Papers by Horst-Holger Boltz

Eur. Phys. J. Special Topics , 2016
We introduce an iterative solution scheme in order to calculate stationary shapes of deformable e... more We introduce an iterative solution scheme in order to calculate stationary shapes of deformable elastic capsules which are steadily moving through a viscous fluid at low Reynolds numbers. The iterative solution scheme couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape
and the velocity of an elastic capsule moving in a viscous fluid governed by the Stokes equation. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical resting shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Karman number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Karman number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical
Föppl-von-Karman numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force.
![Research paper thumbnail of Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)]](https://attachments.academia-assets.com/45287794/thumbnails/1.jpg)
Phys. Rev. E , 2015
We want to point out errors that occurred in the calculation regarding the rotational stability o... more We want to point out errors that occurred in the calculation regarding the rotational stability of sedimenting capsule shapes in Eq. (D4) in Appendix D and in the stability criterion used in Sec. III E resulting in an incorrect Fig. 8. The gravitational torque in Eq. (D4) should read e y · T g = πdαg ds sin ψ r 2 (z − z 0). (D4) Equating this gravitational torque (D4) with the hydrodynamic torque (D3) determines the pivot point z 0 of the rotation. We also want to point out that this pivot point z 0 , which we called the center of hydrodynamic stress, actually differs from the center of hydrodynamic stress as defined in Ref. [1], where it is the point z 0 where the hydrodynamic torque (D3) itself equals zero. The shape is stable with respect to rotations if the pivot point z 0 (or the center of hydrodynamic stress according to Ref. [1]) lies above the center of gravity z c.m.. Using this corrected criterion for rotational stability and the corrected gravitational torque (D4), we obtain a corrected version of Fig. 8, which is shown as Fig. 1. Most of our results are qualitatively unchanged: We find that both of the buckled sedimenting capsule shapes are stable, the pseudospherical shape is only weakly instable for small gravitational forces, and the pear shape is stable for high gravitational forces. Pseudospherical and pear shape develop a pronounced instability only for gravity forces g close to the crossover or transition from pseudospherical to pear shapes, as shown in Fig. 1. Moreover, in the text following Eq. (18) the correct equations for tensions and bending moments should read τ s = λ −1 ϕ ∂w s /∂e s and m s = λ −1 ϕ ∂w s /∂K s .

Phys. Rev. E, 2015
Soft elastic capsules which are driven through a viscous fluid undergo shape deformation coupled ... more Soft elastic capsules which are driven through a viscous fluid undergo shape deformation coupled to their motion. We introduce an iterative solution scheme which couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid at low Reynolds numbers. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical rest shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force. This type of instability should be observable for generic synthetic capsules. All shape bifurcations can be resolved in the force-velocity relation of sedimenting capsules, where up to three capsule shapes with different velocities can occur for the same driving force. All three types of possible axisymmetric stationary shapes are stable with respect to rotation during sedimentation. Additionally, we study capsules pushed or pulled by a point force, where we always find capsule shapes to transform smoothly without bifurcations.
J. Comput. Phys. , Jan 15, 2015
We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallel... more We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.

Phys. Rev. E , Jul 8, 2013
We investigate the localization of stiff directed lines with bending energy by a short-range rand... more We investigate the localization of stiff directed lines with bending energy by a short-range random potential. We apply perturbative arguments, Flory scaling arguments, a variational replica calculation, and functional renormalization to show that a stiff directed line in 1 + d dimensions undergoes a localization transition with increasing disorder for d > 2/3. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1 + 1 dimensions and analyze the properties of the disorder-dominated phase in detail. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in 1 + d dimensions and of directed lines under tension in 1 + 3d dimensions, which is strongly supported by identical free-energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang equation. We support the proposed relation to directed lines via multifractal analysis, revealing an analogous Anderson transition-like scenario and a matching correlation length exponent. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder.

J. Chem. Phys., Jul 23, 2015
We propose an efficient Monte Carlo algorithm for the off-lattice simulation of dense hard sphere... more We propose an efficient Monte Carlo algorithm for the off-lattice simulation of dense hard sphere polymer melts using cluster moves, called event chains, which allow for a rejection-free treatment of the excluded volume. Event chains also allow for an efficient preparation of initial configurations in polymer melts. We parallelize the event chain Monte Carlo algorithm to further increase simulation speeds and suggest additional local topology-changing moves (“swap” moves) to accelerate equilibration. By comparison with other Monte Carlo and molecular dynamics simulations, we verify that the event chain algorithm reproduces the correct equilibrium behavior of polymer chains in the melt. By comparing intrapolymer diffusion time scales, we show that event chain Monte Carlo algorithms can achieve simulation speeds comparable to optimized molecular dynamics simulations. The event chain Monte Carlo algorithm exhibits Rouse dynamics on short time scales. In the absence of swap moves, we find reptation dynamics on intermediate time scales for long chains.

J. Chem. Phys. , Jul 18, 2013
We study the adsorption of semiflexible polymers such as polyelectrolytes or DNA on planar and cu... more We study the adsorption of semiflexible polymers such as polyelectrolytes or DNA on planar and curved substrates, e.g., spheres or washboard substrates via short-range potentials using extensive Monte Carlo simulations, scaling arguments, and analytical transfer matrix techniques. We show that the adsorption threshold of stiff or semiflexible polymers on a planar substrate can be controlled by polymer stiffness: adsorption requires the highest potential strength if the persistence length of the polymer matches the range of the adsorption potential. On curved substrates, i.e., an adsorbing sphere or an adsorbing washboard surface, the adsorption can be additionally controlled by the curvature of the surface structure. The additional bending energy in the adsorbed state leads to an increase of the critical adsorption strength, which depends on the curvature radii of the substrate structure. For an adsorbing sphere, this gives rise to an optimal polymer stiffness for adsorption, i.e., a local minimum in the critical potential strength for adsorption, which can be controlled by curvature. For two- and three-dimensional washboard substrates, we identify the range of persistence lengths and the mechanisms for an effective control of the adsorption threshold by the substrate curvature.

Phys. Rev. E , Jul 2, 2014
Driven elastic manifolds in random media exhibit a depinning transition to a state with nonvanish... more Driven elastic manifolds in random media exhibit a depinning transition to a state with nonvanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than line tension. Their equation of motion is the (quenched) Herring-Mullins equation, which also describes surface growth governed by surface diffusion. Stiff directed lines are particularly interesting as there is a localization transition in the static problem at a finite temperature and the commonly exploited time ordering of states by means of Middleton’s theorems [Phys. Rev. Lett. 68, 670 (1992)] is not applicable. We employ analytical arguments and numerical simulations to determine the critical exponents and compare our findings with previous works and functional renormalization group results, which we extend to the different line elasticity. We see evidence for two distinct correlation length exponents.
Journal of Computational Physics, 2015
We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallel... more We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.

The Journal of Chemical Physics, 2013
We study the adsorption of semiflexible polymers such as polyelectrolytes or DNA on planar and cu... more We study the adsorption of semiflexible polymers such as polyelectrolytes or DNA on planar and curved substrates, e.g., spheres or washboard substrates via short-range potentials using extensive Monte Carlo simulations, scaling arguments, and analytical transfer matrix techniques. We show that the adsorption threshold of stiff or semiflexible polymers on a planar substrate can be controlled by polymer stiffness: adsorption requires the highest potential strength if the persistence length of the polymer matches the range of the adsorption potential. On curved substrates, i.e., an adsorbing sphere or an adsorbing washboard surface, the adsorption can be additionally controlled by the curvature of the surface structure. The additional bending energy in the adsorbed state leads to an increase of the critical adsorption strength, which depends on the curvature radii of the substrate structure. For an adsorbing sphere, this gives rise to an optimal polymer stiffness for adsorption, i.e., a local minimum in the critical potential strength for adsorption, which can be controlled by curvature. For two-and three-dimensional washboard substrates, we identify the range of persistence lengths and the mechanisms for an effective control of the adsorption threshold by the substrate curvature.
Phys. Rev. E , Dec 26, 2012
We investigate the localization of stiff directed lines with bending energy by a short-range rand... more We investigate the localization of stiff directed lines with bending energy by a short-range random potential. Using perturbative arguments, Flory arguments, and a replica calculation, we show that a stiff directed line in 1+ d dimensions undergoes a localization transition with increasing disorder for d> 2/3. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1+ 1 dimensions and analyze the properties of the disorder-dominated phase.
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Papers by Horst-Holger Boltz
and the velocity of an elastic capsule moving in a viscous fluid governed by the Stokes equation. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical resting shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Karman number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Karman number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical
Föppl-von-Karman numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force.
and the velocity of an elastic capsule moving in a viscous fluid governed by the Stokes equation. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical resting shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Karman number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Karman number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical
Föppl-von-Karman numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force.