85 research outputs found
Paraboloidal Crystals
The interplay between order and geometry in soft condensed matter systems is
an active field with many striking results and even more open problems. Ordered
structures on curved surfaces appear in multi-electron helium bubbles, viral
and bacteriophage protein capsids, colloidal self-assembly at interfaces and in
physical membranes. Spatial curvature can lead to novel ground state
configurations featuring arrays of topological defects that would be excited
states in planar systems. We illustrate this with a sequence of images showing
the Voronoi lattice (in gold) and the corresponding Delaunay triangulations (in
green) for ten low energy configurations of a system of classical charges
constrained to lie on the surface of a paraboloid and interacting with a
Coulomb potential. The parabolic geometry is considered as a specific
realization of the class of crystalline structures on two-dimensional
Riemannian manifolds with variable Gaussian curvature and boundary.Comment: 2 page
Cross-talk between topological defects in different fields revealed by nematic microfluidics
Topological defects are singularities in material fields that play a vital
role across a range of systems: from cosmic microwave background polarization
to superconductors, and biological materials. Although topological defects and
their mutual interactions have been extensively studied, little is known about
the interplay between defects in different fields -- especially when they
co-evolve -- within the same physical system. Here, using nematic
microfluidics, we study the cross-talk of topological defects in two different
material fields -- the velocity field and the molecular orientational field.
Specifically, we generate hydrodynamic stagnation points of different
topological charges at the center of star-shaped microfluidic junctions, which
then interact with emergent topological defects in the orientational field of
the nematic director. We combine experiments, and analytical and numerical
calculations to demonstrate that a hydrodynamic singularity of given
topological charge can nucleate a nematic defect of equal topological charge,
and corroborate this by creating , and topological defects in
, , and arm junctions. Our work is an attempt toward understanding
materials that are governed by distinctly multi-field topology, where disparate
topology-carrying fields are coupled, and concertedly determine the material
properties and response.Comment: 18 pages, 9 figure
Complex Spontaneous Flows and Concentration Banding in Active Polar Films
We study the dynamical properties of active polar liquid crystalline films.
Like active nematic films, active polar films undergo a dynamical transitions
to spontaneously flowing steady-states. Spontaneous flow in polar fluids is,
however, always accompanied by strong concentration inhomogeneities or
"banding" not seen in nematics. In addition, a spectacular property unique to
polar active films is their ability to generate spontaneously oscillating and
banded flows even at low activity. The oscillatory flows become increasingly
complicated for strong polarity.Comment: 4 pages, 3 figure
Toroidal Crystals
Crystalline assemblages of identical sub-units packed together and elastically bent in the form of a torus have been found in the past ten years in a variety of systems of surprisingly different nature, such as viral capsids, self-assembled monolayers and carbon nanomaterials. In this Letter we analyze the structural properties of toroidal crystals and we provide a unified description based on the elastic theory of defects in curved geometries. We find ground states characterized by the presence of 5-fold disclinations on the exterior of the torus and 7-fold disclinations in the interior. The number of excess disclinations is controlled primarily by the aspect ratio of the torus, suggesting a novel mechanism for creating toroidal templates with precisely controlled valency via functionalization of the defect sites
Two-Dimensional Matter: Order, Curvature and Defects
Many systems in nature and the synthetic world involve ordered arrangements
of units on two-dimensional surfaces. We review here the fundamental role payed
by both the topology of the underlying surface and its detailed curvature.
Topology dictates certain broad features of the defect structure of the ground
state but curvature-driven energetics controls the detailed structured of
ordered phases. Among the surprises are the appearance in the ground state of
structures that would normally be thermal excitations and thus prohibited at
zero temperature. Examples include excess dislocations in the form of grain
boundary scars for spherical crystals above a minimal system size, dislocation
unbinding for toroidal hexatics, interstitial fractionalization in spherical
crystals and the appearance of well-separated disclinations for toroidal
crystals. Much of the analysis leads to universal predictions that do not
depend on the details of the microscopic interactions that lead to order in the
first place. These predictions are subject to test by the many experimental
soft and hard matter systems that lead to curved ordered structures such as
colloidal particles self-assembling on droplets of one liquid in a second
liquid. The defects themselves may be functionalized to create ligands with
directional bonding. Thus nano to meso scale superatoms may be designed with
specific valency for use in building supermolecules and novel bulk materials.
Parameters such as particle number, geometrical aspect ratios and anisotropy of
elastic moduli permit the tuning of the precise architecture of the superatoms
and associated supermolecules. Thus the field has tremendous potential from
both a fundamental and materials science/supramolecular chemistry viewpoint.Comment: Review article, 102 pages, 59 figures, submitted to Advances in
Physic
Geometry and mechanics of microdomains in growing bacterial colonies
Bacterial colonies are abundant on living and nonliving surfaces and are
known to mediate a broad range of processes in ecology, medicine, and industry.
Although extensively researched, from single cells to demographic scales, a
comprehensive biomechanical picture, highlighting the cell-to-colony dynamics,
is still lacking. Here, using molecular dynamics simulations and continuous
modeling, we investigate the geometrical and mechanical properties of a
bacterial colony growing on a substrate with a free boundary and demonstrate
that such an expanding colony self-organizes into a "mosaic" of microdomains
consisting of highly aligned cells. The emergence of microdomains is mediated
by two competing forces: the steric forces between neighboring cells, which
favor cell alignment, and the extensile stresses due to cell growth that tend
to reduce the local orientational order and thereby distort the system. This
interplay results in an exponential distribution of the domain areas and sets a
characteristic length scale proportional to the square root of the ratio
between the system orientational stiffness and the magnitude of the extensile
active stress. Our theoretical predictions are finally compared with
experiments with freely growing E. coli microcolonies, finding quantitative
agreement.Comment: 10 pages, 7 figure
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