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Chiral fluids – such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids – flow in a different way than ordinary ones. Due to symmetries broken at the microscopic level, chiral fluids may have asymmetric stress and viscosity tensors, for example giving rise to a hydrostatic torque or non-dissipative (odd) and parity-violating viscosities. In this article, we investigate the motion of rigid bodies in such an anisotropic fluid in the incompressible Stokes regime through the mobility matrix, which encodes the response of a solid body to forces and torques. We demonstrate how the form of the mobility matrix, which is usually determined by particle geometry, can be analogously controlled by the symmetries of the fluid. By computing the mobility matrix for simple shapes in a three-dimensional (3-D) anisotropic chiral fluid, we predict counterintuitive phenomena such as motion at an angle to the direction of applied forces and spinning under the force of gravity. [ABSTRACT FROM AUTHOR]

Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales at which the cascade is eventually arrested by dissipation1–6. Here we show how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which can usually be traced to the linear instability of a homogeneous state7. By contrast, the mechanism we propose here is fully nonlinear. It is triggered by the non-dissipative arrest of turbulent cascades: energy piles up at an intermediate scale, which is neither the system size nor the smallest scales at which energy is usually dissipated. Using a combination of theory and large-scale simulations, we show that the tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd viscosity, ubiquitous in chiral fluids ranging from bioactive to quantum systems8–12. Odd viscosity, which acts as a scale-dependent Coriolis-like force, leads to a two-dimensionalization of the flow at small scales, in contrast with rotating fluids in which a two-dimensionalization occurs at large scales4. Apart from odd viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems, including atmospheric flows13–19, stellar plasma such as the solar wind20–22, or the pulverization and coagulation of objects or droplets in which mass rather than energy cascades23–25.Turbulent energy cascades can be arrested by non-dissipative viscosities, resulting in pattern formation at intermediate length scales. [ABSTRACT FROM AUTHOR]

Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries. Here, we show how boundaries can generate and protect spiking when the reacting components can spread out: Even arbitrarily weak diffusion can cause spiking at the edge between two non-excitable media. This edge spiking arises due to a global bistability, which can occur even if amplification and suppression strengths do not allow spiking when mixed. We analytically derive a spiking phase diagram that depends on two parameters: i) the ratio between the system size and the characteristic diffusive length-scale and ii) the ratio between the amplification and suppression strengths. Our analysis explains recent experimental observations of action potentials at the interface between two non-excitable bioelectric tissues. Beyond electrophysiology, we highlight how edge spiking emerges in predator-prey dynamics and in oscillating chemical reactions. Our findings provide a theoretical blueprint for a class of interfacial excitations in reaction-diffusion systems, with potential implications for spatially controlled chemical reactions, nonlinear waveguides and neuromorphic computation, as well as spiking instabilities, such as cardiac arrhythmias, that naturally occur in heterogeneous biological media. [ABSTRACT FROM AUTHOR]

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 nonequilibrium chiral systems. [ABSTRACT FROM AUTHOR]

The Stokes equation describes the motion of fluids when inertial forces are negligible compared with viscous forces. In this article, we explore the consequence of parity-violating and non-dissipative (i.e. odd) viscosities on Stokes flows in three dimensions. Parity-violating viscosities are coefficients of the viscosity tensor that are not invariant under mirror reflections of space, while odd viscosities are those which do not contribute to dissipation of mechanical energy. These viscosities can occur in systems ranging from synthetic and biological active fluids to magnetized and rotating fluids. We first systematically enumerate all possible parity-violating viscosities compatible with cylindrical symmetry, highlighting their connection to potential microscopic realizations. Then, using a combination of analytical and numerical methods, we analyse the effects of parity-violating viscosities on the Stokeslet solution, on the flow past a sphere or a bubble and on many-particle sedimentation. In all the cases that we analyse, parity-violating viscosities give rise to an azimuthal flow even when the driving force is parallel to the axis of cylindrical symmetry. For a few sedimenting particles, the azimuthal flow bends the trajectories compared with a traditional Stokes flow. For a cloud of particles, the azimuthal flow impedes the transformation of the spherical cloud into a torus and the subsequent breakup into smaller parts that would otherwise occur. The presence of azimuthal flows in cylindrically symmetric systems (sphere, bubble, cloud of particles) can serve as a probe for parity-violating viscosities in experimental systems. [ABSTRACT FROM AUTHOR]

Materials made from active, living, or robotic components can display emergent properties arising from local sensing and computation. Here, we realize a freestanding active metabeam with piezoelectric elements and electronic feed-forward control that gives rise to an odd micropolar elasticity absent in energy-conserving media. The non-reciprocal odd modulus enables bending and shearing cycles that convert electrical energy into mechanical work, and vice versa. The sign of this elastic modulus is linked to a non-Hermitian topological index that determines the localization of vibrational modes to sample boundaries. At finite frequency, we can also tune the phase angle of the active modulus to produce a direction-dependent bending modulus and control non-Hermitian vibrational properties. Our continuum approach, built on symmetries and conservation laws, could be exploited to design others systems such as synthetic biofilaments and membranes with feed-forward control loops. Mechanical metamaterials can be engineered with properties not possible in ordinary materials. Here the authors demonstrate and study an active metamaterial with self-sensing characteristics that enables odd elastic properties not observed in passive media. [ABSTRACT FROM AUTHOR]

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecularmotor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics. [ABSTRACT FROM AUTHOR]

Dualities are mathematical mappings that reveal links between apparently unrelated systems in virtually every branch of physics1–8. Systems mapped onto themselves by a duality transformation are called self-dual and exhibit remarkable properties, as exemplified by the scale invariance of an Ising magnet at the critical point. Here we show how dualities can enhance the symmetries of a dynamical matrix (or Hamiltonian), enabling the design of metamaterials with emergent properties that escape a standard group theory analysis. As an illustration, we consider twisted kagome lattices9–15, reconfigurable mechanical structures that change shape by means of a collapse mechanism9. We observe that pairs of distinct configurations along the mechanism exhibit the same vibrational spectrum and related elastic moduli. We show that these puzzling properties arise from a duality between pairs of configurations on either side of a mechanical critical point. The critical point corresponds to a self-dual structure with isotropic elasticity even in the absence of spatial symmetries and a twofold-degenerate spectrum over the entire Brillouin zone. The spectral degeneracy originates from a version of Kramers' theorem16,17 in which fermionic time-reversal invariance is replaced by a hidden symmetry emerging at the self-dual point. The normal modes of the self-dual systems exhibit non-Abelian geometric phases18,19 that affect the semiclassical propagation of wavepackets20, leading to non-commuting mechanical responses. Our results hold promise for holonomic computation21 and mechanical spintronics by allowing on-the-fly manipulation of synthetic spins carried by phonons. Dualities—mathematical mappings between different systems—can act as hidden symmetries that enable materials design beyond that suggested by crystallographic space groups. [ABSTRACT FROM AUTHOR]

Topological states can be used to control the mechanical properties of a material along an edge or around a localized defect. The rigidity of elastic networks is characterized by a topological invariant called the polarization; materials with a well-defined uniform polarization display a dramatic range of edge softness depending on the orientation of the polarization relative to the terminating surface. However, in all 3D mechanical metamaterials proposed to date, the topological modes are mixed with bulk soft modes, which organize themselves in Weyl loops. Here, we report the design of a 3D topological metamaterial without Weyl lines and with a uniform polarization that leads to an asymmetry between the number of soft modes on opposing surfaces. We then use this construction to localize topological soft modes in interior regions of the material by including defect lines--dislocation loops--that are unique to three dimensions. We derive a general formula that relates the difference in the number of soft modes and states of self-stress localized along the dislocation loop to the handedness of the vector triad formed by the lattice polarization, Burgers vector, and dislocation-line direction. Our findings suggest a strategy for preprogramming failure and softness localized along lines in 3D, while avoiding extended soft Weyl modes. [ABSTRACT FROM AUTHOR]

We study the hydrodynamics of fluids composed of self-spinning objects such as chiral grains or colloidal particles subject to torques. These chiral active fluids break both parity and timereversal symmetries in their non-equilibrium steady states. As a result, the constitutive relations of chiral active media display a dissipationless linear-response coefficient called odd (or equivalently, Hall) viscosity. This odd viscosity does not lead to energy dissipation, but gives rise to a flow perpendicular to applied pressure. We show how odd viscosity arises from non-linear equations of hydrodynamics with rotational degrees of freedom, once linearized around a non-equilibrium steady state characterized by large spinning speeds. Next, we explore odd viscosity in compressible fluids and suggest how our findings can be tested in the context of shock propagation experiments. Finally, we show how odd viscosity in weakly compressible chiral active fluids can lead to density and pressure excess within vortex cores. [ABSTRACT FROM AUTHOR]

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 investigate the behavior of ensembles of self-spinning dimers. We find that geometric frustration of dimer rotation by interactions yields spatiotemporal order and active melting with no equilibrium counterparts. At low density, the spinning dimers self-assemble into a triangular lattice with their orientations phase-locked into spatially periodic phases. The phase-locked patterns form dynamical analogs of the ground states of various spin models, transitioning from the three-state Potts antiferromagnet at low densities to the striped herringbone phase of planar quadrupoles at higher densities. As the density is raised further, the competition between active rotations and interactions leads to melting of the active spinner crystal. Emergent edge currents, whose direction is set by the chirality of the active spinning, arise as a nonequilibrium signature of the transition to the active spinner liquid and vanish when the system eventually undergoes kinetic arrest at very high densities. Our findings may be realized in systems ranging from liquid crystal and colloidal experiments to tabletop realizations using macroscopic chiral grains. [ABSTRACT FROM AUTHOR]

We investigate how material rigidity acts as a key control parameter for the failure of solids under stress. In both experiments and simulations, we demonstrate that material failure can be continuously tuned by varying the underlying rigidity of the material while holding the amount of disorder constant. As the rigidity transition is approached, failure due to the application of uniaxial stress evolves from brittle cracking to system-spanning diffuse breaking. This evolution in failure behavior can be parameterized by the width of the crack. As a system becomes more and more floppy, this crack width increases until it saturates at the system size. Thus, the spatial extent of the failure zone can be used as a direct probe for material rigidity. [ABSTRACT FROM AUTHOR]

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--composed of coupled gyroscopes on a lattice--that breaks time-reversal symmetry. The vibrational spectrum displays a sonic gap populated by topologically protected edge modes that propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We demonstrate this functionality in experiment and envision applications of these edge modes to the design of one-way acoustic waveguides. [ABSTRACT FROM AUTHOR]

States of self-stress--tensions and compressions of structural elements that result in zero net forces--play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self-stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely hinged joints, they leave a distinct signature in the nonlinear buckling behavior of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three- dimensional metamaterials built out of stacked kagome lattices. [ABSTRACT FROM AUTHOR]

Any macroscopic deformation of a filamentous bundle is necessarily accompanied by local sliding and/or stretching of the constituent filaments. Yet the nature of the sliding friction between two aligned filaments interacting through multiple contacts remains largely unexplored. Here, by directly measuring the sliding forces between two bundled F-actin filaments, we show that these frictional forces are unexpectedly large, scale logarithmically with sliding velocity as in solid-like friction, and exhibit complex dependence on the filaments' overlap length. We also show that a reduction of the frictional force by orders of magnitude, associated with a transition from solid-like friction to Stokes's drag, can be induced by coating F-actin with polymeric brushes. Furthermore, we observe similar transitions in filamentous microtubules and bacterial flagella. Our findings demonstrate how altering a filament's elasticity, structure and interactions can be used to engineer interfilament friction and thus tune the properties of fibrous composite materials. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials are artificial structures with unusual properties, such as negative Poisson ratio, bistability or tunable vibrational properties, that originate in the geometry of their unit cell. Often at the heart of such unusual behaviour is a soft mode: a motion that does not significantly stretch or compress the links between constituent elements. When activated by motors or external fields, soft modes become the building blocks of robots and smart materials. Here, we demonstrate the existence of topological soft modes that can be positioned at desired locations in a metamaterial while being robust against a wide range of structural deformations or changes in material parameters. These protected modes, localized at dislocations in deformed kagome and square lattices, are the mechanical analogue of topological states bound to defects in electronic systems. We create physical realizations of the topological modes in prototypes of kagome lattices built out of rigid triangular plates. We show mathematically that they originate from the interplay between two Berry phases: the Burgers vector of the dislocation and the topological polarization of the lattice. Our work paves the way towards engineering topologically protected nanomechanical structures for molecular robotics or information storage and read-out. [ABSTRACT FROM AUTHOR]

Measures of the non-Gaussianity of a random field depend on how accurately one is able to measure the field. If a signal measured at a certain point is to be averaged with its surroundings, or coarse-grained, the magnitude of its non-Gaussian component can vary. In this article, we investigate the variation of the 'apparent' non-Gaussianity, as a function of the coarse-graining length, when we measure non-Gaussianity using the statistics of extrema in the field. We derive how the relative difference between maxima and minima-which is a geometrical measure of the field's non-Gaussianity-behaves as the field is coarse-grained over increasingly larger length scales. Measuring this function can give extra information about the non-Gaussian statistics and facilitate its detection. [ABSTRACT FROM AUTHOR]

Networks of rigid bars connected by joints, termed linkages, provide a minimal framework to design robotic arms and mechanical metamaterials built of folding components. Here, we investigate a chain-like linkage that, according to linear elasticity, behaves like a topological mechanical insulator whose zero-energy modes are localized at the edge. Simple experiments we performed using prototypes of the chain vividly illustrate how the soft motion, initially localized at the edge, can in fact propagate unobstructed all of the way to the opposite end. Using real prototypes, simulations, and analytical models, we demonstrate that the chain is a mechanical conductor, whose carriers are nonlinear solitary waves, not captured within linear elasticity. Indeed, the linkage prototype can be regarded as the simplest example of a topological metamaterial whose protected mechanical excitations are solitons, moving domain walls between distinct topological mechanical phases. More practically, we have built a topologically protected mechanism that can perform basic tasks such as transporting a mechanical state from one location to another. Our work paves the way toward adopting the principle of topological robustness in the design of robots assembled from activated linkages as well as in the fabrication of complex molecular nanostructures. [ABSTRACT FROM AUTHOR]

A minimal model for studying the mechanical properties of amorphous solids is a disordered network of point masses connected by unbreakable springs. At a critical value of its mean connectivity, such a network becomes fragile: it undergoes a rigidity transition signaled by a vanishing shear modulus and transverse sound speed. We investigate analytically and numerically the linear and nonlinear visco-elastic response of these fragile solids by probing how shear fronts propagate through them. Our approach, which we tentatively label shear front rheology, provides an alternative route to standard oscillatory rheology. In the linear regime, we observe at late times a diffusive broadening of the fronts controlled by an effective shear viscosity that diverges at the critical point. No matter how small the microscopic coefficient of dissipation, strongly disordered networks behave as if they were overdamped because energy is irreversibly leaked into diverging nonaffine fluctuations. Close to the transition, the regime of linear response becomes vanishingly small: the tiniest shear strains generate strongly nonlinear shear shock waves qualitatively different from their compressional counterparts in granular media. The inherent nonlinearities trigger an energy cascade from low to high frequency components that keep the network away from attaining the quasi-static limit. This mechanism, reminiscent of acoustic turbulence, causes a superdiffusive broadening of the shock width. [ABSTRACT FROM AUTHOR]

We stabilize nematic droplets with handles against surface tension-driven instabilities, using a yield-stress material as outer fluid, and study the complex nematic textures and defect structures that result from the competition between topological constraints and the elasticity of the nematic liquid crystal. We uncover a surprisingly persistent twisted configuration of the nematic director inside the droplets when tangential anchoring is established at their boundaries, which we explain after considering the influence of saddle splay on the elastic free energy. For toroidal droplets, we find that the saddle-splay energy screens the twisting energy, resulting in a spontaneous breaking of mirror symmetry; the chiral twisted state persists for aspect ratios as large as ~20. For droplets with additional handles, we observe in experiments and computer simulations that there are two additional -1 surface defects per handle; these are located in regions with local saddle geometry to minimize the nematic distortions and hence the corresponding elastic free energy. [ABSTRACT FROM AUTHOR]

Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The standard test of non-Gaussianity is to measure higher-order correlation functions. In the present work, we take a different route. We show how geometric and topological properties of Gaussian fields, such as the statistics of extrema, are modified by the presence of a non-Gaussian perturbation. The resulting discrepancies give an independent way to detect and quantify non-Gaussianities. In our treatment, we consider both local and nonlocal mechanisms that generate non-Gaussian fields, both statically and dynamically through nonlinear diffusion. [ABSTRACT FROM AUTHOR]

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 crystals on a plane exhibit fascinating scarred defect patterns on a sphere. Here we show that, for more general curved surfaces, curvature may be relaxed by pleats: uncharged lines of dislocations (topological dipoles) that vanish on the surface and play the same role as fabric pleats. We experimentally investigate crystal order on surfaces with spatially varying positive and negative curvature. On cylindrical capillary bridges, stretched to produce negative curvature, we observe a sequence of transitions-consistent with our energetic calculations-from no defects to isolated dislocations, which subsequently proliferate and organize into pleats; finally, scars and isolated heptagons (previously unseen) appear. This fine control of crystal order with curvature will enable explorations of general theories of defects in curved spaces. From a practical viewpoint, it may be possible to engineer structures with curvature (such as waisted nanotubes and vaulted architecture) and to develop novel methods for soft lithography and directed self-assembly. [ABSTRACT FROM AUTHOR]

We study static and dynamical properties that distinguish 2D crystals constrained to lie on a curved substrate from their flat-space counterparts. A generic mechanism of dislocation unbinding in the presence of varying Gaussian curvature is presented in the context of a model surface amenable to full analytical treatment. We find that glide diffusion of isolated dislocations is suppressed by a binding potential of purely geometrical origin. Finally, the energetics and biased diffusion dynamics of point defects such as vacancies and interstitials are explained in terms of their geometric potential. [ABSTRACT FROM AUTHOR]

The article discusses the role of topology in the study of soft materials. It mentions that it can help in describing intriguing topological structures that exist in knotted proteins and DNA, and topological defects in liquid crystals. It further mentions that Kagome lattice, an arrangement of laths composed of interlaced triangles, have a peculiar elastic response which can help in designing useful soft topological materials that are truly topologically protected.

The authors discuss the study by D. Bi and colleagues on soft materials, such as sands. The authors says that the study, published in December 15, 2011 issue of the journal "Nature," shows that collections of loose, unjammed discs become rigid when sheared under constant volume, building up pressure and resisting further deformation. Moreover, there is an in-between region for the fragile and shear-jammed states, which should meet near the marginal or jamming point to overcome rigidity.