1,503 research outputs found
The Power of Poincar\'e: Elucidating the Hidden Symmetries in Focal Conic Domains
Focal conic domains are typically the "smoking gun" by which smectic liquid
crystalline phases are identified. The geometry of the equally-spaced smectic
layers is highly generic but, at the same time, difficult to work with. In this
Letter we develop an approach to the study of focal sets in smectics which
exploits a hidden Poincar\'e symmetry revealed only by viewing the smectic
layers as projections from one-higher dimension. We use this perspective to
shed light upon several classic focal conic textures, including the concentric
cyclides of Dupin, polygonal textures and tilt-grain boundaries.Comment: 4 pages, 3 included figure
Socio-economic factors Influencing Infant and Child Mortality among the Zou of Manipur
The present study was conducted to find out the influence ofsocio-economic factors on infant and child mortality among the Zou,a tribal population of Manipur. A cross-sectional study was executedamong 533 mothers of age 17- 49 years following house to housevisits from December 2016 to February 2017. The finding showsthere is a significant correlation of the educational level of themother, household income, child immunization to that of infant andchild mortality in the study population
Minimal resonances in annular non-Euclidean strips
Differential growth processes play a prominent role in shaping leaves and
biological tissues. Using both analytical and numerical calculations, we
consider the shapes of closed, elastic strips which have been subjected to an
inhomogeneous pattern of swelling. The stretching and bending energies of a
closed strip are frustrated by compatibility constraints between the curvatures
and metric of the strip. To analyze this frustration, we study the class of
"conical" closed strips with a prescribed metric tensor on their center line.
The resulting strip shapes can be classified according to their number of
wrinkles and the prescribed pattern of swelling. We use this class of strips as
a variational ansatz to obtain the minimal energy shapes of closed strips and
find excellent agreement with the results of a numerical bead-spring model.
Within this class of strips, we derive a condition under which a strip can have
vanishing mean curvature along the center line.Comment: 14 pages, 13 figures. Published version. Updated references and added
2 figure
Topological mechanics of origami and kirigami
Origami and kirigami have emerged as potential tools for the design of
mechanical metamaterials whose properties such as curvature, Poisson ratio, and
existence of metastable states can be tuned using purely geometric criteria. A
major obstacle to exploiting this property is the scarcity of tools to identify
and program the flexibility of fold patterns. We exploit a recent connection
between spring networks and quantum topological states to design origami with
localized folding motions at boundaries and study them both experimentally and
theoretically. These folding motions exist due to an underlying topological
invariant rather than a local imbalance between constraints and degrees of
freedom. We give a simple example of a quasi-1D folding pattern that realizes
such topological states. We also demonstrate how to generalize these
topological design principles to two dimensions. A striking consequence is that
a domain wall between two topologically distinct, mechanically rigid structures
is deformable even when constraints locally match the degrees of freedom.Comment: 5 pages, 3 figures + ~5 pages S
Intermediate Wakimoto modules for Affine sl(n+1)
We construct certain boson type realizations of affine sl(n+1) that depend on
a parameter r. When r=0 we get a Fock space realization of Imaginary Verma
modules appearing in the work of the first author and when r=n they are the
Wakimoto modules described in the work of Feigin and Frenkel
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