Mutual information and breakdown of the Perron-Frobenius scenario in zero-temperature triangular Ising antiferromagnets on cylinders.

A nominally two-dimensional spin model wrapped onto a cylinder can profitably be viewed, especially for long cylinders, as a one-dimensional chain. Each site of such a chain is a ring of spins with a complex state space. Traditional correlation functions are inadequate for the study of correlations in such a system and need to be replaced with something like mutual information.

Erratum: Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions [Phys. Rev. Lett. 123, 037401 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.

Drift-diffusion processes resulting from elimination of fast variables under inhomogeneous conditions.

The problem of eliminating fast-relaxing variables to obtain an effective diffusion process in position is solved in a uniform and straightforward way for models with velocity a function jointly of position and fast variables. A more unified view is thereby obtained of the effect of environmental inhomogeneity on the motion of a diffusing particle, in particular, whether a drift is induced, covering both passive and active particles. Infinitesimal generators (equivalently, drift-diffusion fields) for the contracted processes are worked out in detail for several models.

Distinguishing advective and powered motion in self-propelled colloids.

Self-powered motion in catalytic colloidal particles provides a compelling example of active matter, i.e. systems that engage in single-particle and collective behavior far from equilibrium.

Dynamic stabilization of Janus sphere trans-dimers.

We experimentally investigated the self-assembly of chemically active colloidal Janus spheres into dimers. The trans-dimer conformation, in which the two active sites are oriented roughly in opposite directions and the particles are osculated at their equators, becomes dominant as the hydrogen peroxide fuel concentration increases. Our observations suggest high spinning frequency combined with little translational motion is at least partially responsible for the stabilization of the trans-dimer as activity increases.

Acoustic actuation of bioinspired microswimmers.

Acoustic actuation of bioinspired microswimmers is experimentally demonstrated. Microswimmers are fabricated in situ in a microchannel. Upon acoustic excitation, the flagellum of the microswimmer oscillates, which in turn generates linear or rotary movement depending on the swimmer design.

Spiral diffusion of rotating self-propellers with stochastic perturbation.

Translationally diffusive behavior arising from the combination of orientational diffusion and powered motion at microscopic scales is a known phenomenon, but the peculiarities of the evolution of expected position conditioned on initial position and orientation have been neglected. A theory is given of the spiral motion of the mean trajectory depending upon propulsion speed, angular velocity, orientational diffusion, and rate of random chirality reversal. We demonstrate the experimental accessibility of this effect using both tadpole-like and Janus sphere dimer rotating motors.

Acoustofluidic actuation of in situ fabricated microrotors.

We have demonstrated in situ fabricated and acoustically actuated microrotors. A polymeric microrotor with predefined oscillating sharp-edge structures is fabricated in situ by applying a patterned UV light to polymerize a photocrosslinkable polyethylene glycol solution inside a microchannel around a polydimethylsiloxane axle. To actuate the microrotors by oscillating the sharp-edge structures, we employed piezoelectric transducers which generate tunable acoustic waves.

Geometrical Performance of Self-Phoretic Colloids and Microswimmers.

Within a unified formulation-encompassing self-electrophoresis, self-diffusiophoresis, and self-thermophoresis-we provide a simple integral kernel transforming the relevant surface flux to particle velocity for any spheroid with axisymmetric surface activity and uniform phoretic mobility. Appropriate scaling of the speed allows a dimensionless measure of the motion-producing performance of the motor shape and activity distribution across the surface. For bipartite designs with piecewise uniform flux over complementary surface regions, the performance is mapped out over the entire range of geometry (from discotic through spherical to rodlike shapes) and of bipartitioning, and intermediate aspect ratios that maximize performance are identified.

Guiding chiral self-propellers in a periodic potential.

Ingenious suggestions continue to be made for separation of racemic mixtures according to the inert structural chirality of the constituents. Recently discovered self-motile micro- or nanoparticles express dynamical chirality, i.e.

Systematic Enumeration of sp(3) Nanothreads.

Slow decompression of crystalline benzene in large-volume high-pressure cells has recently achieved synthesis of a novel one-dimensional allotrope of sp(3) carbon in which stacked columns of benzene molecules rehybridize into an ordered crystal of nanothreads. The progenitor benzene molecules function as six-valent one-dimensional superatoms with multiple binding sites. Here we enumerate their hexavalent bonding geometries, recognizing that the repeat unit of interatomic connectivity ("topological unit cell") need not coincide with the crystallographic unit cell, and identify the most energetically favorable cases.

Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics.

We present a self-consistent nonlocal feedback theory for the phoretic propulsion mechanisms of electrocatalytic micromotors or nanomotors. These swimmers, such as bimetallic platinum and gold rods catalyzing decomposition of hydrogen peroxide in aqueous solution, have received considerable theoretical attention. In contrast, the heterogeneous electrochemical processes with nonlocal feedback that are the actual "engines" of such motors are relatively neglected.

Selectively manipulable acoustic-powered microswimmers.

Selective actuation of a single microswimmer from within a diverse group would be a first step toward collaborative guided action by a group of swimmers. Here we describe a new class of microswimmer that accomplishes this goal. Our swimmer design overcomes the commonly-held design paradigm that microswimmers must use non-reciprocal motion to achieve propulsion; instead, the swimmer is propelled by oscillatory motion of an air bubble trapped within the swimmer's polymer body.

Gaussian memory in kinematic matrix theory for self-propellers.

We extend the kinematic matrix ("kinematrix") formalism [Phys. Rev. E 89, 062304 (2014)], which via simple matrix algebra accesses ensemble properties of self-propellers influenced by uncorrelated noise, to treat Gaussian correlated noises.

Kinematic matrix theory and universalities in self-propellers and active swimmers.

We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based Langevin or Fokker-Planck formalisms. The kinematic effects for elementary processes of motion are incorporated into a matrix, called the "kinematrix," from which we immediately obtain correlators and the mean and variance of angular and position variables (and thus effective diffusivity) by simple matrix algebra. The kinematrix formalism enables us recast the behaviors of a diverse range of self-propellers into a unified form, revealing universalities in their ensemble behavior in terms of new emergent time scales.

Nanomotor mechanisms and motive force distributions from nanorotor trajectories.

Nanomotors convert chemical energy into mechanical motion. For a given motor type, the underlying chemical reaction that enables motility is typically well known, but the detailed, quantitative mechanism by which this reaction breaks symmetry and converts chemical energy to mechanical motion is often less clear, since it is difficult experimentally to measure important parameters such as the spatial distribution of chemical species around the nanorotor during operation. Without this information on how motor geometry affects motor function, it is difficult to control and optimize nanomotor behavior.

Crystallites of magnetic charges in artificial spin ice.

Artificial spin ice is a class of lithographically created arrays of interacting ferromagnetic nanometre-scale islands. It was introduced to investigate many-body phenomena related to frustration and disorder in a material that could be tailored to precise specifications and imaged directly. Because of the large magnetic energy scales of these nanoscale islands, it has so far been impossible to thermally anneal artificial spin ice into desired thermodynamic ensembles; nearly all studies of artificial spin ice have either treated it as a granular material activated by alternating fields or focused on the as-grown state of the arrays.

Chiral diffusion of rotary nanomotors.

Neither a purely deterministic rotary nanomotor nor a purely orientational diffuser exhibits long-term translational motion, but coupling rotation to orientational diffusion yields translational diffusion. We demonstrate that this effective translational diffusion can easily dominate the ordinary thermal translational diffusion for experimentally relevant nanomotors, and that this effective diffusion is chiral. Unpowered chiral particles do not exhibit chiral diffusion, but a nanorotor has both handedness and an instantaneous direction of powered motion, thus-unlike an unpowered particle-its diffusional motion can distinguish left from right.

Perpendicular magnetization and generic realization of the Ising model in artificial spin ice.

We have studied frustrated kagome arrays and unfrustrated honeycomb arrays of magnetostatically interacting single-domain ferromagnetic islands with magnetization normal to the plane. The measured pairwise spin correlations of both lattices can be reproduced by models based solely on nearest-neighbor correlations. The kagome array has qualitatively different magnetostatics but identical lattice topology to previously studied artificial spin ice systems composed of in-plane moments.

Ignoring your neighbors: moment correlations dominated by indirect or distant interactions in an ordered nanomagnet array.

We have studied the moment correlations within triangular lattice arrays of single-domain coaligned nanoscale ferromagnetic islands. Independent variation of lattice spacing along and perpendicular to the island axis tunes the magnetostatic interactions between islands through a broad range of relative strengths. For certain lattice parameters, the sign of the correlations between near-neighbor island moments is opposite to that favored by the pairwise interaction.

Curvature-induced D-band Raman scattering in folded graphene.

Micro-Raman scattering from folds in single-layer graphene sheets finds a D-band at the fold for both incommensurate and commensurate folding, while the parent single-layer graphene lacks a D-band. A coupled elastic-continuum/tight-binding calculation suggests that this D-band arises from the spatially inhomogeneous curvature around a fold in a graphene sheet. The polarization dependence of the fold-induced D-band further reveals that the inhomogeneous curvature acts as a very smooth, ideal one-dimensional defect along the folding direction.

Emergent, collective oscillations of self-mobile particles and patterned surfaces under redox conditions.

We have discovered that silver chloride (AgCl) particles in the presence of UV light and dilute hydrogen peroxide exhibit both single-particle and collective oscillations in their motion which arise due to an oscillatory, reversible conversion of AgCl to silver metal at the particle surface. This system exhibits several of the hallmarks of nonlinear oscillatory reactions, including bistability, reaction waves, and synchronized collective oscillations at high particle concentrations. However, unlike traditional oscillatory reactions that take place among dispersed solute species in solution or near a fixed electrode surface, this system of self-mobile catalytic particles evinces a new dynamical length scale: the interparticle spacing, which appears to control wave propagation.

Annealing a magnetic cactus into phyllotaxis.

The appearance of mathematical regularities in the disposition of leaves on a stem, scales on a pine-cone, and spines on a cactus has puzzled scholars for millennia; similar so-called phyllotactic patterns are seen in self-organized growth, polypeptides, convection, magnetic flux lattices and ion beams. Levitov showed that a cylindrical lattice of repulsive particles can reproduce phyllotaxis under the (unproved) assumption that minimum of energy would be achieved by two-dimensional Bravais lattices. Here we provide experimental and numerical evidence that the Phyllotactic lattice is actually a ground state.

Dynamic interactions between fast microscale rotors.

Trimetallic catalytic microrotors were fabricated by electrodeposition of cylindrical Au-Ru rods in the pores of anodic alumina membranes, dissolution of the template membrane, and then sequential vapor deposition of Cr, SiO(2), Cr, Au, and Pt on one side of each rod. This design provides two force vectors for the catalytic motor, including one perpendicular to the rod axis. The rods rotated rapidly (approximately 180 rpm) in 15% aqueous H(2)O(2) solution with minimal orbital or translational movement.

Static and dynamical phyllotaxis in a magnetic cactus.

While the statics of many simple physical systems reproduce the striking number-theoretical patterns found in the phyllotaxis of living beings, their dynamics reveal unusual excitations: multiple classical rotons and a large family of interconverting topological solitons. As we introduce those, we also demonstrate experimentally for the first time Levitov's celebrated model for phyllotaxis. Applications at different scales and in different areas of physics are proposed and discussed.