86 research outputs found
Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
Model lattices consisting of balls connected by central-force springs provide
much of our understanding of mechanical response and phonon structure of real
materials. Their stability depends critically on their coordination number .
-dimensional lattices with are at the threshold of mechanical
stability and are isostatic. Lattices with exhibit zero-frequency
"floppy" modes that provide avenues for lattice collapse. The physics of
systems as diverse as architectural structures, network glasses, randomly
packed spheres, and biopolymer networks is strongly influenced by a nearby
isostatic lattice. We explore elasticity and phonons of a special class of
two-dimensional isostatic lattices constructed by distorting the kagome
lattice. We show that the phonon structure of these lattices, characterized by
vanishing bulk moduli and thus negative Poisson ratios and auxetic elasticity,
depends sensitively on boundary conditions and on the nature of the kagome
distortions. We construct lattices that under free boundary conditions exhibit
surface floppy modes only or a combination of both surface and bulk floppy
modes; and we show that bulk floppy modes present under free boundary
conditions are also present under periodic boundary conditions but that surface
modes are not. In the the long-wavelength limit, the elastic theory of all
these lattices is a conformally invariant field theory with holographic
properties, and the surface waves are Rayleigh waves. We discuss our results in
relation to recent work on jammed systems. Our results highlight the importance
of network architecture in determining floppy-mode structure.Comment: 12 pages, 7 figure
Odd viscosity in chiral active fluids
Chiral active fluids are materials composed of self-spinning rotors that
continuously inject energy and angular momentum at the microscale.
Out-of-equilibrium fluids with active-rotor constituents have been
experimentally realized using nanoscale biomolecular motors, microscale active
colloids, or macroscale driven chiral grains. Here, we show how such chiral
active fluids break both parity and time-reversal symmetries in their steady
states, giving rise to a dissipationless linear-response coefficient called odd
viscosity in their constitutive relations. Odd viscosity couples pressure and
vorticity leading, for example, to density modulations within a vortex profile.
Moreover, chiral active fluids flow in the direction transverse to applied
compression as in shock propagation experiments. We envision that this
collective transverse response may be exploited to design self-assembled
hydraulic cranks that convert between linear and rotational motion in
microscopic machines powered by active-rotors fluids
Optimal power and efficiency of odd engines
Odd materials feature antisymmetric response to perturbations. This anomalous
property can stem from the nonequilibrium activity of their components, which
is sustained by an external energy supply. These materials open the door to
designing innovative engines which extract work by applying cyclic
deformations, without any equivalent in equilibrium. Here, we reveal that the
efficiency of such energy conversion, from local activity to macroscopic work,
can be arbitrarily close to unity when the cycles of deformation are properly
designed. We illustrate these principles in some canonical viscoelastic
materials, which leads us to identify strategies for optimizing power and
efficiency according to material properties, and to delineate guidelines for
the design of more complex odd engines.Comment: 6 pages, 2 figure
Hydrodynamic correlation functions of chiral active fluids
The success of spectroscopy to characterize 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
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