Comment on "Communication: Is directed percolation in colloid-polymer mixtures linked to dynamic arrest?" [J. Chem. Phys. 148, 241101 (2018)].

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 systems.

Active phase field crystal systems with inertial delay and underdamped dynamics.

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 separation.

The thermal jamming transition of soft harmonic disks in two dimensions.

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 particles 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 [Formula: see text], which is smaller than the transition packing fraction of athermal jamming at [Formula: see text]. 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.

Growth of two-dimensional dodecagonal colloidal quasicrystals: Particles with isotropic pair interactions with two length scales vs. patchy colloids with preferred binding angles.

We explore the growth of colloidal quasicrystals with dodecagonal symmetry in two dimensions by employing Brownian dynamics simulations. On the one hand, we study the growth behavior of structures obtained in a system of particles that interact according to an isotropic pair potential with two typical length scales. On the other hand, we consider patchy colloids that possess only one typical interaction length scale but prefer given binding angles. In case of the isotropic particles, we show that an imbalance in the competition between the two distances might lead to defects with wrong nearest-neighbor distances in the resulting structure. In contrast, during the growth of quasicrystals with patchy colloids such defects do not occur due to the lack of a second interaction length scale. However, as a downside, the diffusion of patchy particles along a surface typically is slower such that domains occur where the particles possess different phononic and phasonic offsets. Our results are important to understand how soft matter quasicrystals can be grown as perfectly as possible and to obtain a deeper insight into the mechanisms of the growth of quasicrystals in general.

Shear-induced slab-like domains in a directed percolated colloidal gel.

We explore the structural changes of a gel-forming colloid polymer mixture under shear by employing Brownian dynamics simulations of a colloidal system with short-ranged attractive depletion interaction in a linear flow profile. While the structure of unpercolated systems changes only slightly under shearing, we discover the formation of slab-like clusters in sheared directed percolated gel networks that are confined between two walls. These gel-slabs are stable over a long time and seem to be related to the syneresis phenomena that can be observed in directed percolated colloidal gels. Only at large shear strength the slabs are destroyed and a homogeneous state with many unbounded particles can be observed. We also quantitatively analyze our results by determining void volumes.

Effective substrate potentials with quasicrystalline symmetry depend on the size of the adsorbed particles.

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.

Uncovering the mechanism of trapping and cell orientation during Neisseria gonorrhoeae twitching motility.

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 surfaces.

Comment on "quantum quasicrystals of spin-orbit-coupled dipolar bosons".

A Comment on the Letter by S. Gopalakrishnan, I. Martin, and E. A. Demler, Phys. Rev. Lett. 111, 185304 (2013).. The authors of the Letter offer a Reply.

Particle segregation in a sedimenting bidisperse soft sphere system.

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.

Phason-induced dynamics of colloidal particles on quasicrystalline substrates.

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.

Proliferation of anomalous symmetries in colloidal monolayers subjected to quasiperiodic light fields.

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.

Structural studies of local environments in high-symmetry quasicrystals.

The statistics of how the local environment of a particle looks like, e.g., given by the distribution of nearest neighbor distances or the sizes of Voronoi cells, is important as a starting point for the calculation of many material properties like electronic or photonic band structures. Here we study local environments that occur in quasicrystals with large rotational symmetry. Both with analytical considerations based on geometric arguments and with an analysis of a large number of numerically created patches of high-symmetry quasicrystals we find that the Voronoi area's distribution reaches a bimodal curve and that in the limit of large rotational symmetries the distribution of nearest neighbor distance converges against a universal curve, where [Formula: see text] of the vertices have their nearest neighbor at a normalized distance equal to 1, while for the other [Formula: see text] the nearest neighbor is at a distance less than 1. Therefore, the statistics of local environments is non-trivial but independent of the specific rotational symmetry. Thus properties that only depend on local environments are expected to be universal for all high-symmetry quasicrystals.

What phasons look like: particle trajectories in a quasicrystalline potential.

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.

Mean field approach of dynamical pattern formation in underdamped active matter with short-ranged alignment and distant anti-alignment interactions.

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 ordering.

Active Brownian and inertial particles in disordered environments: Short-time expansion of the mean-square displacement.

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 environments.

Temperature dependence of the transition packing fraction of thermal jamming in a harmonic soft sphere system.

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 crossings.

Random walks with random velocities.

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 simulations.

Ergodicity breaking transition in a glassy soft sphere system at small but non-zero temperatures.

While the glass transition at non-zero temperature seems to be hard to access for experimental, theoretical, or simulation studies, jamming at zero temperature has been studied in great detail. Motivated by the exploration of the energy landscape that has been successfully used to investigate athermal jamming, we introduce a new method that includes the possibility of the thermally excited crossing of energy barriers. We then determine whether the ground state configurations of a soft sphere system are accessible or not and as a consequence whether the system is ergodic or effectively non-ergodic. Interestingly, we find an transition where the system becomes effectively non-ergodic if the density is increased. The transition density in the limit of small but non-zero temperatures is independent of temperature and below the transition density of athermal jamming. This confirms recent computer simulation studies where athermal jamming occurs deep inside the glass phase. In addition, we show that the ergodicity breaking transition is in the universality class of directed percolation. Therefore, our approach not only makes the transition from an ergodic to an effectively non-ergodic systems easily accessible and helps to reveal its universality class but also shows that it is fundamentally different from athermal jamming.

Superdiffusion in a honeycomb billiard.

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.

Anisotropy and memory during cage breaking events close to a wall.

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.