A colloidal model system with tunable disorder: Solid-fluid transition and discontinuities in the limit of zero disorder - Richter, Christian; Schmiedeberg, Michael; Stark, Holger (European Physical Journal E, 2011)
We study a colloidal model system where disorder can be continuously tuned from no disorder-corresponding to a system that can crystallize-to large disorder where geometrical frustration occurs. The model system consists of colloidal particles with screened electrostatic repulsion. They can only move on single lines which are parallel and equidistant to each other. We introduce disorder by modulating the particle line density. The system exhibits a solid-to-fluid transition which we study by the structure factor and the temporal evolution of the mean-square distance of nearest neighbors on neighboring lines. A determining feature is the occurrence of discontinuities when disorder is tuned to zero. We observe that the peak height of the pair correlation function in the solid phase does not extrapolate to the value of the perfect crystal. Similarly, the mean interaction energy and the screening length at which the solid-fluid transition occurs seem to be discontinuous when the limit of zero disorder is approached.

Active Brownian and inertial particles in disordered environments: Short-time expansion of the mean-square displacement - Breoni, Davide; Schmiedeberg, Michael; Löwen, Hartmut (Physical Review E, 2020)
We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behavior adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher-order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is α=3 and α=4. We confirm our theoretical predictions by computer simulations. Moreover, they are verifiable in experiments on self-propelled colloids in random environment
Keywords: Active particles; Brownian motion; Inertia

Active phase field crystal systems with inertial delay and underdamped dynamics - Arold, Dominic; Schmiedeberg, Michael (European Physical Journal E, 2020)
Active matter systems often are well approximated as overdamped, meaning that any inertial momentum is immediately dissipated by the environment. On the other hand, especially for macroscopic systems but also for many mesoscopic ones particle mass can become relevant for the dynamics. For such systems we recently proposed an underdamped continuum model which captures translationally inertial dynamics via two contributions. First, convection and second a damping time scale of inertial motion. In this paper, we ask how both of these features influence the collective behavior compared to overdamped dynamics by studying the example of the active phase field crystal model. We first focus on the case of suppressed convection to study the role of the damping time. We quantify that the relaxation process to the steady collective motion state is considerably prolonged with damping time due to the increasing occurrence of transient groups of circularly moving density peaks. Finally, we illustrate the fully underdamped case with convection. Instead of collective motion of density peaks we then find a coexistence of constant high and low density phases reminiscent of motility-induced phase separatio
Keywords: active matter; microswimmer; inertia; Phase Field Model; non-equillibrium

Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory and simulation study - Härtel, Andreas; Kohl, Matthias; Schmiedeberg, Michael (Physical Review E, 2015)
The fundamental measure approach to classical density functional theory has been shown to be a powerful tool to predict various thermodynamic properties of hard-sphere systems. We employ this approach to determine not only one-particle densities but also two-particle correlations in binary and six-component mixtures of hard spheres in the vicinity of a hard wall. The broken isotropy enables us to carefully test a large variety of theoretically predicted two-particle features by quantitatively comparing them to the results of Brownian dynamics simulations. Specifically, we determine and compare the one-particle density, the total correlation functions, their contact values, and the force distributions acting on a particle. For this purpose, we follow the compressibility route and theoretically calculate the direct correlation functions by taking functional derivatives. We usually observe an excellent agreement between theory and simulations, except for small deviations in cases where local crystal-like order sets in. Our results set the course for further investigations on the consistency of functionals as well as for structural analysis on, e.g., the primitive model. In addition, we demonstrate that due to the suppression of local crystallization, the predictions of six-component mixtures are better than those in bidisperse or monodisperse systems. Finally, we are confident that our results of the structural modulations induced by the wall lead to a deeper understanding of ordering in anisotropic systems in general, the onset of heterogeneous crystallization, caging effects, and glassy dynamics close to a wall, as well as structural properties in systems with confinement.

Anisotropy and memory during cage breaking events close to a wall - Kohl, Matthias; Haertel, Andreas; Schmiedeberg, Michael (Journal of Physics: Condensed Matter, 2016)
The slow dynamics in a glassy hard-sphere system is dominated by cage breaking events, i.e. rearrangements where a particle escapes from the cage formed by its neighboring particles. We study such events for an overdamped colloidal system by the means of Brownian dynamics simulations. While it is difficult to relate cage breaking events to structural mean field results in bulk, we show that the microscopic dynamics of particles close to a wall can be related to the anisotropic two-particle density. In particular, we study cage-breaking trajectories, mean forces on a tracked particle, and the impact of the history of trajectories. Based on our simulation results, we further construct two different one-particle random-walk models-one without and one with memory incorporated-and find the local anisotropy and the history-dependence of particles as crucial ingredients to describe the escape from a cage. Finally, our detailed study of a rearrangement event close to a wall not only reveals the memory effect of cages, but leads to a deeper insight into the fundamental mechanisms of glassy dynamics.
Keywords: cage breaking event; glassy dynamics; structure of liquids; dynamic slowdown; particle memory; random-walk model

Archimedean-like colloidal tilings on substrates with decagonal and tetradecagonal symmetry - Schmiedeberg, Michael; Mikhael, Jules; Rausch, Sebastian; Roth, Johannes; Helden, Laurent; Bechinger, Clemens; Stark, Holger (European Physical Journal E, 2010)
Two-dimensional colloidal suspensions subjected to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction (J. Mikhael et al., Nature 454, 501 (2008)). In experiments as well as in Monte Carlo and Brownian dynamics simulations, we identify a similar phase when the laser field possesses tetradecagonal symmetry. We characterize the structure of both Archimedean-like tilings in detail and point out how the tilings differ from each other. Furthermore, we also estimate specific particle densities where the Archimedean-like tiling phases occur. Finally, using Brownian dynamics simulations we demonstrate how phasonic distortions of the decagonal laser field influence the Archimedean-like tiling. In particular, the domain size of the tiling can be enlarged by phasonic drifts and constant gradients in the phasonic displacement. We demonstrate that the latter occurs when the interfering laser beams are not ideally adjusted.

Asymptotic densities of ballistic Levy walks - Froemberg, D.; Schmiedeberg, Michael; Barkai, E.; Zaburdaev, Vasily (Physical Review E, 2015)
We propose an analytical method to determine the shape of density profiles in the asymptotic long-time limit for a broad class of coupled continuous-time random walks which operate in the ballistic regime. In particular, we show that different scenarios of performing a random-walk step, via making an instantaneous jump penalized by a proper waiting time or via moving with a constant speed, dramatically effect the corresponding propagators, despite the fact that the end points of the steps are identical. Furthermore, if the speed during each step of the random walk is itself a random variable, its distribution gets clearly reflected in the asymptotic density of random walkers. These features are in contrast with more standard nonballistic random walk

Athermal jamming vs. glassy dynamics for particles with exponentially decaying repulsive pair interaction potentials with a cutoff - Wohlleben, Nicolas; Schmiedeberg, Michael (EPL - Europhysics Letters, 2021)
We study athermal jamming as well as the thermal glassy dynamics in systems composed of spheres that interact according to repulsive interactions that exponentially decay as a function of distance. As usual, a cutoff is employed in the simulations. While the athermal jamming transition that is determined by trying to remove overlaps is found to depend on the arbitrary and therefore unphysical choice of the cutoff, we do not find any athermal jamming transition or crossover that only relies on the physical decay length. In contrast, the glassy dynamics mainly depends on the decay length. Our findings constitute another demonstration of the fact that the athermal jamming transition is not related to thermal glassy dynamics. In addition, we argue that interactions without sharp physical cutoff should be considered more often as a model system in jamming. The reevaluation of widely used theoretical approaches or methods of analysis in the field of jamming and the task to change them such that they do not depend on unphysical cutoffs will lead to deeper insights into the nature of athermal and thermal jammin
Keywords: Glass transition; Jamming; cutoff; exponential interaction

Brownian particles in random and quasicrystalline potentials: How they approach the equilibrium - Schmiedeberg, Michael; Roth, Johannes; Stark, Holger (European Physical Journal E, 2007)
We study the Brownian motion of an ensemble of single colloidal particles in a random square and a quasicrystalline potential when they start from non-equlibrium. For both potentials, Brownian dynamics simulations reveal a widespread subdiffusive regime before the diffusive long-time limit is reached in thermal equilibrium. We develop a random trap model based on a distribution for the depths of trapping sites that reproduces the results of the simulations in detail. Especially, it gives analytic formulas for the long-time diffusion constant and the relaxation time into the diffusive regime. Aside from detailed differences, our work demonstrates that quasicrystalline potentials can be used to mimic aspects of random potentials.

Brownian particles on rough substrates: Relation between intermediate subdiffusion and asymptotic long-time diffusion - Hanes, Richard; Schmiedeberg, Michael; Egelhaaf, Stefan (Physical Review E, 2013)
Brownian particles in random potentials show an extended regime of subdiffusive dynamics at intermediate times. The asymptotic diffusive behavior is often established at very long times and thus cannot be accessed in experiments or simulations. For the case of one-dimensional random potentials with Gaussian distributed energies, we present a detailed analysis of experimental and simulation data. It is shown that the asymptotic long-time diffusion coefficient can be related to the behavior at intermediate times, namely, the minimum of the exponent that characterizes subdiffusion and hence corresponds to the maximum degree of subdiffusion. As a consequence, investigating only the dynamics at intermediate times is sufficient to predict the order of magnitude of the long-time diffusion coefficient and the time scale at which the crossover from subdiffusion to diffusion occurs, i.e., when the long-time diffusive regime and hence thermal equilibrium is established. Inversely, theoretical predictions derived for the asymptotic long-time behavior can be used to quantitatively characterize the intermediate behavior, which hardly has been studied so far.

Colloidal Ordering on a 2D Quasicrystalline Substrate - Schmiedeberg, Michael; Stark, Holger (Physical Review Letters, 2008)
By using Monte Carlo simulations, we study the complex phase behavior of charged-stabilized colloidal particles in a two-dimensional substrate potential with quasicrystalline decagonal symmetry. In the regime where the strengths of the substrate and colloidal pair potential are comparable, we identify a novel and unexpected quasicrystalline phase with pure 20-fold bond order and a disordered structure without any apparent rotational symmetry. Furthermore, we demonstrate how phasonic displacements in the substrate potential induce phasonic flips in the colloidal monolayer.

Colloidal Trajectories in Two-Dimensional Light-Induced Quasicrystals with 14-Fold Symmetry due to Phasonic Drifts - Martinsons, Miriam; Sandbrink, Matthias; Schmiedeberg, Michael (POLISH ACAD SCIENCES INST PHYSICS, 2014)
Quasicrystals are structures that are not periodic but possess a long range positional order. They can have any rotational symmetry including those that are forbidden in periodic crystals. The symmetry is classified by the point group and the rank D. In quasicrystals, phasons as additional hydrodynamic modes cause correlated rearrangements of the particles. The number of phasonic degrees of freedom depends on the rank. For colloidal quasicrystals that are induced by laser fields, specific phasonic displacements can be realized by changing the phases of the laser beams in a well-determined way. The arising trajectories of colloids in two-dimensional light-induced colloidal quasicrystals with rank D = 4 have already been analyzed in detail. Here, we analyze the colloidal trajectories in two-dimensional quasicrystals with 14-fold symmetry having rank D = 6. We observe complex paths of the colloids consisting of straight and winding lines as well as jumps.

Colloids in one dimensional random energy landscapes - Hanes, Richard; Dalle-Ferrier, Cecile; Schmiedeberg, Michael; Jenkins, Mathew; Egelhaaf, Stefan (Soft Matter, 2012)
Individual colloidal particles have been studied experimentally in a one dimensional random potential with energies that follow a Gaussian distribution. This rough, noise-like potential has been realised using a holographic optical set-up, which allows the width of the distribution to be varied. For different widths, the particle trajectories were followed and the particle dynamics characterised by, for example, the mean square displacement, non-Gaussian parameter, van Hove function, time-dependent diffusion coefficient and residence time distribution. The values obtained for these observables are consistent with the static properties of the system, in particular the barrier height distribution, which was obtained by a detailed characterisation of the tweezer-like set-up. The dynamics display three distinct behaviours: at short times normal diffusion, subsequently an extended regime of localisation within the different minima of the potential and finally a very slow approach towards long-time diffusive behaviour, for which diffusion coefficients consistent with theoretical predictions have been found.

Comment on "Communication: Is directed percolation in colloid-polymer mixtures linked to dynamic arrest?' - Schmiedeberg, Michael (Journal of Chemical Physics, 2022)
In their Communication [J. Chem. Phys. 148, 241101 (2018)], Richard et al. state that in the work of Kohl et al. [Nat. Commun. 7, 11817 (2016)], a mechanism for dynamical arrest in temporal networks has been proposed that actually has never been proposed (and would be obviously wrong) in this context. The actual findings of Kohl et al. are not tested nor affected by the communication. The work of Richard et al. rests on simulations in a regime of the phase diagram that significantly differs from the one that Kohl et al. consider. In this Comment, it is shown that both the effective density and the rescaled second virial coefficient indicate that the comparison presented by Richard et al. is invalid. Therefore, the implications that are based on this comparison are incorrect. There is no indication for a disagreement between the simulations of Richard et al. and those of Kohl et al., and I am confident that upon consistent comparison and interpretation of the results, both works can contribute to a more comprehensive picture of gel-forming system
Keywords: gel; percolation; network

Comment on "Quantum Quasicrystals of Spin-Orbit-Coupled Dipolar Bosons" - Sandbrink, Matthias; Roth, Johannes; Schmiedeberg, Michael (Physical Review Letters, 2014)

Comparing light-induced colloidal quasicrystals with different rotational symmetries - Schmiedeberg, Michael; Stark, Holger (Journal of Physics: Condensed Matter, 2012)
Quasicrystals are aperiodic structures with long-range orientational order. Unlike crystals, quasicrystals can, in principle, possess any non-crystallographic rotational symmetry. However, only a few of these rotational symmetries have been observed. By using Monte Carlo simulations of colloidal particles in laser interference patterns with quasicrystalline symmetry, we compare the onset of quasicrystalline order for different rotational symmetries in two dimensions. We find that quasicrystals with 5-, 8-, 10-, and 12-fold rotational axes can be induced with lower laser intensities than quasicrystals with other non-crystallographic rotational symmetries. We relate this finding to the number of local symmetry centers in the respective interference patterns.

Compatibility waves drive crystal growth on patterned substrates - Neuhaus, Tim; Schmiedeberg, Michael; Löwen, Hartmut (New Journal of Physics, 2013)
We explore the crystallization in a colloidal monolayer on a structured template starting from a few-particle nucleus. The competition between the substrate structure and that of the growing crystal induces a new crystal growth scenario. Unlike with the crystal growth in the bulk where a well-defined and connected crystal-fluid interface grows into the fluid, we identify a mechanism where a 'compatibility wave' of the prescribed nucleus with the underlying substrate structure dictates the growth direction and efficiency. The growth process is strongly anisotropic and proceeds via transient island formation in front of an initial solid-fluid interface. We demonstrate the validity of this compatibility wave concept for a large class of substrate structures including a square lattice and a quasicrystalline pattern. Dynamical density functional theory that provides a microscopic approach to the crystallization process is employed for colloidal hard spheres. Our predictions can be verified in experiments on confined colloids and also bear consequences for molecular crystal growth on structured substrates.

Connecting the random organization transition and jamming within a unifying model system - Milz, Lars; Schmiedeberg, Michael (Physical Review E, 2013)
While the random organization transition describes the change from reversible to irreversible dynamics in a nonequilibrium system, the athermal jamming transition at zero shear rate occurs when particles can no longer avoid overlaps. Despite the obvious differences between these two transitions, we show that they both occur within the same model packing problem. In this unifying model system the particles are first randomly distributed and then displaced in each step if they overlap. For random displacements we obtain a random organization transition, while jamming occurs in the case of deterministic shifts. We also analyze the critical behavior of random organization. Our results show that random organization and jamming are opposite limits of random sphere packings, and we expect that various equilibrium and nonequilibrium transitions can be formulated as related intermediate packing problems.

Corrigendum: Temperature dependence of the transition packing fraction of thermal jamming in a harmonic soft sphere system (Journal of Physics Condensed Matter (2019) 31 (165101) DOI: 10.1088/1361-648X/ab01e9) - Maiti, Moumita; Schmiedeberg, Michael (Journal of Physics: Condensed Matter, 2019)
In the second to last paragraph of section 3 of our paper [1] there is a mistake in the formula of the rescaling. Instead of (Tμ/2 - bT)-1 it has to be (Tμ/2)-1 - b(T)-1. Note that in the figures 4 (e)–(g) we have employed the correct rescaling but the labels on the x-axes have to read |g,0 - |(Tμ/2)-1 - b(T)-1. We thank Monoj Adhikari for bringing this mistake to our attention.
CRIS-Team Scopus Importer:2019-10-08

Course of dislocation lines in templated three-dimensional colloidal quasicrystals - Sandbrink, Matthias; Schmiedeberg, Michael (Physical Review B, 2014)
We present an approach based on colloidal epitaxy to obtain three-dimensional colloidal quasicrystals, i.e., structures with long-range order but no periodicity. In contrast to other attempts to obtain soft-matter quasicrystals by design, no fine tuning of the colloid-colloid interactions is required. By using Monte Carlo simulations, we explore the development of multiple layers with the desired quasicrystalline symmetry when the colloidal particles sediment onto suitable quasicrystalline substrates. In addition, well-defined defect lines can be induced in the grown colloidal quasicrystal by constructing substrates with well-chosen defects that lead to induced defect lines. We present a study of the three-dimensional course of such dislocation lines by inducing and analyzing stable lines that bend, unstable ones that split up, or defect lines that merge with other defects. Dislocations are characterized by Burgers vectors that are composed of a phononic part as in a periodic crystal and an additional phasonic part that is unique to quasicrystals. As in a periodic crystal, the sum of all Burgers vectors is conserved along defect lines and at all forks. However, unlike in a periodic crystal, the course of a dislocation line in a quasicrystal depends on its position. Furthermore, although in a quasicrystal all Burgers vectors can always be written as sum of Burgers vectors with a smaller phononic part, we find dislocations that do not decompose into dislocations with smaller phononic Burgers vectors. For quasicrystals with eightfold and twelvefold rotational symmetry, we identify basis Burgers vectors that denote stable dislocations. Our results can be verified in experiments and are important for applications of colloidal quasicrystals, e.g., for the development of photonic quasicrystals.

Crystallization induced by multiple seeds: Dynamical density functional approach - Neuhaus, Tim; Schmiedeberg, Michael; Löwen, Hartmut (Physical Review E, 2013)
Using microscopic dynamical density functional theory, we calculate the dynamical formation of polycrystals by following the crystal growth around multiple crystalline seeds imposed to an undercooled fluid. Depending on the undercooling and the size ratio as well as the relative crystal orientation of two neighboring seeds, three possibilities of the final state emerge, namely no crystallization at all, formation of a monocrystal, or two crystallites separated by a curved grain boundary. Our results, which are obtained for two-dimensional hard disk systems using a fundamental-measure density functional, shed new light on the particle-resolved structure and growth of polycrystalline material in general.

Density functional theory of heterogeneous crystallization - Neuhaus, Tim; Härtel, Andreas; Marechal, Mattheus; Schmiedeberg, Michael; Löwen, Hartmut (European Physical Journal - Special Topics, 2014)
This mini-review summarizes recent progress in describing heterogeneous crystallization processes and microstructure formation within microscopic classical density functional theory (DFT). After outlining the basic features of DFT, we discuss several applications ranging from the structure and thermodynamics of fluid-crystal interfaces for hard sphere and Yukawa systems to dynamical phenomena such as crystal growth on structured substrates and induced by externally imposed seeds.

Detection of phonon and phason modes in intrinsic colloidal quasicrystals by reconstructing their structure in hyperspace - Hielscher, Johannes; Martinsons, Miriam; Schmiedeberg, Michael; Kapfer, Sebastian (Journal of Physics: Condensed Matter, 2017)
Phasons are additional degrees of freedom which occur in quasicrystals alongside the phonons known from conventional periodic crystals. The rearrangements of particles that are associated with a phason mode are hard to interpret in physical space. We reconstruct the quasicrystal structure by an embedding into extended higher-dimensional space, where phasons correspond to displacements perpendicular to the physical space. In dislocation-free decagonal colloidal quasicrystals annealed with Brownian dynamics simulations, we identify thermal phonon and phason modes. Finite phononic strain is pinned by phasonic excitations even after cooling down to zero temperature. For the phasonic displacements underlying the flip pattern, the reconstruction method gives an approximation within the limits of a multi-mode harmonic ansatz, and points to fundamental limitations of a harmonic picture for phasonic excitations in intrinsic colloidal quasicrystals.
Keywords: colloids; quasicrystals; phasons; phonons

Dilute gel networks vs. clumpy gels in colloidal systems with a competition between repulsive and attractive interactions - Gimperlein, Matthias; Immink, Jasper N.; Schmiedeberg, Michael (Soft Matter, 2024)
Using Brownian dynamics simulations we study gel-forming colloidal systems. The focus of this article lies on the differences of dense and dilute gel networks in terms of structure formation both on a local and a global level. We apply reduction algorithms and observe that dilute networks and dense gels differ in the way structural properties like the thickness of strands emerge. We also analyze the percolation behavior and find that two different regimes of percolation exist which might be responsible for structural differences. In dilute networks we confirm that solidity is mainly a consequence of pentagonal bipyramids forming in the network. In dense gels, tetrahedral structures also influence solidity.
CRIS-Team Scopus Importer:2024-03-29

Directed percolation identified as equilibrium pre-transition towards non-equilibrium arrested gel states - Kohl, M.; Capellmann, R. F.; Laurati, Marco; Egelhaaf, S. U.; Schmiedeberg, Michael (Nature Communications, 2016)
The macroscopic properties of gels arise from their slow dynamics and load-bearing network structure, which are exploited by nature and in numerous industrial products. However, a link between these structural and dynamical properties has remained elusive. Here we present confocal microscopy experiments and simulations of gel-forming colloid-polymer mixtures. They reveal that gel formation is preceded by continuous and directed percolation. Both transitions lead to system-spanning networks, but only directed percolation results in extremely slow dynamics, ageing and a shrinking of the gel that resembles synaeresis. Therefore, dynamical arrest in gels is found to be linked to a structural transition, namely directed percolation, which is quantitatively associated with the mean number of bonded neighbours. Directed percolation denotes a universality class of transitions. Our study hence connects gel formation to a well-developed theoretical framework, which now can be exploited to achieve a detailed understanding of arrested gels.

Dislocation-free growth of quasicrystals from two seeds due to additional phasonic degrees of freedom - Schmiedeberg, Michael; Achim, Cristian; Hielscher, Johannes; Kapfer, Sebastian; Loewen, Hartmut (Physical Review E, 2017)
We explore the growth of two-dimensional quasicrystals, i.e., aperiodic structures that possess long-range order, from two seeds at various distances and with different orientations by using dynamical phase-field crystal calculations. We compare the results to the growth of periodic crystals from two seeds. There, a domain border consisting of dislocations is observed in case of large distances between the seed and large angles between their orientation. Furthermore, a domain border is found if the seeds are placed at a distance that does not fit to the periodic lattice. In the case of the growth of quasicrystals, we only observe domain borders for large distances and different orientations. Note that all distances do inherently not match to a perfect domain wall-free quasicrystalline structure. Nevertheless, we find dislocation-free growth for all seeds at a small enough distance and for all seeds that approximately have the same orientation. In periodic structures, the stress that occurs due to incommensurate distances between the seeds results in phononic strain fields or, in the case of too large stresses, in dislocations. In contrast, in quasicrystals an additional phasonic strain field can occur and suppress dislocations. Phasons are additional degrees of freedom that are unique to quasicrystals. As a consequence, the additional phasonic strain field helps to distribute the stress and facilitates the growth of dislocation-free quasicrystals from multiple seeds. In contrast, in the periodic case the growth from multiple seeds most likely leads to a structure with multiple domains. Our work lays the theoretical foundations for growing perfect quasicrystals from different seeds and is therefore relevant for many applications.

Effective substrate potentials with quasicrystalline symmetry depend on the size of the adsorbed particles - Rühle, Felix; Sandbrink, Matthias; Stark, Holger; Schmiedeberg, Michael (European Physical Journal E, 2015)
We explore the effective potential landscapes that extended particles experience when adsorbed on the surface of quasicrystals. Commonly, these are solids with long-ranged order but no translational symmetry. The effective potentials significantly depend on the size of the adsorbed particles. We show how changing the particle radius changes the so-called local isomorphism class of the effective quasicrystalline pattern. This means effective potentials for different particle sizes cannot directly be mapped onto each other. Our theoretical predictions are confirmed by Monte Carlo simulations. The results are important for colloidal particles with different sizes that are subjected to laser fields with quasicrystalline symmetry as well as for systems where extended molecules are deposited onto the surface of metallic quasicrystals.

Energy landscape description of the clustering transition for active soft spheres - Maiti, Moumita; Schmiedeberg, Michael (EPL - Europhysics Letters, 2019)
For a system consisting of active soft spheres in three dimensions, we study the transition from a fluid where overlaps between particles can only occur for a short time after a collision to a state where clusters of overlapping particles persist for a long time. In order to determine the properties of the transition, we explore the energy landscape of the system in a similar way as it is done for the determination of the athermal or thermal jamming transition. Note that for zero temperature the competition of particles that attach to existing clusters and particles that detach due to thermal effects does not arise. Therefore, here we do not study such a competition because we consider systems at small or zero energy. Instead, we explore at which packing fractions and what activities cluster formation can occur at all. In case of an athermal system the transition between systems where no clusters develop at all and systems where stable clusters are found is a first order transition for packing fractions below 0.55 while the transition is continuous in case of larger packing fractions. In case of thermal systems the transition is continuous everywhere. While our approach does not deal with the real dynamics of the system, it reveals the nature of the clustering transition and it enables a deeper insight in the consequences of thermal fluctuations and the relation of the clustering transition to jamming. Though Brownian timescales diverge in athermal systems, the activity that we consider can be compared to the active velocity in other simulations if the later is measured in units of the particle size divided by an elastic time scale.<br
Keywords: active particles clustering transition jamming

Ergodicity breaking transition in a glassy soft sphere system at small but non-zero temperatures - Maiti, Moumita; Schmiedeberg, Michael (Scientific Reports, 2018)

Event-chain Monte Carlo simulations of the liquid to solid transition of two-dimensional decagonal colloidal quasicrystals - Martinsons, Miriam; Hielscher, Johannes; Kapfer, Sebastian; Schmiedeberg, Michael (Journal of Physics: Condensed Matter, 2019)
In event-chain Monte Carlo simulations, we model colloidal particles in two dimensions that interact according to an isotropic short-ranged pair potential which supports the two typical length scales present in decagonal quasicrystals. We investigate the assembled structures as we vary the density and temperature. Our special interest is related to the transition from quasicrystal to liquid. In contrast to the KTHNY melting theory for quasicrystals which predicts an intermediate pentahedratic phase, we find a one-step first-order melting transition. However, we discover that the slow relaxation of phasonic flips, i.e. rearrangements of the particles due to additional degrees of freedom in quasicrystals, changes the positional correlation functions, to the extent that structures with long-range orientational correlations, but exponentially decaying positional correlations, are observe
Keywords: quasicrystal; event-chain Monte Carlo; melting

Far from the equilibrium crowd - Schmiedeberg, Michael (Nature Physics, 2023)

Freezing and melting of a colloidal adsorbate on a 1D quasicrystalline substrate - Schmiedeberg, Michael; Roth, Johannes; Stark, Holger (Physical Review Letters, 2006)
Using Monte Carlo simulations and an extended Landau-Alexander-McTague theory, we demonstrate that colloids in a one-dimensional quasicrystalline potential order in triangular and rhombic-alpha crystalline phases. Increasing the strength of the potential further, a new type of light-induced melting is discovered that has its origin in the nonperiodicity of the potential. In contrast to reentrant melting in periodic potentials, the quasicrystalline potential melts the crystalline phases even when they already exist at zero potential.

Growth Modes of Quasicrystals - Achim, Cristian; Schmiedeberg, Michael; Löwen, Hartmut (Physical Review Letters, 2014)
The growth of quasicrystals, i.e., aperiodic structures with long-range order, seeded from the melt is investigated using a dynamical phase field crystal model. Depending on the thermodynamic conditions, two different growth modes are detected, namely defect-free growth of the stable quasicrystal and a mode dominated by phasonic flips which are incorporated as local defects into the grown structure such that random tilinglike ordering emerges. The latter growth mode is unique to quasicrystals and can be verified in experiments on one-component mesoscopic systems.

Growth of two-dimensional decagonal colloidal quasicrystals - Martinsons, Miriam; Schmiedeberg, Michael (Journal of Physics: Condensed Matter, 2018)

Growth of two-dimensional dodecagonal colloidal quasicrystals: Particles with isotropic pair interactions with two length scales vs. patchy colloids with preferred binding angles - Gemeinhardt, Anja; Martinsons, Miriam; Schmiedeberg, Michael (European Physical Journal E, 2018)

Horizons and free-path distributions in quasiperiodic Lorentz gases - Kraemer, Ata; Schmiedeberg, Michael; Sanders, David (Physical Review E, 2015)
We study the structure of quasiperiodic Lorentz gases, i.e., particles bouncing elastically off fixed obstacles arranged in quasiperiodic lattices. By employing a construction to embed such structures into a higher-dimensional periodic hyperlattice, we give a simple and efficient algorithm for numerical simulation of the dynamics of these systems. This same construction shows that quasiperiodic Lorentz gases generically exhibit a regime with infinite horizon, that is, empty channels through which the particles move without colliding, when the obstacles are small enough; in this case, the distribution of free paths is asymptotically a power law with exponent -3, as expected from infinite-horizon periodic Lorentz gases. For the critical radius at which these channels disappear, however, a new regime with locally finite horizon arises, where this distribution has an unexpected exponent of -5, previously observed only in a Lorentz gas formed by superposing three incommensurable periodic lattices in the Boltzmann-Grad limit where the radius of the obstacles tends to zero.

Mapping the glassy dynamics of soft spheres onto hard-sphere behavior - Schmiedeberg, Michael; Haxton, Tom; Nagel, Sidney; Liu, Andrea (EPL - Europhysics Letters, 2011)
We show that the dynamics of soft-sphere systems with purely repulsive interactions can be described by introducing an effective hard-sphere diameter determined using the Andersen-Weeks-Chandler approximation. We find that this approximation, known to describe static properties of liquids, also gives a good description of a dynamical quantity, the relaxation time, even in the vicinity of the glass transition. Copyright (C) EPLA, 2011

Mean field approach of dynamical pattern formation in underdamped active matter with short-ranged alignment and distant anti-alignment interactions - Arold, Dominic; Schmiedeberg, Michael (Journal of Physics: Condensed Matter, 2020)
Many active matter systems, especially on the microscopic scale, are well approximated as overdamped, meaning that any inertial momentum is immediately dissipated by the environment. On the other hand, especially for macroscopic active systems but also for many mesoscopic systems the time scale of translational inertial motion can become large enough to be relevant for the dynamics. This raises the question how collective dynamics and the resulting states in active matter are influenced by inertia. Therefore, we propose a coarse-grained continuum model for underdamped active matter based on a mean field description for passive systems. Furthermore, as an example, we apply the model to a system with interactions that support an alignment on short distances and an anti-alignment on longer length scales as known in the context of pattern formation due to orientational interactions. Our numerical calculations of the under- and overdamped dynamics both predict a structured laning state. However, activity induced convective flows that are only present in the underdamped model destabilize this state when the anti-alignment is weakened, leading to a collective motion state which does not occur in the overdamped limit. A turbulent transition regime between the two states can be characterized by strong density fluctuations and the absence of global orderin
Keywords: active particles; mean field; inertia; non-equilibrium

Multiple reentrant glass transitions of soft spheres at high densities: Monotonicity of the curves of constant relaxation time in jamming phase diagrams depending on temperature over pressure and pressure - Schmiedeberg, Michael (Physical Review E, 2013)
By using molecular-dynamics simulations, we determine the jamming phase diagrams at high densities for a bidisperse mixture of soft spheres that interact according to repulsive power-law pair potentials. We observe that the relaxation time varies nonmonotonically as a function of density at constant temperature. Therefore, the jamming phase diagrams contain multiple reentrant glass transitions if temperature and density are used as control parameters. However, if we consider a new formulation of the jamming phase diagrams where temperature over pressure and pressure are employed as control parameters, no nonmonotonic behavior is observed.

Occurrence of connected clusters in motility-induced phase-separated states of persistent active particles at zero temperature - Schmiedeberg, Michael (EPL - Europhysics Letters, 2023)
To study the interplay of the formation of clusters of overlapping particles and motility-induced phase separation in the zero temperature limit in two dimensions, we consider a simple model system consisting of a bidisperse mixture of disks that are only subject to a repulsion force in case of overlaps and an active force. The orientation of the disks is chosen randomly in the beginning and does not change anytime during the simulation thus corresponding to an infinite persistence length. Simulations with our model system reveal that clusters of overlapping particles occur in the dense phase of a phase-separated state in case of intermediate values of the ratio of active to repulsive force. However, for smaller activities there are only a few overlaps between the particles in the dense phase and the coexistence region ends at a packing fraction below the onset of the formation of clusters with overlapping particles. For large activities small clusters corresponding to small patches of the dense phase are found that are unstable due to the activity. Finally, the occurrence of connected clusters affects the phase separation. Our findings on how cluster formation and phase separation are related are relevant to many active particle systems as after adding thermal noise our model system corresponds to a system of active Brownian particles that have been intensely studied in recent years. Further extensions by adding friction, inertia, or more complex interactions are possible.<br
Keywords: active particles; phase separation; clustering; non-equilibrium

One-bead microrheology with rotating particles - Schmiedeberg, Michael; Stark, Holger (EPL - Europhysics Letters, 2005)
We lay the theoretical basis for one-bead microrheology with rotating particles, i.e., a method where colloids are used to probe the mechanical properties of viscoelastic media. Based on a two-fluid model. we calculate the compliance and discuss it for two cases. We first assume that the elastic and the fluid component exhibit both stick boundary conditions at the particle surface. Then, the compliance fulfills a generalized Stokes law with a complex shear modulus whose validity is only limited by inertial effects, in contrast to translational motion. Secondly, we find that the validity of the Stokes regime is reduced when the elastic network is not coupled to the particle.

On moments and scaling regimes in anomalous random walks - Schmiedeberg, Michael; Zaburdaev, Vasily; Stark, Holger (Journal of Statistical Mechanics-Theory and Experiment, 2009)
Anomalous diffusion is commonly characterized by an exponent in the power law of the mean square displacement as a function of time < r(2)(t)> proportional to t(2 nu). On the other hand, it is known that the probability distribution function of diffusing particles can be approximated by (1/t(alpha))Phi(r/t(alpha)). While for classical normal diffusion this scaling relation is exact, it may not be valid globally for anomalous diffusion. In general, the exponent a obtained from the scaling of the central part of the probability distribution function differs from the exponent nu given by the mean square displacement. In this paper we systematically study how the scaling of different moments and parts of the probability distribution function can be determined and characterized even when no global scaling exists. We consider three rigorous methods for finding, respectively, the mean square displacement exponent nu, the scaling exponent alpha and the profile of the scaling function Phi. We also show that alternatively the scaling exponent alpha can be determined by analyzing fractional moments with q << 1. All analytical results are obtained in the framework of continuous-time random walks. For a wide class of coupled random walks, including the famous Levy walk model, we introduce a new unifying description which allows straightforward generalizations to other systems. Finally, we show how fractional moments help to analyze experimental or simulation data consistentl
Keywords: transport properties (theory); dynamics (theory); diffusion

Oscillations due to time-delayed driving of a ball in a water jet - a challenging problem of the International Physicists' Tournament 2019 - Michalke, Simon; Fösel, Angela; Schmiedeberg, Michael (European Journal of Physics, 2020)
The International Physicists' Tournament (IPT) 2019 dealt with 17 challenging problems. In this article, we present experimental as well as theoretical approaches exemplarily to one of these tasks. A ball placed on a hard and flat surface can show oscillation movement when being hit by a jet of water from above. To explain the oscillations, a theoretical model is introduced and its predictions are compared to the experimental measurements. Furthermore, the structure of the IPT itself is characterized shortly in this article, as well as the idea of a new and innovative seminar which was set up at Erlangen University to prepare and assist students in taking part in International Physicists' Tournament. Furthermore, the educational relevance of physics tournaments like IPT for physics education at university is discussed in detail.<br
Keywords: Physics Competitions; International Physicists' Tournament; German Physicists' Tournament; oscillations; nonlinear dynamics; harmonic oscillator; time-delay

Particle segregation in a sedimenting bidisperse soft sphere system - Kohl, Matthias; Schmiedeberg, Michael (Soft Matter, 2014)
We study the sedimentation process of a binary colloidal soft sphere system where significant overlaps of the particles are possible. We employ estimates of the equation of states in the small and large pressure limit in order to predict the final states of the sedimentation process. Furthermore, Brownian dynamics simulations were performed in order to confirm the predictions and to explore the dynamics of the sedimentation. We observe that the segregation process due to gravity usually consists of multiple steps. Instead of single particles moving upwards or downwards we usually observe that first local segregation occurs, then clusters consisting of particles of one species are formed that finally sink towards their equilibrium position within the final sedimentation profile. The possible final states include complex phases like a phase consisting of large particles on the top and the bottom of the system with small particles in between. We also observe metastable network-like structures.

Phase field crystal model for particles with n-fold rotational symmetry in two dimensions - Weigel, Robert; Schmiedeberg, Michael (Modelling and Simulation in Materials Science and Engineering, 2022)
We introduce a phase field crystal (PFC) model for particles with n-fold rotational symmetry in two dimensions. Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the orientation, and the direction of the orientation, where all these order parameters depend on the position. The functional is constructed such that for particles with axial symmetry (i.e. n = 2) the PFC model for liquid crystals as introduced by Löwen (2010 J. Phys.: Condens. Matter 22 364105) is recovered. We discuss the stability of the functional and explore phases that occur for 1 ⩽ n ⩽ 6. In addition to isotropic, nematic, stripe, and triangular order, we also observe cluster crystals with square, rhombic, honeycomb, and even quasicrystalline symmetry. The n-fold symmetry of the particles corresponds to the one that can be realized for colloids with symmetrically arranged patches. We explain how both, repulsive as well as attractive patches, are described in our model.<br

Phasonic Diffusion and Self-confinement of Decagonal Quasicrystals in Hyperspace - Hielscher, Johannes; Martinsons, Miriam; Schmiedeberg, Michael; Kapfer, Sebastian (Journal of Physics: Conference Series, 2020)
We introduce a novel simulation method that is designed to explore fluctuations of the phasonic degrees of freedom in decagonal colloidal quasicrystals. Specifically, we attain and characterise thermal equilibrium of the phason ensemble via Monte Carlo simulations with particle motions restricted to elementary phasonic flips. We find that, at any temperature, the random tiling ensemble is strongly preferred over the minimum phason-strain quasicrystal. Phasonic flips are the dominant carriers of diffusive mass transport in physical space. Sub- diffusive transients suggest cooperative flip behaviour on short time scales. In complementary space, particle mobility is geometrically restricted to a thin ring around the acceptance domain, resulting in self-confinement and persistent phasonic orde
Keywords: quasicrystal; phason; simulation

Phason-induced dynamics of colloidal particles on quasicrystalline substrates - Kromer, Justus; Schmiedeberg, Michael; Roth, Johannes; Stark, Holger (European Physical Journal E, 2013)
Phasons are special hydrodynamic modes that occur in quasicrystals. The trajectories of particles due to a phasonic drift were recently studied by Kromer et al. (Phys. Rev. Lett. 108, 218301 (2012)) for the case where the particles stay in the minima of a quasicrystalline potential. Here, we study the mean motion of colloidal particles in quasicrystalline laser fields when a phasonic drift or displacement is applied and also consider the cases where the colloids cannot follow the potential minima. While the mean square displacement is similar to the one of particles in a random potential with randomly changing potential wells, there also is a net drift of the colloids that reverses its direction when the phasonic drift velocity is increased. Furthermore, we explore the dynamics of the structural changes in a laser-induced quasicrystal during the rearrangement process that is caused by a steady phasonic drift or an instantaneous phasonic displacement.

Photon channelling in foams - Schmiedeberg, Michael; Miri, MirFaez; Stark, Holger (European Physical Journal E, 2005)
Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction epsilon. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of epsilon.

Physics competitions in the time of a pandemic: 3D printing as a new approach to the quantitative investigation of Cartesian divers at home - Bley, Jonas; Pietz, Antony; Fösel, Angela; Schmiedeberg, Michael; Heusler, Stefan; Pusch, Alexander (European Journal of Physics, 2021)
Despite the difficult circumstances due to the COVID-19 pandemics, physics students can tackle interesting questions that are part of physics competitions as the German Physicists' Tournament (GPT) 2020. Due to the COVID-19 pandemics in 2020, many competitions such as the GPT are held online. Furthermore, the usual options of equipment offered by the supervising university institutions could not be used by the students. The problems of the GPT 2020 therefore had to be chosen in such a way that they could be examined at home using simple means. One of these supposedly simple but profound experiments—the Cartesian diver—is described in this article. The physics of the Cartesian diver has been discussed before Fakhruddin (2003 Phys. Teach. 41 53), Güémez et al (2002 Am. J. Phys. 70 710) and De Luca and Ganci (2011 Phys. Educ. 46 528), as well as various modifications (Ivanov and Nikolov 2019 Phys. Educ. 55 025006). We present a new way of investigating Cartesian divers quantitatively by using 3D printing and common household materials. The paper is addressed to undergraduate students and educators teaching physics at university.<br

Proliferation of anomalous symmetries in colloidal monolayers subjected to quasiperiodic light fields - Mikhael, Jules; Schmiedeberg, Michael; Rausch, Sebastian; Roth, Johannes; Stark, Holger; Bechinger, Clemens (Proceedings of the National Academy of Sciences of the United States of America, 2010)
Quasicrystals provide a fascinating class of materials with intriguing properties. Despite a strong potential for numerous technical applications, the conditions under which quasicrystals form are still poorly understood. Currently, it is not clear why most quasicrystals hold 5- or 10-fold symmetry but no single example with 7- or 9-fold symmetry has ever been observed. Here we report on geometrical constraints which impede the formation of quasicrystals with certain symmetries in a colloidal model system. Experimentally, colloidal quasicrystals are created by subjecting micron-sized particles to two-dimensional quasiperiodic potential landscapes created by n = 5 or seven laser beams. Our results clearly demonstrate that quasicrystalline order is much easier established for n 5 compared to n = 7. With increasing laser intensity we observe that the colloids first adopt quasiperiodic order at local areas which then laterally grow until an extended quasicrystalline layer forms. As nucleation sites where quasiperiodicity originates, we identify highly symmetric motifs in the laser pattern. We find that their density strongly varies with n and surprisingly is smallest exactly for those quasicrystalline symmetries which have never been observed in atomic systems. Since such high-symmetry motifs also exist in atomic quasicrystals where they act as preferential adsorption sites, this suggests that it is indeed the deficiency of such motifs which accounts for the absence of materials with e. g., 7-fold symmetry.
Keywords: 7-fold symmetry; growth mechanism; light patterns

Random walks with random velocities - Zaburdaev, Vasily; Schmiedeberg, Michael; Stark, Holger (Physical Review E, 2008)
We consider a random walk model that takes into account the velocity distribution of random walkers. Random motion with alternating velocities is inherent to various physical and biological systems. Moreover, the velocity distribution is often the first characteristic that is experimentally accessible. Here, we derive transport equations describing the dispersal process in the model and solve them analytically. The asymptotic properties of solutions are presented in the form of a phase diagram that shows all possible scaling regimes, including superdiffusive, ballistic, and superballistic motion. The theoretical results of this work are in excellent agreement with accompanying numerical simulation

Rhombic Preordering on a Square Substrate - Neuhaus, Tim; Marechal, Mattheus; Schmiedeberg, Michael; Löwen, Hartmut (Physical Review Letters, 2013)
A competition of incommensurate symmetries occurs whenever a system is forced to conform to an ordering that is different from the intrinsically preferred structure of the system itself. As a model system of such a competition, we study the rivalry between the triangular ordering of hard disks and the square symmetry induced by a periodic square substrate. By using density functional theory as well as Monte Carlo computer simulations, we determine the full phase behavior for the case of one particle per minimum. We observe a rhombic preordering structure preceding the hexagonal solid as a direct consequence of the competing symmetries. Furthermore, the square-rhombic transition is reentrant with increasing substrate interaction. Our predictions can be verified in experiments of colloids in laser fields. DOI: 10.1103/PhysRevLett.110.118301

Self-assembly of complex structures in colloid-polymer mixtures - Oğuz, Erdal; Mijailović, Aleksandar; Schmiedeberg, Michael (Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2018)
If particles interact according to isotropic pair potentials that favor multiple length scales, in principle, a large variety of different complex structures can be achieved by self-assembly. Here, we study the specific example of colloid-polymer mixtures in which the effective interactions between colloids are dictated by a Aasakura-Osawa–type potential that possesses two length scales. Upon examining the phase behavior of two-dimensional colloid-polymer mixtures, we observe that nontrivial structures only occur in the vicinity of selected densities where triangular ordering is suppressed by the pair potential. Close to these densities, a large number of different phases self-assemble that correspond to tilings containing triangular, rhombic, square, hexagonal, and pentagonal tiles, and including some of the Archimedean tilings. We obtain the ground-state energies by minimizing the corresponding lattice sums with respect to particle positions in a unit cell as well as cell geometry and verify the occurrence of selected phases at finite temperatures by using Brownian dynamics simulations. We explain how the occurrence of nontrivial orderings can be predicted on a two-particle level by employing an enthalpylike pair potentials. Our work provides a manual on how to find the regions of nontrivial phases in parameter space for complex pair interactions in genera

Shear-induced slab-like domains in a directed percolated colloidal gel - Kohl, Matthias; Schmiedeberg, Michael (European Physical Journal E, 2017)

Stability of particles in two-dimensional quasicrystals against phasonic perturbations - Martinsons, Miriam; Schmiedeberg, Michael (Journal of Physics: Conference Series, 2020)
We investigate particles in two-dimensional quasicrystalline interference patterns and present a method to determine for each particle at which phasonic displacement a phasonic flip occurs. By mapping all particles into characteristic areas of reduced phononic and phasonic displacements, we identify the particles that are close to edges of these areas and can easily flip. In contrast, the particles in the center are hardly affected by phasonic fluctuations. Our results are important e.g. for light-induced colloidal structures or cold atomic gases in laser traps. In addition, our approach can help to predict how thermal fluctuations induce phasonic flips in intrinsic quasicrystals with structures close to interference pattern
Keywords: quasicrystals; phasons

Stabilizing quasicrystals composed of patchy colloids by narrowing the patch width - Gemeinhardt, Anja; Martinsons, Miriam; Schmiedeberg, Michael (EPL - Europhysics Letters, 2019)
We explore the behavior of two-dimensional patchy colloidal particles with 8 or 10 symmetrically arranged patches by employing Monte Carlo simulations. The particles interact according to an isotropic pair potential that possesses only one typical length. The patches lead to additional attractions that are anisotropic and depend on the relative orientation of two neighboring particles. We investigate the assembled structures with a special interest in quasicrystals. We found that the patch width is of great importance: Only in the case of narrow patch widths we are able to observe metastable octagonal and decagonal quasicrystals, while dodecagonal quasicrystals can also occur for broad patches. These results are important to understand the role of interactions with preferred binding angles in order to obtain quasicrystals. Our findings suggest that in the case of sharp binding angles, as they occur in metallic alloys, octagonal and decagonal symmetries might be observed more often than in systems with less sharp binding angles as it is the case in soft-matter systems where dodecagonal quasicrystals dominate.

Structural analysis of physical gel networks using graph neural networks - Gimperlein, Matthias; Dominsky, Felix; Schmiedeberg, Michael (European Physical Journal E, 2025)
We employ graph neural networks (GNN) to analyse and classify physical gel networks obtained from Brownian dynamics simulations of particles with competing attractive and repulsive interactions. Conventionally such gels are characterized by their position in a state diagram spanned by the packing fraction and the strength of the attraction. Gel networks at different regions of such a state diagram are qualitatively different although structural differences are subtile while dynamical properties are more pronounced. However, using graph classification the GNN is capable of positioning complete or partial snapshots of such gel networks at the correct position in the state diagram based on purely structural input. Furthermore, we demonstrate that not only supervised learning but also unsupervised learning can be used successfully. Therefore, the small structural differences are sufficient to classify the gel networks. Even the trend of data from experiments with different salt concentrations is classified correctly if the GNN was only trained with simulation data. Finally, GNNs are used to compute backbones of gel networks. As the node features used in the GNN are computed in linear time , the use of GNN significantly accelerates the computation of reduced networks on a particle level. <br
Keywords: Artificial Intelligence; Neural networks; Gels; Graph neural networks; Brownian Dynamics simulation

Structural and dynamical properties of dilute gel networks in colloid–polymer mixtures - Gimperlein, Matthias; Schmiedeberg, Michael (Journal of Chemical Physics, 2021)
The competition of short-ranged depletion attraction and long-ranged repulsion between colloidal particles in colloid–polymer mixtures leads to the formation of heterogeneous gel-like structures. Our special focus will be on the states where the colloids arrange in thin strands that span the whole system and that we will refer to as dilute gel networks. These states occur at low packing fractions for attractions that are stronger than those at both the binodal line of the equilibrium gas–liquid phase separation and the directed percolation transition line. By using Brownian dynamics simulations, we explore the formation, structure, and aging dynamics of dilute gel networks. The essential connections in a dilute gel network are determined by constructing reduced networks. We compare the observed properties to those of clumpy gels or cluster fluids. Our results demonstrate that both the structure and the (often slow) dynamics of the stable or meta-stable heterogeneous states in colloid–polymer mixtures possess distinct features on various length and time scales and thus are richly divers
Keywords: colloidal gel; colloid-polymer mixture; gel network

Structural studies of local environments in high-symmetry quasicrystals - Mendoza Sosa, Alan Rodrigo; Kraemer, Ata; Oğuz, Erdal; Schmiedeberg, Michael (Scientific Reports, 2023)

Superdiffusion in a honeycomb billiard - Schmiedeberg, Michael; Stark, Holger (Physical Review E, 2006)
We investigate particle transport in the honeycomb billiard which consists of connected channels placed on the edges of a honeycomb structure. The spreading of particles is superdiffusive due to the existence of ballistic trajectories which we term perfect paths. Simulations give a time exponent of 1.72 for the mean-square displacement and a starlike, i.e., anisotropic, particle distribution. We present an analytical treatment based on the formalism of continuous-time random walks and explain the anisotropic distribution under the assumption that the perfect paths follow the directions of the six lattice axes. Furthermore, we derive a relation between the time exponent and the exponent of the distribution function for trajectories close to a perfect path. In billiards with randomly distributed channels, conventional diffusion is always observed in the long-time limit, although for small disorder transient superdiffusional behavior exists. Our simulation results are again supported by an analytical analysis.

Temperature dependence of the transition packing fraction of thermal jamming in a harmonic soft sphere system - Maiti, Moumita; Schmiedeberg, Michael (Journal of Physics: Condensed Matter, 2019)
The glassy dynamics of soft harmonic spheres are often mapped onto the dynamics of hard spheres by considering an effective diameter for the soft particles and therefore an effective packing fraction. While in this approach the thermal fluctuations within valleys of the energy landscape are covered, the crossing of energy barriers from one valley into another usually is neglected. Here we argue—motivated by studies of the glass transition based on explorations of the energy landscape—that the crossing of energy barriers can be attributed by an effective decrease of the glass transition packing fraction with increasing temperature T according to T 0.2. Furthermore, we reanalyzing data of soft sphere simulations. Since fitting scaling laws to simulation data always allows for some arbitrariness, we cannot prove based on the simulation data that our idea of a shift of the glass transition packing fraction due to barrier crossings is the only possible way to explain the discrepancies that have been observed previously. However, we show that a possible explanation of the simulation data is given by our approach to characterize the dynamics of soft spheres by both, the previously-considered temperature-dependent effective packing fraction due to the increase of the mean overlap between neighboring particles with stronger thermal fluctuations and the newly introduced increase of the glass transition packing with an increasing probability of barrier crossing
Keywords: glass transition; jamming; colloids

The thermal jamming transition of soft harmonic disks in two dimensions - Maiti, Moumita; Schmiedeberg, Michael (European Physical Journal E, 2019)
By exploring the properties of the energy landscape of a bidisperse system of soft harmonic disks in two dimensions we determine the thermal jamming transition. To be specific, we study whether the ground state of the system where the particle do not overlap can be reached within a reasonable time. Starting with random initial configurations, the energy landscape is probed by energy minimization steps as in case of athermal jamming and in addition steps where an energy barrier can be crossed with a small but non-zero probability. For random initial conditions we find that as a function of packing fraction the thermal jamming transition, i.e. the transition from a state where all overlaps can be removed to an effectively non-ergodic state where one cannot get rid of the overlaps, occurs at a packing fraction of φ_G=0.74, which is smaller than the transition packing fraction of athermal jamming at φ_J=0.842. Furthermore, we show that the thermal jamming transition is in the universality class of directed percolation and therefore is fundamentally different from the athermal jamming transition.<br
Keywords: Jamming Glass Transition

Trajectories of colloidal particles in laser fields with eight-, ten-, or twelve-fold symmetry and phasonic drift - Sandbrink, Matthias; Schmiedeberg, Michael (Aperiodic Crystal, 2013)

Two-dimensional quasicrystals of decagonal order in one-component monolayer films - Comment - Schmiedeberg, Michael; Stark, Holger (Physical Review Letters, 2008)
A Comment on the Letter by A. Patrykiejew and S. Sokolowski, Phys. Rev. Lett. 99, 156101 (2007). The authors of the Letter offer a Reply.

Uncovering the Mechanism of Trapping and Cell Orientation during Neisseria gonorrhoeae Twitching Motility - Zaburdaev, Vasily; Biais, Nicolas; Schmiedeberg, Michael; Eriksson, Jens; Jonsson, Ann-Beth; Sheetz, Michael P.; Weitz, David A. (Biophysical Journal, 2014)
Neisseria gonorrheae bacteria are the causative agent of the second most common sexually transmitted infection in the world. The bacteria move on a surface by means of twitching motility. Their movement is mediated by multiple long and flexible filaments, called type IV pili, that extend from the cell body, attach to the surface, and retract, thus generating a pulling force. Moving cells also use pili to aggregate and form microcolonies. However, the mechanism by which the pili surrounding the cell body work together to propel bacteria remains unclear. Understanding this process will help describe the motility of N. gonorrheae bacteria, and thus the dissemination of the disease which they cause. In this article we track individual twitching cells and observe that their trajectories consist of alternating moving and pausing intervals, while the cell body is preferably oriented with its wide side toward the direction of motion. Based on these data, we propose a model for the collective pili operation of N. gonorrheae bacteria that explains the experimentally observed behavior. Individual pili function independently but can lead to coordinated motion or pausing via the force balance. The geometry of the cell defines its orientation during motion. We show that by changing pili substrate interactions, the motility pattern can be altered in a predictable way. Although the model proposed is tangibly simple, it still has sufficient robustness to incorporate further advanced pili features and various cell geometries to describe other bacteria that employ pili to move on surface

Universal jamming phase diagram in the hard-sphere limit - Schmiedeberg, Michael; Haxton, Tom; Liu, Andrea (Physical Review E, 2011)
We present a new formulation of the jamming phase diagram for a class of glass-forming fluids consisting of spheres interacting via finite-ranged repulsions at temperature T, packing fraction phi or pressure p, and applied shear stress Sigma. We argue that the natural choice of axes for the phase diagram are the dimensionless quantities T/p sigma(3), p sigma(3)/epsilon, and Sigma/p, where T is the temperature, p is the pressure, Sigma is the stress, sigma is the sphere diameter, epsilon is the interaction energy scale, and m is the sphere mass. We demonstrate that the phase diagram is universal at low p sigma(3)/epsilon; at low pressure, observables such as the relaxation time are insensitive to details of the interaction potential and collapse onto the values for hard spheres, provided the observables are nondimensionalized by the pressure. We determine the shape of the jamming surface in the jamming phase diagram, organize previous results in relation to the jamming phase diagram, and discuss the significance of various limits.

VERFAHREN SOWIE EIN GRAPHEN-GENERATOR ZUM ERZEUGEN EINES GRAPHEN DER BEZIEHUNGEN ZWISCHEN OBJEKTEN IN NETZWERKEN BESCHREIBT - Pöschel, Thorsten; Lehmann, Heiko; Mühlbauer, Sebastian; Müller, Patric; Blank, Michael; Schmiedeberg, Michael (2021)
Die Erfindung betrifft ein Verfahren, einen Graphen-Generator zum Erzeugen eines Graphen sowie ein Computersystem auf welchem der erzeugte Graph simuliert werden kann.
Keywords: Netzwerk; Graph; Epidemie; Computervirus; statistisches Verfahren

What Phasons Look Like: Particle Trajectories in a Quasicrystalline Potential - Kromer, Justus; Schmiedeberg, Michael; Roth, Johannes; Stark, Holger (Physical Review Letters, 2012)
Among the distinctive features of quasicrystals-structures with long-range order but without periodicity-are phasons. Phasons are hydrodynamic modes that, like phonons, do not cost free energy in the long-wavelength limit. For light-induced colloidal quasicrystals, we analyze the collective rearrangements of the colloids that occur when the phasonic displacement of the light field is changed. The colloidal model system is employed to study the link between the continuous description of phasonic modes in quasicrystals and collective phasonic flips of atoms. We introduce characteristic areas of reduced phononic and phasonic displacements and use them to predict individual colloidal trajectories. In principle, our method can be employed with all quasicrystalline systems in order to derive collective rearrangements of particles from the continuous description of phasons.