chain of length $N(t) = t^α$, we find two transitions in conformational dynamics. At $α= 1/2$, the propagation of tension and the average shape of the chain change qualitatively, while at $α= 1 $ the average center-of-mass motion stops. These transitions are due to a simple physical mechanism: a race duel between tension propagation and polymer growth. Therefore they should also appear for growing semi-flexible or stiff polymers. The generalized Rouse model inherits much of the versatility of the original Rouse model: it can be efficiently simulated and it is amenable to analytical treatment.

cond-mat.soft↗

arXiv2011

A Monte Carlo study of surface sputtering by dual and rotated ion beams

Several, recently proposed methods of surface manufacturing based on ion beam sputtering, which involve dual beam setups, sequential application of ion beams from different directions, or sample rotation, are studied with the method of kinetic Monte Carlo simulation of ion beam erosion and surface diffusion. In this work, we only consider erosion dominated situations. The results are discussed by comparing them to a number of theoretical propositions and to experimental findings. Two ion-beams aligned opposite to each other produce stationary, symmetric ripples. Two ion beams crossing at right angle will produce square patterns only, if they are exactly balanced. In all other cases of crossed beams, ripple patterns are created, and their orientations are shown to be predictable from linear continuum theory. In sequential ion beam sputtering we find a very rapid destruction of structures created from the previous beam direction after a rotation step, which leads to a transient decrease of overall roughness. Superpositions of patterns from several rotation steps are difficult to obtain, as they exist only in very short time windows. In setups with a single beam directed towards a rotating sample, we find a non-monotonic dependence of roughness on rotation frequency, with a very pronounced minimum appearing at the frequency scale set by the relaxation of prestructures observed in sequential ion beam setups. Furthermore we find that the logarithm of the height of structures decreases proportional to the inverse frequency.

cond-mat.mes-hall↗

arXiv2008

Spreading of EGF Receptor Activity into EGF-free Regions and Molecular Therapies of Cancer

The primary activation of the epidermal growth factor receptor (EGFR) has become a prominent target for molecular therapies against several forms of cancer. But despite considerable progress during the last years, many of its aspects remain poorly understood. Experiments on lateral spreading of receptor activity into ligand-free regions challenge the current standard models of EGFR activation. Here, we propose and study a theoretical model, which explains spreading into ligand-free regions without introducing any new, unknown kinetic parameters. The model exhibits bistability of activity, induced by a generic reaction mechanism, which consists of activation via dimerization and deactivation via a Michaelis-Menten reaction. It possesses slow propagating front solutions and faster initial transients. We analyze relevant experiments and find that they are in quantitative accordance with the fast initial modes of spreading, but not with the slow propagating front. We point out that lateral spreading of activity is linked to pathological levels of persistent receptor activity as observed in cancer cells and exemplify uses of this link for the design and quick evaluation of molecular therapies targeting primary activation of EGFR.

q-bio.MN↗

arXiv2006

Numerical analysis of the quantum dots on off-normal incidence ion sputtered surfaces

We implement substrate rotation in a 2+1 dimensional solid-on-solid model of ion beam sputtering of solid surfaces. With this extension of the model, we study the effect of concurrent rotation, as the surface is sputtered, on possible topographic regions of surface patterns. In particular we perform a detailed numerical analysis of the time evolution of dots obtained from our Monte Carlo simulations at off-normal-incidence sputter erosion. We found the same power-law scaling exponents of the dot characteristics for two different sets of ion-material combinations, without and with substrate rotation.

cond-mat.mtrl-sci↗

arXiv2005

Morphological regions and oblique incidence dot formation in a model of surface sputtering

We study solid surface morphology created by off-normal ion-beam sputtering with an atomistic, solid-on-solid model of sputter erosion. With respect to an earlier version of the model, we extend this model with the inclusion of lateral erosion. Using the 2-dimensional structure factor, we found an upper bound $μ\simeq 2$, in the lateral straggle $μ$, for clear ripple formation. Above this upper bound, for longitudinal straggle $σ\gtrsim 1.7$, we found the possibility of dot formation (without sample rotation). Moreover, a temporal crossover from a hole topography to ripple topography with the same value of collision cascade parameters was found. Finally, a scaling analysis of the roughness, using the consecutive gradient approach, yields the growth exponents $β=0.33$ and 0.67 for two different topographic regimes.

cond-mat.mtrl-sci↗

arXiv2005

Propagation of Ripples in Monte Carlo Models of Sputter Induced Surface Morphology

Periodic ripples generated from the off-normal incidence ion beam bombardment of solid surfaces have been observed to propagate with a dispersion in the velocity. We investigate this ripple behaviour by means of a Monte Carlo model of the erosion process, in conjuction with one of two different surface diffusion mechanisms, representative of two different classes of materials; one is an Arrhenius-type Monte Carlo method including a term (possibly zero) that accounts for the Schwoebel effect, the other a thermodynamic mechanism without the Schwoebel effect. We find that the behavior of the ripple velocity and wavelength depends on the sputtering timescale, qualitatively consistent with experiments. Futhermore, we observe a strong temperature dependance of the ripple velocity, calling for experiments at different temperatures. Also, we observe that the ripple velocity vanishes ahead of the periodic ripple pattern.

cond-mat.mtrl-sci↗

arXiv2002

Long-Time Effects in a Simulation Model of Sputter Erosion

A simple (2+1) dimensional discrete model is introduced to study the evolution of solid surface morphologies during ion-beam sputtering. The model is based on the same assumptions about the erosion process as the existing analytic theories. Due to its simple structure, simulations of the model can be performed on time scales, where effects beyond the linearized theory become important. Whereas for short times we observe the formation of ripple structures in accordance with the linearized theory, we find a rough surface with scaling properties for intermediate times. The long time behavior of the model strongly depends on the surface relaxation mechanism.

cond-mat.mtrl-sci↗

arXiv2001

Pattern Formation of Ion Channels with State Dependent Electrophoretic Charges and Diffusion Constants in Fluid Membranes

A model of mobile, charged ion channels in a fluid membrane is studied. The channels may switch between an open and a closed state according to a simple two-state kinetics with constant rates. The effective electrophoretic charge and the diffusion constant of the channels may be different in the closed and in the open state. The system is modeled by densities of channel species, obeying simple equations of electro-diffusion. The lateral transmembrane voltage profile is determined from a cable-type equation. Bifurcations from the homogeneous, stationary state appear as hard-mode, soft-mode or hard-mode oscillatory transitions within physiologically reasonable ranges of model parameters. We study the dynamics beyond linear stability analysis and derive non-linear evolution equations near the transitions to stationary patterns.

cond-mat.soft↗

arXiv1995

Thermal Equilibrium with the Wiener Potential: Testing the Replica Variational Approximation

We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation functions of the Gibbs states may be calculated exactly as a function of the box length and temperature. This allows for a detailed test of results obtained by the replica variational approximation scheme. We show that this scheme provides a reasonable estimate of the averaged free energy. Furthermore our results shed more light on the validity of the concept of approximate ultrametricity which is a central assumption of the replica variational method.

cond-mat↗