13 citations · 18 across the 10 of their papers we have counts for
10 papers
Stable configurations of entangled systems with repulsive interactions
Motoko Kotani, Hisashi Naito, Naoki Sakata +1
Entangled systems are prevalent in both biological and synthetic materials. This study examines the stable configurations of weaves consisting of two families of intertwined thread…
A Weierstrass Representation Formula for Discrete Harmonic Surfaces
Motoko Kotani, Hisashi Naito
A discrete harmonic surface is a trivalent graph which satisfies the balancing condition in the 3-dimensional Euclidean space and achieves energy minimizing under local deformation…
Construction of weaving and polycatenane motifs from periodic tilings of the plane
Mizuki Fukuda, Motoko Kotani, Sonia Mahmoudi
Doubly periodic (DP) weaves and polycatenanes are complex entangled structures embedded in the Euclidean thickened plane, invariant under translations in two independent directions…
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number
Mizuki Fukuda, Motoko Kotani, Sonia Mahmoudi
A weave is the lift to the Euclidean thickened plane of a set of infinitely many planar crossed geodesics, that can be characterized by a number of sets of threads describing the o…
Construction and Classification of Combinatorial Weaving Diagrams
Mizuki Fukuda, Motoko Kotani, Sonia Mahmoudi
This paper introduces a new systematic algorithm for constructing periodic Euclidean weaving diagrams with combinatorial arguments. It is shown that such a weaving diagram can be c…
Construction of continuum from a discrete surface by its iterated subdivisions
Motoko Kotani, Hisashi Naito, Chen Tao
Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To ab…
A Discrete Surface Theory
Motoko Kotani, Hisashi Naito, Toshiaki Omori
In the present paper, we propose a new discrete surface theory on 3-valent embedded graphs in the 3-dimensional Euclidean space which are not necessarily discretization or approxim…
Long time asymptotics of non-symmetric random walks on crystal lattices
Satoshi Ishiwata, Hiroshi Kawabi, Motoko Kotani
In the present paper, we study long time asymptotics of non-symmetric random walks on crystal lattices from a view point of discrete geometric analysis due to Kotani and Sunada [11…
Quantization of interface currents
Motoko Kotani, Hermann Schulz-Baldes, Carlos Villegas-Blas
At the interface of two two-dimensional quantum systems, there may exist interface currents similar to edge currents in quantum Hall systems. It is proved that these interface curr…
On the fundamental group of the space of harmonic -spheres in the -sphere
M. Furuta, M. A. Guest, M. Kotani +1
We compute the fundamental group of the "moduli space" of classical solutions of the two dimensional Euclidean -model.