Related papers: How periodic surfaces bend
We study the shapes of elastic membranes under the simultaneous exertion of tensile and compressive forces when the translational symmetry along the tension direction is broken. We predict a multitude of novel morphological phases in…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
A one-parameter deformation of a periodic bar-and-joint framework is expansive when all distances between joints increase or stay the same. In dimension two, expansive behavior can be fully explained through our theory of periodic…
We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated…
In this work, a dynamic-Immersed--Boundary method combined with a BGK-Lattice--Boltzmann technique is developed and critically discussed. The fluid evolution is obtained on a three-dimensional lattice with 19 reticular velocities (D3Q19…
We study spatial coherence properties of a system composed of periodic silver nanoparticle arrays covered with a fluorescent organic molecule (DiD) film. The evolution of spatial coherence of this composite structure from the weak to the…
In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the…
The ability to change a surface's profile allows biological systems to effectively manipulate and blend into their surroundings. Current surface morphing techniques rely either on having a small number of fixed states or on directly driving…
Holding a shell in their hands, one can apply six loads: three by pulling and shearing, and three by bending and twisting. Here, it is shown that the shell resists exactly three load cases and comply with the other three, provided the shell…
Bonding between polymeric interfaces is encountered widely in several industrial applications. Many of these bonding processes rely on time-consuming and temperature-dependent classical mechanism of polymer interdiffusion via reptation in a…
The effect of the presence of a finite impedance surface on the wave propagation properties of a two-dimensional periodic array of rigid cylinders with their axes perpendicular to the surface is both numerically and experimentally analyzed…
The geometry of two-dimensional crystalline membranes dictates their mechanical, electronic and chemical properties. The local geometry of a surface is determined from the two invariants of the metric and the curvature tensors. Here we…
The biological membrane, which compartmentalizes the cell and its organelles, exhibit wide variety of macroscopic shapes of varying morphology and topology. A systematic understanding of the relation of membrane shapes to composition,…
We study the pinning of a two-dimensional membrane to a patterned substrate within elastic theory both in the bending rigidity and in the strain dominated regimes. We find that both the in-plane strains and the bending rigidity can lead to…
Solid sheets and fluid membranes exhibit buckling under lateral compression. Here, it is revealed that fluid membranes have anisotropic buckling surface tension contrary to solid sheets. Surprisingly, the surface tension perpendicular to…
Dynamical systems on an infinite translation surface with the lattice property are studied. The geodesic flow on this surface is found to be recurrent in all but countably many rational directions. Hyperbolic elements of the affine…
Edmonds famously proved that every periodic knot of genus g possesses an equivariant Seifert surface of genus g. We show that this is not true if one instead considers nonorientable spanning surfaces of a periodic knot. We demonstrate by…
When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…