William Irvine

University of Chicago | UC · Department of Physics

Inspired by the recent realization of a 2D chiral fluid as an active monolayer droplet moving atop a 3D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2D linear, incompressible, and isotropic fluid, having a viscous shear stress, an active chiral driving stress, and a Hall stre...

The competition between thermal fluctuations and potential forces governs the stability of matter in equilibrium, in particular the proliferation and annihilation of topological defects. However, driving matter out of equilibrium allows for a new class of forces that are neither attractive nor repulsive, but rather transverse. The possibility of ac...

A key aspect of living cells is their ability to harvest energy from the environment and use it to pump specific atomic and molecular species in and out of their system—typically against an unfavourable concentration gradient¹. Active transport allows cells to store metabolic energy, extract waste and supply organelles with basic building blocks at...

Lattices of interacting gyroscopes naturally support band gaps and topologically protected wave transport along material boundaries. Recently the authors and their collaborators found that amorphous arrangements of such coupled gyroscopes also support nontrivial topological phases. In contrast to periodic systems, for which there is a comprehensive...

The competition between thermal fluctuations and potential forces is the foundation of our understanding of phase transitions and matter in equilibrium. Driving matter out of equilibrium allows for a new class of interactions which are neither attractive nor repulsive but transverse. The existence of such transverse forces immediately raises the qu...

Networks of interacting gyroscopes have proven to be versatile structures for understanding and harnessing finite-frequency topological excitations. Spinning components give rise to band gaps and topologically protected wave transport along the system's boundaries, whether the gyroscopes are arranged in a lattice or in an amorphous configuration. H...

Solids built out of active components can exhibit nonreciprocal elastic coefficients that give rise to non-Hermitian wave phenomena. Here, we investigate non-Hermitian effects present at the boundary of two-dimensional active elastic media obeying two general assumptions: their microscopic forces conserve linear momentum and arise only from static...

A passive solid cannot do work on its surroundings through any quasistatic cycle of deformations. This property places strong constraints on the allowed elastic moduli. In this Article, we show that static elastic moduli altogether absent in passive elasticity can arise from active, non-conservative microscopic interactions. These active moduli ent...

Statistical mechanics provides the foundation for describing complex materials using only a fewthermodynamic variables. No such framework currently exists far from equilibrium. In this Letter,we demonstrate how thermodynamics emerges far from equilibrium, using fluids composed of activespinners as a case study. Activity gives rise to a single effec...

Networks of masses with transverse spring-like interactions provide a simple model of solids with energetic gain and loss. In this Letter, we study the non-Hermitian band topology of this model, which applies not only to active solids but also to gyroscopic metamaterials with dissipation. We examine a family of lattices in which topologically charg...

In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent ‘atoms’ is determined by the flow and that viscous stresses damp motion. Activation of the rotational degrees of freedom of a fluid by spinning its atomic building blocks breaks these constraints and has thus been the subject...

We investigate superfluid flow around an airfoil accelerated to a finite velocity from rest. Using simulations of the Gross-Pitaevskii equation we find striking similarities to viscous flows: from production of starting vortices to convergence of airfoil circulation onto a quantized version of the Kutta-Joukowski circulation. We predict the number...

We investigate the development of superfluid flow around an airfoil accelerated to a finite velocity from rest. Using both simulations of the Gross-Pitaevskii equation and analytical calculations we find striking similarities to viscous flows: from the production of starting vortices to the convergence of the airfoil circulation onto a quantized ve...

Hooke's law states that the forces or stresses experienced by an elastic object are proportional to the applied deformations or strains. The number of coefficients of proportionality between stress and strain, i.e., the elastic moduli, is constrained by energy conservation. In this Letter, we lift this restriction and generalize linear elasticity t...

In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent 'atoms' are determined by the flow and that viscous stresses damp motion. Activation of the rotational degrees of freedom of a fluid by spinning its atomic building blocks breaks these constraints and has thus been the subjec...

Gyroscopic metamaterials, mechanical structures composed of interacting spinning tops, have recently been found to support one-way topological edge waves. In these structures, the time-reversal symmetry breaking that enables their topological behavior emerges directly from the lattice geometry. Here we show that variations in the lattice geometry c...

In addition to mass, energy, and momentum, classical dissipationless flows conserve helicity, a measure of the topology of the flow. Helicity has far-reaching consequences for classical flows from Newtonian fluids to plasmas. Since superfluids flow without dissipation, a fundamental question is whether such a conserved quantity exists for superflui...

Gyroscopic metamaterials --- mechanical structures composed of interacting spinning tops --- have recently been found to support one-way topological edge excitations. In these structures, the time reversal symmetry breaking that enables their topological behavior emerges directly from the lattice geometry. Here we show that variations in the lattic...

The discovery that the band structure of electronic insulators may be topologically non-trivial has revealed distinct phases of electronic matter with novel properties1,2. Recently, mechanical lattices have been found to have similarly rich structure in their phononic excitations3,4, giving rise to protected unidirectional edge modes5–7. In all of...

Uniform triangular crystals are the ground state for particles that interact isotropically in two dimensions. However, when immersed in an external potential, for example, one arising from an electric field, a flow field, or gravity, the resulting phases are significantly distorted in a way reminiscent of conformal transformations of planar lattice...

We disclose the unique magnetic properties of cubic hematite particles and show that their self-assembly behavior is driven by competing anisotropic interactions caused by their shape and fixed dipole moment.

For magnetite spherical nanoparticles, the orientation of the dipole moment in the crystal does not affect the morphology of either zero field or field induced structures. For non-spherical particles however, an interplay between particle shape and direction of the magnetic moment can give rise to unusual behaviors, in particular when the moment is...

This contribution to an issue of Comptes rendus Mécanique, commemorating the scientific work of Jean-Jacques Moreau (1923-2014), is intended to give a brief overview of recent developments in the study of helicity dynamics in real fluids and an outlook on the growing legacy of Moreau's work. Moreau's discovery of the conservation of hydrodynamic he...

Topological metamaterials exhibit unusual behaviors at their boundaries, such as unidirectional chiral waves, that are protected by a topological feature of their band structure. The ability to tune such a material through a topological phase transition in real time could enable the use of protected waves for information storage and readout. Here w...

Helicity, a topological measure of the intertwining of vortices in a fluid flow, is a conserved quantity in inviscid fluids but can be dissipated by viscosity in real flows. Despite its relevance across a range of flows, helicity in real fluids remains poorly understood because the entire quantity is challenging to measure. We measured the total he...

In addition to mass, energy, and momentum, classical dissipationless flows conserve helicity, a measure of the topology of the flow. Helicity has far-reaching consequences for classical flows from Newtonian fluids to plasmas. Since superfluids flow without dissipation, a fundamental question is whether such a conserved quantity exists for superflui...

An initially knotted light field will stay knotted if it satisfies a set of nonlinear, geometric constraints, i.e. the null conditions, for all space-time. However, the question of when an initially null light field stays null has remained challenging to answer. By establishing a mapping between Maxwell's equations and transport along the flow of a...

The discovery that the band structure of electronic insulators may be topologically non-trivial has unveiled distinct phases of electronic matter with novel properties. Recently, mechanical lattices have been found to have similarly rich structure in their phononic excitations, giving rise to protected uni-directional edge modes whose existence was...

Collections of interacting, self-propelled particles have been extensively studied as minimal models of many living and synthetic systems from bird flocks to active colloids. However, the influence of active rotations in the absence of self-propulsion (i.e., spinning without walking) remains less explored. Here, we numerically and theoretically inv...

We present a general construction of divergence-free knotted vector fields from complex scalar fields, whose closed field lines encode many kinds of knots and links, including torus knots, their cables, the figure-8 knot and its generalizations. As finite-energy physical fields they represent initial states for fields such as the magnetic field in...

Collections of interacting, self-propelled particles have been extensively studied as minimal models of many living and synthetic systems from bird flocks to active colloids. However, the influence of active rotations in the absence of self-propulsion (i.e. spinning without walking) remains less explored. Here, we numerically and theoretically inve...

Curving a thin material, such as a rubber sheet, can trigger fundamental changes in its structure and behavior. In particular, conforming materials to rigid substrates with Gaussian curvature -- positive for spheres and negative for saddles -- has proven a versatile tool to guide the self-assembly of defects such as scars, pleats, folds, blisters,...

Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them. To understand how this untying works, we simulate the behavior of 1,458 superfluid vortex knots of varying complexity and scale in the Gross-Pitaevskii equation. Without exception, we find that the knots untie efficiently and completely, and...

Guiding the self-assembly of materials by controlling the shape of the individual particle constituents is a powerful approach to material design. We show that colloidal silica superballs crystallize into canted phases in the presence of depletants. Some of these phases are consistent with the so-called "Λ1" lattice that was recently predicted as t...

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial -- comprised of coupled gyroscopes on a lattice -- that breaks time-reversal symmetry. The vibrational spectr...

Epitaxial heterostructures with precise registry between crystal layers play a key role in electronics and optoelectronics. In a close analogy, performance of nanocrystal (NC) based devices depends on the perfection of interfaces formed between NC layers. Here we systematically study the epitaxial growth of NC layers for the first time to enable th...

The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of recent advances, we create vortex knots and links in viscous fluids and simulated superfluids and track their geome...

The conjecture that knottedness is a fundamental conserved physical quantity has a long history in fluid mechanics. In ideal flows, the conservation of helicity arises because the topology of vortex lines is invariant. In real flows (including superfluids), the large scale topology of vortex tubes changes through 'reconnection' events, so helicity...

The idea that the knottedness (hydrodynamic Helicity) of a fluid flow is conserved has a long history in fluid mechanics. The quintessential example of a knotted flow is a knotted vortex filament, however, owing to experimental difficulties, it has not been possible until recently to directly generate knotted vortices in real fluids. Using 3D print...

We construct analytically, a new family of null solutions to Maxwell's equations in free space whose field lines encode all torus knots and links. The evolution of these null fields, analogous to a compressible flow along the Poynting vector that is shear free, preserves the topology of the knots and links. Our approach combines the construction of...

Dislocations, disclinations, and grain boundaries are topological excitations of crystals that play a key role in determining out-of-equilibrium material properties. In this article we study the kinetics, creation, and annihilation processes of these defects in a controllable way by applying "topological tweezers," an array of weak optical tweezers...

Knots and links have been conjectured to play a fundamental role in a wide range of physical fields, including plasmas and fluids, both quantum and classical. In fluids, the fundamental knottedness-carrying excitations occur in the form of linked and knotted vortex loops, which have been conjectured to exist for over a century. Although they have b...

Frustrated ordering processes are of wide interest in condensed matter systems. Experiments on interfacial colloidal systems have resulted in several recent insights into the two dimensional ordering of crystalline lattices frustrated by Gaussian curvature. We study the ordering of two-dimensional lattices of colloids frustrated by spatially varyin...

Recently developed experimental methods have allowed us to generate topologically linked fluid vortices for the first time. The intrinsically geometric nature of vortex dynamics allows us to measure physical quantities, such as energy, by reconstructing the core centerline in three-dimensions using high-speed laser scanning tomography. This novel a...

We investigate the propagation of cracks on curved surfaces. Using a stretched elastic sheet situated at a fluid interface, we generate a surface with spatially varying curvature and observe the trajectory and dynamics of an induced crack. We interpret the results from our experiments using a combination of numerical simulation and analytical consi...

Chirality occupies a central role in fields ranging from biological self assembly to the design of optical meta-materials. The definition of chirality, as given by lord Kelvin in 1893, associates handedness with the lack of mirror symmetry. However, the quantification of chirality based on this definition has proven to be an elusive task. The diffi...

Chirality occupies a central role in fields ranging from biological self assembly to the design of optical meta-materials. The definition of chirality, as given by lord Kelvin, associates it with the lack of mirror symmetry: the inability to superpose an object on its mirror image. While this definition has guided the classification of chiral objec...

Understanding the effect of curvature and topological frustration in crystals yields insights into the fragility of the ordered state. For instance, a one-dimensional crystal of identical charged particles can accommodate an extra particle (interstitial) if all the particle positions are readjusted, yet in a planar hexagonal crystal interstitials r...

Recent experiments have shown that colloidal crystals confined to weakly curved capillary bridges introduce groups of dislocations organized into `pleats' as means to relieve the stress caused by the Gaussian curvature of the surface. We consider the onset of this curvature-screening mechanism, by examining the energetics of isolated dislocations a...

We present a novel method for generating vortex lines of arbitrary shapes. We then image their dynamics using a high speed scanning technique which provides three-dimensional information at up to 500 volumes per second. We create a variety of configurations and study the effect of geometry on their evolution.

Maxwell's equations allow for some remarkable solutions consisting of pulsed beams of light which have linked and knotted field lines. The preservation of the topological structure of the field lines in these solutions has previously been ascribed to the fact that the electric and magnetic helicity, a measure of the degree of linking and knotting b...

We have studied the crystallization behavior of colloidal cubes by means of tunable depletion interactions. The colloidal system consists of novel micron-sized cubic particles prepared by silica deposition on hematite templates and various non-adsorbing water-soluble polymers as depletion agents. We have found that under certain conditions the cube...

We developed a new class of colloidal particles that programmably and reversibly self-assemble into well-defined clusters by virtue of "magnetic patches" carrying a permanent magnetic dipole moment. The resulting clusters form spontaneously in a zero external field, and their geometry is entirely determined by the interplay between magnetic, steric...

We have developed a new simple method to fabricate bulk amounts of colloidal spheres with well defined cavities from monodisperse emulsions. Herein, we describe the formation mechanism of “reactive” silicon oil droplets that deform to reproducible shapes via a polymerization-induced buckling instability. Owing to their unique shape, the resulting p...

Hexagons can easily tile a flat surface, but not a curved one. Introducing heptagons and pentagons (defects with topological charge) makes it easier to tile curved surfaces; for example, soccer balls based on the geodesic domes of Buckminster Fuller have exactly 12 pentagons (positive charges). Interacting particles that invariably form hexagonal c...

Photonic crystal slabs provide unique opportunities for the manipulation of light on semiconductor chips. The patterns of holes in the slabs are typically designed to maximize the width, depth and symmetry of a single photonic band gap. Quasicrystalline patterns are ideal from this point of view; here, we show that, owing to the presence of multipl...

High-quality optical cavities with wavelength-sized end mirrors are important to the growing field of micro-optomechanical systems. We present a versatile method for calculating the modes of diffraction limited optical cavities and show that it can be used to determine the effect of a wide variety of cavity geometries and imperfections. Additionall...

Charged hydrophobic (PMMA) colloids in an oil phase (cyclohexyl bromide) are attracted, without wetting, by image charge effects to an oil-water interface. The micron size spheres form a monolayer and interact via screened coulomb interactions to form a crystalline lattice. By creating curved oil-water interfaces having positive, negative and varyi...

New functional materials can in principle be created using colloids that self-assemble into a desired structure by means of a programmable recognition and binding scheme. This idea has been explored by attaching 'programmed' DNA strands to nanometre- and micrometre- sized particles and then using DNA hybridization to direct the placement of the par...

Single self-assembled InAs quantum dots embedded in GaAs photonic crystal defect cavities are a promising system for cavity quantum electrodynamics experiments and quantum information schemes. Achieving controllable coupling in these small mode volume devices is challenging due to the random nucleation locations of individual quantum dots. We have...

We study two-dimensional crystallography on a curved oil-water interface. Charged hydrophobic (PMMA) colloids in an oil phase (cyclohexyl bromide) are attracted, without wetting, by image charge effects to an oil-water interface. The micron size spheres form a monolayer on the interface and interact via screened coulomb interactions to form a cryst...

Since the publication of Antl, et al. [Colloids and Surfaces 17 (1986) 67--78] more than 20 years ago, several research groups in the soft condensed matter area have attempted the dispersion polymerization of sterically-stabilized PMMA particles. Most have found that success of this particular synthesis depends critically on the quality of the comb...

Certain semiconductors, such as GaAs and GaP, have very high values for the second order optical nonlinear susceptibility. This makes them promising materials for applications in nonlinear (quantum) optics. However, phase matching conditions must be achieved through microstructuring of the materials or in cavities because they possess no intrinsic...

Maxwell's equations allow for curious solutions having linked and knotted field lines. A particularly striking solution is one characterized by the property that all electric and magnetic field lines are closed loops with any two electric(magnetic) field lines linked. These little known solutions, are based on the Hopf fibration and have a remarkab...

Charged hydrophobic (PMMA) colloids in an oil phase (cyclohexyl bromide) are attracted, without wetting, by image charge effects to an oil-water interface. The micron size spheres form a monolayer on the interface and interact via screened coulomb interactions to form a crystalline or hexatic lattice, depending on the tunable ratio of lattice spaci...

Single self-assembled InAs quantum dots embedded in GaAs photonic crystal (PC) defect cavities are a promising system for cavity quantum electrodynamics experiments. Achieving controllable coupling between the PC cavity mode and quantum dot emission is difficult, however, due to the random nucleation locations and spectral properties of individual...

We report on the demonstration of a high finesse micro-optomechanical system and identify potential applications ranging from optical cooling to weak force detection to massive quantum superpositions. The system consists of a high quality diameter flat dielectric mirror cut from a larger substrate with a focused ion beam and attached to an atomic f...

We discuss the observability of strong coupling between single photons in semiconductor microcavities coupled by a chi2 nonlinearity. We present two schemes and analyze the feasibility of their practical implementation in three systems: photonic crystal defects, micropillars, and microdisks, fabricated out of GaAs. We show that, if a weak coherent...

We explore the possibility of generating and manipulating single photon states through all-optical chi(2) nonlinear interactions in photonic crystals. In particular two schemes are presented: one for the generation of entangled-photon pairs by parametric down-conversion in one-dimensional nonlinear photonic crystals (Bragg stacks), and one for the...