arXiv subjects

Vincenzo Vitelli

Publications and source records attributed to Vincenzo Vitelli.

At least 73 records · Page 4Linked to original sources

arXiv2020

Nuts and bolts of supersymmetry

A topological mechanism is a zero elastic-energy deformation of a mechanical structure that is robust against smooth changes in system parameters. Here, we map the nonlinear elasticity of a paradigmatic class of topological mechanisms onto linear fermionic models using a supersymmetric field theory introduced by Witten and Olive. Heuristically, this approach consists of taking the square root of a non-linear Hamiltonian and generalizes the standard procedure of obtaining two copies of Dirac equation from the square root of the linear Klein Gordon equation. Our real space formalism goes beyond topological band theory by incorporating non-linearities and spatial inhomogeneities, such as domain walls, where topological states are typically localized. By viewing the two components of the real fermionic field as site and bond displacements respectively, we determine the relation between the supersymmetry transformations and the Bogomolny-Prasad-Sommerfield (BPS) bound saturated by the mechanism. We show that the mechanical constraint, which enforces a BPS saturated kink into the system, simultaneously precludes an anti-kink. This mechanism breaks the usual kink-antikink symmetry and can be viewed as a manifestation of the underlying supersymmetry being half-broken.

cond-mat.soft↗

arXiv2020

Non-Hermitian band topology and skin modes in active elastic media

Solids built out of active components can exhibit non-reciprocal 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 deformations. Using continuum equations, we demonstrate the existence of the non-Hermitian skin effect in which the boundary hosts an extensive number of localized modes. Furthermore, lattice models reveal non-Hermitian topological transitions mediated by exceptional rings driven by the activity level of individual bonds.

cond-mat.soft↗

arXiv2020

Machine learning active-nematic hydrodynamics

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such hydrodynamic parameters are difficult to derive from microscopics. Seldom is this challenge more apparent than in active matter where the energy cascade mechanisms responsible for autonomous large-scale dynamics are poorly understood. Here, we use active nematics to demonstrate that neural networks can extract the spatio-temporal variation of hydrodynamic parameters directly from experiments. Our algorithms analyze microtubule-kinesin and actin-myosin experiments as computer vision problems. Unlike existing methods, neural networks can determine how multiple parameters such as activity and elastic constants vary with ATP and motor concentration. In addition, we can forecast the evolution of these chaotic many-body systems solely from image-sequences of their past by combining autoencoder and recurrent networks with residual architecture. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems even when no knowledge of the underlying dynamics exists.

cond-mat.soft↗

arXiv2020

Simple views on symmetries and dualities in the theory of elasticity

Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur microscopically in special classes of mechanical structures. Examples of such non-spatial symmetries occur in families of mechanical metamaterials where a duality transformation relates pairs of different configurations. We show on general grounds how the existence of non-spatial symmetries further constrains the elastic tensor, reducing the number of independent moduli. In systems exhibiting a duality transformation, the resulting constraints on the number of moduli are particularly stringent at the self-dual point but persist even away from it, in a way reminiscent of critical phenomena.

cond-mat.soft↗

arXiv2020

Liquid-crystal-based topological photonics

Topological photonics harnesses the physics of topological insulators to control the behavior of light. Photonic modes robust against material imperfections are an example of such control. In this work, we propose a soft-matter platform based on nematic liquid crystals that supports photonic topological insulators. The orientation of liquid crystal molecules introduces an extra geometric degree of freedom which in conjunction with suitably designed structural properties, leads to the creation of topologically protected states of light. The use of soft building blocks potentially allows for reconfigurable systems that exploit the interplay between light and the soft responsive medium.

cond-mat.soft↗

arXiv2020

Hydrodynamic correlation functions of chiral active fluids

The success of spectroscopy to characterise equilibrium fluids, for example the heat capacity ratio, suggests a parallel approach for active fluids. Here, we start from a hydrodynamic description of chiral active fluids composed of spinning constituents and derive their low-frequency, long-wavelength response functions using the Kadanoff-Martin formalism. We find that the presence of odd (equivalently, Hall) viscosity leads to mixed density-vorticity response even at linear order. Such response, prohibited in time-reversal-invariant fluids, is a large-scale manifestation of the microscopic breaking of time-reversal symmetry. Our work suggests possible experimental probes that can measure anomalous transport coefficients in active fluids through dynamic light scattering.

cond-mat.soft↗

arXiv2020

Statistical mechanics of a chiral active fluid

Statistical mechanics provides the foundation for describing complex materials using only a few thermodynamic variables. No such framework currently exists far from equilibrium. In this Letter, we demonstrate how thermodynamics emerges far from equilibrium, using fluids composed of active spinners as a case study. Activity gives rise to a single effective temperature that parameterizes both the equation of state and the emergent Boltzmann statistics. The same effective temperature, renormalized by velocity correlations, controls the linear response through canonical Green-Kubo relations for both the familiar shear viscosity and the odd (or Hall) viscosity observed in chiral fluids. The full frequency dependence of these viscosities can be derived analytically by modeling the active-spinner fluid as a random walker undergoing cyclotron motion in shear-stress space. More generally, we provide a first-principles derivation of the Green-Kubo relations valid for a broader class of fluids far from equilibrium. Besides advancing non-equilibrium thermodynamics, our work demonstrates in silico a non-invasive microrheology of active fluids.

cond-mat.soft↗

arXiv2019

Structuring Stress for Active Materials Control

Active materials are capable of converting free energy into mechanical work to produce autonomous motion, and exhibit striking collective dynamics that biology relies on for essential functions. Controlling those dynamics and transport in synthetic systems has been particularly challenging. Here, we introduce the concept of spatially structured activity as a means to control and manipulate transport in active nematic liquid crystals consisting of actin filaments and light-sensitive myosin motors. Simulations and experiments are used to demonstrate that topological defects can be generated at will, and then constrained to move along specified trajectories, by inducing local stresses in an otherwise passive material. These results provide a foundation for design of autonomous and reconfigurable microfluidic systems where transport is controlled by modulating activity with light.

cond-mat.soft↗

arXiv2019

Anisotropic odd viscosity via time-modulated drive

At equilibrium, the structure and response of ordered phases are typically determined by the spontaneous breaking of spatial symmetries. Out of equilibrium, spatial order itself can become a dynamically emergent concept. In this article, we show that spatially anisotropic viscous coefficients and stresses can be designed in a far-from-equilibrium fluid by applying to its constituents a time-modulated drive. If the drive induces a rotation whose rate is slowed down when the constituents point along specific directions, anisotropic structures and mechanical responses arise at long timescales. We demonstrate that the viscous response of such anisotropic driven fluids can acquire a tensorial, dissipationless component called anisotropic odd (or Hall) viscosity. Classical fluids with internal torques can display additional components of the odd viscosity neglected in previous studies of quantum Hall fluids that assumed angular momentum conservation. We show that these anisotropic and angular momentum-violating odd-viscosity coefficients can change even the bulk flow of an incompressible fluid by acting as a source of vorticity. In addition, shear distortions in the shape of an inclusion result in torques.

cond-mat.soft↗

arXiv2019

A mechanism for anomalous transport in chiral active liquids

Chiral active fluids are known to have anomalous transport properties such as the so-called odd viscosity. In this paper, we provide a microscopic mechanism for how such anomalous transport coefficients can emerge. We construct an Irving-Kirkwood-type stress tensor for chiral liquids and express the transport coefficients in terms of orientation-averaged intermolecular forces and distortions of the pair correlation function induced by a flow field. We then show how anomalous transport properties can be expected naturally due to the presence of a transverse component in the orientation-averaged intermolecular forces and anomalous distortion modes of the pair correlation function between chiral active particles. We anticipate that our work can provide a microscopic framework to explain the transport properties of non-equilibrium chiral systems.

cond-mat.stat-mech↗

arXiv2019

Topological structure and dynamics of three dimensional active nematics

Point-like motile topological defects control the universal dynamics of diverse two-dimensional active nematics ranging from shaken granular rods to cellular monolayers. A comparable understanding in higher dimensions has yet to emerge. We report the creation of three-dimensional active nematics by dispersing extensile microtubule bundles in a passive colloidal liquid crystal. Light-sheet microscopy reveals the millimeter-scale structure of active nematics with a single bundle resolution and the temporal evolution of the associated nematic director field. The dominant excitations of three-dimensional active nematics are extended charge-neutral disclination loops that undergo complex dynamics and recombination events. These studies introduce a new class of non-equilibrium systems whose turbulent-like dynamics arises from the interplay between internally generated active stresses, the chaotic flows and the topological structure of the constituent defects.

cond-mat.soft↗

arXiv2019

Topological waves in fluids with odd viscosity

Fluids in which both time-reversal and parity are broken can display a dissipationless viscosity that is odd under each of these symmetries. Here, we show how this odd viscosity has a dramatic effect on topological sound waves in fluids, including the number and spatial profile of topological edge modes. Odd viscosity provides a short-distance cutoff that allows us to define a bulk topological invariant on a compact momentum space. As the sign of odd viscosity changes, a topological phase transition occurs without closing the bulk gap. Instead, at the transition point, the topological invariant becomes ill-defined because momentum space cannot be compactified. This mechanism is unique to continuum models and can describe fluids ranging from electronic to chiral active systems.

cond-mat.soft↗

arXiv2019

Dualities and non-Abelian mechanics

Dualities are mathematical mappings that reveal unexpected links between apparently unrelated systems or quantities in virtually every branch of physics. Systems that are mapped onto themselves by a duality transformation are called self-dual and they often exhibit remarkable properties, as exemplified by an Ising magnet at the critical point. In this Letter, we unveil the role of dualities in mechanics by considering a family of so-called twisted Kagome lattices. These are reconfigurable structures that can change shape thanks to a collapse mechanism easily illustrated using LEGO. Surprisingly, pairs of distinct configurations along the mechanism exhibit the same spectrum of vibrational modes. We show that this puzzling property arises from the existence of a duality transformation between pairs of configurations on either side of a mechanical critical point. This critical point corresponds to a self-dual structure whose vibrational spectrum is two-fold degenerate over the entire Brillouin zone. The two-fold degeneracy originates from a general version of Kramers theorem that applies to classical waves in addition to quantum systems with fermionic time-reversal invariance. We show that the vibrational modes of the self-dual mechanical systems exhibit non-Abelian geometric phases that affect the semi-classical propagation of wave packets. Our results apply to linear systems beyond mechanics and illustrate how dualities can be harnessed to design metamaterials with anomalous symmetries and non-commuting responses.

cond-mat.mes-hall↗

arXiv2019

Odd elasticity

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 to active media with non-conservative microscopic interactions that violate mechanical reciprocity. This generalized framework, which we dub odd elasticity, reveals that two additional moduli can exist in a two-dimensional isotropic solid with active bonds. Such an odd-elastic solid can be regarded as a distributed engine: work is locally extracted, or injected, during quasi-static cycles of deformation. Using continuum equations, coarse-grained microscopic models, and numerical simulations, we uncover phenomena ranging from activity-induced auxetic behavior to wave propagation powered by self-sustained active elastic cycles. Besides providing insights beyond existing hydrodynamic theories of active solids, odd elasticity suggests design principles for emergent autonomous materials.

cond-mat.soft↗

arXiv2018

Topological protection can arise from thermal fluctuations and interactions

Topological quantum and classical materials can exhibit robust properties that are protected against disorder, for example for noninteracting particles and linear waves. Here, we demonstrate how to construct topologically protected states that arise from the combination of strong interactions and thermal fluctuations inherent to soft materials or miniaturized mechanical structures. Specifically, we consider fluctuating lines under tension (e.g., polymer or vortex lines), subject to a class of spatially modulated substrate potentials. At equilibrium, the lines acquire a collective tilt proportional to an integer topological invariant called the Chern number. This quantized tilt is robust against substrate disorder, as verified by classical Langevin dynamics simulations. This robustness arises because excitations in this system of thermally fluctuating lines are gapped by virtue of inter-line interactions. We establish the topological underpinning of this pattern via a mapping that we develop between the interacting-lines system and a hitherto unexplored generalization of Thouless pumping to imaginary time. Our work points to a new class of classical topological phenomena in which the topological signature manifests itself in a structural property observed at finite temperature rather than a transport measurement.

cond-mat.soft↗

arXiv2018

Cluster formation via sonic depletion forces in levitated granular matter

The properties of small clusters can differ dramatically from the bulk phases of the same constituents. In equilibrium, cluster assembly has been recently explored, whereas out of equilibrium, the physical principles of clustering remain elusive. These principles underlie phenomena from molecular assembly to the formation of planets from granular matter. Here, we introduce acoustic levitation as a platform to experimentally probe the formation of nonequilibrium small structures in a controlled environment. We focus on the minimal models of cluster formation: six and seven millimetre-scale particles in two dimensions. Experiments and modelling reveal that, in contrast to thermal colloids, in non-equilibrium granular ensembles the magnitude of active fluctuations controls not only the assembly rates but also their assembly pathways and ground-state statistics. These results open up new possibilities for non-invasively manipulating macroscopic particles, tuning their interactions, and directing their assembly.

cond-mat.soft↗

arXiv2018

Soft self-assembly of Weyl materials for light and sound

Soft materials can self-assemble into highly structured phases which replicate at the mesoscopic scale the symmetry of atomic crystals. As such, they offer an unparalleled platform to design mesostructured materials for light and sound. Here, we present a bottom-up approach based on self-assembly to engineer three-dimensional photonic and phononic crystals with topologically protected Weyl points. In addition to angular and frequency selectivity of their bulk optical response, Weyl materials are endowed with topological surface states, which allows for the existence of one-way channels even in the presence of time-reversal invariance. Using a combination of group-theoretical methods and numerical simulations, we identify the general symmetry constraints that a self-assembled structure has to satisfy in order to host Weyl points, and describe how to achieve such constraints using a symmetry-driven pipeline for self-assembled material design and discovery. We illustrate our general approach using block copolymer self-assembly as a model system.

cond-mat.soft↗

arXiv2018

Folding mechanisms at finite temperature

Folding mechanisms are zero elastic energy motions essential to the deployment of origami, linkages, reconfigurable metamaterials and robotic structures. In this paper, we determine the fate of folding mechanisms when such structures are miniaturized so that thermal fluctuations cannot be neglected. First, we identify geometric and topological design strategies aimed at minimizing undesired thermal energy barriers that generically obstruct kinematic mechanisms at the microscale. Our findings are illustrated in the context of a quasi one-dimensional linkage structure that harbors a topologically protected mechanism. However, thermal fluctuations can also be exploited to deliberately lock a reconfigurable metamaterial into a fully expanded configuration, a process reminiscent of order by disorder transitions in magnetic systems. We demonstrate that this effect leads certain topological mechanical structures to exhibit an abrupt change in the pressure -- a bulk signature of the underlying topological invariant at finite temperature. We conclude with a discussion of anharmonic corrections and potential applications of our work to the the engineering of DNA origami devices and molecular robots.

cond-mat.soft↗