45 research outputs found
Favoured Local Structures in Liquids and Solids: a 3D Lattice Model
We investigate the connection between the geometry of Favoured Local
Structures (FLS) in liquids and the associated liquid and solid properties. We
introduce a lattice spin model - the FLS model on a face-centered cubic lattice
- where this geometry can be arbitrarily chosen among a discrete set of 115
possible FLS. We find crystalline groundstates for all choices of a single FLS.
Sampling all possible FLS's, we identify the following trends: i) low symmetry
FLS's produce larger crystal unit cells but not necessarily higher energy
groundstates, ii) chiral FLS's exhibit to peculiarly poor packing properties,
iii) accumulation of FLS's in supercooled liquids is linked to large crystal
unit cells, and iv) low symmetry FLS's tend to find metastable structures on
cooling.Comment: 11 pages, 6 figure
From Liquid Structure to Configurational Entropy: Introducing Structural Covariance
We connect the configurational entropy of a liquid to the geometrical
properties of its local energy landscape, using a high-temperature expansion.
It is proposed that correlations between local structures arises from their
overlap and, being geometrical in nature, can be usefully determined using the
inherent structures of high temperature liquids. We show quantitatively how the
high-temperature covariance of these local structural fluctuations arising from
their geometrical overlap, combined with their energetic stability, control the
decrease of entropy with decreasing energy. We apply this formalism to a family
of Favoured Local Structure (FLS) lattice models with two low symmetry FLS's
which are found to either crystallize or form a glass on cooling. The
covariance, crystal energy and estimated freezing temperature are tested as
possible predictors of glass-forming ability in the model system
Connecting local active forces to macroscopic stress in elastic media
In contrast with ordinary materials, living matter drives its own motion by
generating active, out-of-equilibrium internal stresses. These stresses
typically originate from localized active elements embedded in an elastic
medium, such as molecular motors inside the cell or contractile cells in a
tissue. While many large-scale phenomenological theories of such active media
have been developed, a systematic understanding of the emergence of stress from
the local force-generating elements is lacking. In this paper, we present a
rigorous theoretical framework to study this relationship. We show that the
medium's macroscopic active stress tensor is equal to the active elements'
force dipole tensor per unit volume in both continuum and discrete linear
homogeneous media of arbitrary geometries. This relationship is conserved on
average in the presence of disorder, but can be violated in nonlinear elastic
media. Such effects can lead to either a reinforcement or an attenuation of the
active stresses, giving us a glimpse of the ways in which nature might harness
microscopic forces to create active materials.Comment: 9 pages, 4 figure
Fiber networks amplify active stress
Large-scale force generation is essential for biological functions such as
cell motility, embryonic development, and muscle contraction. In these
processes, forces generated at the molecular level by motor proteins are
transmitted by disordered fiber networks, resulting in large-scale active
stresses. While these fiber networks are well characterized macroscopically,
this stress generation by microscopic active units is not well understood. Here
we theoretically study force transmission in these networks, and find that
local active forces are rectified towards isotropic contraction and strongly
amplified as fibers collectively buckle in the vicinity of the active units.
This stress amplification is reinforced by the networks' disordered nature, but
saturates for high densities of active units. Our predictions are
quantitatively consistent with experiments on reconstituted tissues and
actomyosin networks, and shed light on the role of the network microstructure
in shaping active stresses in cells and tissue.Comment: 8 pages, 4 figures. Supporting information: 5 pages, 5 figure
Inferring the dynamics of underdamped stochastic systems
Many complex systems, ranging from migrating cells to animal groups, exhibit
stochastic dynamics described by the underdamped Langevin equation. Inferring
such an equation of motion from experimental data can provide profound insight
into the physical laws governing the system. Here, we derive a principled
framework to infer the dynamics of underdamped stochastic systems from
realistic experimental trajectories, sampled at discrete times and subject to
measurement errors. This framework yields an operational method, Underdamped
Langevin Inference (ULI), which performs well on experimental trajectories of
single migrating cells and in complex high-dimensional systems, including
flocks with Viscek-like alignment interactions. Our method is robust to
experimental measurement errors, and includes a self-consistent estimate of the
inference error
Structural Covariance in the Hard Sphere Fluid
We study the joint variability of structural information in a hard sphere
fluid biased to avoid crystallisation and form fivefold symmetric geometric
motifs. We show that the structural covariance matrix approach, originally
proposed for on-lattice liquids [Ronceray and Harrowell, JCP 2016], can be
meaningfully employed to understand structural relationships between different
motifs and can predict, within the linear-response regime, structural changes
related to motifs distinct from that used to bias the system