22 research outputs found
Shocks near Jamming
Non-linear sound is an extreme phenomenon typically observed in solids after
violent explosions. But granular media are different. Right when they jam,
these fragile and disordered solids exhibit a vanishing rigidity and sound
speed, so that even tiny mechanical perturbations form supersonic shocks. Here,
we perform simulations in which two-dimensional jammed granular packings are
dynamically compressed, and demonstrate that the elementary excitations are
strongly non-linear shocks, rather than ordinary phonons. We capture the full
dependence of the shock speed on pressure and impact intensity by a
surprisingly simple analytical model.Comment: Revised version. Accepted for publication in Phys. Rev. Let
Topological modes bound to dislocations in mechanical metamaterials
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. At the heart of such unusual
behaviour is often 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, 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 nano-mechanical
structures for molecular robotics or information storage and read-out.Comment: 13 pages, 6 figures; changes to text and figures and added analysis
on mode localization; see
http://www.lorentz.leidenuniv.nl/~paulose/dislocation-modes/ for accompanying
video
Heat transport in model jammed solids
We calculate numerically the normal modes of vibrations in 3D jammed packings
of soft spheres as a function of the packing fraction and obtain the energy
diffusivity, a spectral measure of transport that controls sound propagation
and thermal conductivity. The crossover frequency between weak and strong
phonon scattering is controlled by the coordination and shifts to zero as the
system is decompressed towards the critical packing fraction at which rigidity
is lost. Below the crossover, the diffusivity displays a power-law divergence
with inverse frequency, which suggests that the vibrational modes are primarily
transverse waves, weakly scattered by disorder. Above it, a large number of
modes appear whose diffusivity plateaus at a nearly constant value independent
of the inter-particle potential, before dropping to zero above the Anderson
localization frequency. The thermal conductivity of a marginally jammed solid
just above the rigidity threshold is calculated and related to the one measured
experimentally at room temperature for most glasses.Comment: 15 pages, 7 figure
Uniform Shock Waves in Disordered Granular Matter
The confining pressure is perhaps the most important parameter
controlling the properties of granular matter. Strongly compressed granular
media are, in many respects, simple solids in which elastic perturbations
travel as ordinary phonons. However, the speed of sound in granular aggregates
continuously decreases as the confining pressure decreases, completely
vanishing at the jamming-unjamming transition. This anomalous behavior suggests
that the transport of energy at low pressures should not be dominated by
phonons. In this work we use simulations and theory to show how the response of
granular systems becomes increasingly nonlinear as pressure decreases. In the
low pressure regime the elastic energy is found to be mainly transported
through nonlinear waves and shocks. We numerically characterize the propagation
speed, shape, and stability of these shocks, and model the dependence of the
shock speed on pressure and impact intensity by a simple analytical approach.Comment: 12 pages, 11 figure
Motor crosslinking augments elasticity in active nematics
In active materials, uncoordinated internal stresses lead to emergent
long-range flows. An understanding of how the behavior of active materials
depends on mesoscopic (hydrodynamic) parameters is developing, but there
remains a gap in knowledge concerning how hydrodynamic parameters depend on the
properties of microscopic elements. In this work, we combine experiments and
multiscale modeling to relate the structure and dynamics of active nematics
composed of biopolymer filaments and molecular motors to their microscopic
properties, in particular motor processivity, speed, and valency. We show that
crosslinking of filaments by both motors and passive crosslinkers not only
augments the contributions to nematic elasticity from excluded volume effects
but dominates them. By altering motor kinetics we show that a competition
between motor speed and crosslinking results in a nonmonotonic dependence of
nematic flow on motor speed. By modulating passive filament crosslinking we
show that energy transfer into nematic flow is in large part dictated by
crosslinking. Thus motor proteins both generate activity and contribute to
nematic elasticity. Our results provide new insights for rationally engineering
active materials
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
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.Comment: SI Movie 1: https://www.youtube.com/watch?v=9WzIT7OG9pY SI Movie 2:
https://youtu.be/Trc4RyU7-dw SI Movie 3: https://youtu.be/Epm_P_EakH
Vortices in Superfluid Films on Curved Surfaces
We present a systematic study of how vortices in superfluid films interact
with the spatially varying Gaussian curvature of the underlying substrate. The
Gaussian curvature acts as a source for a geometric potential that attracts
(repels) vortices towards regions of negative (positive) Gaussian curvature
independently of the sign of their topological charge. Various experimental
tests involving rotating superfluid films and vortex pinning are first
discussed for films coating gently curved substrates that can be treated in
perturbation theory from flatness. An estimate of the experimental regimes of
interest is obtained by comparing the strength of the geometrical forces to the
vortex pinning induced by the varying thickness of the film which is in turn
caused by capillary effects and gravity. We then present a non-perturbative
technique based on conformal mappings that leads an exact solution for the
geometric potential as well as the geometric correction to the interaction
between vortices. The conformal mapping approach is illustrated by means of
explicit calculations of the geometric effects encountered in the study of some
strongly curved surfaces and by deriving universal bounds on their strength.Comment: 50 pages, 38 figure
Topological sound in active-liquid metamaterials
Liquids composed of self-propelled particles have been experimentally
realized using molecular, colloidal, or macroscopic constituents. These active
liquids can flow spontaneously even in the absence of an external drive. Unlike
spontaneous active flow, the propagation of density waves in confined active
liquids is not well explored. Here, we exploit a mapping between density waves
on top of a chiral flow and electrons in a synthetic gauge field to lay out
design principles for artificial structures termed topological active
metamaterials. We design metamaterials that break time-reversal symmetry using
lattices composed of annular channels filled with a spontaneously flowing
active liquid. Such active metamaterials support topologically protected sound
modes that propagate unidirectionally, without backscattering, along either
sample edges or domain walls and despite overdamped particle dynamics. Our work
illustrates how parity-symmetry breaking in metamaterial structure combined
with microscopic irreversibility of active matter leads to novel
functionalities that cannot be achieved using only passive materials