Delay induced bifurcation of dominant transition pathways

We investigate delay effects on dominant transition pathways (DTP) between metastable states of stochastic systems. A modified version of the Maier-Stein model with linear delayed feedback is considered as an example. By a stability analysis of the {"on-axis"} DTP in trajectory space, we find that a bifurcation of DTPs will be induced when time delay $\tau$ is large enough. This finding is soon verified by numerically derived DTPs which are calculated by employing a recently developed minimum action method extended to delayed stochastic systems. Further simulation shows that, the delay-induced bifurcation of DTPs also results in a nontrivial dependence of the transition rate constant on the delay time. Finally, the bifurcation diagram is given on the $\tau-\beta$ plane, where $\beta$ measures the non-conservation of the original Maier-Stein model.Comment: 14 pages, 6 figure

Flexibility Induced Motion Transition of Active Filament: Rotation without Long-range Hydrodynamic Interaction

We investigate the motion of active semiflexible filament with shape kinematics and hydrodynamic interaction including. Three types of filament motion are found: Translation, snaking and rotation. Change of flexibility will induce instability of shape kinematics and further result in asymmetry of shape kinematics respect to the motion of mass center, which are responsible to a continuous-like transition from translation to snaking and a first-order-like transition from snaking to rotation, respectively. Of particular interest, we find that long-range hydrodynamic interaction is not necessary for filament rotation, but can enhance remarkably the parameter region for its appearance. This finding may provide an evidence that the experimentally found collective rotation of active filaments is more likely to arise from the individual property even without the long-range hydrodynamic interaction.Comment: 5 pages, 4figure

Large-scale Epitaxial Growth Kinetics of Graphene: A Kinetic Monte Carlo Study

Epitaxial growth via chemical vapor deposition is considered to be the most promising way towards synthesizing large area graphene with high quality. However, it remains a big theoretical challenge to reveal growth kinetics with atomically energetic and large-scale spatial information included. Here, we propose a minimal kinetic Monte Carlo model to address such an issue on an active catalyst surface with graphene/substrate lattice mismatch, which facilitates us to perform large scale simulations of the growth kinetics over two dimensional surface with growth fronts of complex shapes. A geometry-determined large-scale growth mechanism is revealed, where the rate-dominating event is found to be $C_{1}$-attachment for concave growth front segments and $C_{5}$-attachment for others. This growth mechanism leads to an interesting time-resolved growth behavior which is well consistent with that observed in a recent scanning tunneling microscopy experiment.Comment: 5 pages, 3 figure

An Efficient Self-optimized Sampling Method for Rare Events in Nonequilibrium Systems

Rare events such as nucleation processes are of ubiquitous importance in real systems. The most popular method for nonequilibrium systems, forward flux sampling (FFS), samples rare events by using interfaces to partition the whole transition process into sequence of steps along an order parameter connecting the initial and final states. FFS usually suffers from two main difficulties: low computational efficiency due to bad interface locations and even being not applicable when trapping into unknown intermediate metastable states. In the present work, we propose an approach to overcome these difficulties, by self-adaptively locating the interfaces on the fly in an optimized manner. Contrary to the conventional FFS which set the interfaces with euqal distance of the order parameter, our approach determines the interfaces with equal transition probability which is shown to satisfy the optimization condition. This is done by firstly running long local trajectories starting from the current interface \l_i to get the conditional probability distribution $P_c$, and then determining \l_{i+1} by equalling $P_c$ to a give value $p_0$. With these optimized interfaces, FFS can be run in a much efficient way. In addition, our approach can conveniently find the intermediate metastable states by monitoring some special long trajectories that nither end at the initial state nor reach the next interface, the number of which will increase sharply from zero if such metastable states are encountered. We apply our approach to a model two-state system and a two-dimensional lattice gas Ising model. Our approach is shown to be much more efficient than the conventional FFS method without losing accuracy, and it can also well reproduce the two-step nucleation scenario of the Ising model with easy identification of the intermidiate metastable state.Comment: 6 pages, 6 figure

Tunable Sorting of Mesoscopic Chiral Structures by External Noise in Achiral Periodic Potentials

Efficient chirality sorting is now highly demanded to separate assembled mesoscopic chiral structures which are of very special physical properties rather than their achiral counterparts or those at the single-particle level. However, the efficiency of conventional methods usually suffers from the thermal or external noise. Here, we propose a mechanism utilizing external noise to attain a tunable sorting of mesoscopic chiral particles in an achiral periodic potential. The complete chirality-separation stems from the path selection by a noise-induced biased flux in a nonequilibrium landscape. Such mechanism provides a practicable way to control the motion of chiral particles by simply adjusting the noise intensity, which is demonstrated by simultaneous separation of several kinds of enantiomorphs with different degrees of chirality. The robustness and generalizability of noise-tuned chirality sorting is further verified in systems with other types of periodic potentials or spatially/temporally correlated noise.Comment: 7 figure

Disordered hyperuniform obstacles enhance sorting of dynamically chiral microswimmers

Disordered hyperuniformity, a brand new type of arrangements with novel physical properties, provides various practical applications in extensive fields. To highlight the great potential of applying disordered hyperuniformity to active systems, a practical example is reported here by an optimal sorting of dynamically chiral microswimmers in disordered hyperuniform obstacle environments in comparison with regular or disordered ones. This optimal chirality sorting stems from a competition between advantageous microswimmer-obstacle collisions and disadvantageous trapping of microswimmers by obstacles. Based on this mechanism, optimal chirality sorting is also realized by tuning other parameters including the number density of obstacles, the strength of driven force and the noise intensity. Our findings may open a new perspective on both theoretical and experimental investigations for further applications of disordered hyperuniformity in active systems.Comment: 6 pages, 5 figure

Nonequilibrium Glass Transition in Mixtures of Active-Passive Particles

We develop a mode coupling theory(MCT) to study the nonequilibrium glass transition behavior of a mono-disperse mixture of active-passive hard-sphere particles. The MCT equations clearly demonstrate that the glass transition is shifted to higher values of total volume fraction when doping a passive system with active particles. Interestingly, we find that the glass transition point may show a non-monotonic dependence on the effective diffusivity of the active component, indicating a nontrivial type of activity induced reentrance behavior. Analysis based on the nonergodic parameters suggest that the glassy state at small activity is due to the caging effect, while that at high activity could result from activity induced dynamic clustering.Comment: 11 pages, 2 figure

Orientation Sensitive Nonlinear Growth of Graphene: A Geometry-determined Epitaxial Growth Mechanism

Although the corresponding carbon-metal interactions can be very different, a similar nonlinear growth behavior of graphene has been observed for different metal substrates. To understand this interesting experimental observation, a multiscale $\lq\lq$standing-on-the-front" kinetic Monte Carlo study is performed. An extraordinary robust geometry effect is identified, which solely determines the growth kinetics and makes the details of carbon-metal interaction not relevant at all. Based on such a geometry-determined mechanism, epitaxial growth behavior of graphene can be easily predicted in many cases. As an example, an orientation-sensitive growth kinetics of graphene on Ir(111) surface has been studied. Our results demonstrate that lattice mismatch pattern at the atomic level plays an important role for macroscopic epitaxial growth.Comment: 5 pages, 3 figures, 2 table

Atomistic Mechanisms of Nonlinear Graphene Growth on Ir Surface

As a two-dimensional material, graphene can be naturally obtained via epitaxial growth on a suitable substrate. Growth condition optimization usually requires an atomistic level understanding of the growth mechanism. In this article, we perform a mechanistic study about graphene growth on Ir(111) surface by combining first principles calculations and kinetic Monte Carlo (kMC) simulations. Small carbon clusters on the Ir surface are checked first. On terraces, arching chain configurations are favorable in energy and they are also of relatively high mobilities. At steps, some magic two-dimensional compact structures are identified, which show clear relevance to the nucleation process. Attachment of carbon species to a graphene edge is then studied. Due to the effect of substrate, at some edge sites, atomic carbon attachment becomes thermodynamically unfavorable. Graphene growth at these difficult sites has to proceed via cluster attachment, which is the growth rate determining step. Based on such an inhomogeneous growth picture, kMC simulations are made possible by successfully separating different timescales, and they well reproduce the experimentally observed nonlinear kinetics. Different growth rates and nonlinear behaviors are predicted for different graphene orientations, which is consistent with available experimental results. Importantly, as a phenomenon originated from lattice mismatch, inhomogeneity revealed in this case is expected to be quite universal and it should also make important roles in many other hetero-epitaxial systems

Inertial Effects on Kinetics of Motility-Induced Phase Separation

Motility-induced phase separation (MIPS) is of great importance and has been extensively researched in overdamped systems, nevertheless, what impacts inertia will bring on kinetics of MIPS is lack of investigation. Here, we find that, not only the phase transition changes from continuous to discontinuous, but also the formation of clusters exhibits a nucleation-like process without any coarsening regime, different from spinodal decomposition in the overdamped case. This remarkable kinetics stems from a competition between activity-induced accumulation of particles and inertia-induced suppression of clustering process. More interestingly, the discontinuity of MIPS still exists even when the ratio of particle mass to the friction coefficient reduces to be very small such as 0.0001. Our findings emphasize the importance of inertia in kinetics of MIPS, and may open a new perspective on understanding the nature of MIPS in active systems.Comment: 5 pages, 4 figure