相关论文: Extrinsic Curvature, Geometric Optics, and Lamella…

This review presents recent progress in understanding constraints and consequences of close-packing geometry of filamentous or columnar materials possessing non-trivial textures, focusing in particular on the common motifs of twisted and…

A new model for lamellar surfaces formed by anisotropic molecules is proposed. The molecules have internal degrees of freedom, associated with their flexible section of length $N$ at zero temperature. We obtain a 2D non-standard six vertex…

The complex morphologies exhibited by spatially confined thin objects have long challenged human efforts to understand and manipulate them, from the representation of patterns in draped fabric in Renaissance art to current day efforts to…

Predicting the alignment of non-spherical particles in dense granular flows under shear remains a central challenge in soft matter physics. We demonstrate that the first-order behavior of granular fabric,the anisotropic distribution of…

A non-relativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression…

In densely-packed two-dimensional systems of growing cells, such as rod-shaped bacteria, a number of experimental and numerical studies report distinct patterns of nematic orientational order in the presence of confinement. So far, these…

Overlaying commensurate optical lattices with various configurations called superlattices can lead to exotic lattice topologies and, in turn, a discovery of novel physics. In this study, by overlapping the maxima of lattices, a new isolated…

The present numerical study aims at shedding light on the mechanism underlying the precessional instability in a sphere. Precessional instabilities in the form of parametric resonance due to topographic coupling have been reported in a…

Surface plasmons dominate the optical response of metal surfaces, and their nature is controlled by surface geometry. Here we study metasurfaces containing singularities in the form of sharp edges and characterized by three quantum numbers…

A fundamental object in a hyperbolic 3-manifold M is its convex core C(M), defined as the smallest closed non-empty convex subset of M. We investigate the way the geometry of the boundary S of C(M) varies as we vary the hyperbolic metric of…

Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…

After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential…

The presence of defects such as vacancies in solids has prominent effects on their mechanical properties. It not only modifies the stiffness and strength of materials, but also changes their morphologies. The latter effect is extremely…

The principles behind the sharp, singular structures in a crumpled sheet are well understood. Here we discuss more general ways of exploiting such sharp structures to control the shape of a sheet by deforming or forcing it elsewhere. Often,…

We develop the theory of the coupling between in-plane order and out-of-plane geometry in twisted, two-dimensionally ordered filament bundles based on the non-linear continuum elasticity theory of columnar materials. We show that twisted…

Everyday experience confirms the tendency of adhesive films to detach from spheroidal regions of rigid substrates -- what is a petty frustration when placing a sticky bandage onto an elbow or knee is a more serious matter in the coating and…

The generalized tight-binding model, with the exact diagonalization method, is developed to investigate optical properties of graphene in five kinds of external fields. The quite large Hamiltonian matrix is transferred into the band-like…

Thin elastic solids are easily deformed into a myriad of three-dimensional shapes, which may contain sharp localized structures as in a crumpled candy wrapper, or have smooth and diffuse features like the undulating edge of a flower.…

A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…

We discuss infinitesimal isometries of the middle surfaces and present some characteristic conditions for a function to be the normal component of an infinitesimal isometry. Our results show that those characteristic conditions depend on…