Fragile aspects of topological transition in lossy and parity-time symmetric quantum walks.

Quantum walks often provide telling insights about the structure of the system on which they are performed. In [Formula: see text]-symmetric and lossy dimer lattices, the topological properties of the band structure manifest themselves in the quantization of the mean displacement of such a walker. We investigate the fragile aspects of a topological transition in these two dimer models.

Discovering a Transferable Charge Assignment Model Using Machine Learning.

Partial atomic charge assignment is of immense practical value to force field parametrization, molecular docking, and cheminformatics. Machine learning has emerged as a powerful tool for modeling chemistry at unprecedented computational speeds given accurate reference data. However, certain tasks, such as charge assignment, do not have a unique solution.

Comparing skyrmions and merons in chiral liquid crystals and magnets.

When chiral liquid crystals or magnets are subjected to applied fields or other anisotropic environments, the competition between favored twist and anisotropy leads to the formation of complex defect structures. In some cases, the defects are skyrmions, which have 180^{∘} double twist going outward from the center, and hence can pack together without singularities in the orientational order. In other cases, the defects are merons, which have 90^{∘} double twist going outward from the center; packing such merons requires singularities in the orientational order.

Clogging and depinning of ballistic active matter systems in disordered media.

We numerically examine ballistic active disks driven through a random obstacle array. Formation of a pinned or clogged state occurs at much lower obstacle densities for the active disks than for passive disks. As a function of obstacle density, we identify several distinct phases including a depinned fluctuating cluster state, a pinned single-cluster or jammed state, a pinned multicluster state, a pinned gel state, and a pinned disordered state.

Using Equation-Free Computation to Accelerate Network-Free Stochastic Simulation of Chemical Kinetics.

The chemical kinetics of many complex systems can be concisely represented by reaction rules, which can be used to generate reaction events via a kinetic Monte Carlo method that has been termed network-free simulation. Here, we demonstrate accelerated network-free simulation through a novel approach to equation-free computation. In this process, variables are introduced that approximately capture system state.

Clogging and transport of driven particles in asymmetric funnel arrays.

We numerically examine the flow and clogging of particles driven through asymmetric funnel arrays when the commensurability ratio of the number of particles per plaquette is varied. The particle-particle interactions are modeled with a soft repulsive potential that could represent vortex flow in type-II superconductors or driven charged colloids. The velocity-force curves for driving in the easy flow direction of the funnels exhibit a single depinning threshold; however, for driving in the hard flow direction, we find that there can be both negative mobility where the velocity decreases with increasing driving force as well as a reentrant pinning effect in which the particles flow at low drives but become pinned at intermediate drives.

High Cooperativity in Negative Feedback can Amplify Noisy Gene Expression.

Burst-like synthesis of protein is a significant source of cell-to-cell variability in protein levels. Negative feedback is a common example of a regulatory mechanism by which such stochasticity can be controlled. Here we consider a specific kind of negative feedback, which makes bursts smaller in the excess of protein.

Avalanches and Criticality in Driven Magnetic Skyrmions.

We show using numerical simulations that slowly driven Skyrmions interacting with random pinning move via correlated jumps or avalanches. The avalanches exhibit power-law distributions in their duration and size, and the average avalanche shape for different avalanche durations can be scaled to a universal function, in agreement with theoretical predictions for systems in a nonequilibrium critical state. A distinctive feature of Skyrmions is the influence of the nondissipative Magnus term.

Extinction and survival in two-species annihilation.

We study diffusion-controlled two-species annihilation with a finite number of particles. In this stochastic process, particles move diffusively, and when two particles of opposite type come into contact, the two annihilate. We focus on the behavior in three spatial dimensions and for initial conditions where particles are confined to a compact domain.

A stochastic and dynamical view of pluripotency in mouse embryonic stem cells.

Pluripotent embryonic stem cells are of paramount importance for biomedical sciences because of their innate ability for self-renewal and differentiation into all major cell lines. The fateful decision to exit or remain in the pluripotent state is regulated by complex genetic regulatory networks. The rapid growth of single-cell sequencing data has greatly stimulated applications of statistical and machine learning methods for inferring topologies of pluripotency regulating genetic networks.

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes.

Single-cell experiments show that gene expression is stochastic and bursty, a feature that can emerge from slow switching between promoter states with different activities. In addition to slow chromatin and/or DNA looping dynamics, one source of long-lived promoter states is the slow binding and unbinding kinetics of transcription factors to promoters, i.e.

Inner Phases of Colloidal Hexagonal Spin Ice.

Using numerical simulations that mimic recent experiments on hexagonal colloidal ice, we show that colloidal hexagonal artificial spin ice exhibits an inner phase within its ice state that has not been observed previously. Under increasing colloid-colloid repulsion, the initially paramagnetic system crosses into a disordered ice regime, then forms a topologically charge ordered state with disordered colloids, and finally reaches a threefold degenerate, ordered ferromagnetic state. This is reminiscent of, yet distinct from, the inner phases of the magnetic kagome spin ice analog.

Locality of interactions for planar memristive circuits.

The dynamics of purely memristive circuits has been shown to depend on a projection operator which expresses the Kirchhoff constraints, is naturally non-local in nature, and does represent the interaction between memristors. In the present paper we show that for the case of planar circuits, for which a meaningful Hamming distance can be defined, the elements of such projector can be bounded by exponentially decreasing functions of the distance. We provide a geometrical interpretation of the projector elements in terms of determinants of Dirichlet Laplacian of the dual circuit.

Speed-of-light pulses in the massless nonlinear Dirac equation with a potential.

We consider the massless nonlinear Dirac (NLD) equation in 1+1 dimension with scalar-scalar self-interaction g^{2}/2(Ψ[over ¯]Ψ)^{2} in the presence of three external electromagnetic real potentials V(x), a potential barrier, a constant potential, and a potential well. By solving numerically the NLD equation, we find different scenarios depending on initial conditions, namely, propagation of the initial pulse along one direction, splitting of the initial pulse into two pulses traveling in opposite directions, and focusing of two initial pulses followed by a splitting. For all considered cases, the final waves travel with the speed of light and are solutions of the massless linear Dirac equation.

Aggregation-fragmentation-diffusion model for trail dynamics.

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively.

Negative differential mobility and trapping in active matter systems.

Using simulations, we examine the average velocity as a function of applied drift force for active matter particles moving through a random obstacle array. We find that for low drift force, there is an initial flow regime where the mobility increases linearly with drive, while for higher drift forces a regime of negative differential mobility appears in which the velocity decreases with increasing drive due to the trapping of active particles behind obstacles. A fully clogged regime exists at very high drift forces when all the particles are permanently trapped behind obstacles.

Dewetting and spreading transitions for active matter on random pinning substrates.

We show that sterically interacting self-propelled disks in the presence of random pinning substrates exhibit transitions among a variety of different states. In particular, from a phase separated cluster state, the disks can spread out and homogeneously cover the substrate in what can be viewed as an example of an active matter wetting transition. We map the location of this transition as a function of activity, disk density, and substrate strength, and we also identify other phases including a cluster state, coexistence between a cluster and a labyrinth wetted phase, and a pinned liquid.

Fast forward to the classical adiabatic invariant.

We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic conditions. Specifically, for a time-dependent Hamiltonian H=p^{2}/2m+U(q,t) in one degree of freedom, and for an arbitrary choice of action I_{0}, we construct a so-called fast-forward potential energy function V_{FF}(q,t) that, when added to H, guides all trajectories with initial action I_{0} to end with the same value of action. We use this result to construct a local dynamical invariant J(q,p,t) whose value remains constant along these trajectories.

Dynamic phases of active matter systems with quenched disorder.

Depinning and nonequilibrium transitions within sliding states in systems driven over quenched disorder arise across a wide spectrum of size scales ranging from atomic friction at the nanoscale, flux motion in type II superconductors at the mesoscale, colloidal motion in disordered media at the microscale, and plate tectonics at geological length scales. Here we show that active matter or self-propelled particles interacting with quenched disorder under an external drive represents a class of system that can also exhibit pinning-depinning phenomena, plastic flow phases, and nonequilibrium sliding transitions that are correlated with distinct morphologies and velocity-force curve signatures. When interactions with the substrate are strong, a homogeneous pinned liquid phase forms that depins plastically into a uniform disordered phase and then dynamically transitions first into a moving stripe coexisting with a pinned liquid and then into a moving phase-separated state at higher drives.

Dynamic Control of Topological Defects in Artificial Colloidal Ice.

We demonstrate the use of an external field to stabilize and control defect lines connecting topological monopoles in spin ice. For definiteness we perform Brownian dynamics simulations with realistic units mimicking experimentally realized artificial colloidal spin ice systems, and show how defect lines can grow, shrink or move under the action of direct and alternating fields. Asymmetric alternating biasing forces can cause the defect line to ratchet in either direction, making it possible to precisely position the line at a desired location.

Emergent inequality and self-organized social classes in a network of power and frustration.

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution of wealth vs.

Collective transport for active matter run-and-tumble disk systems on a traveling-wave substrate.

We examine numerically the transport of an assembly of active run-and-tumble disks interacting with a traveling-wave substrate. We show that as a function of substrate strength, wave speed, disk activity, and disk density, a variety of dynamical phases arise that are correlated with the structure and net flux of disks. We find that there is a sharp transition into a state in which the disks are only partially coupled to the substrate and form a phase-separated cluster state.

Kinetics of aggregation with choice.

We generalize the ordinary aggregation process to allow for choice. In ordinary aggregation, two random clusters merge and form a larger aggregate. In our implementation of choice, a target cluster and two candidate clusters are randomly selected and the target cluster merges with the larger of the two candidate clusters.

Scaling exponents for ordered maxima.

We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running maxima of m independent sequences and investigate the probability S(N) that the maxima are perfectly ordered, that is, the running maximum of the first sequence is always larger than that of the second sequence, which is always larger than the running maximum of the third sequence, and so on.

Self-Trapping of Charge Carriers in Semiconducting Carbon Nanotubes: Structural Analysis.

The spatial extent of charged electronic states in semiconducting carbon nanotubes with indices (6,5) and (7,6) was evaluated using density functional theory. It was observed that electrons and holes self-trap along the nanotube axis on length scales of about 4 and 8 nm, respectively, which localize cations and anions on comparable length scales. Self-trapping is accompanied by local structural distortions showing periodic bond-length alternation.