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Full-Text Articles in Physics
The Shape And Mechanics Of Curved Fold Origami Structures, Marcelo A. Dias, Christian Santangelo
The Shape And Mechanics Of Curved Fold Origami Structures, Marcelo A. Dias, Christian Santangelo
Christian Santangelo
We develop recursion equations to describe the three-dimensional shape of a sheet upon which a series of concentric curved folds have been inscribed. In the case of no stretching outside the fold, the three-dimensional shape of a single fold prescribes the shape of the entire origami structure. To better explore these structures, we derive continuum equations, valid in the limit of vanishing spacing between folds, to describe the smooth surface intersecting all the mountain folds. We find that this surface has negative Gaussian curvature with magnitude equal to the square of the fold's torsion. A series of open folds with …
Slack Dynamics On An Unfurling String, J. A. Hanna, Christian Santangelo
Slack Dynamics On An Unfurling String, J. A. Hanna, Christian Santangelo
Christian Santangelo
An arch will grow on a rapidly deployed thin string in contact with a rigid plane. We present a qualitative model for the growing structure involving the amplification, rectification, and advection of slack in the presence of a steady stress field, validate our assumptions with numerical experiments, and pose new questions about the spatially developing motions of thin objects.
Smectic Pores And Defect Cores, Elisabetta A. Masumoto, Randall D. Kamien, Christian Santangelo
Smectic Pores And Defect Cores, Elisabetta A. Masumoto, Randall D. Kamien, Christian Santangelo
Christian Santangelo
Riemann's minimal surfaces, a one-parameter family of minimal surfaces, describe a bicontinuous lamellar system with pores connecting alternating layers. We demonstrate explicitly that Riemann's minimal surfaces are composed of a nonlinear sum of two oppositely handed helicoids.
Developed Smectics: When Exact Solutions Agree, Gareth P. Alexander, Randall D. Kamien, Christian Santangelo
Developed Smectics: When Exact Solutions Agree, Gareth P. Alexander, Randall D. Kamien, Christian Santangelo
Christian Santangelo
In the limit where the bending modulus vanishes, we construct layer configurations with arbitrary dislocation textures by exploiting a connection between uniformly spaced layers in two dimensions and developable surfaces in three dimensions. We then show how these focal textures can be used to construct layer configurations with finite bending modulus.
Geometric Mechanics Of Curved Crease Origami, Marcelo A. Dias, Levi H. Dudte, L. Mahadevan, Christian Santangelo
Geometric Mechanics Of Curved Crease Origami, Marcelo A. Dias, Levi H. Dudte, L. Mahadevan, Christian Santangelo
Christian Santangelo
Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold, and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases …
Packing Squares In A Torus, D. W. Blair, Christian Santangelo, J. Machta
Packing Squares In A Torus, D. W. Blair, Christian Santangelo, J. Machta
Christian Santangelo
The densest packings of N unit squares in a torus are studied using analytical methods as well as simulated annealing. A rich array of dense packing solutions are found: density-one packings when N is the sum of two square integers; a family of 'gapped bricklayer' Bravais lattice solutions with density N/(N + 1); and some surprising non-Bravais lattice configurations, including lattices of holes as well as a configuration for N = 23 in which not all squares share the same orientation. The entropy of some of these configurations and the frequency and orientation of density-one solutions as N -> infinity …
Frustrated Order On Extrinsic Geometries, Badel L. Mbanga, Gregory M. Grason, Christian Santangelo
Frustrated Order On Extrinsic Geometries, Badel L. Mbanga, Gregory M. Grason, Christian Santangelo
Christian Santangelo
We study, numerically and theoretically, defects in an anisotropic liquid that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the order along the local direction of maximum or minimum bending. This additional frustration is generically unavoidable, and leads to complex ground-state thermodynamics. Using the catenoid as a prototype, we show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic curvature expels disclinations from the region of maximum curvature above a critical coupling threshold. On catenoids lacking an “inside-outside” …